te Ser tes Ret AEBS gy er send MONEE INO EERE, fe * = si: bee o £ 5 + : > SS XS VES 24 * aS Ze. oa SS oe pris: sh watts ras 6a iss ats G Se re nwary 3 ee fais sabe Le SF ahd SS ea met betas SASS MR St N @ leat b TINS Received by bequest from Albert H. Lybyer Professor of History University of Illinois 1916-1949 55 UNIVERSITY AAUP Nois LIBRARY CENTRAL CIRCULATION BOOKSTACKS The person charging this material is re- sponsible for its renewal or its return to the library from which it was borrowed on or before the Latest Date stamped below. You may be charged a minimum fee of $75.00 for each lost book. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. TO RENEW CALL TELEPHONE CENTER, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN When renewing by phone, write new due date below previous due date. L162 Eighth Edition, with 26 pages of new matter, 7. Plates, 624 Woodcuts, and an Appendix of Questions. Crown 8vo. 7s. 6d. NATURAL PHILOSOPHY FOR GENERAL READERS AND YOUNG PERSONS. A Course of Physics divested of Mathematical Formule, expressed in the language of daily life. Translated and Edited from GANov’s Cours Elémentatre de Physique, by E. ATKINSON, Ph. D., F.C.S. DOI FPP LONGMANS, GREEN, & CO., 39 Paternoster Row, London and Bombay. TAIB IIE OF SIPIEGIIRA o ti Ai g 3 a o << eC] a E wy aoe 6 =e g oy Z| Peer vie DOs Rae lone AD Si E ON Pr YOLes Teese ieee ViGEt IN ASEAN, DD) eA PP ee DD HOKMMEMESOSE OH SCOLLEGES AND (SGHOOLS TRANSLATED AND EDITED FROM GANOT’SsELEMENTS DE PHYSIQUE (with the Authors sanction) BY Dee CNS ON an EH). L OlS: LATE PROFESSOR OF EXPERIMENTAL SCIENCE IN THE STAFF COLLEGE FIFTEENTH EDITION, REVISED AND ENLARGED ILLUSTRATED by 95 COLOURED PLATES and MAPS and 1037 WOODCUTS We NG NLAIN Sai G RvE EON’) AN Da, CO: sou PALE RNOS DORR O Ws) WON DON AND BOMBAY 1898 All rights reserved j ah | nl t : % a) “a> be ad AG Pi ¥ 7Ae: ae We ty M ceerted i a a he SSO G Rona 1S9R ADVERTISEMENT iG) brig wnt lel ds abe MIRE ab Di nlc LLOLN THE additions made in the present edition have increased by twenty- one pages the size of the work as it stood in the last edition, and by thirty-six the number of illustrations, notwithstanding the omission of matter which had become of minor importance ; and careful re- vision throughout, has, it is hoped, improved the book beyond the extent represented by a mere statement of the number of added pages and cuts. In issuing this new edition I have to express my acknowledgments to Professor Reinold of the Royal Naval College, who made an inde- pendent revision of the whole book. This has led to many valuable corrections and additions, of which I have been glad to avail myself. I - also have to thank Professor Foster of University College for several valuable suggestions and additions. The continued favour with which the work has been received, as a Text-bock for Colleges and Schools, and also as a book of reference for the general reader, perhaps renders any apology for omissions unnecessary ; it may, however, be as well to point out once more that the book is intended to be a general Elementary _ Treatise on Physics, and that, while it accordingly aims at giving an account of the most important facts and general laws of all branches of Physics, an attempt to treat completely and exhaustively of any one = branch would both be inconsistent with the general plan of the book * and impossible within the available space. | E. ATKINSON. PORTESBERY HILL, CAMBERLEY : /z7e 1898. TRANSLATOR S"PREPACE ORI S i eD / Tur Eléments de Physique of Professor Ganot, of which the present work is a translation, has acquired a high reputation as an Introduction to Physical Science. In France it has passed through Nine large editions in little more than as many years, and it has been translated into German and Spanish. This reputation it doubtless owes to the clearness and conciseness with which the principal physical laws and phenomena are explained, to its methodical arrangement, and to the excellence of its illustrations. In undertaking a translation, I was influenced by the favourable opinion which a previous use of it in teaching had enabled me to form. I found that its principal defect consisted in its too close adaptation to the French systems of instruction ; and accordingly, my chief labour, beyond that of mere translation, has been expended in making such alterations and additions as might render it more useful to the English student. I have retained throughout the use of the Centigrade thermometer, and in some cases have expressed the smaller linear measures on the metrical system. ‘These systems are now everywhere gaining ground, and an apology is scarcely needed for an innovation which may help to familiarise the English student with their use in the perusal of the larger and more complete works on Physical Science to which this work may serve as an introduction. Lee e's ROVAL MILITARY COLLEGE, SANDHURST : 1863. TE IAT OT 6? PAGE ABSORBING powers. wedi s Absorption of gases. 175, 180 heat by gases . 430 ee liquids 424 — vapours 426 hail jee ade various bodies 425, 431 Atmosphere, composition of . eae BAROMETRIC variations 158 Boiling points 347 Breaking weight of substances 85 CAPILLARITY in barometers . 156 Capillary, constant 127 Combustion, heat of 486 Conducting as of solids for heat 396 “a ees Bie liquids for heat 399 Conductors of electricity 726 DENSITIES of gases 322 —____— vapours . 383 Density of water . 313 Diamagnetism : 1002 Diathermanous power . 423 Diffusion of solutions 131 eee heats. 428 Dulong and Petit’s law 451 ELASTICITY : AT Gere Electrical conductivity . . 1028 Electricity, positive and negative . 729 Electromotive force of different elements . 827 Vas series 815 Endosmotic equivalents 129 Expansion, coefficients of solids 302, 303 (ee alee: liquids . 310 gases 318 Eye, dimensions of 618 ——— refractive indices of media of . 618 FREEZING mixtures 333 Fusing points of bodies 323 TABLES PAGE GLAISHER’S factors 390 Gravity, force of, at various places 70 HARDNESS, scale of 86 LATENT heat, of evaporation 9350 —————— fusion a 456 Liquefied gases 370 MAGNETIC declination . 689 inclination . 696 PRESSURE of aqueous vapour 335, 342 LAST OF PPLAT ES ANDAR S' TABLE OF SPECTRA = — vapours of liquids 343 RADIATING powers 413 Radiation of powders 434 Reflecting powers ? 412 Refraction, angle of double 647 Refractive indices 548 of media of eye 618 SOUND, transmission of, in tubes . 215 ' Specific gravity of liquids 113 solids. 110 ze heat of solids and alae H9, 450 ot Cee Bases 454 inductive capacities . 753 ——-— striking distance 798 Surface tension 127 TANGENT galvanometer and volta- meter, comparison between 874 Temperatures, various remarkable. 298 — at different latitudes . 1094 —_———_—— thermal springs 1095 easement Ail: 319 Thermo-electric series . 1005 UNDULATIONS, length of 642 VELOCITY of sound in gases. 218 La LIT 220 rocks. 222 < solids ceed Vibrations of musical scale 236 Frontispiece COLOURED RINGS PRODUCED BY POLARISED LIGHT IN DOUBLE REFRACT- ING CRYSTALS IsOGONIC LINES FOR THE VEAR 1882 IsOCLINIC LINES FOR THE YEAR 1882 LINES FOR THE YEAR 1882 AURORA BOREALIS ISOTHERMAL FOR THE YEAR ISOTHERMAL FOR JANUARY ISOTHERMAL FOR JULY ‘ Zo face p. 668 ni 690 A 695 s 698 5» 1089 99 TO54 % TOy5 Lap Pee ae tah Tacks: 2 13 4| LE: |2 [3 |4 15 16 [7 |3 ee: Millimetres Centimetres The area of the figure within the heavy lines is that of a square decimetre. A cube, one of whose sides is this area, is a cubic decimetre or “tre. A litre of water at the temperature of 4° C. weighs a kilogramme. fig. 23. RS represents the sec- tion of a smooth piece of hard wood hinged at R ; by means of a screw it can be clamped at any angle 2 against the arc- shaped support, by which at the same time the angle can be measured; @ is a cylindrical roller, to the axis of which is attached a string passing over a \ pulley to a scale-pan P. It is thus easy to ascertain P by direct experiments what weights must be placed in the pan P in order to balance a roller of any given weight, or to cause it to move with a given angle of inclination. \ Fig. 23 —43] Inclined Plane ag} The line RS represents the /ength, ST the hezgh¢,and RT the dase of the inclined plane. In ascertaining the theoretical conditions of equilibrium we have a useful application of the parallelogram of forces. Let the line a, fig. 23, represent the force which the weight W of the cylinder exerts acting vertically down- wards ; this may be decomposed into two others; one, ad, acting at right angles against the plane, and representing the pressure which the weight exerts against the plane, and which is counterbalanced by the reaction of the plane ; the other, ac, represents the component which tends to move the weight down the plane, and this component has to be held in equilibrium by the weight P, equal to it, and acting in the opposite direction. It can be readily shown that the triangle adc is similar to the triangle SRT, and that the sides ac and aé are in the same proportion as the sides ST and SR. But the line ac represents the power, and the line ad the weight ; hence SSR Paws that is, on an inclined plane, equilibrium obtains when the power is to the weight as the height of the tnclined plane to tts length. Since the ration, is the sine of the angle x, we may also state the prin- ciple thus eae ato The component da or dc, which represents the actual pressure against the plane, is equal to W cos 2; that is the pressure against the plane is to the weight as the base is to the length of the inclined plane. In the above case it has been considered that the power acts parallel to the inclined plane. It may be applied so as to act horizontally. It will then be seen from fig. 24 that the weight S W may be decomposed into two es forces, one of which, @é, acts at right angles to the plane, and the other, ac, parallel to the base. It is this latter which is to be kept in equilibrium by the power. From the similarity of the two triangles ach and STR, aciéc=ST:TR; # but dc is equal to W, and ac is equal to P ; hence the power which must be applied at 4 to hold the weight W in equilibrium is as the height of the inclined plane is to the base or as the tangent of the angle of inclination x; that is, P=Wtanx The bc pressure upon the plane in this case may be easily shown to be a= aaa 5) af 4) thatis R= _W _ where R is the pressure upon the plane. This is some- cos + times called the relative weighi on the plane. If the force P which is to counterbalance W is not parallel to the plane, but forms an angle, E, with it, this force can be decomposed into one which is parallel to it, and one which is at right angles. Of these only the first is operative, and is equal to P cos E. 28 On Matter, Force, and Motion [43— In most cases of the use of the inclined plane, such as in moving carriages and waggons along roads, in raising casks into waggons or warehouses, the power is applied parallel to the inclined plane. An instance of a case in which a force acts parallel to the base is met with in the screw. Owing to the unevenness of the surfaces in actual use, and the conse- quent frzctéon when one body moves over another, the laws of equilibrium and of motion on an inclined plane undergo modification. Friction must be looked upon as a hindrance to be continually overcome, and must be deducted from the force required to keep a body from falling down an in- clined plane, or must be added to it in the case in which a body is to be moved up the plane. (See art. 47.) Thus if we place on the plane a block of some material, by gradually increasing the inclination it will begin to move at a certain angle, which will depend on the nature of the material ; this angle zs the Limiting angle of resistance, and its tangent is the coefficient of friction for that material. This may serve as a rough illustration of determining this coefficient. 44. The wedge.—The ordinary form of the wedge is that of a three- sided prism of iron or steel, one of whose angles is very acute. Its most frequent use is in splitting stone, timber, &c. Fig. 25 represents in section the application of the wedge to this purpose. The side @é is the back, the vertex of the angle acé which the two faces ac - and dc make with each other represents the edge, — and the faces ac and dc the szdes of the wedge. The power P is usually applied at right angles to the back ; and we may look upon the cohesion be- tween the fibres of the wood as representing the resistance to be overcome; as corresponding to what in other machines is the weight. Suppose this to act at right angles to the two faces of the wedge, and to be represented by the lines fe and ge; complete the parallelogram gef, then the diagonal /e will represent the resultant of the reaction of the fibres tending to force the wedge out ; the force which must be applied to hold this wedge in equilibrium must therefore be equal to ef. Now eff is similar to the triangle ach, therefore ab:ac =ch:ef; but these lines represent the pressure applied at the back of the wedge, and the pressure on the face ac, hence if P repre- sent the former and Q the latter, there is equilibrium when P:Q=abd:ac, that is, when the power is to the resistance in the same ratio as the back of the wedge bears to one of the sides. The relation between power and re- sistance is more favourable the sharper the edge, that is, the smaller the angle which the sides make with each other. The action of all sharp cutting instruments, such as chisels, knives, scissors, &c., depends on the principle of the wedge. It is alsoapplied when very heavy weights are to be raised through a short distance, as in launching ships, and in bracing columns and walls to the vertical. 45. The screw.— Let us suppose a piece of paper in the shape of a —46] Virtual Velocity 29 = right-angled triangle ace’ to be applied with its vertical side ac’e’ against a eylindes and peril! to the axis, and to be wrapped round the eultieeiae the hypotenuse will describe a screw line or felzx on the surface of the cylinder (fig. 26) ; the points adcde will occupy the positions respectively ad’c’d’e’ If the dimensions be so chosen that the base of the triangle, cc’, is equal to the circumference of the cylinder, then the hypotenuse adc becomes an inclined plane traced on the surface of the cylinder ; the distance ac’ being the height of the plane. An ordinary screw consists of an elevation on a solid cylinder ; this elevation may be either square, as in fig. 27, or acute; and such screws are called sguware or sharp screws accordingly. When a corresponding groove is cut in the Hag lil aii : Sey hollow cylinder or nut of the same diameter Tt 4 \= = nag ‘ as the bolt, this gives rise to an internal or s companion screw or 7272, fig. 28. The vertical distance between any two threads of a screw measured parallel to the axis is called the fzfch, and the angle acc’ or aee’ is called the zaclination of the screw. In practice, a raised screw is used with its companion in such a manner that the elevations of the one fit into, and coincide with, the depressions of the other. The screw isa Peigcstion of the inclined albeit and the condi- tions of equilibrium are those which obtain in the case of the plane. The resistance, which is either a weight to be raised, or a pressure to be exerted, acts in the direction of the vertical, and the power acts parallel to the base ; hence we have P:R=:4, and the length of the base is the Citeiateronee of the cylinder ; whence P:R=A:2n7; 7 being the radius of the cylinder, and / the pitch of the screw. The power is usually applied to the screw by means of a lever, as in the bookbinder’s press, the copying press, &c., and the principle of the screw may be stated to be generally that the pow Le of the screw isto the resistance in the same ratio as that of the pitch of the screw to the circumference of the circle through which the power acts. 46. Virtual velocity.—If the point of application of a force be slightly displaced, the resolved part of the displacement in the direction of the force is termed the wzrtual velocity of the force, and is considered as positive or negative, according as it is in the same direction as the force, or in the opposite direction. Thus in fig. 29 let the point of application A of the force P be displaced to A’, and draw A’a perpendicular to AP. Then Aa is the 30 On Matter, Force, and Motion [46— virtual velocity of the force P, and being, in this case, in the direction of P, is to be considered positive. The principle of virtual velocities asserts that if any machine or system be kept in equilibrium by any number of forces, and the machine or system then receive any very small displacement, the algebraic sum of the products formed by multiplying each force by its virtual velocity will be zero. Of course, the displacement of the machine is supposed to be such as not to break the connection of its parts ; thus in the wheel and axle the only possible displacement is to turn it round the fixed axle ; in the inclined plane the weight must still continue to rest on the plane ; inthe various systems of pulleys the strings must still continue stretched, and must not alter in length, &c. Fig. 29 The complete proof of this principle is beyond the scope of the present work, but we may easily establish its truth in any of the machines we have already considered. It will be found in every case that, if the machine receive a small displace- ment, the virtual velocities of P and W will be of opposite signs, and that, neglecting the signs, Px P’s virtual velocity = W x W’s vir- tual velocity. Thus, to take the case of a dent lever, let P and Q ~ be the forces acting at the ex- tremities of the arms of the bent lever AFB (fig. 30), and let the lever be turned slightly round its fulcrum F, bringing A to A’, and B to B’.. Draw A’a and B’d perpendicular to P and Q respec- tively ; then Aa is the virtual rises velocity of P, and Bé that of Q, the former being positive and the latter negative. Let F~, Fg be the perpendiculars from the fulcrum upon P and Q, or what we have called (art. 40) the arms of P and Q. Now, as the displacement is very small, the angles FAA’, FBB’ will be very nearly right angles ; and, therefore, the right-angled triangles AaA’, BOB’ will ultimately be similar to the triangles FAA, FgB respectively, whence eet ; AA’ FA ae ae or eT EY ou = = eat But the triangles FAA’, FBB’ are similar, as they are both isosceles, and their vertical angles are equal, so that ao - whence Bp E pO as we may put it, Fp" Os Fy Now the denominators of these two equal fractions are equal if the lever be in equilibrium (art..40).. Hence the numerators are equal, or P x P’s virtual velocity = Q x Q’s virtual velocity. As a further and simpler example, take the case of the block and tackle described in article 41. Suppose the weight to be raised through a space / ; 47] Friction 31 then the virtual velocity of the weight is #, and is negative. Now, as the distance between the block and tackle is less than before by the space /, and as the rope passes over this space z times, in order to keep the rope still tight the power will have to move through a space equal to zZ. This is the virtual velocity of P, and is positive, and as W=z2P, we see that W x W’s virtual velocity = P x P’s virtual velocity. 47. Friction.—In the cases of the actions of machines which have hitherto been described, the resistances which are offered to motion have not been at all considered. The surfaces of bodies in contact are never perfectly smooth ; even the smoothest present inequalities which can neither be detected by the touch nor by ordinary sight ; hence when one body moves over the surface of another, the elevations of one sink into the depressions of the other, like the teeth of wheels, and thereby offer a certain resistance to motion ; thisis what is called /rvzctzon. It must be regarded as a force which continually acts in opposition to actual or possible motion. Friction is of two kinds: sd¢ding, as when one body glides over another ; this is least when the two surfaces in contact remain the same, as in the motion of an axle in its bearing ; and vol/ing friction, which occurs when one body rolls over another, as in the case of an ordinary wheel. The latter is less than the former, for by the rolling the inequalities of one body are raised over those of the other. As rolling friction is considerably less than sliding friction, it is agreat saving of power to convert the latter into the former ; as is done in the case of the casters of chairs and other furniture, and also in that of friction wheels. This, however, is not always the case ; thus a sledge experiences less friction on snow than a carriage, for in this case the wheels sink and friction on the sides results. On the other hand, it is sometimes useful to change rolling into sliding friction, as when drags are placed on carriage wheels. , Friction is directly proportional to the pressure of the two surfaces against each other. That fraction of the pressure which must act as moving force merely to overcome friction is called the coefficzent of friction. Friction is independent of the extent of the surfaces in contact if the pres- sure is the same. Thus, suppose a board with a surface of a square deci- metre resting on another board to be loaded with a weight of a kilogramme. If this load be distributed over a similar board of two square decimetres’ surface, the total friction will be the same, while the friction per square centimetre is one-half, for the pressure on each square centimetre is one-half of what it was before. So, too, a rectangular stone experiences the same friction whether it is laid on the narrow or on the broad side. Friction is diminished by polishing and by smearing, but is increased by heat. It is greater as a body passes from the state of rest to that of motion than during motion, but seems independent of the velocity. The coefficient of friction depends on the nature of the substances in contact ; similar bodies experience in general greater friction than dissimilar ones, for with the former the in- equalities fit more into one another ; thus for oak upon oak it is 0-418 when the fibres are parallel, and 0:293 when they cross ; for beech upon beech it is 0°36. Greasy substances, which are not absorbed by the body, diminish friction, but increase it if they are absorbed. Thus moisture and oil increase, 32 On Matter, force, and Motion [47— while tallow, soap, and graphite diminish, the friction of wooden surfaces. In the sliding friction of cast iron upon bronze the coefficient was found to be 0°25 wont grease ; with oil it was 0°17, fat o°1f, soap 0°03, and with a mixture of fat and graphite 0-002. The coefficient of rolling friction for cast- iron wheels on iron rails as in railways is about 0-004; for ordinary wheels on an ordinary road it is o'o4, hence a horse can draw ten times as great a load on rails as on an ordinary road, and this is indeed a main use of rail and tram ways. The coefficient of steel upon smooth ice has been determined by a skater holding in his hand a spring balance (89) attached to a cord by which he was drawn along bya second skater. At starting the spiral showed a pullof 5 to 6 kilos, but during the motion this varied between 1 and 2 kilos. As the weight of the skater was 62 kilos, the coefficient of friction during the motion was ,4 to 2, or 1°6 to 3°2 per cent. Without friction on the ground, neither man nor animals, neither ordinary carriages nor railway carriages, could move. Friction is necessary for the transmission of power from one wheel to another by means of bands or ropes ; and without friction we could hold nothing in the hands. 48. Resistance to motion in a fluid medium.—A body in moving through any medium, such as air or water, experiences a certain resistance ; for the moving body sets in motion those parts of the medium with which it is.in contact, whereby it loses an equiva- i lent amount of its own motion. . | This resistance increases with the surface of the i moving body ; thus a soap-bubble or a snow-flake falls more slowly than does a drop of water of the same weight. It also increases with the density of the medium ; in rarefied air, therefore, it is less than in air under the ordinary pressure ; and in this again it is less than in water. The influence of this resistance may be illustrated by means of the apparatus represented in fig. 31, which consists of two vanes, w w, fixed toa horizontal axis, xx, to which is also attached a bobbin s. The rotation of the vanes is effected by means of the falling of a weight attached to the string coiled round the bobbin. The vanes can be adjusted either at right angles or parallel to the axis. In the former position the vanes rotate rapidly when the weight is allowed to act ; in the latter, however, where they press with their entire surface against the air, the resistance greatly lessens the rapidity of rotation. The resistance increases with the velocity of the moving body, and for moderate velocities is proportional to the square ; for, supposing the velocity of a body made twice as great, it must displace twice as much matter, and must also impart to the displaced particles twice the velocity. For high velocities the resistance in a medium increases in a more rapid ratio than that of the square, for some of the medium is carried along with the moving body, and this, by its friction against the other portions of the medium, causes a loss of velocity. It is this resistance which so greatly increases the difficulty and cost of 49] Uniformly Accelerated Rectilinear Motion 23 attaining very high speeds in steam-vessels, to which must be added the pro- duction of waves on the surface, and of eddy currents. Use is made, on the other hand, of this resistance in parachutes (fig. 183) and in the windvanes for diminishing the velocity of falling bodies (fig. 57), the principle of which is illustrated by the apparatus, fig. 31. Light bodies fall more slowly in air than heavy ones of the same surface, for the moving force is smaller com- pared with the resistance. The resistance to a falling body may ultimately equal its weight ; it then moves uniformly forward with the velocity which it has acquired. Thus, a raindrop falling from a height of 3,000 feet should, when near the ground, have a velocity of nearly 440 feet, or that of a musket-shot ; owing, however, to the resistance of the air, its actual velocity is probably not more than 30 feet in a second. On railways the resistance of the air is appreciable ; with a carriage exposing a surface of 22 square feet, it amounts to 16 or 17 pounds when the speed of the train is 16 feet a second, or 11 miles an hour. By observing the rate of diminution in the number of oscillations of a horizontal disc suspended by a thread when immersed in water, Meyer determined the coefficient of the frictional or internal resistance of water, and found that at 10° it was equal to 001567 gramme on a square centi- metre ; and for air it was about 4 as much. 49. Uniformly accelerated rectilinear motion.—Let us suppose a body containing 77 units of mass to move from rest under the action of a force of F units ; the body will move in the line of action of the force, and will acquire in each second an additional velocity / given by the equation ay ke consequently, if v is its velocity at the end of ¢ seconds, we have v =f. (1) To determine the space it will describe in ¢ seconds, we may reason as follows :—The velocity at the time ¢ being /%, that at a time 7+7 will be f (é+7). Ifthe body moved uniformly during the time 7 with the former velocity, it would describe a space s squal to f¢r; if with the latter velocity, a space s, equal to f(¢+7)r. Consequently, Cees we Gace oe ee therefore, when r is indefinitely small, the limiting values of s and s, are equal. Now, since the body’s velocity is continually zzcreasing during the time 7, the space actually described is greater than s and less than s,. But since the limiting values of s and s, are equal, the limiting value of the space described is the same as that of s or s, In other words, if we suppose the whole time of the body’s motion to be divided into any number of equal parts, if we determine the velocity of the body at the beginning of each of these parts, and if we ascertain the spaces described on the supposition that the body moves uniformly during each portion of time, the limiting value of the sum of these spaces will be the space actually described by the body. Draw D 34 On Matter, Force, and Motion [49- a line AC (fig. 32), and at A construct an angle CAB, whose tangent equals ff; divide AC into any number of equal parts in D, E, F,...and draw PD, OE, RF;...BC at right angles to AC ; then smce PD=ADx/, QE=AEx 7, RF=AF x f, BC=ACx f/f, &c., PD will represent the velocity of the body at the end of the time represented by AD, and similarly QE, RF,...BC, will re- present the velocity at the end of the times AE, AF,...AC. Complete the rect- angles De, Ef, Fg... These rectangles represent the space described by the body, on the above supposition, during the second, third, fourth,...portions of the time. Consequently, the space actually described during the time AC is the limit of the sum of the rectangles ; the limit being continually approached as the number of parts into which AC is divided is continually increased. But this limit is the area of the triangle ABC ; that is AC x CB or $AC xACxf Therefore, if AC represents the time ¢ during which the body describes a space s, we have s=4/ft. | (2) Since this equation can be written PAREN ad we find, on comparison with equation (1), that U = 2fs. (3) To illustrate these equations, let us suppose the accelerative effect of the force to be 6 ; that 1s to say that, in virtue of the action of the force, the body acquires in each successive second an additional velocity of 6 feet per second ; and let it be asked what, on the supposition of the body moving from rest, will be the velocity acquired, and the space described, at the end of 12 seconds ; equations I and 2 enable us to answer that at that instant it will be moving at the rate of 72 feet per second, and will have described 432 feet. The following important result follows from equation (2). At the end of the first, second, third, fourth, &c., second of the motion, the body will have described 3f, 3fx 4, f/x 9, 4fx 16, &c., feet ; and consequently durving the first, second, third, fourth, &c., second of the motion will have described 3/7, fx 3, 4f~x 5, 3/7, &c., feet, namely spaces in arithmetical progression. The results of the above article can be stated in the form of laws which apply to the condition of a body moving from a state of rest under the action of a constant force :— I. The velocities are proportional to the times during which the motion has lasted. Il. Zhe spaces described are proportional to the squares of the times em- ployed tn thetr description. III. The spaces described are proportional to the squares of the velocities acquired during thetr description. IV. Lhe spaces described in equal successive periods of time increase by a constant quantity. Instead of supposing the body to begin to move from a state of rest, we may suppose it to have an initial velocity V, in the direction of the force. In this case equations I, 2, and 3 can be easily shown to take the following forms, respectively :— —51] Motion of Projectiles 35 GaN STi, S=Vi+s fe’, UT? a VP 2 5 If the body move in a direction opposite to that of the force, f must be reckoned negative. The most important exemplification of the laws stated in the present article is in the case of a body falling freely zz vacuo. Here the force causing the acceleration is that of gravity, and the acceleration produced is denoted by the letter @: it has already been stated (29) that the numerical value of £ 1S 32°1912 at London, when the unit of time is a second and the unit of length a foot. Adopting the metre as unit of length, the value of gat London is 9°8117. 50. Motion on an inclined plane.—Referring to (43), suppose the force P not to act ; then the mass M is acted on by an unbalanced force M g sin 2, in the direction SR ; consequently the acceleration down the plane is ¢ sin x, and the motion becomes a particular case of that discussed in the last article. If it begins to move from rest, it will at the end of ¢ seconds acquire a velocity v given by the equation U= et sin x, and will describe a length s of the plane given by the equation Se-ec7 Sill 2. Also, if v is the velocity acquired while describing s feet of the plane, Vis OG Si Ye Hence (fig. 23), if a body slides down the plane from S to R, the velocity which it acquires at R is equal to ./ 2¢. RS sinRor V 2g¢.ST; that isto say, the velocity which the body has at R does not depend on the angle x, but only on the perpendicular height ST. The same would be true if for RS we substituted any smooth curve ; and hence we may state generally that when a body moves along any smooth line under the action of gravity, the change of velocity it experiences in moving from one point to another is that due to — the vertical height of the former point above the latter. 51. Motion of projectiles—The equations given in the above article apply to the case of a body thrown vertically upwards or downwards with a certain initial velocity. We will now consider the case of a heavy body thrown in a horizontal direction. Let a, fig. 33, be such a body thrown with an initial velocity of v feet in a second, and let the line ad represent the space described in any interval ; then at the end of the 2nd, 3rd, 4th... equal interval, the body, in virtue of its inertia, will have reached the points ¢, d, e, &c. But during all this time the body is under the influence of gravity, which, if it alone acted, would cause the body to fall through the distances repre- sented on the vertical line; these are determined by the successive values of 4g¢*, which is the formula for the space described by a freely falling body (50). The effect of the combined action of the two forces is that at the end of the first interval, &c., the body will be at 6’, at the end of the second interval at c’, of the third at a’, &c., the spaces 00’ cc’ dd’... being propor- D2 36 [51- tional to the squares of ad, ac, ad, respectively, and the line joining these points represents the path of the body. By taking the intervals of time sufficiently small we get a regularly curved line of the form known as the parabola. In order to demonstrate motion with horizontal and inclined direction the appa- ratus represented in fig. 34 may be made use of. It consists of a bottle from which a steady stream of water issues through a caoutchouc tube terminating ina jet. This can be discharged in front of a slate or blackboard on which the path of the curve in each case can be chalked. If the direction in which the body is thrown makes an angle of a with the horizon (fig. 35), then after ¢ seconds it would have travelled a distance a=v7, where v is the original velocity ; during this time, however, it will have fallen through a distance dc = 4¢7? ; the height which it will have actually reached is =bd—bc=vt sin a—tgt?; and the hori- zontal distance will be ad=ab cos a=vt COS a. The vange of the body, or the greatest distance through which itis thrown, will be reached when the On Matter, Force, and Motion that wi \! mi mil Ht iT f ss ii _—SS SS = TT } Mn ao NNT q # i A | 1 | ‘ } i ~ _ \\ I SA St vu itt an if | \ —s —— —— NN height is again=o; is, when v¢ sin a—4g¢? =0, : 2U Si from which ¢ = 2752 @, Introducing this value of ¢# into the equation for the distance, d, we have is da 2U" SiN @ COS a, Vey Si by a trigonometrical : v* sin 2a transformation = caine The greatest height is attained in half the time of ysina flight, or when 7= - from which we_ get 9. Se, v? sin* a hk =— wt It follows from the formula that the Aezgh¢ is greatest when sin a is greatest, which is the case when it = 90°, or when the body is thrown vertically upwards ; the range is greatest where sin 2a is a maximum, that is, when 2a=90° or a= 45°. -53] Motion in a Ctrcle—Centrifugal Force 37 In these formule it has been assumed that the air offers no resistance. This is, however, far from the case, and in practice, particularly if the velocity of projection is very great, the path differs from that of a parabola. - Fig. 35 approximately represents the path, allowing for the resistance of the air. 6b Fig. 35 The divergence from the true theoretical path is affected by the fact that in the modern rifled arms the projectiles are not spherical in shape ; and also because, along with their motion of translation, they have, in consequence of the rifling, a rotatory motion about their axis. 52. Composition of velocities.—The principle for the composition of velocities is the same as that for the composition of forces: this follows evi- dently from the fact that forces are measured by the momentum they com- municate, and are therefore to one another in the same ratio as the velocities they communicate to the same body. Thus (fig. 8, art. 33), if the point has at any instant a velocity AB in the direction AP, and there is communicated to it a velocity AC in the direction AQ, it will move in the direction AS with a velocity represented by AD. And, conversely, the velocity of a body re- presented by AD can be resolved into two component velocities AB and AC. This suggests the method of determining the motion of a body when acted on by a force in a direction transverse to the direction of its velocity ; namely, suppose the time to be divided into a great number of intervals, and suppose the velocity actually communicated by the force to be communicated at once ; then by the composition of velocities we can determine the motion during each interval, and therefore during the whole time ; the actual motion is the limit to which the motion, thus determined, approaches when the number of intervals is increased. 53. Motion in a circle—Centrifugal force.—When a body is once in motion, unless it be acted upon by some force, it will move uniformly forward in a straight line with unchanged velocity (26). If, therefore, a body moves uniformly in any other path than a straight line—in a circle, for instance—this must be because some force is constantly at work which continuously deviates it from this straight line. We have already seen an example of this in the case of the motion of projectiles (51), and will now consider it in the case of central motion or motion in a circle, of which we have an example in the motion of the celestial bodies, or in the motion of a s/z7g. In the latter case, if the string is cut, the stone, ceasing to be acted upon by the tension of the string, will move in a straight line with the velocity which it already possesses—that is, in the direction of the tangent to the curve at the point where the stone was when the string was cut. The tension 38 On Matter, Force, ana Motion [53- of the string, the effect of which is to pull the stone towards the centre of the circle and to cause the stone to move in its circular path, is called the centripetal or central force ; the reaction of the stone upon the string, which is equal and opposite to this force, is called the centrifugal force. The amount of the forces may be arrived at as follows :— Let us suppose a body moving in a circle with given uniform velocity to be at the point a (fig. 36); then, had it not been acted on by a force in the direction ac, it would, in a small succeeding interval of time Z, have continued to move in the direction of the tangent at a,and have passed through a distance which we will represent by ad. In consequence, however, of this force, it has not followed this direction, but has arrived at the point @ on the curve ; hence the force has made it traverse the distance dd=ae in this interval. If/fbe the acceleration with which the body is drawn towards the centre ae=43/¢*, and if ad be very small, it may be taken as equal to @6 or wé, where v is the velocity of the moving body. Now if az is the diameter of the circle, the triangle adz is inscribed in a semicircle and is right-angled, whence ad! = ae x an =aex2r. Substituting their values for ad and ae in this equation, we find that v2? =4// x 27, from which oye iy == 5 that is, in order that a body with a certain velocity may move in a circle, it must be drawn to the centre by a force which is directly as the square of the velocity with which the body moves, and inversely as the radius of the circle. In‘order to express this in the ordinary units of weight, we must multiply the above expression by the mass, which 2 . V1 . . ives vl c= ZANT G keep the body in a circle, an r attraction towards the centre is needed, which is constantly equal to”, and this attraction is also a Fig. 36 constantly neutralised by the centrifugal force. The above expression may be put in a form which is sometimes more convenient. If T be the time in seconds aio to traverse the circum- 4mn*r Tas If a rigid body rotates about a fixed axis, all parts of the body describe circumferences of various diameters, but all in the same time. The velocity of the motion of individual particles increases with the distance from the axis of rotation. By angular velocity is understood the velocity of a point at unit distance from the axis of rotation. If this is denoted by a, na velocity v of a ference 277 with the velocity wv, then v? = oor from which F = 3 : Bled : Uv point at a distance from the axis is #7, from which o=< =~ and F=mro. r 7 The existence of centrifugal force may be demonstrated by means of numerous instructive experiments, such as the centrifugal railway. Ifasmall —54] Motion in a Vertical Circle 39 can of water hung by the handle to a string be rapidly rotated in a vertical circle, no water will fall out, for, at a suitable velocity, the liquid will press against the bottom of the vessel with a force at right angles to the circle and greater than its own weight. Centrifugal force has been used in chemical laboratories to separate crystals from the mother-liquors, and also to promote the deposition of fine precipitates which under ordinary circumstances settle very slowly ; it is also applied industrially in sugar factories to purify sugar from syrup, in dyeworks to dry yarn and cloth rapidly, and in laundries. 54. Motion in a vertical circle.—Let ACBD (fig. 37) be a circle whose plane is vertical and radius denoted by 7 Suppose a point placed at A, and allowed to slide down the curve, what velocity will it have acquired on reaching any given point P? Draw D the vertical diameter CD, join CA, CP, and draw the horizontal lines AMB and PNP’. Now, assuming the curve to be smooth, the velocity acquired in falling from A to P is that due to MN, the vertical height of A above P (51); if therefore v denote the velocity of the point at P, we shall have U = 20 NIN" Now by similar triangles DCP, PCN, we have DONC? aCe EZ eines consequently, if we denote by s the chord CP, Z2rNC=s", In like manner, if a denote the chord CA, 2MOA therefore 27M N =a?—s”, and y? =F (a? — 5s), rv Now wz will have equal values when s has the same value, whether positive or negative, and for any one value of s there are two equal values of v, one positive and one negative. That is to say, since CP’ is equal to CP, the body will have the same velocity at P’ that it has at P, and at any point the body will have the same velocity whether it is going up the curve or down the curve. Of course it is included in this statement that if the body begins to move from A it will just ascend to a point B on the other side of C, such that A and B are in the same horizontal line. It will also be seen that at C the value of sis zero; consequently, if Vis the velocity acquired by the body in falling from A to C, we have r and, on the other hand, if the body begins to move from C with a velocity V, 40 On Matter, Force, and Motion [54- it will reach a point A such that the chord AC or ais given by the same equation. In other words, the velocity at the lowest point is proportional to the chord of the are described. 55. Motion of a simple pendulum.—By a simple pendulum is meant a heavy particle suspended by a fine thread from a fixed point, about which it oscillates without friction. So far as its changes of velocity are concerned, they will be the same as those of the point in the previous article, for the tension of the thread, acting at each position in a direction at right angles to that of the motion of the point, will no more affect its motion than the re- action of the smooth curve affects that of the point in the last article. The time of an oscillation—that is, the time in which the point moves from A to B—can be easily ascertained when the arc of vibration is small; that is, when the chord and the arc do not sensibly differ. Thus, let AB (fig. 38) equal the arc or chord ACB (fig. 37) ; with centre C and radius AC or a describe a circle, and suppose a point to describe the circumference of that circle with a uniform velocity am V ora J At any instant let the point be at Q, r L XQ join CQ, draw the tangent QT, also draw QP at right angles and QN parallel to AB, then the angles NQT and CQP are equal. Now the velocity of Q resolved parallel to AB is V cos TQN or ay/€ , cos CQP;; that is,ifCP equals s, the velocity of Q parallel to AB is Fig. 38 A/£PQ oa Ae (a? -s°). But if we suppose a point to move along AB in such a manner that its velocity in each position is the same as that of the oscillating body, its velocity at P would also equal Je &(a?—s*); and, therefore, this point would describe AB in the same time that Q describes the sey UO he AQB. If then 7 be the required time of an oscillation, we have o Yr fanasay /€ = raft. r = This result is independent of the length of the arc of vibration, provided its amplitude, that is AB, be small—not exceeding 4 or 5 degrees, for instance. It is evident from the formula that the time of a vibration is directly pro- portional to the square root of the length of the pendulum, and inversely proportional to the square root of the accelerating force of gravity. As an example of the use of the formula we may take the following :—It has been found that 39°13983 inches is the length of a single pendulum whose time of oscillation at Greenwich is one second ; the formula at once leads to an accurate determination of the accelerating force of gravity ¢ ; for using feet and seconds as our units we have ¢=1, r= 3°26165, and w stands for the known number 3°14159 ; therefore the formula gives us. —57] Linpulstve Forces 41 PS(BTAT 59)? * 3°26165)= 3271012: This is the value employed in (29). Other examples will be met with in the Appendix. 56. Graphic representation of the changes of velocity of an oscil- lating body.—The changes which the velocity of a vibrating body under- goes may be graphically represented as follows :—Draw a line of indefinite length and mark off AH (fig. 39) to represent the time of one vibration, HH’ to represent the time of the second vibration, and so on. During the first vibration the velocity increases from zero toa maximum at the half-vibration, and then decreases during the second half-vibration from the maximum to zero. Consequently, a curved line or arc AQH may be drawn, whose ordinate QM at any point Q will represent the velocity of the body at the 8— ek Pye ea iett M A ig Eger Fig. 39 time represented by AM. Ifa similar curved line or arc HPH’ be drawn, the ordinate PN of any point P will represent the velocity at a time denoted by AN. But since the arection of the velocity in the second oscillation is contrary to that of the velocity in the first oscillation, the ordinate NP must be drawn in the contrary direction to that of MQ. If then the curve be continued ‘by a succession of equal arcs alternately on opposite sides of AD, the variations of the velocity of the vibrating body will be completely represented by the varying magnitudes of the ordinates of successive points of the curve. The last article shows this to be the curve of sines for a pendulum 57. Impulsive forces.—When a force acts on a body for an inappre- ciably short time, and yet sensibly changes its velocity, it is termed an zmstan- taneous or tmpulsive force. Such a force is called into play when one body strikes against another. A force of this character is nothing but a finite though very large force, acting for atime so short that its duration is nearly, or quite, insensible. In fact, if M is the mass of the body, and the force contains Mf units, it will, in a time 4 communicate a velocity /¢; now, how- ever small ¢ may be, Mf and therefore f may be so large that /¢ may be of sensible or even considerable magnitude. Thus if M containsa pound of matter, and if the force contains ten thousand units, though ¢ were so short as to be only the ;54, of a second, the velocity communicated by the force would be one of ten feet per en It is also to be remarked that the body will not sensibly move while this velocity is being communicated; thus in the case supposed, the body would only move through 3/2 or the 345 of a foot whilst the force acts upon it. When one body impinges on another, it follows from the law of the equality of action and reaction (39) that whatever force the first body exerts upon the second, the second will exert an equal force upon the first in the opposite direction. Now forces are proportional to the momenta generated 42 On Matter, Force, and Motion [57- in the same time : consequently, these forces generate, during the whole or any part of the time of impact, in the bodies respectively, equal momenta K G ad k HH with contrary signs; and therefore the sum of the ean ue of the two bodies will remain constant during and at the end ofthe. impact: It ist#éfi. Course understood that if the two bodies move in contrary directions, their momenta have opposite signs, and their sum is an algebraical sum. In order to test the Fig. «oe physical validity of this conclusion, Newton made a series of experiments, which may be thus briefly described—Two balls A and B (fig. 40) are hung from points C, D in the same horizontal line by threads in such a manner that their centres A and B are in the same horizontal line. With centre C and radius CA describe a semicircle EAF, and with centre D and radius DB describe a semicircle GBH, on the wall in front of which the balls hang. Let A be moved back to R, and be allowed to descend to A; it there impinges on B; A and B will now move along the arcs AF and BH respectively ; let A and B come to their highest points at and £ respectively. Now if V denotes the velocity with which A reaches the lowest point, v and wz the velocities with which A and B leave the lowest points after impact, and 7 the radius AC, it follows from (54) that =chd AR, /¥,v=chd Arq /$,and v= cha Bea /€ ; rv therefore if A and B are the masses of the two balls, the momentum at the instant before impact was proportional to A x chd AR, and the momentum after impact was proportional to Ax chd Ar+Bxchd B&. Now when the position of the points R, ~, and & had been properly corrected for the resistance of the air, it was found that these two expressions were equal to within quantities so small that they could be properly referred to errors of observation. The experiment succeeded equally under every modification, whether A impinged on B at rest or in motion, and whatever the materials of A and B might be. 58. Direct collision of two bodies.—Let A and B be two _ bodies moving with velocities V and U respectively along the same line, and let their mutual action take place in that line; if the one overtake the other, what will be their respective velocities at the instant after impact? We will answer this question in two extreme cases. (i.) Let us suppose the bodies to be guz¢e znelastic. In this case, when A ° touches B, it will continue to press against B until their velocities are equalised, when the mutual action ceases. For whatever deformation the . bodies may have undergone, they have no tendency to recover their shapes. If, therefore, x is their common velocity after impact, we shall have Ax + Br their joint momentum at the end of impact ; but their momentum before impact was AV + BU whence (A+B)r=AV+BU, an equation which determines »*. —59] Work: Meaning of the Term 43 (i1.) Let us suppose the bodies Zerfectly elastic. In this case they recover their shapes, with a force exactly equal to that with which they were com- pressed, Consequently the whole momentum lost by the one and gained by the other must be exactly double that lost while compression took place ; that is, up to the instant at which their velocities were equalised. But these are respectively AV — Ax and Ba— BU ; therefore if v and w are the required final velocities, Av=AV—-2(AV—-Ax) orv=—-Vt2r Bu=BU+2(Br—BU) or w=2x—U ; hence (A+ B)v=2BU +(A—B)V, and (A + B)w=2AV—(A-—B)U. The following conclusion from these equations may be noticed : suppose a ball A, moving with a velocity V, to strike directly an equal ball B at rest. In this case A=B and U =o, consequently v=o and z=V; that is, the former ball A is brought to rest, and the latter B moves on with a velocity V. If now B strike on a third equal ball C at rest, B will in turn be brought to rest, and C will acquire the velocity V. And the same is true if there is a fourth, or fifth, or indeed any number of balls. This result may be shown with ivory balls, and is a very remarkable experiment. 59. Work: meaning of the term.—It has been pointed out (19, 26) that a moving body has no power of itself to change either the direction or the speed of its motion, and that, if any such change takes place, it is a proof that the body is acted upon by some external force. But although change of motion thus always implies the action of force, forces are often exerted with- out causing any change in the motion of the bodies on which they act. For instance, when a ship is sailing at a uniform speed, the force exerted on it by the wind causes no change in its motion, but simply prevents such a change being produced by the resistance of the water ; or, when a railway-train is running with uniform velocity, the force of the engine does not change, but only maintains its motion in opposition to the forces, such as friction and the resistance of the air, which tend to destroy it. These two classes of cases—namely, first, those in which forces cause a change of motion ; and, secondly, those in which they prevent, wholly or in part, such a change being produced by other forces—include all the effects to which the action of forces can give rise. When acting in either of these ways, a force is said to do work: an expression which is used scientifically in a sense somewhat more precise, but closely accordant with that in which it is used in common language. A little reflection will make it evident that, in all cases in which we are accustomed to speak of work being done— whether by men, horse-power, or steam-power, and however various the pro- ducts may be in different cases—the physical part of the process consists solely in producing or changing motion, or in keeping up motion in opposition to resistance, or in a combination of these actions. The reader will easily convince himself of this by calling to mind what the definite actions are which constitute the work done by (say) a navvy, a joiner, a mechanic, a weaver ; that done bya horse, whether employed in drawing a vehicle or in turning a gin ; or that of a steam-engine, whether it be used to draw a railway-train or to 44 On Matter, Force, and Motion [59— drive machinery. In all cases the work done is reducible, from a mechanical point of view, to the elements that have been mentioned, although it may be performed on different materials, with different tools, and with different degrees of skill. It is, moreover, easy to see (53) that any possible change or motion may be represented as a gain by the moving body of an additional (positive or negative) velocity either in the direction of its previous motion, or at right angles to it; but a body which gains velocity is (27) said to be ac- celerated. Hence, what has been said above may be summed up as follows :—When a force produces acceleration, or when tt maintains motion unchanged in opposition to reststance, tt 1s satd to do WORK. 60. Measure of work.—In considering how work is to be measured, or how the relation between different quantities of work is to be expressed numerically, we have, in accordance with the above, to consider, first, work of acceleration; and, secondly, work against resistance. But in order to make the evaluation of the two kinds of work consistent, we must bear in mind that one and the same exertion of force will result in work of either kind according to the conditions under which it takes place: thus, the force of gravity acting on a weight let fall from the hand causes it to move with a continually accelerated velocity until it strikes the ground ; but if the same weight, instead of being allowed to fall freely through the air, be hung to a cord passing round a cylinder by means of which various degrees of friction can be applied to hinder its descent, it can be made to fall with a very small and practically uniform velocity. Hence, speaking broadly, it may be said that, in the former case, the work done by gravity upon the weight is work of acceleration only, while in the latter case it is work against resistance (friction) only. But it is very important to note that an essential condition, without which a force, however great, cannot do work either of one kind or the other, is that the thing acted on by it shall szove while the force continues to act. This is obvious, for if no motion takes place it clearly cannot be either accelerated or maintained against resistance. The motion of the body on which a force acts being thus necessarily involved in our notion of work being done by the force, it naturally follows that, in estimating how much work is done, we should consider how much—that is to say, how far—the body moves while the force acts upon it. This agrees with the mode of estimating quantities of work in common life, as will be evident if we consider a very simple case—for instance, that of a labourer employed to carry bricks up to a scaffold : in such a case a double number of bricks carried would represent a double quantity of work done, but so also would a double height of the scaffold, for whatever amount of work is done in raising a certain number to a height of twenty feet, the same amount must be done again to raise them another twenty feet, or the amount of work done in raising the bricks forty feet is twice as great as that done when they are raised only twenty feet. It is also to be noted that no direct reference to é7me enters into the conception of a quantity of work : if we want to know how much work a labourer has done, we do not ask how long he has been at work, but what he has done—for instance, how many bricks he has carried, and to what height ; and our estimate of the total amount of work is the same whether the man has spent hours or days in doing it. —60] Measure of Work 45 The foregoing relations between force and work may be put into definite mathematical language as follows :—-If the point of application of a force moves ina straight line, and if the part of the force resolved along this line acts in the direction of the motion, the product of that component and the length of the line is the work done by the force. If the component acts in the opposite direction to the motion, the component may be considered as a resistance, and the product is work done against the resistance. Thus, in (43), 1f we suppose @ to move up the plane from R to S, the work done by P is Px RS: the work done against the resistance W is W sinx x RS. It will be observed that if the forces are in equilibrium during the motion, so that the velocity of ais uniform, P equals W sin x, and consequently the work done by the power equals that done against the resistance. Also, since RS sin x equals ST, the work done against the resistance equals W x ST. In other words, to raise W from R to S requires the same amount of work as to raise it from T to S. If, however, the forces are not in equilibrium, the motion of a willnot be uniform, but accelerated ; the work done upon it will nevertheless still be represented by the product of the resultant force resolved along the direction of motion into the distance through which it moves. In order to ascertain the relation between the amount. of work done and the change produced by it in the velocity of the moving mass, we must recall one or two elementary mechanical principles. Let F be the resultant force resolved along the direction of motion, and S. the distance through which its point of application moves: then, according to what has been said, the work done by the force=FS. Further, it has been pointed out (28) that a constant force is measured by the momentum produced by it in a unit of time : hence, if T be the time during which the force acts, V the velocity of the mass M at the beginning of this period, and V, the velocity at the end, the momentum produced during the time T is MV, — MV, and consequently the momentum produced in a unit of time, or, in other words, the measure of the force, is MEV ea) oe Pei The distance S through which the mass M moves while its velocity changes from the value V to the value V, is the same as if it had moved during the whole period T with a velocity equal to the average value of the varying velocity which it actually possesses. But a constant force acting upon a constant mass causes its velocity to change at auniform rate; hence, in the present case, the average velocity is simply the arithmetical mean of the actual and final velocities : S=4(V,+ V)T. Combining this with the last equation, we get as the expression for the work done by the force F : FS=3$M(V2-V°); or, in words, when a constant force acts on a mass so as to change tts velocity, the work done by the force ts equal to half the uae of the mass into the change of the square of the veloctty. 46 On Matter, Force, and Motion [60- The foregoing conclusion has been arrived at by supposing the force F to be constant, but it is easy to show that it holds good equally if F is the average magnitude of a force which varies from one part to another of the total distance through which it acts. To prove this, let the distance S be subdivided into a very great number z of very small parts, each equal to s, so that zs=S. Then, by supposing s to be sufficiently small, we may with- out any appreciable error consider the force as.constant within each of these intervals, and as changing suddenly as its point of application passes from one interval, to’the’ next:; Let) F,) F7F,)2. .. Fy; be the forcessacting throughout the 1st, 2nd, 3rd... . #th interval, and let the velocity at the end of the same intervals be v,, U, Us . +--+ Un (=V,) respectively ; then, for the work done in the successive intervals, we have : Fis Pr +M(v,?— V?) Fs =3M(uv,? —v,”*) F,s=3M(v,’ —v,”) £8 =3M(v," — Yn? -1) = 3M(V 1? — 9,2 — 1); or, for the total work, (eo to a ee + Fn)s=43M(V,?-V?); where the quantity of the left-hand side of the equation may also be e+ koto. FE 1 arithmetical mean) of the forces F,, F,, &c. An important special case of the application of the above formula arises when either the initial or the final velocity of the mass M is nothing ; that is to say, when the effect of the force is to make a body pass from a state of rest into one of motion, or from a state of motion into one of rest. The general expression then assumes one of the following forms, namely :— FS =4}MV,? or, —FS=}MV?; written ms = FS, if we put F to stand for the average (or the first of which denotes the quantity of work which must be done on a body of mass M in order to give to it the velocity V,, while the second expresses the work that must be done in order to bring the same mass to rest when it is moving with the velocity V, the negative sign in the latter case showing that the force here acts zz opposition to the actual motion, and is therefore to be regarded as a resistance. In practice, the case which most frequently occurs is where work of ac- celeration and work against resistance are performed simultaneously. Thus, recurring to the inclined plane already referred to in art. 43, let M be the mass of a and W its weight. If the force P (where P is the constant force with which the string pulls M up the plane) be greater than W sin x, the mass M will move up the incline with a continually increasing velocity, and —62] Unit of Work. Power 47 if the point of application of P be displaced from R to S, the total amount of work done, namely, P x RS, consists of a portion= W sin x RS, done against the resistance of the weight W, and of a portion=(P—W sin x) RS expended in accelerating the weight. Hence, to determine the velocity wv with which W arrives at the top of the incline, we have the equation (P—W sin +) RS=4Mv’*; for the portion of P which is in excess of what is required to produce equili- brium with the weight W, namely, P— W sin x, corresponds to the resultant force F supposed in the foregoing discussion, and RS to the distance through which this resultant force acts. 61. Unit of work. Power.—-For strictly scientific purposes a unit of work is taken to be the work done by a unit of force when its point of appli- cation moves through the unit distance in the direction of its action ; but, as a convenient and sufficiently accurate standard for practical purposes, the quantity of work which is done in lifting 1 pound through the height of 1 foot is commonly adopted as the unit, and this quantity of work is spoken of as one ‘foot-pound.’ It is, however, important to observe that the foot-pound is not perfectly invariable, since the weight of a pound, and therefore the work done in lifting it through a given height, differs at different places, being a little greater near the Poles than near the Equator. On the metrical system the clogrammetre is the unit; it is the work done when a weight of a kilogramme is raised through a height of a metre. This is equal to 7°23 foot-pounds, and one foot-pound = "1383 of a kilogrammetre. . In estimating the usefulness of any motor it becomes necessary to know the time required by it for doing a given amount of work. The amount of work per second is the ower of the motor. The unit of power is the power required to do a unit of work in a unit of time. For measuring the power of engines the unit used is the horse-fower, which represents a rate of work of 33,000 foot-pounds per minute. It is to be observed that in every case the unit is of the same denomina- tion as the thing or quantity measured. The unit of length must bea length ; the unit of value must be a definite quantity of some valuable commodity. The numbers, to determine which is one of the objects of physical research, are to be considered as abstract numbers, representing how many times the unit is taken. | 62. Systems of units.—The units of mass, length, and time are said to be fundamental units, as all other units, such as those of area, velocity, acceleration, power, &c., are referred to them. These latter units are there- fore called derived units. The magnitudes of the fundamental units are, however, arbitrary. A large class of writers use the centimetre, gramme, and second, and this system is usually called the C.G.S. system ; others use the foot, pound,.and second. It thus becomes important to have a systematic method of reducing measurements from one system of units to another. Let L, M, T represent respectively the magnitude or dmenszons of the centimetre, the gramme, and the second, and L’, M’, T’ represent the 48 On Matter, Force, and Motion [62- dimensions of the foot, the pound, and the minute. Then, if a wire is found to be Z cm. or / ft. in length, its length may be represented either by ZL or Ui /fwvand hence Li orth - Os 7 UV de Ot. b= Th The ratio 2 is the length of a foot in gute what and has been found by direct comparison to be 30°4797.. Hence any measurement, Z’ in feet, is converted into centimetres by multiplying 7” by this number. In a similar manner, if #z and 7’ represent the number of units of mass in a piece of matter in the two systems, / We ei M where the unit ratio is the number of grammes in a pound, or 453°59. For converting a volume v’ into the equivalent v, (/L’) = (IL), or 2 = fe ) ve or Ux (-)~ ; For density, a =D) Yin WN Pies 7° 1373" 179 Dol’. (LY: Here the ratio [3 is said to bea measure of the magnitude or dimensions of the unit of density, in terms of the dimensions of the fundamental units of mass and length. Ifa substance is saidto have a unit density, then if M were the gramme and L? the cubic centimetre, the density of the substance would be that of water. If, however, M were the kilogramme and L* the cubic ‘centimetre, the density would be a thousand times that of water. If, again, L® represent a cubic decimetre, and M the kilogramme, the density would again be that of water. It appears, then, that the magnitude of the unit of density is directly proportional to the magnitude of the unit of mass, and inversely as the magnitude of the unit of volume or the cube of the unit of length. As unit density is the density of a unit mass for unit volume, it is clear that Ts meneures the dimensions of the unit of density. Similar explanations apply in the succeeding cases. For velocity, v 2 ie ca ‘dep d bua tinged Vg 1a iee as VU=.- = POA -62] 5 ‘ystems of Units The ratio T _second _ 1 IT’ minute 60. 49 If the units of time were the same, the unit factor ae I, and the velocity in centimetres would be oi Nes o)/ 0 = Se, where w” is the velocity in feet per second. el for Momentum, mv = my mie MUL_m'l’ M’L’ find ees or MU = gee mv" pew BL BRR one for Acceleration, a=—= ca dem Wiles 231) PEN eT Ce LL cee a= (7): 4 where a’ is the acceleration in feet per minute. ml For Porte, F =ma= a mel ML_ ml Nis Pp.) pe pe? ML /T\2 poML M67 M~LOA\T In the C.G.S. system the unit is called the Dye. For Work, W=Fl= a TON Par Yip rem es LL? Pe Ty? Pee ee In the C.G.S. system the unit of work is called the Erg. Rate of Work, or Power, ea Le ANG NY Ca St Bi ge Te” ae If work is expressed in foot-pounds or kilogramme-metres, the unit of E 50 On Matter, Force, and Motion [62- force being the weight of a pound or kilogramme, then to convert a certain number of foot-pounds into kilogramme-metres we have 21) WL =r Wwe “W’ Work (kgr.-m) = = work, foot-pounds, W aL W*" pound 7 h = wltere 7 alee: ee Ly foo ee L metre pede: the unit factor being thus 0°1383. Similarly, to convert foot-pounds per minute into kilogr.-metres per second, aye gee”: where the conversion factor becomes 0°00230. The units commonly used for measuring the power of engines are the horse-power, which is 33,000 times as great as the unit in which P’ of the last equation was measured, and the force de cheval, which is 75 times as great as the unit in which P was measured. Hence, if P’ is to be in horse- power, and P in force de cheval, the equation will become P =0:00230 x 33:09 py 75 = 1°O120gh and hence one British horse-power = 1°0139 force de cheval. These examples will be sufficient to indicate the method of converting measurements from one system of units to any other, and the treatment of other derived units may be deferred until they are needed. 63. Energy.—The fact that any agent is capable of doing work is usually expressed by saying that it possesses Hvergy, and the quantity of energy it possesses is measured by the amount of work it can do. For example, in the case of the inclined plane above referred to, the working power or energy of the force P is Px RS; and if this force acts under the conditions last supposed, by the time its own energy is exhausted (in consequence of its point of application having arrived at S, the limit of the range through which it is supposed able to act), it has one upon the mass M a quantity of energy equal to that which has been expended ; for, in the first place, M has been raised through a vertical height equal to ST, and could by falling again through the same height do an amount of work represented by W x ST ; and in the second place M can do work by virtue of the velocity that has been imparted to it, and can continue moving in opposition to any given resistance R through a distance s, such that Rs=4Mv. The energy possessed by the mass M in consequence of its having been raised from the ground is commonly distinguished as exergy of position or potential energy, and is measured by the product of the force tending to cause motion into the distance through which the point of application of the force —65] Transformation of Energy 51 is capable of being displaced in the direction in which the force acts. The energy possessed by a body in consequence of its velocity is commonly dis- tinguished as energy of motion, or kinetic energy : it is measured by half the product of the moving mass into the square of its velocity. 64. Varieties of energy.—On considering the definition of work given above, it will be seen that a force is said to do work when it produces any change in the condition of bodies ; for the only changes which, according to the definition of force given previously (26), a force is capable of producing, are changes in the state of rest or motion of bodies, and changes of their place in opposition to resistances tending to prevent motion or to produce motion in an opposite direction. There are, however, many other kinds of physical changes which can be produced under appropriate conditions, and the recent progress of investigation has shown that the conditions under which changes of all kinds occur are so far analogous to those required for the production of work by mechanical forces that the term work has come to be used in a more extended sense than formerly, and is now often used to signify the production of any sort of physical change. Thus work is said to be done when a body at a low temperature is raised to a higher temperature, just as much as when a weight is raised from a lower to a higher level ; or, again, work is done when an electrical, magnetic, or chemical change is produced. This extension of the meaning of the term work involves a similar extension of the meaning of exergy, which in this wider sense may be defined as the capacity for producing physical change. As examples of energy in this more general sense, the following may be mentioned :—(a@) The energy possessed by gunpowder in virtue of the mutual chemical affinities of its constituents, whereby it is capable of doing work by generating heat or by acting on a cannon-ball so as to change its state of rest into one of rapid motion ; (8) the energy of a charged Leyden jar, which, according to the way in which the jar is discharged, can give rise to changes’ of temperature, to changes of chemical composition, to mechanical changes, or to changes of magnetic or electrical condition ; (c) the energy of a red-hot ball, which, amongst other effects it 1s capable of producing, can raise the temperature and increase the volume of bodies colder than itself, or can change ice into water or water into steam; the energy of the stretched string of a bow: here work has been consumed in stretching the string ; when it is released the work reappears in the velocity imparted to the arrow. 65. Transformation of energy.—It has been found by experiment that when one kind of energy disappears or 1s expended, energy of some other kind is produced, and that, under proper conditions, the disappearance of any one of the known kinds of energy can be made to give rise to a greater or less amount of any other kind. One of the simplest illustrations that can be given of this transformation of energy is afforded by the oscillations of a pendulum. When the pendulum is at rest in its lowest position it does not possess any energy, for it has no power of setting either itself or other bodies in motion, or of producing in them any kind of change. In order to set the pendulum oscillating, work must be done upon it, and it thereafter possesses an amount of energy corresponding to the work that has been expended. E 2 U. OF ILL, LIB. 52 On Matter, Force, and Moton [65— When it has reached either end of its path, the pendulum is for an instant at rest ; but it possesses energy by virtue of its position, and can do an amount of work while falling to its lowest position, which is represented by the product of its weight into the vertical height through which its centre of gravity de- scends. When at the middle of its path, the pendulum is passing through its position of equilibrium, and has no power of doing work by falling lower ; but it now possesses energy by virtue of the velocity which it has gained, and this energy is able to carry it up on the second side of its lowest position to a height equal to that from which it has descended on the first side. By the time it reaches this position the pendulum has lost all its velocity, but it has regained the power of falling ; this, in its turn, is lost as the pendulum returns again to its lowest position, but at the same time it regains its pre- vious velocity. Thus, during every quarter of an oscillation the energy of the pendulum changes from potential energy of position into actual energy or energy of motion, or wice versa. A more complex case of the transformation of energy is afforded by a thermo-electric pile, the terminals of which are connected by a conducting wire ; the application of energy in the form of heat to one face of the pile gives rise to an electric current in the wire, which, in its turn, reproduces heat, or by proper arrangements can be made to produce chemical, magnetic, or mechanical effects, such as those described below in the chapters on Electricity. It has also been found that the transformations of energy always take place according to fixed proportions. For instance, when coal or any other combustible is burned, its chemical energy, or power of combining with oxygen, vanishes, and heat or thermal energy is produced, and the quantity of heat produced by the combustion of a given amount of coal is fixed and invariable. If the combustion takes place under the boiler of a steam-engine, mechanical work can be obtained by the expenditure of part of the heat pro- duced, and here again the quantitative relation between the heat expended and the work gained in place of it is perfectly constant. 66. Conservation of energy.—Another result of great importance, which has been arrived at by experiment, is that the total amount of energy possessed by any system of bodies is unaltered by any transformations arising from the action of one part of the system upon another, and can only be increased or diminished by effects produced on the system by external agents. In this statement it is of course understood that in reckoning the sum of the energy of various kinds which the system may possess, those amounts of the different forms of energy which are mutually convertible into each other are taken as being numerically equal; or, what comes virtually to the same thing, the total energy of the system is supposed to be reduced—either ac- tually, or by calculation from the known ratio of transformation of the various forms of energy—to energy of some one kind ; then the statement is equivalent to this: that the total energy of any one form to which the energy of a given system of bodies is reducible is unalterable so long as the system is not acted on from without. Practically it is always possible, in one way or another, to convert the whole of the energy possessed by any body or system of bodies into heat, but it cannot be all converted without loss into any other form of energy ; hence the principle stated at the beginning of this article can be 66] Conservation of Energy eis: enunciated in the closest conformity with the direct results of experiment by saying that, so long as any system of bodies is not acted on from without, the total quantity of heat that can be obtained from it is unalterable by any changes which may go on within the system itself. Forinstance, a quantity of air compressed into the reservoir of an air-gun possesses energy which is represented partly by the heat which gives to it its actual temperature above the absolute zero (508), and partly by the work which the air can do in expand- ing. This latter portion can be converted into heat in various ways, as, for example, by allowing the air to escape through a system of capillary tubes so fine that the air issues from them without any sensible velocity ; if, how- ever, the expanding air be employed to propel a bullet from the gun, it produces considerably less heat than in the case previously supposed, the deficiency being represented for a time by the energy of the moving bullet, but reappearing in the form of heat in the friction of the bullet against the air, and, when the motion of the bullet is destroyed, by striking against an inelastic obstacle at the same level as the gun. But whatever the mode and however numerous the intermediate steps by which the energy of the com- pressed air is converted into heat, the total quantity of heat finally obtainable from it is the same. 54 Gravitation and Molecular Attraction [67— BOOK II GRAVITATION AND MOLECULAR ATTRACTION CHAPTER TI GRAVITY. CENTRE OF GRAVITY. THE BALANCE 67. Universal attraction: its laws.—Universal attraction is a force in virtue of which the material particles of all bodies tend incessantly to approach each other ; it is an action, however, which all bodies, at rest or in motion, exert upon one another, no matter how great or how small the space between them may be, or whether this space be occupied or un- occupied by other matter. A vague hypothesis of the tendency of the matter of the earth and stars o a common centre was adopted even by Democritus and Epicurus. Kepler assumed the existence of a mutual attraction between the sun, the earth, and the other planets. Bacon, Galileo, and Hooke also recognised the existence of universal attraction. But Newton was the first who established the law, and the universality of gravitation. After Newton’s time the attraction of matter by matter was experimentally established by Cavendish. This eminent English physicist succeeded, by means of a delicate'torsion balance (90), in rendering visible the attraction between a large leaden and a small copper ball. The attraction between any two bodies is the resultant of the attractions. of each molecule of the one upon every molecule of the other according to the law of Newton, which may be thus expressed: the attraction between two material particles ts directly proportional to the product of their masses and invers:ly broportional to the square of their distances asunder. To ‘illustrate this, we may take the case of two spheres, which, owing to their symmetry, attract each other just as if their masses were concentrated in their centres. If without other alteration the mass of one sphere were doubled, tripled, &c., the attraction between them would be doubled, tripled, &c. If, however, the mass of one sphere being doubled, that of the other were increased three times, the distance between their centres remaining the same, the attraction would be increased six times. Lastly, if, without alter- ing their masses, the distance between their centres were zzcreased from I to 2,3,4.... units, the attraction would be azmznished to the 4th, oth, —68] Lerrestrial Gravitation 55 16th .... part of its former intensity. In short, if we define the unit of attraction as that which would exist between two units of mass whose distance asunder was the unit of length, the attraction of two molecules having the masses #7 and m’, at the distance 7, would be expressed by mene’ 68. Terrestrial gravitation—The tendency of any body to fall towards the earth is due to the mutual attraction of that body and the earth, or to terrestrial gravitation, and is, in fact, merely a particular case of universal attraction. At any point of the earth’s surface, the direction of gravity—that is, the line which a falling body describes—is called the ver¢zcal line. The vertical lines drawn at different points of the earth’s surface converge very nearly to the earth’s centre. For points situated on the same meridian the angle con- tained between the vertical lines equals the difference between the latitudes of those points. The directions of the earth’s attraction upon neighbouring bodies, or upon different molecules of one and the same body, must| therefore be considered as parallel, for the two vertical lines form the sides of a triangle whose vertex is near the earth’s centre, about 4,000 miles distant, and whose base is the small distance between the molecules under consideration. A plane or line is said to be horizontal when it 1s perpendicular to the vertical line. The vertical line at any point of the globe is generally Herermined by the plumb-line (fig. 41), which consists of a weight attached to the end of a string. It is evident that the weight cannot be in equilibrium unless the direction of the earth’s attraction upon it passes through the point of support, and therefore co- incides with that of the string. The horizontal plane is also determined with creat ease, since it coincides, as will be afterwards shown, an the /eve/ surface of every liquid when in a state of equili- brium. When the mean figure of the earth has been approxi- mately determined, it becomes possible to compare the direction of the plumb-line at any place with that of the normal to the mean figure at that place. When any differ- ence in these directions can be detected, it constitutes a deviation of the plumb-line, and is due to the attraction of some great mass of matter in the neighbourhood, such as a mountain. Thus, in the case of the mountain of Schiehallion, in Perthshire, it was found by Dr. Maskelyne that the angle between the directions of two plumb-lines, one at a station to the north, and the other to the south, of the mountain was greater by 11/6 than the angle between the normals of the mean surface of the earth at those points ; in other words, each plumb-line was deflected by about 6” towards the mountain. By calculating the volume and mass of the mountain, it was inferred from this observation that the mean density of the mountain was to that of the earth in the ratio of 5:9, and that the mean density of the earth is about five times that of water—a Ang ANNI Cf: Fig. 41 56 Gravitation and Molecular Attraction [68— result agreeing pretty closely with that deduced from Cavendish’s experi- ment referred to in the last article. 69. Centre of gravity; its experimental determination.—Into what- ever position a body may be turned with respect to the earth, there is a certain point invariably situated with respect to the body, through which the resultant of the attracting forces between the earth and its several mole- cules always passes. This point is called the centre of gravity ; it may be within or without the body, according to the form of the latter ; its existence, however, is easily established by the following considerations : let 77 72’ m2’’ m’”’’. ... (fig. 42) be molecules of any body. The earth’s attraction upon these molecules wlll constitute a system of parallel forces, having a common vertical direction, whose resultant will be found by seeking first the resultant of the forces which act on any two molecules, 7#z and 7’, then that of this resultant and a third force acting on m’’, and so on until we arrive at the final resultant W, representing the weight of the body and applied ata certain point G. If the body be now turned into the position shown in fig. 43, the molecules 7 m’ m’’. . . . will continue to be acted on by the Ee eee a= ---- - Fig. 42 same forces as before, the resultant of the forces on 7 and wm’ will pass through the same point o in the line mz’, the following resultant will again - pass through the same point o’ in o72’’, and so on up to the final resultant P, which will still pass through the same point C, which is the centre of gravity. To find the centre of gravity of a body is a purely geometrical problem ; in many cases, however, it can be at once determined. For instance, the centre of gravity of a right line of uniform density is the point which bisects its length ; in the circle and sphere it coincides with the geometrical centre ; in cylindrical bars it is the middle point of the axis. The centre of gravity of a plane triangle is in the line which joins any vertex with the middle of the opposite side, and at a distance from the vertex equal to two-thirds of this line : in a cone or pyramid it is in the line which joins the vertex with the centre of gravity of the base, and at a distance from the vertex equal to three-fourths of this line. These rules, it must be remembered, presuppose that the several bodies are of uniform density. In order to determine experimentally the centre of gravity of a body, it is suspended by a string in two different positions, as shown in figs. 44 and 45; the point where the directions AB and CD of the string in the two —71] Different States of Equitibrium 57 experiments intersect each other is the centre of gravity required. For, the resultant of the earth’s attraction being a vertical force applied at the centre of gravity, the body can only be in equilibrium when the point lies vertically under the point of suspension ; that is, in the prolongation of the suspended string. But the centre of gravity, being in AB as well as in CD, must coincide with the point of intersec- tion of these two lines. The centre of gravity of a thin piece of cardboard of irregular shape, for instance, may be found by balancing it in two positions on a knife-edge ; the centre of gravity will then lie in the intersection of the two lines. 70. Equilibrium of heavy bodies. —Since the action of gravity H upon a body reduces itself to a single vertical force applied at the centre of gravity and directed to- wards the earth’s centre, equili- brium will be established only when this resultant is balanced by the resultant of other forces and resistances acting on the body at the fixed point through which it passes. When only one point of the body is fixed, it will be in equilibrium if the vertical line through its centre of gravity passes through the fixed point. If more than one point is supported, the body will be in equilibrium if a vertical line, through the centre of gravity, passes through a point within the polygon formed by joining the points of support. The Leaning Tower of Pisa continues to stand because the vertical line drawn through its centre of gravity passes within its base. It is easier to stand on our feet than on stilts, because in the latter case the smallest motion is sufficient to cause the vertical line through the centre of gravity of our bodies to pass outside the supporting base, which is here reduced to a mere line joining the feet of the stilts. A man carrying a load on his back must lean forward : if he carries it in the left hand he must incline the upper part of his body to the right, for otherwise the centre of gravity of the body and of the load would fall outside the line joining the feet and he would fall. Again, it is impossible to stand on one leg if we keep one side of the foot and head close to a vertical wall, because the latter prevents us from throwing the body’s centre of gravity vertically above the supporting base. 71. Different states of equilibrium.—Although a body supported by a fixed point is in equilibrium whenever its centre of gravity is in the vertical line through that point, the fact that the centre of gravity tends, incessantly to occupy the lowest possible position leads us to distinguish between three states of equilibrium—s/able, unstable, neutral. A body is said to be in stadle equilibrium if it tends to return to its first position after the equilibrium has been slightly disturbed. Every body is in 58 Gravitation and Molecular Attraction [71- this state when its position is such that the slightest alteration of the same elevates its centre of gravity; for the centre of gravity will descend again when permitted, and after a few oscillations the body will return to its original position. The pendulum of a clock continually oscillates about its position of stable equilibrium, and an egg on a level table is in this state when its long axis is horizontal. We have another illustration in the toy represented in the adjoining fig. 46. A small figure cut in ivory is made to stand on one foot at the top of a pedestal by being loaded with two leaden balls, a, 6, placed sufficiently low to throw the centre of gravity g of the whole compound body below the foot of the figure. After being disturbed, the little figure oscillates like a pendulum, having its point of sus- pension at the toe, and its centre of gravity at a lower point, & A body is said to be in wsstable equilibrium when, after the slightest disturbance, it tends to depart still more from its original position. A body is in this state when its centre of gravity is vertically above the point of support, or higher than it would be in any adjacent position of the body. An egg standing on its end, or a stick balanced upright on the finger, is in this state. Lastly, if in any adjacent position a body still remains in equilibrium, its state of equilibrium is said to be zeztral or labile. In this case an altera- tion in the position of the body neither raises nor lowers its centre of gravity. A perfect sphere resting on a horizontal plane is in this state. Fig. 47 represents three cones, A, B, C, placed respectively in stable, unstable, and neutral equilibrium upon a horizontal plane. The letter g in each shows the position of the centre of gravity. 72. The balance.— The balance is an in- strument for determin- ing the relative weights or masses of bodies. There are many varie- ties. The ordinary balance (fig. 48) consists of a lever of the first kind, called the deam, AB, with its fulcrum in the middle ; at the extremities of the beam are suspended two scale-pans, C and D, one intended to receive the object to be weighed, and the other the counterpoise. The fulcrum consists of a steel prism, 7, commonly called a kvzfe-edge, which passes through the beam, and rests with its sharp edge, or axzs of susfenston, upon two supports ; these are formed of agate, in order to diminish the friction. A needle or pointer is fixed to the beam, and oscillates with it in front of a graduated arc, a: when the beam is perfectly horizontal the needle points to the zero of the graduated arc (fig. 51). Since by (40) two equal forces in a lever of the first kind cannot be in —73] Conditions to be satisfied by a Balance 59 equilibrium unless their leverages are equal, the length of the arms 7A and 2B ought to remain equal during the process of weighing. To secure this the scales are suspended from hooks, whose curved parts have sharp edges, ard rest on similar edges at the ends of the beam. In this manner the scales are in effect supported on mere points, which remain unmoved during the oscillations of the beam. This mode of suspension is represented in fig. 48. 73. Conditions to be satisfied by a balance.—A good balance ought to satisfy the following conditions :— 1. The two arms of the beam ought to be precisely equal; otherwise, according to the principle of the lever, unequal weights will be required to produce equilibrium. To test whether the arms of the beam are equal, AU SYTAANYVANEETGDETUUTATVIUU TOMTOM SE HA AAA TO OT Fig. 48 weights are placed in the two scales, until the beam becomes horizontal ; the contents of the scales being then interchanged, the beam will remain horizontal if its arms are equal, but if not, it will descend on the side of the longer arm. u. Lhe balance ought to be in equilibrium when the scales are empty, for otherwise unequal weights must be placed in the scales in order to produce equilibrium. It must be borne in mind, however, that the arms are not necessarily equal, even if the beam remains horizontal when the scales are empty ; for this result might also be produced by giving to the longer arm the lighter scale. ili. The beam being horizontal, its centre of gravity ought to be in the same vertical line with the edge of the fulcrum, and a little below the latter, for otherwise the beam would not be in stable equilibrium (71). 60 Gravitation and Molecular Attraction [73- The effect of changing the position of the centre of gravity may be shown by means of a beam (fig. 49), whose fulcrum, being the nut of a screw, a, can be raised or lowered by turning the screw head, 0. When the fulcrum is at the top of the groove c, in which it slides, the centre of gravity of the beam is below its edge, and the latter oscillates freely about a position of stable equilibrium. By gradually lowering the fulcrum its edge may be made to pass through the centre of gravity of the beam when the latter is in neutral equilibrium ; that is to say, it no longer oscillates, but remains in equilibrium in all positions. When the fulcrum is lowered still more, the centre of gravity passes above its edge, the beam is in a state of unstable equilibrium, and is overturned by the least displacement. 74. Delicacy of the balance.—A balance is said to be delicate or sensible when a very small difference between the weights in the scales causes a per- ceptible deflection of the pointer. Let A and B (figs. 50 and 51) be the point from which the scale-pans are suspended, and C the axis of suspension of the beam. A, B, and C are assumed to be in the same straight line, according to the usual arrangement. Suppose weights P and Q to be in the pans, suspended from A and B re- spectively, and let G be the centre of gravity of the beam ; then the beam will come to rest in the position shown in the figure, where the line DCN is vertical, and ECG is the direction of the pointer. According to the above statement, the greater the angle ECD for a given difference between P and Q, the greater is the sensibility of the balance. Draw GN at right angles to CG: Let W be the weight of the beam ; then from the properties of the lever (40) it follows that measuring moments with respect to C, the moment of P equals the sum of the moments of Q and W—a condition which at once leads to the relation (P—OQ)AC=WxGN. -75] Physical and Chemical Balances OI e Now it is clear that fora given value of CG the angle GCN (that is, ECD, which measures the delicacy) is greater as GN is greater; and from the formula it is clear that for a given value of P—Q we shall have GN greater as AC is greater, and as W is less. Again, for a given value of GN the angle GCN is greater as GC is less. Hence the means of rendering a balance delicate are— i. Zo make the arms of the balance long. u. Zo make the weight of the beam as small as ts consistent with its rigidity. ii. Zo bring the centre of gravity of the beam a very little below the point of support. Moreover, since friction will always oppose the action of the force that tends to preponderate, the balance will be rendered more delicate by diminish- ing friction. To secure this advantage, the edges from which the beam and scales are suspended are made as sharp and as hard as possible, and the supports on which they rest are very smooth and hard. This is effected by the use of agate knife-edges. And, further, the pointer is made long, since its elongation renders a given deflection more perceptible by increasing the arc which its end describes. The sensitiveness of a balance is expressed by the ratio of the smallest weight, which will produce a measurable deflection of the pointer, to the load. 75. Physical and chemical balances.—Fig. 52 represents one of the accurate balances ordinarily used for chemical analysis. Its sensitiveness is ir TMT Tm TTT ATTN TT Tui AAA rE such that when charged with a kilogramme (1,000 grms.) in each scale an excess of a tenth of a milligramme (z5455 of a grm.)in either scale produces a very perceptible deflection of the index. 62 Gravitation and Molecular Attraction [75- + In order to protect the balance from air currents, dust, and moisture, it is always, even when weighing, surrounded by a glass case, whose front slides up and down, to enable the operator to introduce the objects to be weighed. Where extreme accuracy is desired the case is constructed so that the space may be exhausted, and the weighing made zz vacuo. In order to preserve the edge of the fulcrum as much as possible, the whole beam, BB, with its fulcrum K, can be raised from the support on which the latter rests by simply turning the button O outside the case. The horizontality of the beam is determined by means of a long index, which points downwards to a graduated arc near the foot of the supporting pillar. Lastly, the button C serves to alter the sensitiveness of the balance ; by turning it, the centre of gravity of the beam can be made to approach or recede from the fulcrum (73). 76. Method of double weighing.—Even if a balance be not perfectly accurate, the true weight of a body may still be determined by its means. To do so, the body to be weighed is placed in one scale, and shot or sand poured into the other until equilibrium is produced ; the body is then replaced by known weights until equilibrium is re-esta- blished. The sum of these weights will neces- sarily be equal to the weight of the body, for, acting under precisely the same circumstances, both have produced precisely the same effect. The exact weight of a body may also be deter- mined by placing it successively in the two pans of a balance, and then deducing its true weight. For having~placed in one pan the body to be weighed, whose true weight is #, and in the other the weight Z, required to balance it, let a and 6 be the arms of levers corresponding to x and 7. Then from the principle of the lever (40) we have ax=pb. Similarly, if , is the weight when the body is placed in the other pan, then dx=af,. Hence abs =abpp,, from which x=,/ff,. This method was invented by Pére Amiot, but is ordinarily known as Borda's Method. Jolly made use of a very sensible balance to determine the constant of gravity. The balance (fig. 53) was placed in a room in the tower of the University of Miinich, and to each of the scale-pans was attached, by a wire 21 metres in length, a second scale-pan. A mass of mercury of 5 kilogrammes contained in a glass vessel was first counterpoised in the upper scale-pan ; it was then moved to the lower one, and it was found necessary to add 31°683 mgr. to the upper pan in order to counterbalance the increase in attractiveness due to the greater force in the lower pan. Taking the radius of the earth at Munich at 6,365,722 metres, the number —76] Method of Double Weighing 63 calculated from the formula in (83) is 33 mgr.; a sufficiently close result when the difficulties of the experiments are taken into account. A large lead sphere was then placed immediately below the mass in the lower pan, and produced a measurable attraction. From the attraction thus produced by the known mass of the lead it was possible to deduce the mass and the mean density of the earth (68); the number obtained was 5°69. Similar experiments made by Prof. Poynting have led to the number 5°5: 64. LAWS OF Gravitation and Molecular Attraction [77- CHAPTER FALLING BODIES. INTENSITY OF TERRESTRIAL GRAVITY. THE PENDULUM 77. Laws of falling bodies.—Since a _ body falls to the ground in consequence of the earth’s attraction on each of its molecules, it follows that, everything else being the same, all bodies, great and small, light and heavy, ought to fall with equal rapidity, and a lump of sand without cohesion should during its fall retain its original form as perfectly as if it were compact stone. The fact that a stone falls more rapidly than a feather is due solely to the unequal resistances opposed by the air to the descent of these bodies ; 27 a vacuum all bodies fall with equal rapidity. To demonstrate this, by experiment a glass tube about two yards long (fig. 54) may be taken, having one of its ends completely closed, and a brass cock fixed to the other. After having introduced bodies of different weights and densities (pieces of lead, paper, feathers, &c.) into the tube, the air is withdrawn from it by an air-pump, and the cock closed. If the tube be now suddenly re- versed, all the bodies will fall equally quickly. On introducing a little air and again inverting the tube, the lighter bodies become slightly retarded, and this retardation increases with the quantity of air introduced. The resistance opposed by the air to falling bodies is especially remarkable in the case of liquids. The Staubbach in Switzerland is a good illustration ; an immense mass of water is seen fall- ing over a high precipice, but before reaching the bottom it is shattered by the air into the finest mist. In a vacuum, however, liquids fall lke solids without separation of their molecules. The water-hammer illustrates this : the instrument con- sists of a thick glass tube about a foot long, half filled with water, the air having been expelled by ebullition previous to closing one extremity with the blowpipe. When such a tube is suddenly inverted, the water falls in one undivided mass against the ~78] Atwood’s Machine 65 other extremity of the tube, and produces a sharp dry sound, resembling that which accompanies the shock of two solid bodies. From Newton’s law (67) it follows that when a body falls - to the earth the force of attrac- tion which causes it to do so increases as the body ap- proaches the earth. Unless the height from which the body falls, however, be very great, this increase will be altogether inappreciable, and the force in question may be considered as constant and continuous. If the resistance of the air were removed, therefore, the motion of all bodies falling to the earth would be uniformly accelerated, and would obey the laws already explained (49). 78. Atwood’s machine.— Severa! instruments have been invented for illustrating and experimentally verifying the laws of falling bodies. Galileo, who discovered these laws in the early part of the seven- teenth century, illustrated them by means of bodies falling down inclined planes. The great object of all such instruments is to diminish the rapidity of the fall of bodies without altering the character of their motion, for by this means their motion may not only be _ better observed, but it will be less modified by the resistance of the air (48). The most convenient instru- ment of this kind is that invented by Atwood at the end of the last century, and represented in fig. 55. It consists of a stout pillar of wood, about 2} yards high, at the top of which is a brass pulley, whose axlerests and turns upon four other wheels, called /r¢ctton wheels, inasmuch as they serve to diminish friction. Two equal weights M and M’, are attached to the F ahi Ww mya X a | | AN i Alina me ( i i || Sena rani ana Se ik = UII = “i Teasers ee ETE ST Ernepoer eee PRuEnp rnp SEPT j pay Fo epee (oe 66 Gravitation and Molecular Attractton [78- extremities of a fine silk thread, which passes round the pulley ; a timepiece, H, fixed to the pillar, is regulated by a seconds pendulum, P, in the usual way ; that is to say, the oscillations of the pendulum are communicated to a ratchet, whose two teeth, as seen in the figure, fit into those of the ratchet wheel. The axle of this wheel gives motion tothe seconds hand of the dial, and also to an eccentric behind the dial, as shown at E bya separate figure. This eccentric plays against the extremity of a lever, D, which it pushes until the latter no longer supports the small plate z; and thus the weight M, which at first rested on this plate, is suddenly exposed to the free action of gravity. The eccentric is so constructed that the little plate z falls precisely when the hand of the dial points to zero. The weights M and M’, being equal, hold each other in equilibrium ; the weight M, however, is made to descend slowly by putting a small bar or overweight 7z upon it ; and, to measure the spaces which it describes, the rod or scale Q is divided into feet and inches, commencing from the plate z. To complete the instrument there are a number of plates, A, A’, C, C’, and a number of rings, B, B’, which may be fixed by screws at any part of the scale. The plates arrest the descending weight M, the rings only arrest the bar or overweight 77, which was the cause of motion, so that after passing through them the weight M, in consequence of its inertia, will move on uniformly with the velocity it had acquired on reaching the ring. The several parts of the apparatus being described, a few words will suffice to explain the method of experimenting. Let the hand of the dial be placed behind the zero point, the lever D adjusted to support the plate z, on which the weight M with its overweight m rests, and the pendulum put in motion.. As soon as the hand of the dial points to zero, the plate z will fall, the weights M and wz will descend, and by a little attention and a few trials it will be easy to place a plate A so that M may reach it exactly as the dial indicates the expiration of one second. To make a second experiment let the weights M and 7, the plate z, and the lever D be placed as at first ; remove the plate A, and in its place put aring, B, so as to arrest the overweight 7 just when the weight M would have reached A ; on putting the pendulum in motion again it will be easy, after a few trials, to put a plate, C, so that the weight M may fall upon it precisely when the hands of the dial point to two seconds. Since the overweight in this experiment was arrested by the ring B at the expiration of one second, the space BC was described by M in one second purely in virtue of its own inertia, and consequently by (29). BC will indicate the velocity of the falling mass at the expiration of one second. Proceeding in the same manner as before, let a third experiment be made in order to ascertain the point B’ at which the weights M and w arrive after the lapse of two seconds, and putting a ring at B’, ascertain by a fourth experiment the point C’ at which M arrives alone, three seconds after the descent commenced ; B’C’ will then express the velocity acquired after a descent of twoseconds. Ina similar manner, by a fifth and sixth experiment, ‘we may determine the space OB” described in three seconds, and the velo- city B’C’” acquired during those three seconds, and so on; we shall find that B’C’ is twice and B”’C” three times as great as BC—in other words, that the velocities BC, B’C’, B’C” increase in the same proportion as the ~79] | Morin’s Apparatus a7 times (I, 2, 3, . . . seconds) employed in their acquirement. By the defi- nition (49), therefore, the motion is uniformly accelerated. The same ex- periments will also serve to verify and illustrate the four laws of uniformly accelerated motion as enunciated in (49). For example, the spaces OB, Of OB. 0 say.described froma, state of rest. in)J, 2,,3,.-, ...-..seconds, will be found to be proportional to the numbers I, 4,9 ...; that is to say, to the squares of those numbers of seconds, as stated in the third law. Lastly, if the overweight 7z be changed, the acceleration or velocity BC acquired per second will also be changed, and we may easily verify the assertion in (27), that force is proportional to the product of the mass moved, into the acceleration produced in a given time. For instance, assuming the pulley to be so light that its inertia can be neglected, then if #z weighed half an ounce, and M and M’ each 153 ounces, the acceleration BC would be found to be six inches ; whilst.if #z weighed one ounce, and M and M’ each 633 ounces, the acceleration BC would be found to be three inches. Now in these cases the forces producing motion, that is the overweights, are in the ratio of 1:2; while the products of the masses and the accelera- tions are in the ratio of ($+ 153+15%) x 6 to (1 + 634 + 634) x 3; that is, they are also in the ratio 1:2. Now the same result is obtained in whatever way the magnitudes of #, M, and M’ are varied, and consequently in all cases the ratio of the forces producing motion equals the ratio of the mo- menta generated. 79. Morin’s apparatus.—The principle of this apparatus, the original idea of which is due to General Poncelet, is to make the falling body trace its own path. Fig. 56 gives a view of the whole apparatus, and fig. 57 gives the details. The apparatus consists of a wooden framework, about 7 feet high, which holds in a vertical position a very light wooden cylinder, M, which can turn freely about its axis. This cylinder is coated with paper divided into squares by equidistant horizontal and vertical lines. The latter measure the path traversed by the body falling along the cylinder, while the horizontal lines are intended to divide the duration of the fall into equal parts. The falling body is a mass of iron, P, provided with a pencil, which is pressed against the paper by a small spring. The iron is guided in its fall by two light iron wires which pass through guide-holes on the two sides. The top of this mass is provided with a tipper which catches against the end of a bent lever, AC. This being pulled by the string K attached at A, the weight falls. Ifthe cylinder M were fixed, the pencil would trace a Straight line on it; but if the cylinder moves uniformly, the pencil traces the line mn, which serves to deduce the law of the fall. The cylinder is rotated by means of a weight, Q, suspended to a cord which passes round the axle G. At the end of this are two toothed wheels, c and 9, which turn two endless screws, a and 4, one’ of which turns the cylinder, and the other two vanes, + and x’ (fig. 57). At the other end is a ratchet wheel, in which fits the aa of a lever, B ; by pulling at a cord fixed to the other end of B, the wheel is liberated, the weight Q descends, and the whole system begins to turn. The motion ig at first accelerated, but as the air offers a resistance to the vanes (48), which increases as the rotation becomes more rapid, the resistance finally equals the acceleration which F 2 68 Gravitation and Molecular Attraction [79— gravity tends to impart. From this time the motion becomes uniform. This is the case when the weight Q has traversed about three-quarters of its course ; at this moment the weight P is detached by pulling the cord K, and the pencil then traces the curve 777. If, by means of this curve, we examine the double motion of the pencil on the small squares which divide the paper, we see that for displacements Oi: i a mi) Eats in —=—= SSS —— : Fig. 56 I, 2,3... in a horizontal direction, the displacemeénts are 1,4,9 4.5 ~= 5 in a vertical direction. This shows that the paths traversed in the direction of the fall are directly as the squares of the lines in the direction of the rotation, which verifies the second law of falling bodies. From the relation which exists between the two dimensions of the curve wn, it is concluded that this curve is a parabola (51). —80] The Length of the Compound Pendulum 69 8o. The length of the compound pendulum.—The formula deduced in article (55), and the conclusions which follow therefrom, refer to the case of the simple or mathematical pendulum; that is, to a single heavy point suspended by a thread without weight. Such a pendulum has only an imaginary existence, and any pendulum which does not realise these con- ditions is called a compound or physical pendulum. The laws for the time of vibration of a compound pendulum are the same as those for the motion of the simple pendulum, though it will be necessary to define accurately what is meant by the /eneth of such a pendulum. A compound pendulum being formed of a heavy rod terminated by a greater or less mass, it follows that the several material points of the whole system will strive to perform their oscillations in different times, their distances from the axis of suspension being different, and the more distant points requiring a longer time to complete an oscillation. From this, and from the fact that being points of the same body they must all oscillate together, it follows that the motion of the points near the axis of suspension will be retarded, whilst that of the more distant points will be accelerated, and between the two extremities there will necessarily be a series of points whose motion will be neither accelerated nor retarded, but which will oscillate precisely as if they were perfectly free and unconnected with the other points of the system. These points, being equi- distant from the axis of suspension, constitute a parallel axis known as the axzs of oscillation ; and it is to the distance be- tween these two axes that the term length of the compound pen- dulum is applied: we may say, therefore, that the length of a compound pendulum ts that of the simple pendulum which would describe tts oscillations in the same time. Huyghens, the celebrated Dutch physicist, discovered that the axes of suspension and oscillation are mutually convertible ; that is to say, the time of oscillation will remain unaltered when the pendulum is suspended from its axis of oscillation. This enables us to determine experimentally the length of the com- pound pendulum. For this purpose the reversible pendulum devised by Bohnenberger and Kater may be used. One form of this (fig. 58) is a rod with the knife-edges a and 6 turned towards each other. W and V are lens-shaped masses the relative posi- tions of which may be varied. By a series of trials a position can be found such that the number of oscillations of the pemdu- lum in a given time is the same whether it oscillates about the axis @ or the axis 6. This being so, the distance aé represents the length 7 of a simple pendulum which has the same time of oscillation. From the value of /, thus obtained, it is easy to determine the length of the seconds pendulum. The length of the seconds pendulum—that is to say, of the pendulum which makes one oscillation in a second—varies, of course, with the force of gravity. The following table gives its value at the sea-level at various places as determined by observation. The accelerative effect of gravity at these places, according to formula (55). is obtained in feet and 70 Gravitation and Molecular Attraction [80— metres, by multiplying the length of the seconds pendulum, reduced to feet and metres respectively, by the square of 3°14159 or 9°8696. | Acceleration of Gravity in : ; | Length of Pen- | ms 4 | Latitude = qulumininches ] | | Feet Metres | Hammerfest . S| 70" AO Nes 80 1040. a mann cea 50d 9°8258 | Aberdeen : , 57°9 Pm) Sor 55a" ) 432-3000 9°8164 _K6nigsberg . : 54°42 39°1507. | 32°2002 oSi42 _Manchester . bi hice) 39°1466 32°1968 9°8134 | Dublin . : Tie At |. 39°1461 32°1963 yu) oSIsae a | Berlin: -. : ; 52°30 | 39°1439 32°1945 9°8124 | Greenwich : : 51°29 eeO 1306 32°19012 g°8115 Paris : : . | 48°50 |. 207285 32°1819 9°8039 | Rome, . : eA TS 4 39° L145 | Wl. 32ye3 9°8053 New York : GAS 301012 | |) 32°) 504uuae 070010 Washington . ao 54 29°090S 4 321k So 9°8006 | Madras . arr SA 39°02608. 1’ 2°32°0082 "ENG 7530 Ascension ¢ Sn) Fats 39°0242 | 32°0961 9°7817 St homas) ir é O'25 43970207 A005 maz ORs 9°7826 Cape of Good Hope | 33°55S. | 39:0780 | 3271404 | 9°7962 - Consequently, 4g or the space described in the first second of its motion by a body falling zz vacuo from a state of rest (49) is 16'0466 feet or 4°891 metres at St. Thomas, TO'00560) 4. 4514005 tay re eOnUOn cane LO711827,, 05, 2018 we cate aminerics.. In all calculations, which are merely used for the sake of illustration, we may take 32 feet, or 9°38 metres, as the accelerative effect due to gravity. The metre (22) and the seconds pendulum differ in length at Greenwich, by less than a quarter of an inch. From observations with the pendulum, after applying the necessary corrections, and taking into account the effect of rotation (83), the form of the earth ‘can be deduced. 81. Verification of the laws of the pendulum.—In order to verify the laws of the.simple pendulum (55) we are compelled to employ a compound one, whose construction differs as little as possible from that of the former. For this purpose a small sphere of a very dense substance, such as lead or platinum, is suspended from a fixed point by means of a very fine metal wire. A pendulum thus formed oscillates almost like a simple pendulum, whose length is equal to the distance of the centre of the sphere from the point of suspension. In order to verify the isochronism of small oscillations, it is merely necessary to count the number of oscillations made in equal times, as the amplitudes of these oscillations diminish from 3 degrees to a fraction of a degree ; this number is found to be constant. That the time of vibration is proportional to the square root of the length is verified by causing pendulums, whose lengths are as the numbers I, 4, —82] Application of the Pendulum to Clocks. 71 9,.... to oscillate simultaneously. The corresponding numbers of oscil- lations in a given time are then found to be proportional to the fractions 1, 3, 4, &c., . . . . which shows that the times of oscillation increase as the Dim Weyvont. 2,93, tees ee: By taking several pendulums of exactly equal length, B, C, D (fig 59), but with spheres of different substances—lead, copper, ivory—it is found that, neglecting the resistance of the air, these pendulums oscillate in equal times, thereby show- : ing that the accelerative effect of gravity on all (rt bodies is the same at the same place. / By means of an arrangement resembling the | above, Newton verified the fact that the asses i of bodies are determined by the balance; which, : Pe it will be remarked, lies at the foundation of the | measure of force (28). For it will be seen on / comparing (54) and (55) with (49) that the law of | the time of a small oscillation is obtained on the I supposition that the force of gravity on all bodies | is represented by Mg, in which M is determined by the balance. In order to verify this, he had i two round equal wooden boxes made ; one he i filled with wood, and as nearly as possible in the | centre of oscillation of the other he placed an | equal weight of gold. He then suspended the j boxes by threads eleven feet Jong, so that they formed pendulums exactly equal so far as weight, figure, and resistance of the air were concerned. Their oscillations were performed in exactly the same time. The same results were obtained when other substances were used, such as silver, lead, glass, sand, salt, wood, water, corn. Now Fig. 59 all these bodies had equal weights, and, being contained in the same boxes they experienced the same resistance by the air, and if the inference that therefore they had equal masses had been erroneous, by as little as the one- thousandth part of the whole, the experiment would have detected it. 82. Application of the pendulum to clocks.—The regulation of the motion of clocks is effected by means of pendulums, that of watches by dalance- springs. Pendulums were first applied to this purpose by Huyghens in 1658, and in the same year Flooke applied a spiral spring to the balance of a watch. The manner of employing the pendulum is shown in fig. 60. The pendulum rod passing between the prongs of a fork, 2, communicates its motion to a rod, 4, which oscillates on a horizontal axis, 0. To this axis is fixed a piece, 727, called an escapement or crutch, terminated by two pro- jections or fallefs, which work alternately with the teeth of the escadement wheel R. This wheel being acted on by the weight tends to move con- tinuously, let us say, in the direction indicated by the arrow-head. Now, if the pendulum is at rest, the wheel is held at rest by the pallet 7, and with it the whole of the clockwork and the weight. If, however, the pendulum moves and takes the position shown by the dotted line wz is raised the 72 Gravitation and Molecular Attraction [82— wheel escafes from the confinement in which it was held by the pallet, the weight descends, and causes the wheel to turn until its motion is arrested by the other pallet 7 ; which, in consequence of the motion of the pendulum, will be brought into contact with another tooth of the escapement wheel. In this manner the descent of the weight is alternately permitted and arrested—or, in a word, regulated—by the pendulum. By means of a proper train of wheelwork the motion of the escape- ment is communicated to the hands of the clock ; and consequently their motion, also, is regulated by the pendulum. In watches the watch-spring plays the part of the weight in clocks. The pendulum has also been used for measuring great velocities. A large wooden box filled with sand and weighing from 3 to 5 tons is coated with iron ; against this arrangement, which is known as a daldistic pendulum, a shot is fired, and the deflection thereby produced is observed. From the laws of the impact of inelastic bodies, and from those of the pendulum, the velocity of the ball may be calculated from the - amount of this deflection. The gun may also be fastened to a pendulum arrangement ; and, when fired, the reaction causes an angular deflection, from which the pressure of the en- closed gases can be deduced, and therefrom the initial velocity of the shot. An interesting application of the pendulum is to the metronome, which consists of a short rod witha fixed bob ; on the rod and above the axis is a sliding weight. By raising this the rate of the pendulum is Fig. 60 _ lengthened ; by lowering it accelerated ; and thus even with a short pendulum the beats can be made pretty long. Maelzel connected this with a clockwork arrangement so that the beats are quite audible. 83. Causes which modify the intensity of terrestrial gravitation.—The intensity of the force of gravity—-that is, the value of g—is not the same in all parts of the earth. It is modified by several causes, of which the form.of the earth and its rotation are the most important. i. The attraction which the earth exerts upon a body at its surface is the sum of the partial attractions which each part of the earth exerts upon that body, and the resultant of all these attractions may be considered to act from a single point—the centre. Hence, if the earth were a perfect sphere, a given body would be equally attracted at any part of the earth’s surface. The attraction would, however, vary with the height above the surface. For small alterations of level the differences would be inappreciable ; but for greater heights and in accurate measurements observations of the value of g must be reduced to the sea-level. The attraction of gravitation being inversely as the square of the distance from the centre (67), we shall have —83] Causes which modify Terrestrial Gravitation 73 Peg = : EP where g 1s the value of the acceleration of gravity at the sea-level, ¢, its value at any height Z, and R is the radius of the earth. From this, seeing that / is very small compared with R, and that therefore its square may be neglected, we get by simple algebraical transformation ip Ae TERE R But even at the sea-level the force of gravity varies in different places in consequence of the form of the earth. The earth is not a true sphere, but an ellipsoid, the major axis of which is 12,754,796 metres, and the minor 12,712,160 metres. The distance, therefore, from the centre being greater at the Equator than at the Poles, and the attraction on a body being inversely as the square of these distances, calculation shows that the attraction due to this cause is x4, greater at the Poles than at the Equator. This is what would be true if, other things being the same, the earth were at rest. i. In consequence of the earth’s rotation, the force of gravity is further modified. If we imagine a body relatively at rest on the Equator, it really shares the earth’s rotation, and describes, in the course of one day, a circle, whose centre and radius are the centre and radius of the earth. Now, since a body in motion tends by reason of its inertia to move in a straight line, it follows that to make it move ina circle, a force must be employed at each instant to deflect it from the tangent (53). Consequently, a certain portion of the earth’s attraction must be employed in keeping the above body on the surface of the earth, and only the remainder is sensible as weight. It appears from calculation that at the Equator the s3,5th part of the earth’s attraction on any body is thus employed, so that the magnitude of g at the Equator is less by the 32,5th part of what it would be were the earth at rest. iii. As the body goes nearer the Poles the force of gravity is less and less diminished by the effect of centrifugal force. For in any given latitude it will describe a circle coinciding with the parallel of latitude in which it is placed; but as the radii of D these circles diminish, so does the centrifugal force ey up to the Pole, where the radius is null. Further, on NC the Equator the centrifugal force is directly opposed to gravitation: in any other latitude only a com- E E ponent of the whole force is thus employed. This is seen in fig. 61,in which PP’ represents the axis of rotation of the earth, and EE’ the Equator. At any given point Eon the Equator the centrifugal force Pp’ is directed along CE, and acts wholly in diminishing Biche: the intensity of gravitation ; but on any other point, a, nearer the Pole, the centrifugal force acting on a right line @é at right angles to the axis PP’, while gravity acts along aC, gravity is no longer directly diminished by centrifugal force, but only by its component ad, which is less the nearer a is to the Pole. The combined effect of these two causes—the flattening of the earth at the Poles, and the centrifugal force—is to make the attraction of gravitation at the Equator less by about the ;4,nd part of its value at the Poles. 74 Gravitation and Molecular Attraction [84- CHAPTER wit MOLECULAR FORCES 84. Nature of molecular forces.—The various phenomena which bodies present show that their molecules are under the influence of two contrary forces, one of which tends to bring them together, and the other to separate them from each other. The first force, which is called molecular attraction, varies in one and the same body with the distance only. The second force is due to the vzs viva, or moving force, which the molecules possess. It is the mutual relation between these forces, the preponderance of the one or the other, which determines the molecular state of a body (4)—whether it be solid, Jiquid, or gaseous. Molecular attraction is only exerted at infinitely small distances. Its effect is inappreciable when the distance between the molecules becomes appreciable. According to the manner in which it is regarded, molecular attraction is designated by the terms cohesion, affinity, or adhesion. 85. Cohesion.—Coheston is the force which unites adjacent molecules of the same nature ; for example, two molecules of water, or two molecules of iron. Cohesion is strongly exerted in solids, less strongly in liquids, and scarcely at all in gases. Itsstrength decreases as the temperature increases, because then the wzs vzva of the molecules increases. Hence itis that when solid bodies are heated they first liquefy, and are ultimately converted into the gaseous state, provided that heat produces in them no chemical change. Cohesion varies not only with the nature of bodies, but also with the arrangement of their molecules ; thus, the difference between tempered and untempered steel (95) is due to a difference in the molecular arrangement produced by tempering. Many of the properties of bodies, such as tenacity, hardness and ductility, are due to the modifications which this force undergoes. In large masses of liquids the force of gravity overcomes that of cohesion. Hence liquids acted upon by the former force have no special shape ; they take that of the vessel in which they are contained. But in smaller masses cohesion gets the upper hand, and liquids assume then the spheroidal form. This is seen in the drops of dew on the leaves of plants. It is also seen when a liquid is placed ona solid which it does not moisten ; as, for example, mercury upon wood. The experiment may also be made with water, by sprinkling upon the surface of the wood some light powder such as lyco- podium or lampblack, and then dropping a little water on it. The following experiment is an illustration of the force of cohesion causing a liquid to as- sume the spheroidalform. A saturated solution of zinc sulphate is placed ina =87] Adhesion 75 narrow-necked bottle (fig. 62), and a small quantity of carbon bisulphide, coloured with iodine, made to float on the surface. If pure water be now carefully added, so as to rest on the surface of the zinc sulphate solution, its specific gravity being less than that of the saturated solution, the bisulphide collects in the form of a flattened spheroid, which presents the appearance of blown coloured glass, and is larger than the neck of the bottle, pro- vided a sufficient quantity has been taken. ~ The force of cohesion of liquids may be illustrated and even measured as follows. A plane, perfectly smooth disc, D jill (fig. 63), is suspended horizontally to one scale-pan, Z, of a li delicate balance, and is accurately equipoised. A some- — what wide vessel of liquid is placed below, and the position of the disc regulated by means of the sliding screw S until it just touches the liquid. Weights are then carefully added to the other scale-pan until the disc is detached from the liquid. In this way it has been found that the weights required to detach the disc vary with the nature of the liquid ; with a disc of 118 mm. diameter the numbers for waters, alcohol, and turpentine were 59:4, 31, and 34 grammes respectively. The results were the same whether the disc was of glass, of copper, or of other metals, showing thus that they only depend on the nature of the liquid. It is a measure of the cohesion of the liquid, for a layer remains adhering to the disc ; hence the weight on the other side does not separate the disc from the liquid, but separates the particles of liquid from each other. 86. Affinity.— Chemical affinity, or chemical attraction, is the force which is exerted between molecules not of the same kind. Thus, in water, which is composed of oxygen and hydrogen, it is affinity which unites these ele- ments, but it is cohesion which binds together two molecules of water. In compound bodies cohesion and affinity operate simultaneously, while in simple bodies or elements cohesion has alone to be considered. To affinity are due all the phenomena of combustion and of chemical combination and decomposition. Those causes which tend to weaken cohesion are most favourable to affinity ; for instance, the action of affinity between substances is facilitated by their division, and still more by reducing them to a liquid or gaseous state. It is most powerfully exerted by a body in tts zascent state—that is, the state in which the body exists at the moment it is disengaged from a compound ; the body is then free and ready to obey the feeblest affinity. An increase of temperature modifies affinity differently under different circumstances. In some cases by diminishing cohesion, and increasing the distance between the molecules, heat promotes combination ; thus, sulphur and oxygen, which at the ordinary temperature are without action on each other, combine to form sulphur dioxide when the temperature is raised. In other cases heat tends to decompose compounds by imparting to their elements an unequal expan- sibility ; hence it is that many metallic oxides—as, for example, those of silver and mercury—are decomposed, by the action of heat, into gas and metal. 87. Adhesion.—The molecular attraction exerted between the szvrfaces of bodies in contact is called adhesion. i. Adhesion takes place between solids. If two leaden bullets are cut Fig. 62 76 Gravitation and Motecular Attraction [87— with a penknife so as to form two equal and brightly polished surfaces, and the two faces are pressed and turned against each other, until they are in the closest contact, they adhere so strongly as to require a force of more than Ioo grammes to separate them. The same experiment may be made with two equal pieces of glass which are polished and made perfectly plane. When they are pressed one against the other, the adhesion is so powerful that they cannot be separated without breaking. As the experiment succeeds in vacuo, it cannot be due to atmospheric pressure, but must be attributed to a reciprocal action between the two surfaces. The attraction also in- creases as the contact is prolonged, and is greater in proportion as the con- tact is closer. It appears, however, from optical considerations that plates may be separated from each other by a distance of o‘o001 mm. As this is greater than the diameter of the sphere of molecular action (3), it is probable that the connection of the platesis effected by layers of air condensedon the surface (196). In the operation of glueing the adhesion is complete, for the pores and crevices of the fresh surfaces being filled with liquid glue, so that there is no empty space on drying, wood and glue form one compact whole. In some cases the adhesion of cemented objects 1s so powerful that the mass breaks more readily at other places than at the cemented parts. Both in glueing and cementing the layer should be thin. Spring exposed various powders, such as salt- petre, sawdust, fine sand, and chalk, to a pressure of 10,000 atmospheres (166). He thus obtained masses of greater hardness and tenacity than the original substances possessed, and destitute of crystalline form. Soldering 1s due to adhesion ; the surface of the metals must be quite clean, which is effected by removing the layer of oxide, with which they are usually coated, by acid or by borax. The _solder when it solidifies only adheres to clean metal surfaces, There is no real difference between adhesion - and cohesion; thus when two freshly cut surfaces of caoutchouc are pressed together, they adhere with considerable force, and ultimately form one compact solid mass. iu. Adhesion also takes place between solids and liquids. If we dip a glass rod into water, and then withdraw it, a drop will be found to collect at its lower extremity, and remain suspended there. As the weight of the drop tends to detach it, there must necessarily be some force superior to this weight which maintains it there ; this force is the force of adhesion. This is the cause why liquids when poured out of a vessel so easily run —87] Adhesion a7 down the outside ; it is prevented by greasing the outer edge, and thus doing away with the adhesion. The adhesion between liquids and solids is more powerful than that between solids. Thus, if in the above experiment a thin layer of oil is inter- posed between the plates they adhere firmly, but when pulled asunder each plate is moistened by the oil, showing therefore that in separating the plates the cohesion of the liquid is overcome, but not the adhesion of the oil to the metal. In the above case the solid is wetted by the liquid ; that is, some remains adhere even when the drop falls. But liquids adhere to solids even when they are not wetted. Thus if a smooth glass plate be suspended horizontally from one arm of a balance, and be counterpoised as in fig. 63 ; on sliding a level surface of mercury under the plate, so that the plate touches the mercury, a considerable weight must be placed in the other panso as to detach the plate from the mercury. Small drops of mercury, too, adhere to the under side of a glass or porcelain plate. iii. The force of adhesion operates, lastly, between solids and gases. If a glass or metal plate be immersed in water, bubbles will be found to appear on the surface. As air cannot penetrate into the pores of the plate, the bubbles could not arise from the air which has been expelled. It is solely due to the layer of air which covered the plate and mozstened it like a liquid. In many cases when gases are separated in the ascent state on the surface of metals—as in electrolysis—the layer of gas which covers the plate has such a density that it can produce chemical actions more powerfu! than those which it can bring about in the free state. The collection of dust on walls, writing and drawing with chalks and pencils, depend on the adhesion of solids. Yet these are easily rubbed out, for the adhesion is only to the surface layer. In writing with ink, and in water-colour painting, the liquid penetrates into the pores, taking the solid with it, which is left behind as the liquid evaporates, and hence the adhesion of such writing and painting is far more complete. 78 Gravitation and Molecular Attraction [88- CHAP They, PROPERTIES PECULIAR TO SOLIDS 88. Various special properties.—After having described the principal properties common to solids, liquids, and gases, we shall discuss the proper- ties peculiar to solids. They are elasticity, tenacity, ductility, and hardness. With regard to elasticity we must distinguish between elasticity of volume, longitudinal elasticity, and torsional elasticity or simple rigzdity. Let us first define the terms s¢vess and strazm commonly used in the theory of elasticity. A change in the size or shape of a body due to the application of force to the body is called a strain, while the force in the interior of the body producing this strain is called a stvess. If the displacements of the molecules of a body due to the action of stress are small, the strains produced are proportional to the stresses pro- ducing them, and hence the ratio stress strain coefictent of elasticity of the body, this coefficient being greatest in those cases where a small displace- ment requires a very large force to produce it. Thus, steel and glass are highly elastic bodies because in them the application of evena large force will produce only a small change of shape or volume. For by force of elasticity is under- stood the force with which the dis- placed particles tend to revert to their original position, and which force is equivalent to that which has brought about the change. Considered from this point of view, is constant and is called the gases have the least force of elasticity ; that of liquids is considerably greater, and is, indeed, greater that that of many solids. Thus the force of elasticity 89] Volume Elastectty. Longitudinal Elasticity 79 of mercury is greater than that of caoutchouc, glass, wood, and stone. It is, however, less than that of the other metals, with the exception of lead. This mode of defining elasticity differs somewhat from ordinary ideas according to which bodies, such as india-rubber, are considered highly elastic which undergo considerable change of form on the application of a small force. A body is perfectly elastic when any given stress produces no permanent set, restitution being always complete. It is imperfectly elastic when it does retain permanently such a set. Within the limits of elasticity all bodies may be regarded as perfectly elastic. 89. Volume elasticity. Longitudinal elasticity.—Elasticity of volume is the only kind of elasticity a liquid or a gas possesses, for liquids and gases have no definite shape. A solid may by the application of stress have not only its volume but also its shape altered. The volume elasticity of a body is measured, as we have said, by the ratio stress/strain. The stress is the force per unit area uniformly applied to the body to compress it ; the strain is the resulting compression, that is the ratio of the change of volume to the original volume. If the original volume V be reduced to V-v when sub- jected to uniform pressure (force per unit area) P, the strain is v/V, and U U V The dimensions (62) of P are those of a force divided by an area, Z.e. iL’ or M/LT.? Since the strain is the ratio of a volume to a volume, its dimensions are zero. Thus the dimensions of K, the coefficient of volume elasticity, are the same as those of a pressure. The reciprocal of £ is called the coefficient of compressibility or simply the compressibility of the body. In order to study the laws of longitudinal elasticity, Savart used the apparatus represented in fig. 64. It consists of a wooden support from which are suspended the rods or wires taken for experiment. At the lower ex- tremity there is a scale-pan, and on the wire two points, A and B, are marked, the distance between which is measured by means of the cathetometer before the weights are added. The cathetometer consists of a strong upright brass support, K, divided nto millimetres, which can be adjusted in an exactly vertical position by means of levelling screws and the plumb-line. A small telescope, exactly at right angles to the scale, can be moved up and down, and is provided with a vernier which measures fiftieths of a millimetre. By adjusting the telescope successively on the two points A and B, as represented in the figure, the distance between these points.is obtained on the graduated scale. Placing, then, weights in the pan, and measuring again the distance from A to B, the elongation is obtained. By experiments of this kind it has been ascertained that— The alteration in length within the limits of elasticity 7s in proportion to the length and to the load acting on the body, and is inversely as the cross Section Let 7 be the radius of the wire, Z its length, and e the elongation produced 80 Gravitation and Molecular Attraction [89- by the application of aload W. ‘Thestress, or force per unit of cross section of the wire, is W/m7*, and since the length / is stretched by an amount g, the strain is e/7. Thus by the definition, errs Ley Ww wil Co-efficient of longitudinal ‘Gale ae Elasticity, or Young’s Modulus t Z We see from this expression that if the wire have unit cross section (77? = I) and be stretched to double its length (e=7), »=W. In other words, we may define Young’s Modulus as the stretching force which must be applied to a wire of unit cross section to double its length. This cannot be directly observed, for no substance has elastic limits so wide as to undergo stretching to double its length without permanent set ; n, however, may be calculated from any accurate observations by means of the above formula. In the following table the values of » and e are given for a number of substances, the units being 1 kilogramme, 1 millimetre, and 1 second. To obtain the corresponding numbers in C.G.S. units (62) divide the values of p by 981 and multiply by 10'! ; multiply the values of e by 981 and divide by POW: pe Py Wrought-iron : 2 A a 20,869 0°000048 Steeliron |": : : ae 18,809 0°000053 _ Platinuin~ si: : ; 3 onl 17,044 0°000058 Copper : : ; : : ay 12,500 | 0'000080 Slate . : : , : : : 11,035 | 0000090 Zico ee ; : mA 8,734 | O'OOOI 14 | Brass . é ‘ ; , | 8,543 O‘OOO1 17 | Crown Glass : “ : A a 7,917 | 0'0001 26 Plate Glass . ; : , 3 cr 7,015 | O‘0001 42 Rock Salt. : 4,230 | 91000236 | Marble : ‘ : : al 2,309 0°000382 Geaduar ; : , : : sid 1,803 | 07000555 | Bonerg, ...: oy yp ae 1,635 | 0000612 | Acacia . ; p : ; ; 2 Loe | 0°000792 Prac lee : , : : 5 ay Tbr | 0°000890 WON dl 1 ‘ : ; : : y g2I | O°001085 | Whalebone . ; se 700 | 0°001 428 ml Geet. : : Tenia hy 650 O°Ol1167 | Sandstone . ‘ a 631 | 0001521 | Fir : ; : : : ; | 564 | 0°001 768 | Gypsum ; ; ; | 400 | 0°002500 | ie SS a Se at Ee fetes SS ee ee ee —___—— | Thus, to double the length of a wrought-iron wire a square millimetre in section would (if this were possible) require a weight of 19,000 kilogrammes ; but a weight of 15 kilogrammes produces a permanent alteration in length of +3'szth, and this is the limit of elasticity. The weight, which when applied to a body of unit section just brings about an appreciable permanent change, is a measure of the /z7z¢ of elasticity. _Whalebone has only a modulus of -89] _ Elasticity of Traction 8I 700, and experiences a permanent elongation by a weight of 5 kilogrammes ; its limit is, therefore, relatively greater than that of iron. Steel has a high modulus, along with a wide limit. Longitudinal stretching is accompanied by a lateral contraction, and the ratio of the contraction to the proportional stretching is known as Potsson’s coefficient. It was taken by him to be 0°25, but later experiments have found the ratio to vary from o to o°5 ; it is about 0°25 for glass, and nearly o5 for caoutchouc. When a wire is stretched by a load to within the limit of elasticity, some time often elapses before the full effect is produced, and conversely when the load is removed the wire does not at once wholly resume its original condition, but a small portion of the deformation remains, and it only reverts to its initial state after the lapse of some time. This phenomenon, first observed by Weber, which is met with in most elastic changes of form, is called the elastic after-action or effect, or the elastic fatigue. This phenomenon is probably due to the fact that the mole- cules of bodies are not spherical, but are variously extended in different directions, and in elastic deformation are not only displaced in reference to each other, but are also twisted. This may be illustrated by the following experiment. A piece of caoutchouc tube is closed by a glass plug at the bottom, while the open end is passed over a piece of glass tube. (oloured liquid is then poured in so that it stands ata certain height in this tube. If then a weight is suspended to the lower end of the india-rubber tube, the liquid at once sinks to a considerable distance, and afterwards very slowly a little further. Onremoving the weight it rises again, but not immediately to the old height. This it only reaches after some time. Both calculation and experiment show that when bodies are lengthened by traction their volume increases. When weights are placed on a bar, the amount by which it is shortened, or the coefficient of contraction, is equal to the elongation which it would experience if the | same weights were suspended to it, and is represented by the above numbers. The influence of temperature on the elasticity of iron, copper, and brass was investigated by Kohlrausch and Loomis. They found thatthe alteration in the coefficient of elasticity by heat is the same as that which heat pro- duces in the coefficient of expansion and in the refractive power ; it is also much the same as the change in the . permanent magnetism, and in the specific heat, while it : is less than the alteration in the conductivity for elec- tricity. As an application of elasticity may be mentioned Jolly’ s spring balance. This consists of a long steel wire, aé (fig. 65), wound in the form of a spiral, which is suspended in front of an Accurately graduated scale. To the lower end of the spiral two scale-pans, c and d, are hung by G Fig. 65 82 Gravitation and Molecular Attraction [89- a thread, the lower one, d@, dipping in a small vessel of water on an adjust- able support. The instrument is graduated empirically by observing what displacement of the mark vz is produced by putting a known weight in the scale-pan d@. Knowing then once for all the constant of the instrument, it is easy to determine the weight of a body by reading the displacement which it produces along the scale. go. Elasticity of torsion.—The laws of the torsion of wires were deter- mined by Coulomb, by means of an apparatus called the zorszon balance (fig. 66). It consists essentially of a metal wire, clamped at one end in a support, A, and holding at the other a metal sphere, B, to which is affixed an index, C. Immediately below this there is a graduated circle, CD. If the needle is turned from its position of equilibrium through a certain angle, which is the angle of torsion, the force necessary to produce this effect is the force of torston. When, after this deflection, the sphere is left to itself, the reaction of torsion produces its effect, the wire untwists itself, and the sphere rotates © about its vertical axis with increasing rapidity until it reaches its position of equilibrium. It does not, however, rest there: in virtue of its inertia it passes this position, and the wire undergoes a torsion in the opposite direc- tion. The equilibrium being destroyed, the wire tends to untwist itself, the same alterations are again produced, and the needle does not rest at zero of the scale until after a certain number of oscillations about this point have been completed. By means of this apparatus, Coulomb found that when the amplitude of the oscillations is within certain limits, the oscillations are repre- sented by the following laws : I. Zhe oscillations are very nearly tsochronous. Il. For the same wire, the angle of torsion ts proportional to the moment of the force of torsion. Ill. With the same force of torsion, and with wires of the same diameter, the angles of torsion are proportional to the length of the wires. IV. Zhe same force of torsion being applied to wzres of the same length, the angles of torsion are in- versely proportional to the fourth powers of the dia- meters. Wertheim examined the elasticity of torsion in the case of stout rods by means of a different appa- ratus, and found that it 1s also subject to these laws. He further found that, all dimensions being the same, different substances undergo different degrees of tor- sion for the same force, and each substance has its own coefficient of torsion, which is usually denoted by wm. The value of this coefficient is about 4 that of the modulus of elasticity. The laws of torsion may be enunciated in the formula o = ae ; in which mr w is the angle of torsion, F the moment of the force of torsion, 7 the length of the wire, 7 its radius, and z the torsion-coefficient or simple rigidity. As the angle of torsion is inversely proportional to the fourth power of -91} Determination of Young’s Modulus by Flexure 83 the radius, rods of some thickness require very great force to produce even small twists. With very small diameters, such as those of a cocoon or glass thread, the proportionality between the angle of torsion and the twisting force holds even for several complete turns. We may here mention a very ingenious method of obtaining very fine threads of glass, and even of quartz and other minerals, which has been de- vised by Professor Boys. It consists in attaching a stout thread of the sub- stance in question to a small arrow of straw, melting the end so as to form a small drop. When the arrow is shot from a small crossbow, the drop remains behind in virtue of its inertia (19), and a thread practically uniform but of excessive tenuity is spun out from it and carried along with the arrow. In this way glass threads go feet in length and ;,/g5th of an inch in diameter have been produced. By the same method, melting quartz with the oxy- hydrogen blowpipe, threads of this substance have been produced which are not more than o‘oooo! inch in diameter. Such threads are of great value in torsion experiments, for, while they possess great tenacity, they are almost destitute of the property of elastic fatigue (89). gt. Determination of Young’s modulus by flexure.—A solid, when cut into a rod or thin plate, and fixed at one end, after having been more or less bent, strives to return to its original position when left to itself. This property is known as the elasticity of flexure, and is very marked in steel, caoutchouc, wood, and paper. If a rectangular bar AB be clamped at one end and loaded at the other end by a weight W (fig. 67), a flexure will be produced which may be ob- served by the catheto- meter. If the amount of this flexure is denoted by h, Young’s modulus 1s given by the formula _4WPR ON where W is the load, / the length of the bar, @ its breadth, % its depth or thickness, and & a con- stant, which depends on the manner in which the rod is supported, the three principal cases _ being represented in fig. 68 ; a is that in which the rod is supported at one end, as in fig. 67 ; in 8 the rod rests on knife-edges, with both ends free ; while ny both ends are rigid ; if one and the same a be fastened in these differ- ent ways, the values of \ are respectively as 64:4:1. If the section of the bar is a circle of radius 7, then It will thus be seen that if for a given load the depression is not to be greater with a long beam than with a short one, the height must increase in the same ratio as the length. ‘ G2 84 Gravitation and Molecular Attraction [91- The elasticity of flexure is applied in a vast variety of instances—for example, in bows, watch-springs, carriage-springs ; in spring balances it is used to determine weights, in dynamometers to determine the force of agents in prime movers ; and, as a property of wool, hair, and feathers, it is applied to domestic uses in cushions and mattresses. Fig. 68 Whatever be the kind of elasticity, there is, as has been already said (89), a limit to it—that is, there is a molecular displacement beyond which bodies are broken, or at any rate do not regain their primitive form. This limit is affected by various causes. The elasticity of many metals is increased by hardening, whether by cold, by means of the draw-plate, by rolling, or by hammering. Some substances, such as steel], cast iron, and glass, become both harder and more elastic by tempering (95). Elasticity, on the other hand, is diminished by azzealing, which consists in raising the body to a temperature lower than that necessary for tempering, and allowing it to cool slowly. By this means the elasticity of springs may be regulated at pleasure. Glass, when it is heated, undergoes a true tempering in being rapidly cooled, and hence, in order to lessen the fragility of glass objects, they are reheated in a furnace, and are carefully allowed to cool slowly, so that the particles have time to assume their most stable position (95). 92. Tenacity.—7Zenacity is the resistance which a body opposes to the total separation of its parts. According to the manner in which the external force acts, we may have various kinds of tenacity ; ¢emaczty in the ordinary sense, or resistance to traction ; ve/ative tenacity, or resistance to fracture ; reactive tenacity, or resistance to crushing ; sheevzmg tenacity, or resistance to displacement of particles in a lateral direction ; and ¢orszonal tenacity, or resistance to twisting. Ordinary tenacity is determined in different bodies by forming them into cylindrical or prismatic wires, and ascertaining the weight necessary to break them. Mere increase in length does not influence the breaking weight, for the weight acts in the direction of the length, and stretches all parts as if it had been directly applied to them. Tenacity ts adtrectly proportional to the breaking weight, and inversely proportional to the area of a transverse section of the wire. Tenacity diminishes with the duration of the traction. A small force continuously applied for a long time will often break a wire, which would not at once be broken by a larger weight. Not only does tenacity vary with different substances, but it also varies with the form of the body. Thus, with the same sectional area, a cylinder has greater tenacity than a prism. The quantity of matter being the same, a hollow cylinder has greater tenacity than a solid one; and the tenacity of this hollow cylinder is greatest when the external radius is to the internal —92] Tenacity 85 one in the ratio of 11 to 5. The shape has also the same influence on the resistance to crushing as it has on the resistance to traction. A hollow cylinder with the same mass, and the same weight, offers a greater resistance than a solid cylinder. Thus it is that the bones of animals, the feathers of birds, the stems of corn and other plants, offer greater resistance than if they were solid, the mass remaining the same. Tenacity, like elasticity, is not the same in all directions in bodies. In wood, for example, both the tenacity and the elasticity are greater in the direc- tion of the fibres than in a transverse one. And this difference obtains in general in all bodies, the texture of which is not uniform. Wires by being worked acquire greater tenacity on the surface, and have therefore a higher coefficient than even somewhat thicker rods of the same material; and, according to some physicists, solids have a surface tension analogous to that of liquids (135). 1,45 +T,,; hence the two forces T,, and T,, cannot counter- balance the force T,,, and the point A must move in the direction of the pull T,., until the whole surface is covered with a thin layer of oil. Although oil zs spread over water by the pull T,., it is usual to say that oil spreads itself on water. That surface tension is only exhibited at the boundary of two liquids is well seen by an experiment of Professor Boys: If a camel’s-hair brush is dry the hairs are separately visible, and to make them come to a point they must be wetted ; this adherence is not due to moisture, for if the Jencz7 is wholly immersed in water the separate hairs are as visible as when the pencil is dry. 140. Formation of drops in a capillary orifice.—When a liquid is con- tained in a vessel terminating in a narrow capillary opening, such as a dropping tube, a certain excess of pressure is required to make the lquid flow out. If this pressure is limited, the lower meniscus has an invariable shape, and the drop does not increase. But as the pressure increases the drop gradually expands like a small elastic bag, the tension of which is less in the degree in which the surface increases, and when the drop is so large that its weight exceeds the normal component of the surface tension, it contracts at the upper part, and finally breaks across a circumference o0’o’, which is nearly equal to that of the orifice oo. ty Tate has found that the weights of drops Sormed with different capillary tubes are for the ae same liguid proportional to the diameters of the “eaue orifice. The weights of the drops are independent of the substance of the tube, provided it is moistened ; they diminish with rise of temperature. When a small but very hot flame is directed against the point of a fine je TER el ie abet) Wek Wn a 128 On Liquids [140- metal wire, such as gold or platinum, the metal is melted and falls in drops, the weight P of which is found to be very uniform. P is the greatest weight which the melted mass can support, and is equal to 277T, where T is the constant of capillarity and 27 the diameter of the wire. Quincke has applied this method of determining the constant in cases where other methods are not applicable, such as in the case of the noble metals, salts, selenium, phosphorus, &c. 141. Osmose.—Other shares are observed when two different liquids miscible with each other are separated by a porous diaphragm. This may be best illustrated by means of the apparatus represented in fig. 123, in which a vessel open at the bottom is tied round with a bladder. In the neck a long narrow tube, @a, is fitted. This vessel is filled with solution of copper sulphate, so that it stands at a certain height, 7, in the tube, and is then placed in a larger vessel containing pure water, at the level a mm. If the temperature remains stationary, it will be seen that after some time the liquid in the tube aa, which was originally at the level 7, has risen, while the level of 77 has become somewhat lower ; it will also be seen that the outer liquid has acquired a faint bluish tinge. This process continues for some time until the liquid has attained a certain height, It thus appears that there is an interchange of the two liquids, but the quantity of water which passes into the sulphate of copper is greater than that of the solution which passes out. If the experiment be reversed—that is, if water is contained in 4, and copper sulphate in the i outer vessel—the phenomena are reversed ; that is, the | level in 7 sinks, while that in 77 rises. Dutrochet, who first investigated these phenomena, applied the term exosmose to the current which passes from the denser liquid to the less dense, and ezdosmose to the opposite current, and the apparatus itself he called an endosmometer. The phenomena are now known as those of dosmose or osmose. For the occurrence of osmose the membrane must be permeable to at least one of the liquids, and the liquids must be different, but capable of mixing, such as alcohol and water; there is none, for instance, between water and oil. Osmose may occur between two liquids of the same kind, but of different densities, such as solutions of acids or salts of different strengths ; here the current is from the weaker towards the stronger solution, and this is general, osmose usually taking place towards the denser liquid. Alcohol and ether form an exception ; although they are specifi- cally lighter than water, they behave in this respect like liquids which are denser. If a tube filled with water is closed at both ends by a bladder (fig. 124), and one end is placed in a vessel of water, the other being in contact with the air, the water gradually evaporates through the bladder ; it is, however, —141] Osmose 129 as rapidly replaced, so that, in consequence of evaporation, water moves towards the place where this occurs. Hence osmose plays a part in the motion. The evaporation from the skin of animals brings about a motion of liquids from the interior towards the evaporating surface. In like manner, the passage of water to the rootlets of plants, as well as the ascent of sap to the highest points of the trees, is favoured by evaporation from branchlets, leaves, flowers, and fruit. The well-known fact that dilute alcohol kept in a porous vessel becomes concentrated depends on osmose. If a mixture of alcohol and water be kept for some time in a bladder, the volume diminishes, but the alcohol becomes much more concentrated. The reason doubtless is that the bladder absorbs water more readily than alcohol, and accordingly water evaporates on the surface, and thus brings about a concentration of the residue. Dutrochet’s method is not adapted for quantitative measurements, for it does not take into account the hydrostatic pressure produced by the column, Jolly examined the endosmose of various liquids by determining the weights of the bodies diffused. He called the exdosmotic equivalent of a substance the number which expresses how many parts by weight of water pass through the bladder in exchange for one part by weight of the substance. The fol- lowing are some of the endosmotic equivalents which he determined :— Sulphuric acid : o'4 Copper sulphate. : 9°5 Alcohol . : i ‘ 4'2 Magnesium sulphate . I1'7 Sedium chloride . : 4°3 Caustic potash : er ZERO Sugar. ; ; ; 7°1 He also found that the endosmotic equivalent increases with the temperature, and that the quantities of substances which pass in equal times through the bladder are proportional to the strengths of the solutions. Porous diaphragms differ very greatly in the facility with which they permit osmose ; of all substances goldbeater’s skin is the best, being twice as good as vegetables, and sixty or seventy times as good as porous earthenware, which, however, is necessary in some cases, for organic membranes are apt to decompose. Pfeffer has constructed what he calls sesmzpermeable membranes, by immersing a porous cell, such as is used for voltaic cells, in solution of copper sulphate, and then in one of ferrocyanide of potassium. By double decomposition, a coherent layer of ferrocyanide of copper is found, which is permeable to the molecules of water, but not to those of sugar, for instance. If a solution of sugar be exposed to pressure in such a vessel, pure water filters through ; the membrane acts asa molecular sieve. The whole phenomena and laws of osmose have, in recent times, acquired great importance from the theoretical considerations of Van’t Hoff, on the nature of solutions, of which we may indicate the general results. If a one-per-cent. solution of sugar be placed in the vessel in such an arrangement as that represented in fig. 123, when the semi-permeable dia- K 130 On Liquids [141-— phragm is of ferrocyanide of copper, it will be found that after the lapse of some time the liquid will rise in the tube to a maximum height of 53°5 cm. 5 this height is a measure of the osmotic pressure. Dealing with dilute solutions, it is found that this pressure is proportional to the concentration ; thus, with solutions of 1, 2, 4, and 6 per cent. respectively, the corresponding osmotic pressures are 53°5, 101°6, 2082, and 307°5, respectively. We shall afterwards see (296) that we conceive a mass of gas as made up of a very large number of molecules moving in all directions with extreme velocity, and that the pressure of a gas is due to the impacts of these molecules against the sides of the containing vessel. Now in what are called zdeal solutions—those, that is to say, in which the dimensions of the molecules (3) of the body dis- solved may be disregarded in comparison with the space in which they are contained—Van ’t Hoff considers that the molecules of the body dis- solved are animated by just such a motion as they possess in the case of gases. If the pressure on a given volume of gas be gradually increased its volume will be diminished, and it is found that to reduce it to one-half, the temperature remaining constant, the original pressure must be doubled. For a given mass of gas, the product of pressure and volume is constant ; this is what is known as Boyle’s law (183). Osmotic pressure in liquids is exactly analogous to the pressure of gases; if we double the number of molecules in a given volume of liquid, we double the pressure, just as we can force two volumes of gas into the space occupied by one if we double the pressure. . This analogy between osmotic and gaseous pressure is not a fanciful one, but holds good in details so far asit has been tried. It can be shown, for instance, that the osmotic pressure of sugar in solution is the same as would be exerted by the same weight of sugar if it existed in the state of gas in the same space as that occupied by the solution. Gases, as will afterwards be shown, expand by a certain definite propor- tion of their volume when heated, the pressure remaining constant ; or, if the volume be kept constant, the increase of pressure is proportional to the increase of temperature. This is also found to hold with the osmotic pres- sure ; it increases in direct proportion to the temperature. 142. Diffusion of liquids.—If oil be poured on water, no tendency to intermix is observed, and even if the two liquids be violently agitated to- gether, two separate layers are formed on allowing them to stand. With alcohol and water the case is different; if alcohol, which is specifically lighter, be carefully poured upon water, so as to form two distinct layers, it will be seen that the heavier water rises in opposition to gravity with the lighter alcohol, which, in turn, passes into the denser liquid below; the liquids gradually intermix, in spite of the difference of the specific gravities ; they diffuse into one another. This point may be illustrated by the experiment represented in fig. 125. A tall jar contains water coloured by solution of blue litmus ; by means of a funnel some dilute sulphuric acid is carefully poured in, so as to form a layer at the bottom ; the colour of the solution is changed into red, pro- gressing upwards, and after forty-eight hours the change is complete—a result of the action of the acid, and a proof, therefore, that it has diffused throughout the entire mass. —142] Diffusion of Liquids 131 The laws of this diffusion, in which no porous diaphragm is used, were completely investigated by Graham. The method by which his latest ex- periments were made was the following :—A small wide-necked bottle, A (fig. 126), filled with the liquid whose rate of diffusion was to be examined, was closed by a thin glass disc and placed. in a larger vessel, B, in which water was poured to a height of about an inch above the top of the bottle. The disc was carefully removed, and then after a given time successive layers were carefully drawn off by means of a siphon or pipette, and their contents examined. The general results of these investigations may be thus stated :— i. When solutions of the same substance, but of different strengths, are taken, the quantities diffused in equal times are proportional to the strengths of the solutions. ii. In the case of solutions containing equal weights of different substances, the quantities diffused vary with the nature of the substances. Saline sub- Fig. 125 Fig. 126 stances may be divided into a number of eguzdiffustve groups, the rates of diffusion of each group being connected with the others by a simple numerical relation. ili, The quantity diffused varies with the temperature. Thus, taking the rate of diffusion of hydrochloric acid at 15° C. as unity, at 49° C, it is 2°18. iv. If two substances which do not combine be mixed in solution, they may be partially separated by diffusion, the more diffusive one passing out most rapidly. In some cases chemical decomposition even may be effected by diffusion. Thus, potassium bisulphate is decomposed into free sulphuric acid and neutral sulphate. v. If liquids be dilute, a substance will diffuse into water containing another substance Biceled as into pure water ; but the rate is materially reduced if a portion of the same diffusing substance be already present. The following table gives the approximate times of equal diffusion :— Hydrochloric acid. LO Magnesium sulphate . 7:0 Sodium chloride ; 23 Albumen : . . 49°0 Sugar F : : oualy es: Caramel : ; 2050 K 2 132 On Ligutds [142— It will be seen from the above table that the difference between the rates of diffusion is very great. Thus magnesium sulphate, one of the least diffusible saline substances, diffuses 7 times as rapidly as albumen and 14 times as rapidly as caramel. These last substances, like hydrated silicic acid, starch, dextrine, gum, &c., constitute a class of substances which are characterised by their incapacity for taking the crystalline form, and by the mucilaginous character of their hydrates. Considering gelatine as the type of this class, Graham called them colloids (kodXa, glue), in contradistinction to the far more easily diffusible cvystallotd substances. Colloids are for the most part bodies of high molecular weight, and it is probably the larger size of their molecules which hinders their passing through minute apertures. Graham devised a method of separating bodies based on their unequal diffusibility, which he called dialysts. His dialyser (fig. 127) consists of a ring of gutta-percha, over which is stretched while wet a sheet of parchment paper, forming thus a vessel about two inches high and ten inches in dia- > NX ‘uaa awe sae oy | Fig. 127 meter, the bottom of which is of parchment paper. After pouring in the mixed solution to be dialysed, the whole is floated on a vessel containing a very large quantity of water (fig. 128). In the course of one or two days a more or less complete separation will have been effected. Thus a solution of arsenious acid mixed with various kinds of food readily diffuses out. The process has received important applications to laboratory and pharmaceutical purposes. Emulsions, such as are of frequent use in medicine, are prepared by intimately mixing oil with a solution of gum, albumen, or some other colloid, and water. As stated above, the reason Bt the difficulty which a eelion experiences in diffusing through the membrane of another colloid, is probably that its molécules are too Jarge and too near each other—in other words, that the pores are too small. Withan ordinary emulsion, the minute droplets of oil are dispersed among the large and difficult mobile particles of the colloid, which thus hinder their motion, and thereby prevent them from uniting and forming a coherent layer. ~145] Direction of the Jet from Lateral Orifices 133 CHAPTER 1 El HYDRODYNAMICS 143. Hydrodynamics.—The science which treats of the motion of liquids is called hydrodynamics ; and the application of the principles of this science to conducting and raising water in pipes and to the use of water as a motive power is known by the name of hydraulics. 144. Velocity of efflux. Torricelli’s theorem.—Let us imagine an aperture made in the bottom of any vessel, and consider the case of a particle of liquid on the surface, without reference to those which are beneath. If this particle fell freely, it would have a velocity on reaching the orifice equal to that of any other body falling through the distance between the level of the liquid and the orifice. This, from the laws of falling bodies, is ,/2g, in which ¢ is the acceleration due to gravity, and /# the height. If the hquid be maintained at the same level, for instance, by a stream of water running into the vessel, sufficient to replace what has escaped, the particles will follow one another with the same velocity, and will issue in the form of a stream. Since pressure is transmitted equally in all directions, a liquid would issue from an orifice in the side with the same velocity, provided the depth were the same. The law of the velocity of efflux was discovered by Torricelli. It may be stated as follows :—TZhe velocity of efflux is the velocity which a freely jalling body would have on reaching the orifice after having started from a@ State of rest at the surface. It is expressed by the formula v=,/2¢h. It follows directly from this law that the velocity of efflux depends on the depth of the orifice below the surface, and not on the nature of the liquid. Through orifices of equal size and of the same depth, water and mercury would issue with the same velocity ; for although the density of the latter liquid is greater, the weight of the column, and consequently the pressure, are greater too. It follows further that the velocities of efflux are directly proportional to the square roots of the depth of the orifices. Water could issue from an orifice Too inches below the surface with ten times the velocity with which it would issue from one an inch below the surface. ‘The quantities of water which issue from orifices of different areas are very nearly proportional to the size of the orifice, provided the level remains constant. 145. Direction of the jet from lateral orifices.—From the principle of the equal transmission of pressure, water issues from an orifice in the side of a vessel with the same velocity as from an aperture in the bottom of a vessel at the same depth. Each particle of a jet issuing from the side of a 134! | On Liguzds [145- vessel begins to move horizontally with the velocity above mentioned, but it is at once drawn downward by the force of gravity in the same manner as a bullet fired from a gun, with its barrel horizontal. It is well known that the bullet describes a parabola (51) with a vertical axis, the vertex being the muzzle of the gun. Now, since each particle of jet moves in the same curve, the jet itself takes the para- bolic form. In every parabola there is a certain point called the focus, and the distance from the vertex to the x focus fixes the magnitude of a para- \ bola in much the same manner as wae the distance from the centre to the Ee circumference fixes the magnitude ~ of acircle. Now it can easily be .. proved that the focus is as much \ below as the surface of the water is above the orifice. Accordingly, if water issues through orifices which are small in comparison with the contents of the vessel, the jets from orifices at different depths below the surface take different forms, as shown in fig. 129. If these are traced on paper held behind the jet, then, knowing the horizontal and vertical distances of any point of the jet from the orifice, it is easy to demonstrate that the jet forms a parabola. 146. Height of the jet.—If a jet issuing from an orifice in a vertical direction has the same velocity as a body would have which fell from the surface of the liquid to that orifice, the jet ought to rise to the level of the liquid. It does not, however, reach this ; for the particles which fall hinder it. But by inclining the jet at a small angle with the vertical it reaches about 5%, of the theoretical height, the difference being due to friction and to the resistance of the air. By experiments of this nature the truth of Torricelli’s law has been demonstrated. (47. Quantity of efflux. Vena contracta.—If we suppose the sides of a vessel containing water to be thin, and the orifice to be a small circle whose area is A, we might think that the quantity of water, E, discharged in a second would be given by the expression A./2g¢%, since each PR BP. particle has, on the average, a velocity equal to ./2gh, and dhe particles issue from each point of the orifice. But this is by \ A No B nomeans the case. This may be explained by reference to ! | fig. 130, in which AB represents an orifice in the bottom of | a vessel—what is true in this case being equally true of an ! Fig. 129 to orifice in the side of the vessel. Every particle above AB endeavours to pass out of the vessel, and in so doing exerts a pressure on those near it. Those that issue near A and B Wig 3 exert pressures in the directions MM and NN ; those near the centre of the orifice in the direction RQ, those in the intermediate parts in the directions PQP. In consequence, the water. within the space PQP is unable to escape, and that which does escape, instead of assuming a cylindrical form, at first contracts, and takes the form -148] Jnfluence of Tubes on the Quantity of Effiux 135 of a truncated cone. It is found that the escaping jet continues to contract until at a distance from the orifice about equal to the diameter of the orifice. This part of the jet is called the vena contracta. It is found that the area of its smallest section is about 3 or 0°625 of that of the orifice. Accord- ingly, the true value of the efflux per second is given approximately by the formula E = 0°62A ./2¢h, or the actual value of E is about 0°62 of its theoretical value. 148. Influence of tubes on the quantity of efflux.—The result given in the last article has reference to an aperturein a thin wall. If a cylindrical or conical efflux tube, or ajutage, is fitted to the aperture, the amount of the efflux is considerably increased, and in some cases falls but little short of its theoretical value. A short cylindrical ajutage, whose length is from two to three times its dia- meter, has been found to increase the efflux per second to about 0°82A,/2gh. In this case the water on entering the ajutage forms a contracted vein (fig. 131), just as it would do on issuing freely into the air ; but afterwards it ex- pands, and, in consequence of the adhesion of the water to the interior surface of the tube, has, on leaving the ajutage, a section greater than that of the contracted vein. The contraction of the jet within the ajutage causes a par- tial vacuum. If an aperture is made in the ajutage, near the point of greatest contraction, and is fitted with a vertical tube, the other end of which dips into water (fig. 131), it is found that water rises in the vertical tube, thereby proving the formation of a partial vacuum. If the ajutage has the form of a conic frustum whose larger end is at the aperture, the efflux in a second may be raised to 0'92A ./2¢%, provided the dimensions are properly chosen. If the smaller end of a frustum of a cone of suitable dimensions be fitted to the orifice, the efflux may be still further increased, and fall very little short of the theoretical amount. When the ajutage has more than a certain length, a considerable diminution takes place in the amount of the efflux ; for example, if its length is 48 times its diameter, the efflux is reduced to 0°63A,/2gh. This arises from the fact that, when water passes along cylindrical tubes, the resistance in- creases with the length of the tube ; for a thin layer of liquid is attracted to the walls by adhesion, and the internal flowing liquid rubs against this. The resistance which gives rise to this result is called Aydraulic friction ; it is independent of the material of the tube, provided it be not roughened ; but depends in a considerable degree on the viscosity of the liquid; for instance, ice-cold water experiences a greater resistance than lukewarm water. According to Prony, the mean velocity v of water in a cast-iron pipe of the length /, and the diameter @, under the pressure Z, is in metres I pe | 136 On Liguzds [148— This is on the assumption that the tubes are straight. Any angle or curvature of the tube diminishes the velocity, seeing that part of the motion is used up in pressure against the sides. Thus Venturi found the time requisite to fill a small vessel by means of a tube 38 inches in length by 3°3 in diameter was 45, 50, or 70 seconds, according as the tube was straight, curved, or bent at a right angle. By means of hydraulic pressure Tresca submitted solids such as silver, lead, iron and steel, powders like sand, soft plastic substances such as clay, and brittle bodies like ice, to such enormous pressures as 100,000 kilo- grammes per square cm, and has found that they then behave like fluid bodies. His experiments show also that these bodies transmit pressure equally in all directions when the pressure is considerable enough. 149. Efflux through capillary tubes.—This was investigated by Poiseuille by means of the apparatus represented in fig. 132, in which the capillary tube AB is sealed to a glass tube on which a bulb is blown. The volume of the space between the marks M and N is accurately determined, and the apparatus, having been filled with the liquid under examination by suction, is connected at the end M with a reservoir of compressed air, in which the pressure is measured by means of a mercury mano- meter (186. The time is then noted which is required for the level of the liquid to sink from M to N, the pressure remaining constant. It is thus found that v, the volume which flows out in a given time, is, with close approxi- mation, represented by the formula mesa 8 Z where / is the length and 7 the diameter of the tube, J the pressure, and 7 the coeffictent of internal friction (48) ; which may be defined as the resistance to motion offered by two layers of the liquid of unit surface, at unit distance, and moving away from each other with unit velocity. Knowing the dimensions, a determination of the volume which flows OULU LIN Aaviven Unie moms ready means of obtaining this coefficient. If the liquid which flows out through the tube is one which moistens it, a layer of liquid adheres to the side ; and accordingly the friction which the liquid experiences is not that against the sides, but is due to that of the particles against each other. The co- efficient of internal friction is represented in the above formula by 7. Bodies with a high coefficient of internal friction are said to be viscous (97). The liquids ether, water, sulphuric acid, linseed oil, Venice turpentine, represent, for instance, a series with increasing viscosity. The reciprocal of the -150] Form of the Jet 137 viscosity, or ' , iscalled the fiuidity ; it appears probable that this increases “i! with the temperature in the same ratio as the conductivity for electricity. The coefficient of internal friction is greater in the case of solution of salts than with water, and increases with the strength of the solution. It greatly diminishes with the temperature, and, for water, at 60° is one-third what it is at zero. A convenient apparatus for the purpose, more particularly for comparative measurements, is that given by Ostwald (fig. 133). It consists essentially of a tube, ac, which is narrowed at c, and opens into a bulb, to which is. attached the capillary ad, which again terminates in the wider tube de. The tube is filled with liquid from the bottle up to the point c, by aspiration through the caoutchouc tube ¢; the liquid is then allowed to flow out, and the time noted which its surface takes in falling from c toa mark, a. If the experiment be made with water, which is taken as standard, then, using the same apparatus, other liquids may be compared with it ; this has the advantage of dispensing with a deter- mination of the dimensions of the tube, and par- ticularly of the diameter—a matter of importance, since its fourth power occurs in the formula, and thus “any error in its determination greatly affects the result. If ¢ is the time required for the flow of the given volume of water, and 2’ that of a liquid whose coefficient is 7 and sp. gr. o, then i ball ni il i, I ee Tl | | ih | \ Wy ll HT MATTIE: I | HA Ht the coefficient of water and its specific gravity being each unity. A lubricating substance applied between an axle and its bearing adheres on the one hand to the axle, and on the other to the bearing, the outer layer is at rest, the inner one rotates with the axle. The internal friction acts in opposition to the motion, and the advantage of lubricators is that this internal friction is far less than the sliding friction. By observing the rate of diminution in the number of oscillations of a horizontal disc suspended by a thread when immersed in water, Meyer de- termined the coefficient of the frictional or internal resistance of water, and found that at 10° it was equal to 001567 granime on a square centimetre : . and for air it was about 34 as much. 150. Form of the jet.—After the contracted vein, the jet has the form of a solid rod for a short distance, but then begins to separate into drops, which present a peculiar appearance. Theyseem to form a series of ventral and nodal segments (fig. 134). The ventral segments consist of drops extended in a horizontal direction, and the nodal segments in a longitudinal direction. And as the ventral and nodal segments have respectively a fixed position, each drop must alternately become elongated and flattened while it is 138 On Liquids [150- falling (fig. 135). Between any two drops there are smaller ones, so that the whole jet has a tube-like appearance. These alterations in form have been explained as being due to vibrations in the mouth of the vessel itself. Their position is modified by extraneous influences, such as musical and other sounds, but only when these influences affect the edges themselves. When the vibrations of the vessel itself are stopped, the enlargements and contractions in the jet cease also ; they are strengthened, on the contrary, if a violoncello, for instance, is sounded. If the jet is momentarily illuminated by the electric spark, its structure is well seen ; the drops appear then to be stationary, and separate from each other. Ifthe aperture is not circular, the form of the jet undergoes curious changes. 0 " . » ' . 7 q U ' e =\ UNONTVONULAALOET AU ALN BS ay ie) ——— i ws eae es a 2 EP (chp Bh es e FQ Lonl bo a = = 0Q o Ut Fig. 136 When air issues from a gasholder under a pressure of 48 atmospheres, the jet can be ascertained by photography to be resolved into a series of drops of air following each other at equal intervals. 151. Barker’s mill—If water be contained in a vessel, and an aperture be made in one of the sides, the pressure at this point is removed, for it is expended in sending out the water ; but it remains on the other side ; and if the vessel were movable in a horizontal direction, it would move in a direc- tion opposite to that of the issuing jet. This is illustrated by the apparatus known as the Aydraulic tourniquet or Barker's mili (fig. 136). It consists of a glass vessel, M, containing water, and capable of moving about its vertical axis. At the lower part there is a tube, C, bent horizontally in oppo- site directions at the two ends. If the vessel were full of water and the tubes closed, the pressure on the sides of C would balance each other, being equal and acting in contrary directions ; but, being open, the water runs out, and the —152] Water-wheels. Turbines 139 pressure is not exerted on the open part, but only on the opposite side, as shown in the figure A. And this pressure, not being neutralised by an opposite pressure imparts a rotatory motion in the direction of the arrow, the velocity of which increases with the height of the liquid and the size of the aperture. The same principle may be illustrated by the following experiment. A tall cylinder containing water, and provided with a lateral stopcock near the bottom, is placed on a light shallow dish on water, so that it easily floats. On opening the stopcock so as to allow water to flow out, the vessel is observed to move in a direction diametrically opposite to that in which the water is issuing. Similarly, if a vessel containing water be suspended by a string on opening an aperture in one of the sides the water will jet out, and the vessel be deflected away from the vertical in the opposite direction. Segner water-wheel and the reaction machine depend on this principle. So also do rotating fireworks; that is, an unbalanced reaction from the heated gases which issue from openings in them gives them motion in the opposite irection. 152. Water-wheels. Turbines.—When water is continuously flowing from a_igher to a lower level, it may be made use of as a motive power. The motive power of water is generally utilised either by means of wafer- wheels, turbines, rams, or hydraulic engines. Water-wheels are wheels provided with buckets or float-boards at the circumference, on which the water acts either by pressure or by impact. They are made to turn in a vertical plane round a horizontal axis, and are of two principal kinds, wzdershot and overshot. In undershot wheels the float boards are placed radially—that is, at right angles to the circumference of the wheel. The lowest flat-boards are immersed in the water, which flows with a velocity depending on the height of the fall. Such wheels are applicable where the quantity of water is great but the fall inconsiderable. Overshot wheels are used with a small quantity of water which has a high fall, as with small mcuntain streams. On the circumference of the wheel there are buckets of a peculiar shape. The water falls into the buckets on the upper part of the wheel, which is thus moved by the weight of the water, and as each bucket arrives at the lowest point of revolution it discharges all the water, and ascends empty. An overshot wheel driven by an extraneous force may be used for raising water, as in dredging machines ; and an undershot one for moving a vessel to which its axis is fixed, as in the paddles of steam-vessels. The furbine is a horizontal water-wheel, and is similar in principle to the hydraulic tourniquet or reaction wheel (151). It consists of a pair of discs, one above the other, connected together by a number of specially shaped thin -arms or blades, which divide the space between the discs into an equal number of curved radial chambers. The wheel works generally upon a vertical axis, and one of the discs is cut away at the centre. In an outward Jlow turbine, the water enters through the opening so made into the space between the discs, and passes outwards radially through the chambers above mentioned, causing the wheel to rotate by its reaction upon their curved walls. In order to prevent waste of energy in giving useless rotation to the water, the peripheral openings of the wheel are surrounded by a series of 140 On Liquids [152- corresponding fixed chambers, whose sides (gu¢de-b/ades) are so curved that the water when it leaves them has lost all its rotational motion, and simply flows away at right angles to the axis. In an zzward flow turbine the water enters the peripheral opening of the wheel through the guide-blades, and leaves the wheel at the centre. The total theoretical effect of a fall of water is never realised ; for the water, after acting on the wheel, still retains some velocity, and therefore does not impart the whole of its energy to the wheel. In many cases water flows past without acting at all; if the water acts by impact, vibrations are produced which are transmitted to the earth and lost ; the same effect is produced by the friction of water over an edge of the sluice, in the channel which conveys it, or against the wheel itself, as well as by the friction of this latter against the axle. A wheel working freely in a stream, as with the corn-mills on the Rhine near Mainz, does not utilise more than 50 per cent. of the theoretical effect. One of the most perfect forms of turbines will work up to over 80 per cent. Turbines also, when properly designed, may be made to have a very high efficiency either with high or low falls ; while, on account of the great speed at which they run, they are very much smaller than water-wheels in proportion to their power. They are thus more ‘ effi- cient’ motors than steam engines, which, even if perfect, can only transform into work from 25 to 30 per cent. of the energy represented by the coal they burn, and seldom in practice utilise more than half of this percentage. 153. The hydraulic ram.—If a quantity of water flow through a pipe open at one end, and if this aperture be quickly closed, a sudden impact will be exerted on the closure as well as on the sides of the pipe. Some of the energy of the falling water is thereby converted into heat, and some exerts a dangerous pressure on the pipe. The existence of this pressure may be readily observed in any town with a high-pressure water supply, by the sharp click heard if the tap through which water is flowing is suddenly closed. Le i i am = YW WWW iD 7777777 8 WII) os KS YL] VY ee — S 7 Yj yy, VM LMA The hydraulic ram invented by Montgolfier is an arrangement by which the energy of falling water is applied so as to raise a portion of it to a greater height than the reservoir from which it is fed. The principle of such an arrangement is represented in fig. 137, in which E is the reservoir, A the pipe in which the water falls, B the channel, which should be long and straight, a and 0 the valves, C the wind-chest, and D the rising main. Water first flows out in quantity through the valve a, and as -154] Hydraulic Ram 141 soon as it has acquired a certain velocity it raises that valve, and the aperture is shut. The impact thus produced, acting on the sides of the pipe and on the valve 4, raises this valve, and a quantity of water passes into the wind-chest, shutting off air and compressing it in the space above the mouth d@ of the rising main D. This air by its elastic force closes the valve 6, and the water which has entered is raised in the main pipe D. As soon as the impulsive action is over, and the water in the channel is at rest, the valve a falls again by its own weight, the flow begins afresh, and when it has acquired sufficient velocity the valve 6 is again closed, and the whole process is repeated. In this way water can be raised to a height several times as great as the difference in level from E to the valve 6. If no energy were lost in friction, and in raising the valves, the height of ascent would be to the fall as the quantity of water which flows out at ais to that which is raised. Thus + of the water flowing out of the channel could be raised to 4 times the height of the available fall. 154. Hydraulic engine.—Historically, falling water was one of the earliest sources of power ; but it is only in recent times that attention has been called (first by Lord Armstrong) to the advantage of using hydraulic power in towns and other places where there is no watwra/ fall of water for driving certain classes of machines, in those cases more especially where the use of the machinery is only intermittent. ——/ - ~ y yg | SY A ili x Z \ (nu La ff Z RQ N NANA ASS SS S , uit \ ; WY LHL i | i js! " ; \ HHT IT TAHT HP | | i | | i V4 waey dS ii SS \ t } 4 SS RK Uf, Fig. 13% For this purpose the most important docks and large warehouses are now generally furnished with means of obtaining a water-supply at a very high pressure, generally about 700 pounds to the square inch. Steam- pumping engines are employed to pump water more or less continuously into what are practically large cylinders with immensely heavy pistons loaded to the required pressure. These vessels are called accumulators, and pipes 142 On Liquids f154- from them are led away to the various places (lock gates, sluice valves, cranes, capstans, &c.) where power may be wanted. At each of these places there is some kind of hydraulic motor suitable to the particular work to be done, and this motor can be instantaneously set to work by opening the communication between it and the high-pressure water in the accumulator. The motor used is not uncommonly a small engine similar in principle to a steam engine, and one of the best of these engines is that illustrated in fig. 138, which is the invention of Schmidt of Zitirich. It consists of a cylinder fitted with a piston, c, whose rod is.connected directly to a crank upon a horizontal shaft. The cylinder has two forts or passages, a and 4, one at each end, both terminating below in openings upon a convex curved face, which is kept continually pressed against a similar concave face upon the framing of the engine. In this fixed face are also an inlet port or passage A, and outlet passages B. When the cylinder is in the position shown in the figure, the high-pressure water is passing through A and 4, forcing the piston along, and driving out the already used water through a and B. As the piston moves and turns the crank, the cylinder oscillates on its bearings, and by the time the piston has got to the end of its stroke, the cylinder then being horizontal, the process is just being reversed, water passing in through A and a, and out through 4 and B. W is an air-vessel for preventing shocks. This motor utilises 90 per cent. of the available power ; in this respect it far exceeds a steam-engine which does not utilise more than Io per cent. of the power due to the consumption of the coal burnt. The chief drawback to the use of water power, except where there is a large natural supply under pressure, is its expense. For each revolution of the crank shaft two complete cylinders full of water must be passed through such an engine, as, whether the power be wanted or not, the water cannot be expanded like steam. With any given pressure it is easy to find out how much water will be required for a given power. Ata pressure of 30 pounds per square inch, for instance, one horse-power will require, supposing the effictency of the 33000 x 60 492), 30 x 144 x 0°7 gallons per hour, a quantity the cost of which would in most cases put the use of this power out of the question. The pressure in town mains generally lies between 20 and 4o pounds per square inch, and it is therefore only in cases where a special high-pressure supply is available that the power can be economically used. In London, water is supplied to consumers by the Hydraulic Power Company under a pressure of 700 pounds; and the quantity required for one horse- power would be about 175 gallons. The cost of power supplied in this way is about fourpence per horse-power per hour, which, although expensive for continuous working, is not so when it is intermittently used, and when only the quantity actually consumed is paid for. Water-power is usually represented by the weight of the water multiplied into the height of the available fall; or it may also be represented by half the product of the mass into the square of the velocity. Both measurements machine to be 70 per cent. ( = about 655 cubic feet or 4,000 ~154] Hydraulic Engine 143 give the same result (60). The mass of water falling every hour over Niagara is estimated at 100,000,000 tons ; taking the vertical depth at 150, and adding to this 150 as representing the velocity, we have a total fall from lake to lake of 300 feet. The force which the chief fall alone would furnish represents 16,800,000 horse-power, which, if furnished by steam, would require an annual consumption of 260,000 ooo tons of coal, taking 4 pounds per hour for the horse-power. This is more than all the coal raised in the year in the whole world. 144 On Gases [155- BOOK LY. ON GASES CHAP Tivive! PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS 155. Physical properties of gases..-Gases are bodies which, unlike solids, have no independent shape, and, unlike liquids, have no independent volume. Their molecules possess almost perfect mobility ; they are con- ceived as darting about in all directions, and are continually tending to occupy a greater space. This property of gases is known by the names expansibility, tenston, or elastic force, from which they are often called elastic huids. Gases and liquids have several properties in common, and some in which they seem to differ are in reality only different degrees of the same property. Thus, in both, the particles are capable of moving ; in gases with almost perfect freedom ; in liquids not quite so freely, owing to a greater degree of viscosity (149). Both are compressible, though in very different degrees. If a liquid and a gas both exist under the pressure of one atmosphere, and then the pressure be doubled, the water is compressed by about the zt y5 part, while the gas is compressed by one-half. In density there is a great difference : water, which is the type of liquids, is 770 times as heavy as air, the type of gaseous bodies, while under the pressure of one atmosphere. A gas has no original volume ; it is always elastic, or, in other words, it is always striving to attain a greater volume ; this tendency to indefinite ex- pansion is the chief property by which gases are distinguished from liquids. A spiral spring only shows elasticity when it is compressed; it loses its tension when it has returned to its primitive condition. By the aid of pressure and of low temperatures, the force of cohesion may be so far increased in many gases that they are readily converted into liquids, and we know now that with sufficient pressure and cold they may all be liquefied. On the other hand, heat, which increases the vzs vzva of the molecules, converts liquids, such as water, alcohol, and ether, into the aeriform state in which they obey all the laws of gases. An aeriform substance is called a vapour or a gas according as it can or cannot without change of temperature be compressed into a liquid ; that is, it is a gas if its tempera- —158] Weight of Gases 145 ture be above its critical temperature (374) and a vapour if below. Formerly, it was usual to describe as a vapour a substance which at ordinary tempera- tures is liquid (for instance, steam) and as a gas a substance which, at ordinary temperatures and pressures, exists only in the gaseous state. In describing the properties of gases we shall, for obvious reasons, refer to atmospheric air as their type. 156. Expansibility of gases.—This property of gases, their tendency to assume continually a greater volume, is exhibited by means of the following experiment :—A bladder, closed by a stop- cock and about half full of air, is placed under the receiver of the air-pump (fig. 139), and a vacuum is produced, on which the bladder immediately distends. This arises from the fact that the molecules of air flying about in all directions (297) press against the sides of the bladder. Under ordinary conditions, this internal pressure is counterbalanced by the air in the receiver, which exerts an equal and contrary pressure. But when this pres- sure is removed, by exhausting the receiver, the internal pressure becomes evident. When air is admitted into the receiver, the bladder resumes its original form. ; 157. Compressibility of gases.—The compressibility of gases is readily shown by the pneumatic syringe (fig. 140). This con- Fieticd sists of a stout glass tube closed at one end, and provided with a tight-fitting solid piston. When the rod of the piston is pressed it moves down in the tube, and the air becomes compressed into a smaller volume; but as soon as the force is removed the air regains its original volume, and the piston rises to its former position. al cin | zi , | 158. Weight of gases.—From their extreme fluidity and expansibility, gases seem to be uninfluenced by the force of gravity: they nevertheless possess weight like solids and liquids. To show this, a glass globe of 3 or 4 quarts capacity is taken (fig. 141), the neck of which is provided with a stop- cock, which hermetically closes it, and by which it can be screwed to the plate of the air-pump. The globe is then exhausted, and its weight deter- mined by means of a delicate balance. Air is now allowed to enter, and the L 146 On Gases [158- globe again weighed. The weight in the second case will be found to be greater than before, and if the capacity of the vessel is known, the increase will obviously be the weight of that volume of air. By a modification of this method, and with the adoption of certain pre- cautions, the weight of air and of other gases has been determined. Perhaps the most accurate are those of Regnault, who found that a litre of dry air at o° C., and under a pressure of 760 milli- metres, weighs 1°293187 gramme. Since a litre of water (or 1,000 cubic centimetres) at o° weighs ‘999877 gramme, the density of air is 000129334 that of water under the same circumstances ; that is, water is 773 times as heavy as air. Expressed in English measures, 100 cubic inches of dry air under the ordinary atmospheric pressure of 30 in. and at the temperature of 16° C. weigh 31 grains ; the same volume of carbonic acid gas under the same circumstances weighs 47°25 grains; 1oo cubic inches of hydrogen, the lightest of all gases, weigh 2°14 grains; and too cubic inches of hydriodic acid gas weigh 146 grains. 159. Pressure exerted by gases.—Gases exert on their own molecules, and on the sides of vessels which contain them, pressures which may be regarded from two points of view. First, we may neglect the weight of the gas; secondly, we may take account of its weight. It we neglect Fig. 14x the weight of any gaseous mass at rest, and only consider its expansive force, it will be seen that the pressures due to this force act with the same strength on all points, both of the mass itself and of the vessel in which it is contained. For itisanecessary consequence of the elasticity and fluidity of gases that the repulsive force between the molecules is the same at all points, and acts equally in all directions. This principle of the equality of the pressure of gases in all directions may be shown ex- perimentally by means of an apparatus resembling that by which the same principle is demonstrated for liquids (fig. 71). If we consider the weight of any gas, we shall see that it gives rise to pressures which obey the same laws as those produced by the weight of liquids. Let us imagine a cylinder, with its axis vertical, several miles high, closed at both ends and full of air. Let us consider any small portion of the air enclosed between two horizontal planes. This portion must sustain the weight of all the air above it, and transmit that weight to the air beneath it, and likewise to the curved surface of the cylinder which contains it, and at each point in a direction at right angles to the surface. Thus the pressure increases from the top of the column to the base; at any given layer it acts equally on equal surfaces, and at right angles to them, whether they are horizontal, vertical, or inclined. The pressure acts on the sides of the vessel, and on any small surface it is equal to the weight of a column of gas whose base is this surface, and whose height its distance from the summit of the column, The pressure is also independent of the shape and dimensions of the supposed cylinder, provided the height remain the same. For a small quantity of gas the pressures due to its weight are quite insignificant, and may be neglected ; but for large quantities, like the atmo- sphere, the pressures are considerable, and must be allowed for. ~161] Atmospheric Pressure 14 7 160. The atmosphere: its composition. —The atmosphere is the layer of air which surrounds our globe in every part. It partakes of the rotatory motion of the globe, and would remain fixed relatively to terrestrial objects but for local circumstances, which produce winds, and are constantly dis- turbing its equilibrium. It is essentially a mixture of oxygen and nitrogen gases ; its average composition by volume being as follows :— Nitrogen ; : ; : , 3 : : eo AG Oxygen . : AES : , : : : re 08 Aqueous vapour. : : : ; : é nae Od, Carbonic acid : ‘ : : : : ood T00°00 The nitrogen of the atmosphere has recently been found by Lord Rayleigh and Prof. Ramsay to contain about I per cent. of a new gaseous element to which, in consequence of its extraordinary nertness, its discoverers have given the name avgov. Argonisabout half as dense again as ordinary nitrogen, and is condensed at a temperature of — 121° C., under a pressure of 51 atmospheres, to a colourless liquid. When cooled to —190° C. it solidifies. The carbonic acid arises from the respiration of animals, from the pro- cess of combustion, and from the decomposition of organic substances. Boussingault estimated that in Paris the following quantities of carbonic acid are produced every 24 hours :— By the population and by animals . . 11,895,000 cubic feet By processes of combustion . ; 492,101,000 i 103,996,000 i Notwithstanding this enormous continual production of carbonic acid the composition of the atmosphere does not vary ; for plants in the process of vegetation decompose the carbonic acid, assimilating the carbon, and restoring to the atmosphere the oxygen, which is being continually consumed in the processes of respiration and combustion. 161. Atmospheric pressure.—If we neglect the perturbations to which the atmosphere is subject, as being inconsiderable, we may consider it as a fluid sea of a certain depth, surrounding the earth on all sides, and exercising the same pressure as if it were a liquid of very small density. Consequently, the pressure on the unit of area is constant at a given level, being equal to the weight of the column of atmosphere above that level whose horizontal section is the unit of area (Ioo). It will act at right angles to the surface, whatever be its position. It will diminish as we ascend, and ‘Increase as we descend from that level. Consequently, at the same height, the atmospheric pressures on unequal plane surfaces will be proportional to the areas of those surfaces, provided they be small in proportion to the height of the atmosphere. In virtue of the expansive force of the air, it might be supposed that the molecules would expand indefinitely into the planetary spaces. But, in pro- portion as the air expands, its expansive force decreases, and is further weakened by the low temperature of the upper regions of the atmosphere, so ie 148 On Gases [161- that, at a certain height, equilibrium is established between the expansive force which separates the molecules and the action of gravity which draws them towards the centre of the earth. It is therefore concluded that the atmosphere is limited. From the weight of the atmosphere, and its increase in density, and from the observation of certain phenomena of twilight, its height has been esti- mated at from 30 to 4omiles. Above that height the air is extremely rarefied, and at a height of 60 miles it is assumed that there is a perfect vacuum. On the other hand, meteorites have been seen at a height of 200 miles, and, as their luminosity is undoubtedly due to friction against air, there must be air at such a height. This higher estimate is supported by observations made at Rio Janeiro on the twilight arc, by M. Liais, who estimated the height of the atmosphere at between 198 and 212 miles. The question as to the exact height of the atmosphere must therefore be considered as still awaiting settlement. As it has been previously stated that 100 cubic inches of air weigh 31 grains, it will readily be conceived that the whole atmosphere exercises a considerable pressure on the surface of the earth. The existence of this pressure is shown by the following experiments. 162. Crushing force of the atmosphere.—On one end of a stout glass cylinder, about 5 inches high, and open at both ends, a piece of bladder is tied quite air-tight. The other end, the edge of which is ground and well greased, is pressed on the plate of the air-pump (fig. 142). As soon as the air in the vessel is rarefied by working the air-pump, the bladder is depressed by the weight of the atmosphere above it, and finally bursts with a loud report caused by the sudden entrance of the air. Mi | i 163. Magdeburg hemispheres.—The preceding experiment only serves to illustrate the downward pressure of the atmosphere. By means of the -164] Torricelle’s Experiment 149 Magdeburg hemispheres (figs. 143 and 144), the invention of which is due to Otto von Guericke, burgomaster of Magdeburg, it can be shown that the pressure acts in all directions. This apparatus consists of two hollow brass hemispheres of 4 to 43 inches diameter, the edges of which are made to fit tightly, and are well greased. One of the hemispheres is provided with a stopcock, by which it can be screwed on to the air-pump, and on the other there isa handle. As long as the hemispheres contain air they can be separated without any difficulty, for the external pressure of the atmosphere is counter- balanced by the elastic force of the air in the interior. But when the air in the interior is pumped out by means of the air-pump, the hemispheres cannot be separated without a powerful effort: and as this is the case in whatever position they are held, it follows that the atmospheric pressure is transmitted in all directions. DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS. 164. Torricelli’s experiment.—The above experiments demonstrate the existence of the atmospheric pressure, but they give no precise indication as to its amount. The following experiment, which was first made in 1643 by Torricelli, a pupil of Galileo, gives an exact measure of the pressure of the atmosphere. A glass tube is taken, about a yard long and a quarter of an inch internal diameter (fig. 145). It is sealed at one end, and is quite filled with mercury. The aperture C being closed by the thumb, the tube is inverted, the open end placed in a small mercury trough, and the thumb removed. The tube being in a vertical position, the column of mercury sinks, and, after oscillating some time, it finally comes to rest at a height, A, about 301nches above the mercury in the trough. The mercury is raised in the tube by the pressure of the atmosphere on the mer- cury in the trough. There is no contrary pressure on the mercury in the tube, because it is closed ; but, if the end of the tube be opened, the atmosphere will press equally inside and outside the tube, and the mercury will sink to the level of that in the trough. It has been shown in Hydrostatics (108) that the heights of two columns of liquid in communication with each other are inversely as their densities ; and hence it follows that the Fig. 145 pressure of the atmosphere is equal to that of a column of mercury the height of which is 30 inches. If the pressure of the atmosphere diminishes, the height of the column which it can sustain must also diminish. 150 On Gases [165- 165. Pascal’s experiments.—Pascal, who wished to ascertain whether the force which sustained the mercury in the tube was really the pressure of the atmosphere, made the following experiments. (i.) If it were the case, then the column of mercury ought to be lower in proportion as we ascend in the atmosphere. He accordingly requested one of his relatives to repeat Torricell’s experiment on the summit of Puy de Dome in Auvergne. This was done, and it was found that the column of mercury was about 3 inches lower, thus proving that it is really the pressure due to the weight of the atmosphere which supports the mercury, since, when this weight diminishes, the height of the column also diminishes. (i1.) Pascal repeated Torricelli’s experiment at Rouen in 1646, with other liquids. He closed a tube nearly 50 feet long at one end, and, having filled it with water, placed it vertically in a vessel of water, and found that the water stood in the tube at a height of 34 feet ; that is, 13°6 times as high asmercury. SButsince the mercury is 13°6 times as heavy as water, the height of the column of water was exactly equal to that of a column of mercury in Torricelli’s experiment, and it was consequently the same force, the pressure of the atmosphere, which succes- sively supported the two liquids. Pascal’s other experiments with oil and with wine gave similar results. 166. Amount of the atmospheric pressure.—Let us assume that the tube in the above experiment is a cylinder, the section of which is equal toa square inch ; then, since the height of the column of mercury, in round num- bers, is 30 inches, the column will contain 30 cubic inches ; and as a cubic inch of mercury weighs 3,433°5 grains = 0°49 of a pound, the pressure of such a column ona square inch of surface is equal to 14°7 pounds. In round numbers, the pressure of the atmosphere is taken at 15 pounds on the square inch. A surface of a foot square contains 144 square inches, and therefore the pressure upon it is equal to 2,160 pounds, or nearly a ton. Expressed in the metrical system the standard atmospheric pressure at o° and the sea- level is 760 millimetres, which is equal to 29:9217 inches ; anda calculation similar to the above shows that the pressure on a square centimetre is = 1:032896 kilogramme, or 1°‘01327 x 10° dynes per sq. cm. For convenience of calculation Everett has proposed to adopt the pressure of a megadyne per sq. cm. or 10 C.G.S. units of pressure-intensity, as the standard pressure ; this with a value of g=981'17 at Greenwich for this country would represent a height of 74:96 cm. or 29°513 inches. A gas or liquid which acts in such a manner that a square inch of surface is exposed to a pressure of 15 pounds is called a pressure of one atmosphere. If, for instance, the elastic force of the steam of a boiler isso great that each square inch of the internal surface is exposed to a pressure of 90 pounds (=6x 15), we say it is under a pressure of six atmospheres. The surface of the body of a man of middle size is about 16 square feet ; the pressure, therefore, which a man supports on the surface of his body is 35,560 pounds, or nearly 16 tons. Such an enormous pressure might seem impossible to be borne ; but it must be remembered that, in all directions, there are equal and contrary pressures which counterbalance one another. It might also be supposed that the effect of this force, acting in all directions, would be to press the body together and crush it. But the solid parts of the skeleton could resist a far greater pressure ; and as to the air and liquids -168] Cistern Barometer I51 contained in the organs and vessels, the air has the same density as the external air, and cannot be further compressed by the atmospheric pressure ; and from what has been said about liquids (98), it is clear that they are vir- tually incompressible. Only by considerable variations in pressure is the body affected, as by ascending great heights, or by divers in diving bells and the like. When the external pressure is removed from any portion of the body, either by means of a cupping-vessel or by the air-pump, the pressure from within is seen by the distension of the surface. 167. Different kinds of barometers.—The instruments used for measur- ing the atmospheric pressure are called darometers. In ordinary barometers the pressure is measured by the height of a column of mercury, as in Torri- celli’s experiment ; the barometers which we are about to describe are of this kind. But there are barometers without any liquid, one of which, the aneroid (190), is remarkable for its simplicity and portability. 168. Cistern barometer.—The céstern barometer consists of a straight glass tube closed at one end, about 33 inches long, filled with mercury, and dipping into a cistern also containing mercury. In order to render the barometer more portable, and the variations of level in the cistern less perceptible when the mercury rises or falls in the tube, several different forms have been constructed.. Fig. 146 represents one form of the cistern barometer. The apparatus is fixed to a mahogany stand, on the upper part of which there is a scale graduated in millimetres or inches from the level of the mercury in the cistern ; a movable index, z, shows on the scale the level of the mercury. A thermometer on one side indicates the temperature. There is one fault to which this barometer is liable, in common with all others of the same kind. The zero of the scale does not always correspond to the level of the mercury in the cistern. For, as the atmospheric pressure is not always the same, the height of the mercurial column varies ; some- times mercury is forced from the cistern into the tube, and sometimes from the tube into the cistern, so that in the majority of cases the graduation of the barometer does not indicate the true height. If the diameter of the cistern is large, relatively to that of the tube, the error from this source, which is known as the error of capacity, is lessened. The height of the barometer is the distance between the levels of the mercury in the tube and in the cistern. Hence the barometer should always be perfectly vertical ; for if not, the tube being inclined, the column of mercury is elongated (fig. 147), and the number read off on the scale is too great. As the pressure which the mercury exerts by its weight at the base of the tube is independent of the form of the tube and of its diameter (102), provided it is not capillary, the height of the barometer is independent of the diameter of the tube and of its shape, but is inversely as the density of the liquid. With mercury the mean height at the level of the sea is 29°92, Or, in round numbers, 30 inches ; in a water barometer it would be about 34 feet, or 10°33 metres. In marine barometers the error of capacity is got rid of by graduating the scale, not in the true measurements, but by an empirical correction depending on the relative diameters of the tube and cistern. Thus if a rise of 1o mm. in the tube produced a fall of 1 mm. in the cistern, the true change would not be iIomm. but 11 mm. This is obviously allowed for by dividing the space 152 On Gases [168- of 1o mm. on the scale into 11 mm: The correctness of such an instrument depends on the accuracy with which the scale is laid off. 169. Fortin’s barometer.—/fortin’s barometer differs in the shape of the cistern from that just described. The base of the cistern is made of leather, and can be raised or lowered by means of a screw; this has the advantage that a constant level can be obtained, and also that the instru- ment is made more portable. For, in travelling, it is only necessary to raise Fig. 146 Fig. 147 the leather until the mercury, which rises with it, quite fills the cistern and the tube ; the barometer may then be inclined, and even inverted, without any fear that a bubble of air may enter, or that the shock of the mercury may crack the tube. Fig. 148 represents the arrangement of the barometer, the tube of which is placed in a brass case. At the top of this case there are two longitudinal slits on opposite sides, so that the level of the mercury, B, is seen. The scale on the case is graduated in millimetres. An index, A, moved by the -169] Fortin’s Barometer 153 hand, gives by means of a vernier the height of the mercury to 4th of a millimetre. At the bottom of a case is the cistern, 6, containing mercury, o. Fig. 149 shows the details of the cistern on a larger scale. It consists of a glass cylinder, 4, through which the mercury can be seen ; this is closed at the top by a boxwood disc fitted on the under surface of the brass cover M. Through this passes the barometer tube E, which is drawn out at the end, and dips in the mercury ; the cistern and the tube are connected by a piece of buckskin, ce, which is firmly tied at ¢ to a contraction in the tube, and at e to a brass tubulure in the cover of the cistern. This mode of closing prevents the mercury from escaping when the barometer is inverted, while the pores of the leather transmit the atmospheric pressure. The bottom of the cylinder 6 is cemented on a boxwood cylinder, zz, on a contraction in which, 22, is firmly tied the buckskin, 77, which forms the base of the cistern. On this skin is fastened a wooden button, 1+, which rests against the end of a screw, C. According as this is turned in one direction or the other the skin sz is raised or lowered, and with it the mer- cury. In using this barometer the mercury is first made ex- actly level with the point a, which is effected by turning the screw C either in one direction or the other. The graduation of the scale is counted from this point a, and thus the distance of the top of the column of mercury from a gives the height of the barometer. The bottom of the cistern is surrounded by a_ brass case, which is fastened to the cover M by screws, &, k, k. We have already seen (168) the importance of having the barometer quite vertical, which is effected by the following plan, known as Cardan’s SUSPENSION. The metal case containing the barometer is fixed in a copper sheath X by two screws, a and 4 (fig. 150). This is provided with two axles (only one of which, 9, is seen in the figure), which turn freely in two holes in a ring, Y. In a direction at right angles to that of the axles, 00, the ring has also two similar axles, #z and 2, resting on a support, Z. By means of this double suspension the barometer can oscillate freely about the axes mm and vo, in Fig. 149 Fig. 150 154 On Gases [169— two directions at right angles to each other. But as care is taken that the point at which these axes cross corresponds to the tube itself, the centre of gravity of the system, which must always be lower than the axis of sus- pension, is below the point of intersection, and the barometer is thus perfectly vertical. 170. Gay-Lussac’s syphon barometer.—The syphon barometer is a bent glass tube, one of the branches of which is much longer than the other. Fig. 154 Fig. 155 The longer branch, which is closed at the top, is filled with mercury as in the cistern barometer ; while the shorter branch, which is open, serves as a cistern. The difference between the two levels is the height of the barometer. Fig. 151 represents the syphon barometer as modified by Gay-Lussac. In order to render it more available for travelling, by preventing the entrance of air, he joined the two branches by a capillary tube (fig. 152); when the ~171] Precautions in reference to Barometers 155 instrument is inverted (fig. 153) the tube always remains full in virtue of its capillarity, and air cannot penetrate into the longer branch. A sudden shock, however, might separate the mercury and admit some air. To avoid this, Bunten introduced an ingenious modification into the apparatus. The longer branch is drawn out to a fine point, and is joined to a tube, B, of the form represented in fig. 154. This arrangement forms an az-trap ; for if air passes through the capillary tube it cannot penetrate the drawn-out extremity of the longer branch, but lodges in the upper part of the enlargement B. In this position it does not affect the observations, since the vacuum is always at the upper part of the tube ; it is, moreover, easily removed. In the syphon barometer the shorter branch is closed, but there is a capillary aperture in the side z, through which the atmospheric pressure is transmitted. The barometric height is determined by means of a o scales, which have a common zero at O, towards the middle of the longer branch, ed are gra- duated in contrary directions, the one from O to FE, and the other from O to B, either on the tube itself, or on brass rules fixed parallel to the tube. Two sliding verniers, 7 and , indicate tenths of a millimetre. The total height of the barometer, AB, is the sum of the distances from O to A and from O to B. Fig. 155 represents a very convenient mode of arranging the open end of a syphon barometer for transport. The quantity of mercury is so arranged that when the Torricellian space is quite filled with mercury, by inclining the tube the enlargement is just filled to d@. This is closed by a carefully fitted cork, fixed on the end of a glass tube, do, about a millimetre in diameter, which allows for the expansion of mercury by heat. When the barometer is to be used, the cork and tube are raised. 171. Precautions in reference to barometers.—In the construction of barometers mercury is chosen in preference to any other liquid, since, being the densest of all liquids, it stands at the least height. When the mercury barometer stands at 30 inches, the water barometer would stand at about 34 feet (168). It also deserves preference because it does not moisten the glass. It is necessary that the mercury be pure and free from oxide, other- wise it adheres to the glass and tarnishes it. Moreover, if it is impure, its density is changed, and the height of the barometer is too great or too small. Mercury is purified, before being used for barometers, by treatment with dilute nitric acid, and by distillation. The space at the top of the tube (figs. 146 and 151), which is called the Lorricellian vacuum, must be quite free from air and from aqueous vapour, for otherwise either would depress the mercurial column by its elastic force. To obtain this result, a small quantity of pure mercury is placed in the tube and boiled for some time. It is then allowed to cool, and a further quantity, previously warmed, added, which is boiled, and so on, until the tube is quite full ; in this manner the moisture and the air which adhere to the sides of the tube (196) pass off with the mercurial vapour. A barometer tube should not be too narrow, for otherwise the mercury is moved with difficulty ; and before a reading is taken, the barometer should be tapped so as to get rid of the Be esion, to the glass. A Paina | is free from air and moisture if, when it is inclined, the 150 On Gases _ [171- mercury strikes with a sharp metallic sound against the top of the tube. If there is air or moisture in it, the sound is deadened. 172. Correction for capillarity.x—In cistern barometers there is always a certain depression of the mercurial column due to capillarity, unless the internal diameter of the tube exceeds o'8 inch. To make the correction due to this depression, it is not enough to know the diameter of the tube ; we must also know the height of the meniscus, od (fig. 156), which varies according as the meniscus has been formed during an ascending or descending motion of the mercury in the tube. Consequently, the height of the meniscus must be determined by bringing the pointer to the level a4, and then to the level d, when the difference of the readings will give the height, od, required. These two terms—namely, the internal diameter of the tube and the height of the meniscus—being known, the resulting correction can be taken out of the following table : Fig. 156 Height of sagitta of meniscus in inches | Internal | diameter | 5 rh | in inches | | | | O‘OIO O°OI5 | 0°020 0°025 | 0'030 0°035 0040 O°157 0'0293 | 070431 | 0°0555 | 00677 | 0:0780 | 0:0870 | 0°0948 0'236 | OOIIQ | O°0176 | 0°O231 | 0°0294 | 0°0342 | 0°0398 | 0°0432 0°315 | 010060 | 0:0088 | o-0118 | 00144 | 00175 | 0°0196 | 0:0221 07394 | 0°0039 | 0°0048 | 0:0063 | 0°0078 | 070095 | O;OIIO O'0I25 0°472 | 0°0020 | 00029 | 0°0036 | 00045 | 0°0053 | 0°0063 0°0073 O°550 | O'001O | O'00I7 | 0'0024 | 00029 | 0°0034 0°0039 0°0044 \ In the syphon barometer the two tubes are of the same diameter, so that the error caused by the depression in the one tube very nearly corrects that caused by the depression in the other. As, however, the meniscus in the one tube is formed by a column of mercury with an ascending motion, while that in the other is formed by a column with a descending motion, their heights will not be the same, and the reciprocal correction will not be quite exact. 173. Correction for temperature.—In all observations with barometers, whatever be their construction, a correction must be made for temperature. Mercury contracts and expands with change of temperature, hence its density changes, and consequently the barometric height for a given pressure is inversely as the density of the mercury, so that for different atmospheric pressures the mercurial column might have the same height. Accordingly, in each observation the height observed must be reduced to a standard temperature. The choice of this is quite arbitrary, but that of melting ice is always adopted in practice. It will be seen in the book on Heat how this correction is made. 174. Variations in the height of the barometer.—When the barometer is observed for several days, its height, corrected for temperature, is found —175] Causes of Barometric Variations Tse to vary in the same place, not only from one day to another, but also during the same day. The extent of these variations—thatis, the difference between the greatest and the least height—is different in different places. It increases from the equator towards the poles. Except under extraordinary circumstances, the greatest variations do not exceed six millimetres under the equator, 30 under the tropic of Cancer, 40 in France, and 60 at 25 degrees from the pole. The greatest variations are observed in winter. The mean datly height is the height obtained by dividing the sum of 24 successive hourly observations by 24. In our latitudes the barometric height at noon corresponds to the mean daily height. The mean monthly height is obtained by adding together the mean daily heights for a month and dividing by 30. The sean yearly height is similarly obtained. Under the equator the mean annual height at the level of the sea is o™-758, or 29°84 inches. It increases from the equator, and between the latitudes 30° and 4o° it attains a maximum of 0™°763, or 30°04 inches. In lower latitudes it decreases, and in Paris it does not exceed 0o™°7568. The general mean at the level of the sea is o™-761, or 29°96 inches. The mean monthly height is greater in winter than in summer, in conse- quence of the cooler atmosphere. Two kinds of variations are observed in the barometer :—Ist, the acc7- dental variations, which present no regularity ; they depend on the seasons, the direction of the winds, and the geographical position, and are common in our climates ; 2nd, the dazly variations, which are produced periodically at certain hours of the day. At the equator, and between the tropics, no accidental variations are observed ; but the daily variations take place with such regularity that a barometer may serve to a certain extent as a clock. The barometer sinks from midday till towards four o’clock ; it then rises, and reaches its maximum at about ten o’clock in the evening. It then again sinks, and reaches a second minimum towards four o’clock in the morning, and a second maxi- mum at ten o’clock. In the temperate zones there are also daily variations, but they are detected with difficulty, since they occur in conjunction with accidental variations. The hours of the maxima and minima appear to be the same in all climates, whatever be the latitude ; they merely vary a little with the seasons. 175. Causes of barometric variations.—It is observed that the course of the barometer is generally in the opposite direction to that of the thermo- meter ; that is, that when the temperature rises the barometer falls, and vzce versa ; which indicates that the barometric variations at any given place are produced by the expansion or contraction of the air, and therefore by its change in density. If the temperature were the same throughout the whole extent of the atmosphere, no currents would be produced, and at the same height atmospheric pressure would be everywhere the same. But when any portion of the atmosphere becomes warmer than the neighbouring parts its specific gravity is diminished, and it rises and passes away through the upper regions of the air, whence it follows that the pressure is diminished and the barometer falls. If any portion of the atmosphere retains its temperature, while the neighbouring parts become cooler, the same 158 On Gases [175- effect is produced ; for in this case, too, the density of the first-mentioned portion is less than that of the others. Hence, also, it usually happens that an extraordinary fall of the barometer at one place is counterbalanced by an extraordinary rise at another place. The daily variations appear to result from the expansions and contractions which are periodically pro- duced in the atmosphere by the heat of the sun during the rotation of the earth. 176. Relation of barometric variations to the state of the weather.— It has been observed that, in our climate, the barometer in fine weather is generally above 30 inches, and is below this point when there is rain, snow, wind, or storm ; and also, that for any given number of days at which the barometer stands at 30 inches there are as many fine as rainy days. From this coincidence between the height of the barometer and the state of the weather, the following indications have been marked on the barometer, counting by thirds of an inch above and below 30 inches :— Height State of the weather 31 inches . : ; : Very "dary: 502 CEUs : } ; . Settled weather, BOTY , | Fine weather. 30.) Sees ; ; . Variable. aoe 0) ee : é . Rain or wind. 5 Loy Ee : ; ; . Much rain. ete ky dls : ; ; .- Tempest: In using the barometer as an indicator of the state of the weather, we must not forget that it really only serves to measure the pressure of the atmo- sphere, and that it only rises or falls as the pressure in- creases or diminishes; and although a change of weather frequently coincides with a change in the pressure, they are not necessarily connected. This coincidence arises from meteorological conditions peculiar to our climate, and does not occur every- where. That a fall in the barometer usually precedes rain in our latitudes is caused by the position of Europe. The prevailing winds here are the south- west and north-east. The former, coming to us from the equatorial regions, are warmer and lighter. They often, therefore, biow for hours or even days in the higher regions of the atmosphere before manifesting themselves on the surface of the earth. The air is therefore lighter, and the pressure lower. Hence a fall of the barometer is a probable indication of the south-west winds, which gradually extend downwards, and, reaching us, after having traversed large tracts of water, are charged with moisture, and bring us rain. The north-east wind blows simultaneously aboveand below, but the hindrances to the motion of the current on the earth, by hills, forests, and houses, cause the upper current to be somewhat in Bitanee of the lower ones, fought not so much so as the south-west wind. The air is therefore LSE heavier 4 178] Fixed Barometer 159 even before we perceive the north-east, and a rise in the barometer affords a forecast of the occurrence of this wind, which, as it reaches us after having passed over the immense tracts of dry land in Central and Northern Europe, is mostly dry and fine. When the barometer rises or sinks slowly, that is, for two or three days, towards fine weather or towards rain, it has been found from a great number of observations that the indications are then extremely probable. Sudden variations in either direction indicate bad weather or wind. 177. Wheel barometer.—The wheel barometer, which was invented by Hooke, is a syphon barometer, and is especially intended to indicate good and bad weather (fig. 157). In the shorter leg of the syphon there is a float which rises and falls with the mercury. 1, OG PV, =I+e, the gas —184] Boyle's Law 169 : ‘ ; id is ismore compressible than Boyle’s law requires. If ey << 1b OF ay BV Pay. the gas is less compressible than it would be in accordance with the law. The following table gives the results of a series of experiments made on ait, nitrogen, carbonic acid, and hydrogen :— sae ALES Air Nitrogen Carbonic acid Hydrogen Pav, Pay PoV 12 ovo P ov%o P ACR) Pp SON P,V, ‘ P.V, A PVG 5 PV, mm mm mm mm 738°72 | YZ'oor414 75346 r°000988 764°03 I°007597 = oe 2II2°53 I°002765 495392 | 1°002952 3486°13 1°028698 2211°18 0°998584 4140°82 1°003253 8628°54 1°004768 4879°77 1°045625 5845718 o’996121 9330°41 1°006366 10g81"42 1'000456 9619°97 1155865 g176°50 =| 0°992933 Regnault’s conclusions were :— 1. That no gas rigorously obeys Boyle’s law. The divergence is small for small pressures, but increases with the pressure. 2. That «¢ is positive for all the gases experimented on except hydrogen. Hydrogen then is less compressible, all the other gases more compressible, than Boyle’s law requires. 3. The divergence from the law is greater for the easily liquefiable gases, such as carbonic acid, sulphurous acid, ammonia, and cyanogen, than for the gases called in Regnault’s time permanent gases, viz. oxygen, nitrogen, methane, nitric oxide, and carbon monoxide. F Thus to reduce air to 345 of its original volume, a pressure of 19°7199 atm. was required instead of 20; and while carbonic acid only required 16°705, hydrogen required 20:269 atmospheres. Very much higher pressures have been employed in similar experiments by Natterer, who applied.pressures of 2,900 atmospheres, and by Andrews. Natterer’s experiments’ showed that air, oxygen, nitrogen, and carbonic oxide are for moderate pressures more compressible and for high pressures less compressible than in accordance with Boyle’s law. Andrews’s experi- ments will be described later (374). Cailletet used a special apparatus by which the pressure could be raised to 600 atmospheres. Amagat made a remarkable series of experiments by a method based on Boyle’s experiment. The pressure could be applied directly by means of mercury in a steel tube about 1,300 feet: in length, arranged in the shaft of a deep coalpit, and suitably connected at the bottom with a carefully calibrated glass compression tube. In this way pressures of as much as 500 atmospheres could be applied ; the temperatures were kept constant by sur- rounding the compression tube by a jacket through which water circulated. The general result of these experiments is exhibited by the curves in fig. 166, which are plotted with pressures as abscissz and the products PV as ordinates. Were Boyle’s law true for these gases, the curves would be straight lines parallel to the axis of pressures. The curves show that PV diminishes at first for all the gases examined (except hydrogen). The deviation from Boyle’s law reaches a maximum, different for different gases, and then diminishes ; further, that at a certain pressure, which for atmo- 170 On Gases [184- spheric air is 175 atmospheres, or a little over one ton weight per square inch, each gas accurately obeys Boyle’s law. From this point the devia- tion from the law is in the same direction as that exhibited by hydrogen, and appears to increase indefinitely with the pressure. \ome ENR a da ERNNK fe ia = Rezeakt = FENCN: aL eR ENG CAcmaa A bn intnt > "& S Le Fig. 166 Experiments have been made as to the validity of Boyle’s law for pres- sures much lower than one atmosphere, but the variations observed are within the errors of observation. 185. Van der Waals’ formula.—Under high pressures gases do not, as we have seen, follow Boyle’s law with strictness. In order to account for these discrepancies, Van der Waals has introduced a modification into the formula PV =const. (183) which is based on the following considerations. We shall afterwards see (296) that Boyle’s law may be deduced from the dynamical theory of gases, which assumes that they are made up of infinitely small particles moving with great velocities ;, it is also assumed that these particles have no cohesion or specificattraction for each other, and further, that they are mere mathematical points. ) Van der Waals takes account of these limitations. He considers that the cohesion a, which the particles possess, though small, has still a certain value, the effect of which is to add itself to the pressure ; its force will be proportional to the number of acting and attracting particles, and will be directly propor- tional to the square of the density, or inversely proportional to the square of the volume. The other correction is for the volume of the particles them- selves, 6, which, though exceedingly small, has a certain value. The pressure of a given mass of gas being due to the number of impacts which take place 186] Manometers 171 in a given time, it is clear that if the particles have a certain magnitude they must collide against each other more frequently than if they are mere mathe- matical points ; the influence on the formula will be that the volume V will be diminished by an amount which represents a multiple of the molecular volume, or the space actually occupied by the particles. The formula of Boyle’s law, as thus modified by Van der Waals, becomes ( + vi) (V — 6) = const. It will thus be seen that the two influences mentioned affect Boyle’s law in opposite directions. With hydrogen, where the molecules have little or no attraction, there is no cohesion, and accordingly the pro- duct PV increases continuously with the pressure, and there is NO maximum of compressibility. With other gases @ has a definite value ; at low pres- sures the product PV is less than that required by Boyle’s law, and the influence of @ preponderates ; but asthe pressure continuously increases this diminishes in comparison with the influence of 4, and the product now increases, and at |,,; high pressures the gases behave as does hydrogen at low : ones. Between these a maximum compressibility is seen, which varies with different gases according to the values of | a and 6 in each case. Van der Waals deduced from the experimental results obtained by Regnault for the comparison of various gases and for their expansion by heat, values for a@ and 4 for the respective gases, which when introduced into the formula satisfactorily represent the numbers obtained by experiment. Thus for 4 in the case of hydrogen he obtained the number 0:00069 ; this is confirmed by Budde, who obtained 0°0007 by an entirely different method. 186. Manometers.—Manometers are instruments for measuring the pressure of gases or vapours. In all such in- struments the unit chosen is the pressure of one atmosphere, or thirty inches of mercury at the standard temperature, which, as we have seen, is nearly ‘15 Ib. to the square inch. The open-air manometer consists of a bent glass tube BD (fig. 167), fastened to‘ the bottom of a reservoir AC, of. the same material, containing mercury, which is connected with the closed recipient containing the gas or vapour the pres- sure of which is to be measured. The whole is fixed on a long plank kept in a vertical position. In graduating this manometer, C is left open, and the number 1 marked at the level of the mercury, for this repre- sents one atmosphere. From this point the numbers 2, 3, 4, 5, 6, are marked at each 30 inches, indicating so many atmo- spheres, since a column of mercury 30 inches represents a pressure of one atmosphere. The intervals from 1 to 2, and from 2 to 3, &c., are divided into tenths. C -being then placed in connection with a boiler, for example, the mercury rises in the tube BD to a herght mol a 3 trol fn 5 utitsols bo ts|> on 3 wu) oo —) dob « Se) ae = toot S = ith = sy ois o i & totus by botortorites = binitibyit Ed co Fig. 167 172 On Gases [186— which measures the tension of the vapour. In the figure the manometer marks 2 atmospheres, which represents a height of 30 inches or 76 cm., RWW WS SS SSG TTR HL 7, Fig. 169 plus the atmospheric pressure exerted at the top of the column through the aperture D. This manometer is only used where the pressures do not exceed 5 to 6 atmospheres. Beyond this, the length of tube necessary makes it very inconvenient, and the following apparatus is commonly used. 187. Manometer with compressed air.—The manometer with conipressed air is founded on Boyle’s law: one form is represented in fig. 168, which may be screwed into a boiler or steam-pipe where pressure is to be measured. The pres- sure is transmitted through the opening @ into the closed space 6. In this is an iron vessel containing mercury, in which dips the open end of the manometer tube, which is screwed airtight in the tubulure. In the graduation of this manometer, the quantity of air contained in the tube is such that when the aperture @ com- municates freely with the atmosphere, the level of the mercury is the same in the tube and in the tubulure. Consequently, at this level, the number 1 is marked on the scale to which the tube is affixed. As the pressure acting through the tubulure @ increases, the mercury rises' in the tube, until its weight, added to the pressure of the compressed air, is equal to the external pressure. It would consequently be incorrect to mark two atmospheres in the middle of the tube ; for since the volume of the air is reduced to one-half, its pressure is equal to two atmospheres, and, together with the weight of the mercury raised in the tube, is therefore more than two atmospheres. The position of the number is at such a height that the elastic force of the compressed air, together with the weight of the column of mercury in the tube, is equal to two atmospheres. The exact position of the numbers 2, 3, 4, &c. on the manometer scale can only be determined by calculation. 188. Volumenometer.—An interesting application of Boyle’s law is met with in the volumenometer, which is used in determinations of the specific gravity of solids which cannot be brought into contact with water or other liquids.: A simple form consists of a glass tube with a cylinder G at the top (fig. 169), the edges of which are carefully ground, and which can be closed hermetically by means of a ground-glass plate D. The top being open, the tube is immersed until the level of the mercury inside and outside is the same ; this is represented by the mark Z. The apparatus is then closed airtight by the plate, and is raised until the mercury stands at a height 4, above the level Q in the bath. The original volume of the enclosed air V, which was under the pressure of the atmosphere, 1 now increased to V + v, since the pressure has diminished by the height of 3 ~190] Anerod Barometer 173 the column of mercury /. Calling the height of the barometer at the time of observation 4, we shall have V : V+ ee hii : Placing now in the cylinder a body Kk, whose volume x is unknown, the same operations are repeated; the tube is raised until the mercury again stands at the same mark as before, but its height above the bath is now different ; a second reading, /,, is obtained and we have (V —%) : (V—2).+v =b—h,:6. Combining and reducing, we getx = (V+ v) (1 - é j= The volume V+v is constant, and is determined numerically, once for all, by making the experiment with a substance of known volume, such as a glass bulb. This apparatus is also known as the stereometer. It is of great value in determining the geometrical or true density of gunpowder ; this averages from 1°67 to 1°84, and is thus materially different from its apparent density, or the weight of a given volume compared with that of an equal volume of water, which is from 0°89 to 0-94. “ 189. Regnault’s barometric manometer.—For measuring pressures of less than one atmosphere, Regnault devised the following arrangement, which is a modification of his fixed barometer (fig. 158). In the barometer cistern dips a second tube a of the same diameter, open at both ends, and provided at the top with a three-way cock, one aperture of which is connected with an air-pump and the other with the space to be exhausted. | The further the exhaustion is carried the higher the mercury rises in the tube a. _ The differences of level in the tubes 4 and a give the pressures.. Hence, by measuring the height a4, by means of the cathetometer, the pressure in the space that is being exhausted is accurately given. This apparatus is also called a differential barometer or a barometer gauge. 190. Aneroid barometer.—This instrument derives its name from the circumstance that no liquid is used in its construction (d, without ; »mpds, moist). Fig. 170 represents one of the forms of this instrument ; it consists of a cylindrical metal box, exhausted of air, the top of which is made of thin corrugated metal, so elastic that it readily yields to alterations in-the pressure of the atmosphere. When the pressure increases, the top is pressed inwards ; when, on the contrary, it decreases, the elasticity of the lid, aided by a spring, tends to move it inthe opposite direction. These motions are transmitted by delicate multiplying levers to an index which moves on a scale. The instrument is graduated empirically by comparing its indications, under different pressures, with those of an ordinary mercury barometer. The aneroid has the advantage of being portable, and can be constructed of such delicacy as to indicate the difference in pressure between the height of an ordinary table and the ground. It is hence much used in determining heights in mountain ascents. But it is somewhat liable to get out of order, especially when it has been subjected to great sudden variations of pressure ; and its indications must from time to time be controlled by comparison with those of a standard barometer. The errors arising from the use of the aneroid are mainly due to the trans- mission of the motion of the lid by the multiplying arrangement. Goldschmid of Ziirich devised a form in which the motion of the lid is directly observed. 174 On Gases | [190- In this instrument, as in other aneroids, the lid of a box a@ (fig. 171), in which the alterations of pressure are determined, is of fine corrugated sheet metal. To this is fixed a horizontal metal strip 4, on the front end of which is a small square e, acting as index. This rises and falls with the movement of the lid, and indicates on a scale 7’, on the sides of the slit dd’, alterations of pressure in centimetres. To this strip a second and more delicate one, ¢, is attached, on the front end of which is also fixed an indexe’. Before making an observation, the horizontal line of this index is made to coincide with that st . a; re aja 5 6 2 i * NOR wa ia 1 20 or ’ «Bhs Sp mun ck = OLS GOee SCHMID, iN We of ao KA The whole subject of gas absorption has been investigated by Bunsen. The general rules are the following :— . I. For the same gas, the same liquid, and the same temperature, the weight of gas absorbed is proportional to the pressure. This may also be expressed by saying that at all pressures the volume dissolved is the same ; or that the density of the gas absorbed is in constant relation with that of the external gas which is not absorbed. Accordinels when the pressure diminishes, the quantity of dissolved gas decreases. Ifa solution of gas be placed ander the receiver of an air- pump and the pressure be chenimasaed) the gas ale its expansive force, and escapes with effervescence. Il. Lhe guantity of gas absorbed decreases with zncrease of the tempera- ture; that is to say, when the elastic force of the gas is greater. Thus at 15% water absorbs only 1:00 of carbonic acid. Ill. Zhe quantity of gas which a liquid can dissolve zs independent of the nature and of the quantity ike Sunes gases which tt may already hold in solution. This absorption of gases may be determined by the absorptiometer re- presented in fig. 173, yhien consists of a graduated measuring tube, A, connected by a caoutchouc tube with a tube of equal diameter, B. The absorption vessel, C, is connected with A by means of a thin flexible capillary lead tube ; @ and @ are three-way stop- cocks, and ¢ an ordinary one. The vessel C is fitted with air-free liquid, and A with the gas, which by means of the two three-way stopcocks is easily effected. The tube B is raised or lowered until the level of the mercury is the same as in A, and the volume of gas is read off. A is now put in connection with C, and, the stopcock c having been opened, B is raised so that a determinate volume of liquid runs out. An equal volume of the gas then passes into C, and the absorption proceeds, C being constantly shaken. In order to work at constant tempera- ture, A and C may be surrounded by water. In every gaseous mixture each gas exercises the same pressure as it would if its volume occu- pied the whole space ; and the total pressure is equal to the sum of the individual pressures, When a liquid is in contact with a gaseous mixture, it absorbs a certain part of each gas, but less than it would if the whole space were occupied by each gas. The quantity of each gas dissolved is proportional to the pressure which the unabsorbed gas exercises alone. For instance, oxygen forms only about + the quantity of air ; and water under ordinary conditions absorbs exactly the same quantity of oxygen as it would if the atmosphere were entirely formed of this gas under a pressure equal to # that of the atmosphere. 193. Diffusion of gases, —Phenomena analogous to those of endosmose (141) are seen in a high degree in the case of gases. When two different Fig. 173 -193] Diffusion of Gases 177 gases are separated by a porous diaphragm, an interchange takes place between them, and ultimately the composition of the gas on both sides of the diaphragm is the same ; but the rapidity with which different gases diffuse into each other under these circumstances varies considerably. There is, however, an essential difference between the phenomena of endosmose and those of diffusion ; for while the inequality in the currents in the former case is due to the different attraction of the material of the diaphragm for the con- stituents, in the diffusion of gases the nature of this material has no influence ; from the smallness of the pores the actions are molecular, and not molar, and the rate of interchange depends only on the size of the molecules, that is on the specific gravities of the gases. The laws of the diffusion of gases were investigated by Graham. Numerous experiments illustrate them, some of the most interesting of which are the following :— A glass cylinder closed at one end is filled with carbonic acid gas, its open end tied over with a bladder, and the whole placed under a jar of hydrogen. Diffusion takes place between them through the porous dia- phragm, and after the lapse of a certain time hydrogen has passed through Fig. 174 the bladder into the cylindrical vessel in much greater quantity than the carbonic acid which has passed out, so that the bladder becomes very much distended outwards (fig. 174). If the cylinder be filled with hydrogen and the bell-jar with carbonic acid, the reverse phenomenon will be produced— the bladder will be pressed inwards (fig. 175). A tube about 12 inches long, closed at one end by a plug of dry plaster of Paris, is filled with dry hydrogen, and its open end then immersed in a mercury bath. Diffusion of the hydrogen towards the air takes place so rapidly that a partial vacuum is produced, and mercury rises in the tube to a height of several inches (fig. 176). If several such tubes are filled with different gases, and allowed to diffuse into the air in a similar manner, in the same time, different quantities of the various gases will diffuse, and Graham found that the law regulating these diffusions is that ‘re guantity of a gas which passes through a porous diaphragm in a given time ts inversely as the square root of the density of the gas. Thus, if two vessels of equal capacity, containing oxygen and hydrogen, be separated by a porous plug, diffusion takes place ; and after the lapse of some time, for every one part of N 178 On Gases [193- oxygen which has passed into the hydrogen, four parts of hydrogen have passed into the oxygen. Now, the density of hydrogen being 1, that of oxygen is 16 ; hence the force of diffusion is inversely as the square roots of these numbers. It is four times as great in the one which has ;% the density of the other. Let the stem of an ordinary tobacco pipe be cemented, so that its ends project, in an outer glass tube, which can be connected with an air-pump and thus exhausted. On allowing then a slow current of air to enter one end of the pipe, its nitrogen diffuses more rapidly on its way through the porous pipe than the heavier oxygen, so that the gas which emerges at the ‘other end of the porous pipe, and which can be collected, is richer in oxygen, and by repeating the operation on the gas which has passed through, the proportion of oxygen is so much increased that the gas can relight a semi-extinguished taper. To this process, in which one gas can be separated from another by diffusion, the term azmolyszs is given. Fig. 177 is an excellent illustration of the action of diffusion. A porous pot, A, such as is used for voltaic cells, is fixed by means of a cork to the glass tube, which contains water up to the bulb, C, the upper part containing air. Whena beaker containing hydrogen, B, is placed over the | pot, the diffusion of the hydrogen into it is so SRI rapid that the water is at once driven down and ! jets out. When the beaker is removed, the gas inside the pot, being richer in hydrogen, now diffuses out with great rapidity, and the water rises in the tube much higher than its original level. 194. Effusion of gases.—A gas can only flow from one space to another space occupied by the same gas when the pressure in the one is greater than in the other. fusion is the term applied to the phenomenon of the passage of gases into vacuum, through a minute aperture not much more or less than o’o13 millimetre in diameter, in a thin plate of metal or of glass ; for in a tube we are dealing with masses of gases, and friction comes into play, and in a larger aperture the particles would strike against one another, and form eddies and whirlpools. The velocity of the efflux is measured by the formula v=.4/2gh, in which / represents the pressure under which the gas flows, expressed in terms of the height of a column of the gas which would exert the same pressure as that of the effluent gas. Thus for air under the ordinary pressure flowing into a vacuum the pressure is equivalent to a column of mercury 76 centimetres high ; and as mercury is approximately 10,500 times as dense as air, the equivalent column of air will be 76 x 10,500= 7,980 metres. Hence the velocity of efflux of air ~195] ' Transpiration of Gases 179 into vacuum is = 1/2 x 9°8 x 7980= 395°5 metres. ‘This velocity into vacuum only holds, however, for the first moment, for the space contains a continu- ally increasing quantity of air, so that the velocity becomes continually smaller, and is null when the pressure on each side is the same. If the height of the column of air, corresponding to the' external pressure, is known, the velocity may be calculated by the formula v= ./2¢ (h-/,). For gases lighter than aira greater height must be inserted in the formula, and for heavier gases a lower height ; and this change must be inversely as the change of density. Hence the veloctties of efflux of various gases must be tnversely as the square roots of their densitzes. A simple inversion of this statement is that the demszties of two gases are inversely as the squares of their velocities of effusion. On this law Bunsen has based an interesting method of determining the densities of gases and vapours, which is of great service where only small quantities of the substances are available. The gas in question is contained (fig. 178) in a glass tube A, closed at the top with a stopper, S,in the neck, B. Inalittle enlargement here a thin platinum plate V is fixed, in which is a fine capillary aperture. The tube is depressed in a deep mercury trough, CC, until the top 7 of a glass float D is level with the mercury. The stopper S having been removed, the gas issues through the capillary aperture, and the time is noted which elapses until a mark ¢ in the float is level with the mercury. Working in this way with different gases, Bunsen found that the ratios of the times of effusion are directly as the sguare roots of the densities, which is another form of the above statement. By this method it may often be ascertained whether a gas is a mixture or not. Thus marsh gas (CH,) has the same specific gravity (07554) as a mixture in equal volumes of dimethyl (C,H,, sp. gr. 1°039) and hydrogen (sp. gr. 0'069), and would furnish the same results on chemical analysis. But if the composition of the gas which had been subjected to effusion were examined in the two cases, it would be found that the residual marsh gas would retain the same composition, while that of the mixture would be different, for a relatively larger volume of the specifically lighter hydrogen would have passed out. 195. Transpiration of gases.—If gases issue through long, fine capillary tubes into a vacuum, the phenomenon is called transpiration ; and the rate of efflux, or the velocity of transpiration, is not the same as the rate of diffusion, either through a single aperture or through a series of fine capillary tubes, as in a porous diaphragm. This property of gases may be investigated by means of an apparatus N 2 180 On Gases f[195-— analogous to that represented in fig. 133, and consisting essentially of an arrangement by which gas under known pressure is allowed to flow through a capillary tube of known length and diameter. The volume which flows out in a given time, or the rate of transpiration, is represented by a formula which is identical with that for liquids (149) namely, s _(p—-p,)7* SSAA Sp lal where # is the pressure of the gas on entering, and 7, that on leaving the capillary tube ; ~ is the diameter, and / the length of the tube, and 7 is the coefficient of internal friction of the gas. This furnishes an easy method of determining the value of y in this formula, as all the other magnitudes are capable of direct accurate measurement. This is a most important physical constant, as it occurs in many formulze by which molecular magnitudes are determined, such as the length of the mean free path of gases (298), the number of impacts in a second, and even the dimensions of the molecules themselves. Expressed in CGS units, the value of n for air 1s 0°0,18. 196. Absorption of gases by solids.—The surfaces of all solid bodies exert an attraction on the molecules of gases with which they are in contact of such a nature that they become covered with a more or less thick layer of condensed gas. When a porous body, such as a piece of charcoal, which conse- quently presents an immensely increased surface in proportion to its size, is placed in a vessel of ammonia gas over mercury (fig. 179), the great diminution of volume which ensues indicates that considerable quan- tities of gas are absorbed. Now, although there is no absorption such as arises ~ from chemical combination between the solid and the gas (as with phosphorus and oxygen), still the quan- tity of gas absorbed is not entirely dependent on the physical conditions of the solid body ; it is influenced in some measure by the chemical nature both of the solid and the gas. Boxwood charcoal has very great absorptive power. The following table gives the volumes of gas, under standard conditions of tempera- ture and pressure, absorbed by one volume of boxwood charcoal and of meerschaum respectively :— Charcoal Meerschaum Ammonia . : : . : { : go 15 Hydrochloric acid . . é ‘ ; £ 85 — Sulphurous acid. : ‘ : : ; 65 <4 Sulphuretted hydrogen . : , ‘ ; 55 II Carbonic acid : } ‘ : : 35 553 Carbonic oxide. : s : 4 9°4 Le Oxygen ; F ; ’ : 2 I°5 Nitrogen : : : : : 7°4 1°6 Hydrogen. ; F : ‘ : see ehdo765 0'5 197] Occlusion of Gases ISI The absorption of gases is in general greatest in the case of those which are most easily liquefied. Cocoa-nut charcoal is even more highly absorbent; it absorbs 171 of ammonia, 73 of carbonic acid, and 108 of cyanogen at the ordinary pressure ; the amount of absorption increases with the pressure. The absorptive power of pine charcoal is about half as much as that of boxwood. The charcoal made from cork wood, which is very porous, is not absorbent ; neither is graphite. Platinum, in the finely divided form known as platinum sponge, is said to absorb 250 times its volume of oxygen gas. Many other porous substances, such as gypsum, silk, &c., are also highly absorbent. If a coin is laid on a plate of glass or metal, after some time, when the plate is breathed on, an image of the coin appears. If a figure is traced on a glass plate with the finger, nothing appears until the plate is breathed on, when the figure is at once seen. Indeed, the traces of an engraving which has long lain on a glass plate may be produced in this way. These phenomena are known as Moser’s zmages, for they were first in- vestigated by Moser, although he explained them erroneously. The correct explanation was given by Waidele, who ascribed them to alterations in the layer of gas, vapour, and fine dust which is condensed on the surface of all solids. If this layer is removed by wiping, on afterwards breathing against the surface more vapour is condensed on the marks in question, which then present a different appearance from the rest. ; If a die or a stamp is Jaid on a freshly polished metal plate, one ‘therefore which has been deprived of its atmosphere, the layer of vapour from the coin will diffuse on to the metal plate, which thereby becomes altered ; so that when this is breathed on an impression is seen. Conversely, if a coin is polished and placed on an ordinary glass plate, it will partially remove the layer of gas from the parts in contact, so that on breathing on the plate the image is visible. Ordinary glass kept in moist air becomes covered with a layer of water, which can be weighed. This is due to an action of the alkali in glass which attracts moisture, and is absent in glass free from alkali ; it can be consider- ably diminished by boiling with water, by which the alkali on the surface is removed. In addition to this layer, which appears rather to be chemically than physically attracted, there is a temporary one which escapes in a vacuum at the ordinary temperature. 197. Occlusion of gases.—Graham found that at a high temperature platinum and iron allow hydrogen to traverse them even more readily than does caoutchouc in the cold. Thus, while a square metre of caoutchouc o-or4 millimetre in thickness allowed 129 cubic centimetres of hydrogen at 20° to _ traverse it in a minute, a platinum tube 11 millimetre in thickness and of the same surface allowed 489 cubic centimetres to traverse it at a bright red heat. This is probably connected with the property which some metals, though destitute of physical pores, possess of absorbing gases either on their surface or in their mass, and to which Graham has applied the term occlusion. It is best observed by allowing the heated metal to cool in contact with the gas. The gas cannot then be extracted by the air-pump, but is disengaged on heating. In this way Graham found that platinum occluded four times its volume of hydrogen ; iron wire 0°44 its volume of hydrogen, and 4°15 182 On Gases [197- volumes of carbonic oxide ; silver, reduced from the oxide, absorbed about seven volumes of oxygen, and nearly one volume of hydrogen when heated to dull redness in these gases. This property is most remarkable in palla- dium, which absorbs hydrogen not only in cooling after being heated, but also in the cold. When, for instance, a palladium electrode is used in the decomposition of water, one volume of the metal can absorb 98o times its volume of the gas. This gas is again driven out on being heated, in which respect there is a resemblance to the solution of gases in liquids. By the occlusion of hydrogen the volume of palladium is increased by 0°09827 of its original amount, from which it follows that the hydrogen, which under ordinary circumstances has a density of 0:000089546 that of water, has herea density nearly 9,868 times as great, or about 0°88 that of water. Hence the hydrogen must be in the liquid or even solid state ; it probably forms thus an alloy with palladium, like a true metal—a view of this gas which is strongly supported by independent chemical considerations. The physical properties, too, in so far as they have been examined, support this view of its being an alloy. The phenomenon of occlusion may be illustrated by the following experi- ment (fig. 180). A platinum wire, dc, is stretched between supports on a glass plate; one end of a _ palladium @ @ ~ wire, jg, is also fixed, the other end being attached to the short arm of a light lever movable about 0, the long arm of which is loaded with a weight (not repre- sented in the figure) to keep the wire tight. The platinum wire is connected with the positive pole a, and the palladium with the negative pole @, of a voltaic battery, and the apparatus is partially immersed in acidulated water; the water is thereby decomposed into its constituent gases ; oxygen is liberated in bubbles from the platinum wire, but there is no visible dis- Pigs sso engagement atthe palladium. The latter becomes longer, however, as is seen by the motion of the lever. If the current is reversed, the wire again contracts, and the lever resumes its original position. ~198] Archimedes Principle applied to Gases 183 CHAPTER: IT! PRESSURE ON BODIES IN AIR. BALLOONS 198. Archimedes’ principle applied to gases.—The pressure exerted by gases on bodies immersed in them is transmitted equally in all directions, as has been shown by the experiment with the Magdeburg hemispheres (163). It therefore follows that all which has been said about the equilibrium of bodies in liquids applies to bodies in air; they lose apparently a part of their weight equal-to that of the air which they displace. The loss of weight in air is demon- strated by means of the Jdavoscofe, which consists of a scalebeam, at one end of which a small leaden weight is supported, and at the other there is a hollow copper sphere (fig. 181). In the air they exactly balance each other; but when they are placed under the receiver of an air-pump, = ies : and a vacuum is produced, the sphere ————————————— sinks, thereby showing that in reality Pittey it is heavier than the smaller leaden r weight. Before the air is exhausted each body is buoyed up by the weight of the air which it displaces. But as the sphere is much the larger of the two, its weight undergoes most apparent diminution, and thus, though in reality the heavier body, it is balanced by the small leaden weight. It may be proved by means of the same apparatus that this loss is equal to the weight of the displaced air. Suppose the volume of the sphere is 10 cubic inches. The weight of this volume of air is 3°1 grains. If now this weight be added to the leaden weight, it will overbalance the sphere in air, but will exactly balance it in vacuo. . The principle of Archimedes is true for bodies in air; all that has been said about bodies immersed in liquids apples to them ; that is, that when a body is heavier than air it will sink, owing to the excess of its weight over the buoyancy. If it is as heavy as air, its weight will exactly counterbalance the buoyancy, and the body will float in the atmosphere. If the body is lighter than air, the buoyancy of the air will prevail and the body will rise 184 On Gases [198- in the atmosphere until it reaches ‘a layer of the same density as its own. ' The force causing ascent is equal to the excess of the buoyancy over the weight of the body. This is the reason why smoke, vapours, clouds, and air- balloons rise in the air. It will be understood that by dueyancy is meant the weight of the medium displaced whatever that medium may be. AIR-BALLOONS 199. Air-balloons.—H-—A’, if k’>h. Thus water will flow from the vessel if AB is greater than DC. If AB=DC, there will be no flow ; and if AB is less than DC, the liquid will flow in the opposite direction. It follows from the explanation of the siphon that it would not work in vacuo, nor if the height CD were greater than that of a column of liquid which counterbalances the atmospheric pressure. 217. The intermittent siphon.—In the zz¢termizttent siphon the flow is not continuous. It is arranged in a vessel, so that the shorter leg is near the bottom of the vessel, while the longer leg passes through it (fig. 209). Being fed by a constant supply of water, the level gradually rises both in. the vessel and in the tube to the top of the siphon, which it fills, and water begins to flow out. But the apparatus is arranged so that the flow of the siphon is more rapid than that of the tube which supplies the vessel, and consequently the level sinks in the vessel until the shorter branch no longer dips in the liquid ; the siphon is then empty, and the flow ceases. But as the vessel is continually fed from the same source the level again rises, and the same series of phenomena is reproduced. The theory of the intermittent siphon explains the natural intermittent springs which are found in many countries, and of which there is an excel- lent example near Giggleswick in Yorkshire. Many of these springs fur- nish water for several days or months, and then, after stopping for a certain interval, again recommence. In others the flow stops and recommences several times in an hour. These phenomena are explained by assuming that there are subterranean fountains, which are more or less slowly filled by springs, and which are then emptied by fissures so occurring in the ground as to form an intermittent siphon. 218. Different kinds of pumps.—/zzszfs are machines which serve to raise water either by suction, by pressure, or by both effects combined ; they Fig. 209 —219] Suction-pump 205 are consequently divided into szction or lift pumps, force-pumps, and suction and forcing pumps. The various parts entering into the construction of a pump are the barrel, the piston, the valves, and the pipes. The éarre/ is a cylinder of metal or of wood, in which is the fzstom. The latter is a metal or wooden cylinder wrapped with tow, and work- , ing with gentle friction the ul TN Ih} whole length of the barrel. LAS | The valves are discs of metal or leather, which alter- nately close the apertures which connect the barrel with the pipes. The most usual valves are the clack valve (fig. 210) and the conzcal valve (fig. 211). The former is a metal disc fixed to a hinge on the edge of the orifice to be closed. In order more effectually to close it, the lower part of the disc is covered with thick leather. Sometimes the valve consists merely of a leather disc, of larger diameter than the orifice, nailed on the edge of the orifice. Its flexibility enables it to act as a hinge. The conical valve consists of a metal cone fitting in an aperture of the same shape. Below this is aniron hoop, through which passes a bolt-head . Afi fixed to the valve. The object of this es is to limit the play of the valve when i it is raised by the water, and to pre- i vent its removal. | | WU pe TOM Na Fig. 210 Fig. 211 muta) TC gnaw me i} 219. Suction-pump.—Fig. 212 re- presents a model of a suction-pump i such as is used in lectures, but which | has essentially the same arrangement | s Ne Win Hi) ) mui ATETEGE HH! a is ||| \ | as the pumps in common use. It | consists, Ist, of a glass cylinder, B, at the bottom of which is a valve, S, / opening upwards ; 2nd, of a szction- / | tube, A, which dips into the reservoir WJ from which water is to be raised ; 3rd, of a gzston, which is moved up and down by a rod worked by a handle, P. The piston is perforated by a hole ; the upper aperture is closed by a valve, O, opening upwards. When the piston rises from the bottom of the cylinder B, a vacuum is = produced below, and the valve O is SSS kept closed by the atmospheric pres- == —— sure, while the air in the pipe A, in SSS SSS SS consequence of its elasticity, raises the valve S, and partially passes into the cylinder. The air being thus rarefied, water rises in the pipe until the pres- (G — i = / = if i iN , bse on =a: uw E =| . ba) — SSS ATI Tn Fig. 212 206 On Gases [219- sure of the liquid column, together with the pressure of the rarefied air which remains in the tube, counterbalances the pressure of the atmosphere on the water of the reservoir. When the piston descends, the valve S closes by its own weight, and prevents the return of the air from the cylinder into the tube A. The air compressed by the piston opens the valve O, and escapes into the atmosphere by the pipe C. With a second stroke of the piston the same series of phenomena is produced, and after a few strokes the water reaches the cylinder. The effect is now somewhat modified ; during the descent of the piston the valve S closes, and the water raises the valve O, and passes above the piston by which it is lifted into the upper reservoir D. There is now no more air in the pump, and the water forced by the atmospheric pressure rises with the piston. It is essential for the action of the pump that the valve S should be less than 34 feet above the level of the water in which the tube A dips, for we have seen (165) that a column of water of this height is equal to the pressure of the atmosphere. In practice the height of the tube A does not exceed 26 to 28 feet ; for although the atmospheric pressure can support a higher column, the vacuum produced in the barrel is qos not perfect, owing to the ge —— | fact that the piston does eu | ! not fit exactly on the | sd bottom ofthe barrel. But when the water has passed the piston, itis the ascend- ing force ofthe latter which raises it, and the height to which it can be brought depends on the power which works the piston. 220. Suction- and force-pump.—The action of this pump, a model of which is represented in fig. 213, depends both on exhaustion and on _pres- sure. At the base of the barrel, where it is cone nected with the tube A, there is a valve, S, which opens upwards. Another valve, O, opening in the same direction, closes the aperture of a conduit, which passes from a hole, o, near the valve S, into a vessel, M, which is called the az7-chamber. From this chamber there is another tube, D, up which the water is forced. At each ascent of the piston B, which is solid, the water rises through the 221] Load which the Piston supports 207 tube A into the barrel. When the piston sinks the valve S closes, and the water is forced through the valve O into the reservoir M, and thence into the tube D. The height to which it can be raised in this tube depends solely on the motive force which works the pump. If the tube D were a prolongation of the tube Jao, the flow would be intermittent ; it would take place when the piston descended, and would cease as soon as it ascended. But between these tubes there is an interval, which, by means of the air in the reservoir M, ensures a continuous flow. The water forced into the reservoir M divides into two parts, one of which, rising in D, presses on the water in the reservoir by its weight ; while the other, in virtue of this pressure, rises in the reservoir above the lower orifice of the tube D, compressing the air above. Consequently, when the piston ascends, and no longer forces the water into M, the air of the reser- voir expands, and raises the liquid in the tube D, until the piston again descends, so that the jet is continuous. aed thy il 221. Load which the piston supports.—In the suction-pump, when once the water fills the pipe, and the barrel, as far as the spout, the effort necessary to raise the piston is equal to the weight of a column of water the base of which ts this piston, and the height the vertical distance tn the Spout from the level of the water tn the reservotr; that ts, the height to which the water ts ratsed. For if H is the atmospheric pressure, / the height of the water above the piston, and 4%’ the height of the column which fills the suction-tube A (fig. 213), and the lower part of the barrel, the pressure above the piston is obviously H+, and that below is H—/’, since the weight of the column /’ tends to counterbalance the atmospheric pressure. 208 On Gases [221 But as the pressure H —/’ tends to raise the piston, the effective resistance is equal to the excess of H+ over H—/’; that is to say, to +h’. In the suction- and force-pump it is readily seen that the pressure which the piston supports is also equal to the weight of a column of water the base of which is the section of the piston, and the height that to which the water is raised. 222. Fire-engine._--The /ive-engine is a force-pump in which a steady jet is obtained by the aid of an air-chamber, and also by two pumps working alternately (fig. 214). The two pumps 7z and , worked by the same lever, PQ, are immersed in a tank, which is kept filled with water as long as the pump works. From the arrangement of the valves it will be seen that when one pump, 7, draws water from the tank, the other, 7, forces it into the az7- chamber, R.; whence, by an orifice, Z, it passes into the delivery tube, by which it can be sent in any direction. Without the air-chamber the jet would be intermittent. But as the velo- city of the water on entering the reservoir is less than on emerging, the level of the water rises above the orifice Z, compressing the air which fills the reservoir. Hence, whenever the piston stops, the air thus compressed, reacting on the liquid, forces itout during its momentary stoppage, and thus keeps up a constant flow. —225] Cause of Sound 209 BOOK V ON SOUND j CHAPTER I PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND 223. Province of acoustics.—The study of sounds and that of the vibra- tions of elastic bodies form the province of the science of sownds, or ACOUSTICS. « Music considers sounds with reference to the pleasurable feeling they are calculated to excite. Acoustics is concerned with the questions of the pro- duction, transmission, and comparison of sounds ; to which may be added the physiological question of the perception of sounds, 224. Sound and noise.—Sowzd is the peculiar sensation excited in the organ of hearing by the vibratory motion of bodies, when this motion is transmitted to the ear through an elastic medium. Sounds are distinguished from zozses. Sound properly so called, or musical sound, is that which produces a continuous sensation, the musical value of which can be estimated; while noise is either a sound of too short a duration to be determined, like the report of a cannon ; or else it is a confused mixture of many discordant sounds, like the rolling _ of thunder or the noise of the waves. Nevertheless, the difference between sound and noise is by no means precise; Savart showed that there are relations of height in the case of noise, as well as in that of sound; and there are said to be certain ears sufficiently well organised to determine the musical value of the sound produced by a carriage rolling on the pavement. 225. Cause of sound.—Sound is always the result of rapid oscillations - imparted to the molecules of elastic bodies, when the state of equilibrium of these bodies has been disturbed either bya shock or by friction. Such bodies tend to retain their first position of equilibrium, but only reach it after per- forming, on each side of that position, very rapid vibratory movements, the amplitude of which quickly decreases. A body which is capable of pro- ducing a sound is called a sonorous or sounding body. As understood in England and Germany, a vibration comprises a motion to and fro ; in France, on the contrary, a vibration means a movement to 07 P 210 On Sound [225- fro. ‘The French vibrations are with us semi-vibrations ; an osczllation or vibration is the movement of the vibrating molecule in only one direction ; a double or complete vibration comprises the oscillation both backwards and forwards. Vibrations of sounding bodies are very readily observed. If a light powder is sprinkled on a body which is in the act of yielding a musical sound, a rapid motion is imparted to the powder, which renders visible the vibrations of the body ; and, in the same manner, if a stretched cord is smartly pulled and let go, its vibrations are apparent to the eye. A bell-jar is held horizontally Fig. 215 in one hand (fig. 215), and made ' to vibrate by being struck with the other; if then a piece of meta! is placed in it, it is rapidly raised by the vibrations of the side ; touching the bell-jar with the hand, the sound ceases, and with it the motion of the metal. 226. Sounds not propagated in vacuo.—The vibrations of elastic bodies can only produce the sensation of sound in us by the intervention of a medium interposed between the air and the sonorous body and vibrating with.it. This medium is usually the air; but all gases, vapours, liquids, and solids also transmit sounds. . The following experiment shows that the presence of a ponderable medium is neces- sary for the propagation of sound. A small metal bell, which is continually struck by a small hammer by means of clockwork, or else an ordinary musical box, is placed under the receiver of an air-pump (fig. 216). So long as the receiver is full of air at the ordi- nary pressure the sound is transmitted ; but in proportion as the air is exhausted the sound becomes feebler, and cannot be heard in a vacuum. To ensure the success of the experiment, the bellwork or the musical box must be placed on wadding or on a block of vulcan- ised rubber; for otherwise the vibrations would be transmitted to the air through the | plate of the pump. 227. Sound is propagated in all elastic bodies.—If, in the above experiment, any vapour or gas be admitted after the vacuum has been made, the sound of the bell will be heard, showing that sound is propagated in this medium as in air. Sound is also propagated in liquids. When two stones are struck against each other under water, the shock is distinctly heard ; and a diver at the Fig. 216 —228] Propagation of Sound in Atr 211 bottom of the water can hear the sound of voices on the bank. The sound is, however, enfeebled, as a considerable portion is reflected at the boundary of the two media. The conductibility of solids is such that the faint scratching of a pen or the ticking of a watch at one end of a long horizontal wooden rod is heard much more distinctly when the ear is directly applied against the other end of the rod than when it is at the same distance in the air. Sound may even reach the ear through solids alone without passing through the air ; for if the ears be closed, and the rod be put between the teeth, the ticking is distinctly heard. The earth conducts sound so well that at night, when the ear is applied to the ground, the stepping of horses, or any other noise at a great distance, is heard. 228. Propagation of sound in air.—In order to simplify the theory of the propagation of sound in air, we shall first consider the case in which it is propagated in a cylindrical tube of indefinite length. Let MN (fig. 217) be a tube filled with air at a constant pressure and temperature, and let P be a piston oscillating rapidly from A toa. When the piston starts from A, it compresses the air in front of it and the compression increases until P Fig. 217 reaches the position halfway between A and a, when it is a maximum, after which it diminishes as P reaches a. Suppose that as the piston moves from A to a, the disturbance of the air in the tube travels to H. Thus in @H the pressure of the airis greater than normal, the compression being greatest at the centre. When the piston returns in the direction aA, the pressure behind it is diminished and the diminution of pressure is a maximum when P is halfway back. This reduction of pressure or rarefaction travels along the tube in the same way and at the same rate as the compression, so that when the piston has reached A, the point from which it started, the compres- sion has advanced to the position HH’, and its place has been taken by the rarefied portion. Thus after one complete oscillation of the piston the beginning of the air disturbance is at H’and theend at a. The whole length aH’ is a wave or undulation. It consists of two equal parts in one of which the air is more compressed and in the other is more rarefied than in the undisturbed tube. __ When the piston has made another complete oscillation, the wave aH’ will have advanced by a distance equal to itself, and its place will have been taken by another wave, and so on. The velocity with which the disturbance travels is the velocity of sound in the air of the tube. If A denote the length of a wave, and z be the number of oscillations of the piston per second, 7A is equal to the total distance travelled by the beginning of the distance in one second. If this distance is vw, the velocity of sound, then v= za. It is important to remark that if we consider a single row of particles, which when at rest occupy a line parallel to the axis of the cylinder—for P2 212 On Sound [228— instance, those along AH” (fig. 217)—we shall find they will have respectively at the same instant all the various velocities which the piston has had suc- cessively while oscillating from A to @ and back to A. Sothat ifin fig. 39 - AH’ represents the length of one undulation, the curved line H’PQA will represent the several velocities which all the points in the line AH’ have simultaneously ; for instance, at the instant the piston has returned to A, the particle at M will be moving to the right with a velocity represented by QM ; the particle at N will be moving to the left with a velocity represented by PN, and so on of the other particles. When an undulatory motion is transmitted through a medium, the motions of any two particles are said to be in the same phase when those particles move with equal velocities in the same direction ; the motions are said to be in opposite phases when the particles move with the same velocities in opposite directions. It is plain from an inspection of fig. 39 that when any two particles are separated by a distance equal to half an undulation, their motions are always in opposite phases, but if their distance equals the length of a complete undulation their motions are in the same phase. ‘It is an easy transition from the explanation of the motion of sound- waves in acylinder to that of their motion in an unenclosed medium. It is simply necessary to apply in all directions to each molecule of the vibrating body what has been said about a piston movable ina tube. A series of spherical waves alternately condensed and rarefied is produced around each centre of disturbance. As these waves are contained within two concentrical spherical surfaces, whose radii gradually increase while the length of the undulation remains the same, their mass increases with the distance from the centre of disturbance, so that the amplitude of the vibration of the mole- cules gradually lessens, and the intensity of the sound diminishes. It is these spherical waves, consisting of portions alternately condensed and expanded, which in being propagated transmit sound. If many points are disturbed at the same time, a system of waves is produced around each point. But all these waves are transmitted one through the other without modifying either their lengths or their velocities. When two waves meet each other the effect will be an augmentation or diminution of sound accord- ing to the relative phases in which the waves meet. If the surface of still water is disturbed at two or more points, the co-existence of waves becomes sensible to the eye. | 229. Causes which influence the intensity of sound.—Many causes modify the force or the zzfensity of sound. These are the distance of the sounding body, the amplitude of the vibrations, the density of the air at the place where the sound is produced, the direction of the currents of air, and, lastly, the neighbourhood of other sounding bodies. i. The intensity of sound ts inversely as the square of the distance of the sounding body from the ear. This law has been deduced by calculation, but it may be also demonstrated experimentally. Let us suppose several sounds of equal intensity—for instance, bells of the same kind, struck by hammers of the same weight, falling from equal heights. If four of these bells are placed at a distance of 20 yards from the ear, and one at a distance of Io yards, it is found that the single bell produces a sound of the same intensity as the four bells struck simultaneously. Consequently, for double the dis- —230] Apparatus to strengthen Sound BER tance the intensity of the sound is only one-fourth. A method of com- paring the intensities of different sounds will be described afterwards (293). The distance at which sounds can be heard depends on their intensity. The report of a volcano at St. Vincent was heard at Demerara, 300 miles off, and the firing at Waterloo was heard at Dover. u. Lhe intensity of sound increases with the amplitude of the vibrations of the sonorous body. The connection between the intensity of the sound and the amplitude of the vibrations is readily observed by means of vibrating strings (269). For, if the strings are somewhat long, the oscillations are per- ceptible to the eye, and it is seen that the sound is feebler in proportion as the amplitude of the oscillations decreases. The intensity varies as the square of the amplitude of oscillation. ui. Zhe tntensity of sound depends on the density of the air in the place tn which tt ts produced. As we have already seen (226), when an alarum actuated by clockwork is placed under the bell-jar of an air-pump, the sound becomes weaker in proportion as the air is rarefied. In hydrogen, which is about 4 the density of air, sounds are much feebler, although the pressure is the same. In carbonic acid on the con- trary, whose density is 1°529, sounds are more intense. On high mountains, where the air is much rarefied, it is necessary to speak with some effort in order to be heard, and the discharge of a gun produces only a feeble sound. The ticking of a watch is heard in water ata distance of 23 feet, in oil of 163, in alcohol of 13, and in air of only Io feet. iv. Zhe intensity of sound ts modified by the motion of the atmosphere and the direction of the wind. \n calm weather sound is always better propagated than when there is wind ; in the latter case, for an equal distance, sound is more intense in the direction of the wind than in the contrary direction. v. Lastly, sound ts strengthened by the netghbourhood of a sonorous body. A string made to vibrate in free air has but a very feeble sound ; but when it vibrates above a sounding-box, as in the case of the violin, guitar, or violon- cello, its sound is much stronger. This arises from the fact that the box and the air which it contains vibrate in unison with the string. Hence the use of Ssounding-boxes in stringed instruments. Attempts have been made to get a measure of the loudness of sound which should serve as a standard, by allowing leaden bullets to fall from various heights on an iron plate of some size. It appears that within certain limits the loudness is nearly proportional to the square root of the height from which the bullet falls, and not to the height itself. It thus appears that only a portion of the energy of the falling body is expended in producing vibrations of the plate. 230. Apparatus to strengthen sound.—The apparatus represented .in fig. 218 was used by Savart to show the influence of boxes in strengthening sound. It consists of a hemispherical brass vessel, A, which is set in vibra tion by means of a violin bow. Near it isa hollow cardboard cylinder, B, closed at the further end. By means of a handle this cylinder can be turned on its support, so as to be inclined at any given degree towards the vessel. The cylinder is fixed on a slide, C, by which means it can be placed at any distance from A. When the vessel is made to vibrate, the strengthen- 214 On Sound [230- ing of the sound is very remarkable. But the sound loses almost all its intensity if the cylinder is turned away, and it becomes gradually weaker when the cylinder is re- moved to a greater dis- tance, showing that the strengthening is due to the vibration of the air in the cylinder. The air in the cylinder B is made to vibrate in Zp si unison with the brass vessel by adjusting it toa bi, AS ss certain depth, which is py ity 6 ~—s effected by making one ; part of the cylinder slide into the other. Vitruvius states that in the theatres of the ancients resonant brass vessels were placed to strengthen the voices of the actors. 231. Influence of tubes on the transmission of sound.—The law that the intensity of sound decreases in proportion to the square of the distance does not apply to the case of tubes, especially if they are straight and cylindrical. The sound-waves in that case are not propagated in the form of increasing concentric spheres, and sound can be transmitted to a great distance with- out any perceptible alteration. Biot found that in one of the Paris water- pipes, 1,040 yards long, the voice lost so little of its intensity that a con- versation could be kept up at the ends of a tube ina very low tone. The weakening of sound becomes, however, perceptible in tubes of large diameter, or where the sides are rough. This property of transmitting sounds was first used in England for sfeaking tubes. They consist of caout- chouc or metal tubes of small diameter passing from one room to another. If a person speaks at one end of the tube, he is distinctly heard by a person with his ear at the other end. From Biot’s experiments it is evident that a communication might be made between two towns by means of speaking tubes. The velocity of sound is 1,125 feet in a second at 16°°6 C., so that a distance of 50 miles would be traversed in four minutes. 232. Regnault’s experiments.—Theoretically, a sound-wave should be. propagated in a straight cylindrical tube witha constant intensity. Regnault found, however, that in these circumstances the intensity of sound gradually diminishes with the distance, and that the distance at which it ceases to be audible is nearly proportional to the diameter of the tube. He reproduced sound-waves of equal strength by means of a small pistal charged with a gramme of powder, and fired at the open ends of tubes of various diameters ; and he then ascertained the distance at which the sound could no longer be heard, or at which it ceased to act on what he calls a —233] Velocity of Sound in Aur 215 sensitive membrane. This was a very flexible membrane which could be fixed across the tube at various distances, and was provided with a small metal disc in its centre. When the membrane begins to vibrate, this disc struck against a metallic contact, and thereby closed a voltaic circuit, which traced on a chronograph the exact moment at which the membrane received the sound-wave. Experimenting in this manner, Regnault found that the report of a pistol charged as stated is no longer audible at a distance of moso metres in.a.tube of, .. , : : . o@108 diameter 3,810 = dane . ‘ : : mt 2 ZOO pe 9,540 be _ . . ; : Pe eda OO 3 These numbers represent the limit of distance at which the sound-wave is no longer heard, but it still acts on the membrane at the distances of 4,156, 11,430, and 19,851 metres respectively. According to Regnault the principal cause of this diminution of intensity is the loss of vzs vzva against the sides of the tube ; he found also that sounds of high pitch are propagated in tubes less easily than those of low pitch: a bass voice would be heard at a greater distance than a treble voice. 233. Velocity of sound in air.—Since the propagation of sound-waves is gradual, sound requires a certain time for its transmission from one place to another, as is seen in numerous phenomena. For example, the sound of thunder is only heard some time after the flash of lightning has been seen, although both the sound and the light are produced simultaneously ; and in like manner we see a mason at a distance in the act of striking a stone, or a man felling a tree, before we hear the sound. The velocity of sound in air has often been the subject of experimental research. One of the most accurate of the direct measurements was made by Moll and Van Beck in 1823. Two hills, near Amsterdam, Kooltjesberg and Zevenboomen, were chosen as stations: their distance from each other as determined trigonometrically was 57,971 feet, or nearly eleven miles. Cannons were fired at stated intervals simultaneously at each station, and the time which elapsed between seeing the flash and hearing the sound was noted by chronometers. This time could be taken as that which the sound required to travel between the two stations ; for it will be subsequently seen that light takes an inappreciable time to traverse the above distance. In- troducing corrections for the barometric pressure, temperature, and hygro- metric state, and eliminating the influence of the wind, Molland Van Beck’s results as recalculated by Schréder van der Kolk gave 1,092°78 feet as the velocity of sound in one second in dry air at o° C., and under a pressure of 760 mm. Kendall, in a North Pole expedition, found that the velocity of sound at a temperature of — 40° was 314 metres or 103074 feet. Stone’s _ determinations, made at the Cape of Good Hope with very great care, gave 1,090°57 or 332°4 metres, as the velocity of sound at 0°, The velocity of sound at o° may be taken at 1,093 feet, or 333 metres. It increases with increase of temperature, and may be calculated for a tem- perature 7° from the formula UV = 1093.V/(1 + 0'0036057) 216 On Sound [233- where 1,093 is the velocity in feet at 0° C., and 0'003665 the coefficient of expansion for 1° C. This amounts to an increase of nearly two feet for every degree Centigrade. For the same temperature it is independent of the density of the air, and consequently of the pressure. It is the same for the same temperature with all sounds, whether they be strong or weak, deep or acute. Biot found, in his experiments on the conductivity of sound. in tubes, that when a well-known air was played on a flute at one end of a tube 1,040 yards long, it was heard without alteration at the other end, from which he concluded that the velocity of different sounds is the same. For the same reason the tune played by a band is heard at a great distance without alteration, except in loudness, which could not ,be the case if sounds differ- ing in pitch and intensity travelled with different velocities. This cannot, however, be admitted as universally true. Earnshaw, as the result of a mathematical investigation of the laws of the propagation of sound, concluded that the velocity of a sound depends on its strength ; and, accordingly, that a violent sound ought to be propagated with greater velocity than a gentler one. This conclusion is confirmed by an observation made by Captain Parry on his Arctic expedition. During artillery practice it was found, by persons stationed at a considerable distance from the guns, that the report of the cannon was heard before the command to fire given by the officer. And, more recently, Mallet made a series of experiments on the velocity with which sound is propagated in rocks, by observing the times _ which elapsed before blastings, made at Holyhead, were heard at a distance. He found that the larger the charge of gunpowder, and therefore the louder the report, the more rapid was the transmission. With a charge of 2,000 pounds of gunpowder the velocity was 967 feet in a second, while with a charge of 12,000 it was 1,210 feet in the same time. Jacques made a series of experiments by firing different weights of powder from a cannon, and determining the velocity of the report at different distances from the gun by means of an electrical arrangement. He thus found that, close to the gun, the velocity is least, and that it increases to a certain maximum which is considerably greater than the average velocity. The velocity is also greater with the heavier charge. ‘Thus with a charge of 13 pound the velocity was 1187, and with a charge of } pound it was 1032 at a distance of from 30 to 50 feet ; while at a distance of 70 to 80 it was 1267 and 1120: and at 90 to 100 feet it was 1262 and 1114 respectively. Bravais and Martins found, in 1844, that sound travelled with the same velocity from the base to the summit of the Faulhorn as from the summit to the base. A laboratory method of determining the velocity of sounds consists in using a metronome (82) which is beating slowly, and is approached to a wall until a position is found at which the echo of one beat coincides with the sound of another heard directly. The distance from the wall is then half the distance, which sound traverses in the interval between two beats of the metrono me. ; 234. Calculation of the velocity of sound in gases.—From theoretical considerations Newton gave a rule for calculating the velocity of sound in gases, which may be represented by the formula ay dhe fe a 5 —234] Calculation of the Velocity of Sound in Gases 217 in which v represents the velocity of the sound, or the distance it travels in a second, ¢ the elasticity of the gas, and d its density. This formula expresses that the velocity of the propagation of sound in gases ts directly as the square voot of the elasticity of the gas, and tnversely as the square root of tts density. It follows that the velocity of sound is the same under any pressure ; for although the elasticity increases with increased pressure, according to Boyle’s law, the density increases in the same ratio. At Quito, where the mean pressure is only 21°8 inches, the velocity is the same as at the sea-level, provided the temperature is the same. Now the elasticity of a gas is measured by the ratio of a small applied pressure to the compression thereby produced, and it may be easily proved that, supposing the changes of pressure and volume to take place isotherm- ally—that is, supposing Boyle’s law to hold—the elasticity of the gas is equal to the pressure P to which it is subjected. If Z be the height of the barometer, 6 the density of mercury, and g the acceleration due to gravity, the pressure = 96h ; further, if Z be the density of the gas at 7°C. and d, the density at o°C., d,=d (1 +aZ), where a is the coefficient of expansion of the gas (335). Thus Newton’s formula becomes oer + at) 10) a => < é Substituting in this formula the values in centimetres and grammes, =981, = 76, d+0°001293, we get for the value v a number 29,795 centi- metres = 297°95 metres, which is about one-sixth less than the experimental result. The reason for this discrepancy was given by Laplace, who pointed out that when sound waves are travelling through air the heat which is pro- duced by the increase of pressure in the compressed part of any wave does not rapidly escape into the surrounding air. Similarly the cold- due to the diminution of pressure in the rarefied portion of the wave is not at once compensated by the ingress of heat from the surrounding space. Con- sequently the temperature in the two parts of any wave cannot be regarded as constant, and therefore Boyle’s law does not hold. Although the average temperature of the air is unaltered, its elasticity is increased and is no longer measured by the pressure P. It may be shown that the elasticity is greater than the isothermal elasticity P in the proportion in which the specific heat of the gas at constant pressure is greater than the specific heat at constant volume. If these specific heats are denoted by ¢, c’ respectively, ¢ the elasticity = P _ Py, and the expression for the velocity of sound in Oe ° the gas is (pe Ve po ay (I+at)y he =\/' ne aee 4 The value of y for air is 1°41, and if the value of the velocity obtained above, viz. 297°95 metres, be multiplied by ./1‘41 or 1° 187 5, the calculated numbers agree with the Experimental results. Knowing the velocity of sound, we can calculate. approximately the dis- tance at which it is produced. Light travels with such velocity that the flash or the smoke accompanying the report of a gun may be considered to 218 On Sound [234— be seen simultaneously with the occurrence of the explosion. Counting then the number of seconds which elapse between seeing the flash and hearing the sound, and multiplying this number by 1,125, we get the distance in feet at which the gun is discharged. In the same way the distance of thunder may be estimated. 235. Velocity of sound in various gases.—Approximately the same results have been obtained for the velocity of sound in air by another method, by which the velocity in other gases could be determined. As the wave- length X is the distance which sound travels during the time of one oscillation, that is, Sotaa second, the velocity of sound or the distance traversed in a nt second is v=, (233). Now the length of an open pipe is half the wave- length of the fundamental note of that pipe ; and that of a closed pipe is a quarter of the wave-length (279). Hence, if we know the number of vibra- tions of the note emitted by any particular pipe, which can be easily ascer- tained by means of a sirene, and we know the length of this pipe, we can calculate v. Taking the temperature into account, Wertheim found in this way 1,086 feet for the velocity of sound in air at zero. Further, since in gases which differ in density, but are subjected to the same pressure, the velocity of sound varies inversely as the square root of the density, knowing the velocity of sound in air, we may calculate it for other gases ; thus in hydrogen it will be 100 Dies feet. /0°'0688 creed Velocities calculated in this way cannot be universally accurate, for the coefficient £,or y differs somewhat in different gases. And when pipes were C sounded with different gases, and the number of vibrations of the notes multiplied with twice the length of the pipe, numbers were obtained which differed for those calculated by the above formula. When, however, the proper value of y for each gas was introduced into the calculation, the theo- retical results agreed very well with the observed ones. By the above method the following values have been obtained :— Chlorine : s : : : : 677 feet in a second Carbonic acid 5 : : ; ; 856 ys Oxygen : ; : : : . 1040 # Air ; ; : ; : : 1003 i Carbonic oxide. ; Peri toOG a Hydrogen . : ‘ : : Se ato3 és 236. Doppler’s principle—When a sounding body approaches the ear, the note perceived is somewhat higher than the true one; but if the source of sound recedes from the ear, the note perceived is lower. The truth of this, which is known as Dopfler’s principle, will be apparent from the follow- ing considerations :—When the source of sound and the ear are relatively at rest, the ear receives 7 waves in a second; but if the ear approaches the sound, or the sound approaches the ear, it receives more; just as a ship 237] Doppler's Principle 219 meets more waves when it ploughs through them than if it is at rest. Conversely, the ear receives a smaller number when it recedes from the source of sound. The effect in the first case is as if the sounding body emitted more vibrations in a second than it really does, and in the second case fewer. Hence in the first case the note appears higher ; in the second case lower. If the distance which the ear traverses in a second towards the source of sound (supposed to be stationary) is s feet, and the wave-length of the par- ticular note is A feet, then there are ~ waves ina second; this is equal to nS U : for A=—, where vis the velocity of sound (233). Hence the. ear re- c m0 * . Fewias ne ceives not only the z original waves, but also —— in addition. Therefore the YU number of waves per second which enter the ear is Wi I oan (I+ Se On, U for an ear which approaches the sound ; and by similar reasoning it is / Wap 2H (1 a) U v for an ear receding from the sound. To test Doppler’s theory Buys Ballot stationed trumpeters on the Utrecht railway and also upon locomotives, and had the height of the approaching or receding notes compared with stationary ones by musicians. He thus found both the principle and the formula fully confirmed. Similar conclu- sive experiments were made by Scott Russell on English railways. The observation may often be made as a fast train passes a station in which an electrical alarum is sounding. Independently of the difference in loud- ness, an attentive ear can detect a difference in pitch on approaching and on leaving the station. A speed of about 4o miles an hour sharpens the note of the whistle of an approaching train by a semitone, and flattens it to that extent as the train recedes. Doppler’s principle may also be established by direct laboratory ex- periments. Rollmann fixed a long rod on a turning table, at the end of which was a large glass bulb with a slit in it, which sounded like a humming-top when a tangential current of air was blown against the slit. The uniform and sufficiently rapid rotation of the sphere developed such a current, and produced a steady note, the pitch of which was higher or lower in each rotation according as the bulb came nearer, or receded from, the observer. The principle may also be illustrated by means of a tuning-fork with wide branches, and producing a very high note of 2,046 vibrations. When this is loudly sounded, and, being held in front of a smooth wall, is moved towards it with a velocity of a metre in a second, the direct note and that reflected. from the wall undergo opposite changes, so that an observer hears distinctly twelve beats in a second (266). 237. Velocity of sound in liquids.—The velocity of sound in water was 220 Ox Sound [237- experimentally determined in 1827 by Colladon and Sturm. They moored two boats at a known distance apart in the Lake of Geneva. The first supported a bell immersed in water, and a bent lever provided at one end with a hammer which struck the bell, and at the other with a lighted wick, so arranged that it ignited some powder the moment the hammer struck the bell. To the second boat was affixed an ear-trumpet, the bell of which was in water, while the mouth was applied to the ear of the observer, so that he could measure the time between the flash of light and the arrival of sound by the water. By this method the velocity was found to be 4,708 feet in a second at the temperature 8°'1, or four times as great as in air. The velocity of sound, which is different in different liquids, can be cal- culated by a formula identical with that given above (234) as applicable to gases—that is, v= IN / In this formula, ¢ is the volume elasticity of the liquid—that is, the ratio of pressure applied to the compression produced— and @ the density. The compression per unit of volume due to the applica- tion of a pressure of one atmosphere is called the compressibility of the liquid. The numbers given in the following table were computed from the above formula. As in the case of gases, the velocity varies with the tem- perature, which is therefore appended in each case. River water (Seine) ‘ : . 13°C. = 4714 feet in a second ” ” ” : ‘ Dies ohed on Ee ” Artificial sea water : : SRO S761 : Mercury ; i : : Awe bs) = 4866 - Solution of common salt , eA lbs: = MS132 i Absolute alcohol . : : pos = 3854 He Turpentine . . : ; Sey = 30976 xs Hihera oe } : ; t ‘ =n 3801 mis It will be seen how close is the agreement between the two values for the velocity of sound in water, the only case in which they have been directly compared. There is considerable uncertainty about the values for other liquids, owing to the doubt as to the values for their compressibility. 238. Velocity of sound in solids.—As a general rule, the elasticity of solids, as compared with the density, is greater than that of liquids, and consequently the propagation of sound is more rapid. The difference is well seen in an experiment by Biot, who found that when a bell was struck by a hammer, at one end of an iron tube 3,120 feet long, two sounds were distinctly heard at the other end. The first of these was transmitted by the tube itself with a velocity, +; and the second by the en- closed air with a known velocity, a. The interval between the sounds was 2°5 seconds. The value of x obtained from the equation SEAS LP a x shows that the velocity of sound in the tube is nearly 9 times as great as that in air. -238] Velocity of Sound in Solids 221 That the report of the firing of cannon is heard at far greater distances than peals of thunder is doubtless owing to the fact that the sound in the former case is mainly transmitted through the earth. To this class of phenomena belongs the fact that if the ear is held against a rock in which a blasting is being made at a distance, two distinct reports are heard—one transmitted through the rock to the ear, and the other trans- mitted through the air. The propagation of sound in solids is also well illustrated by the fact that in manufacturing telegraph wires the filing at any particular part can be heard at distances bf miles by placing one end of the wire in the ear. The Zoy telephone also is based on this fact. The velocity of sound in wires has also been determined theoretically, by Wertheim and others, by the formula v= Fin which pis the longi- y » DY A, a ‘ed 5 tudinal elasticity (Young’s modulus) of the material (89), while @ is the density. This may be illustrated from a determination by Wertheim of the velocity of sound in a specimen of annealed steel wire, the density s of which was 7631 and longitudinal elasticity 21,000 (89). That is, a weight of 21,000 kilogrammes would double the length of a wire I sq. mm. in cross section, if this were possible, without exceeding the limit of elasticity. This is equal to 2,100,000,000, or 21 x IO* grammes on a wire I sq. cm. in cross section. fence U= Neo oe = 519581 cm, =17047 feet. 3} The following table gives the velocity in various bodies, expressed in feet per second, mostly from the experimental determinations of Wertheim and of Stefan :— Caoutchouc . - 100 to 200 Copper : : . 12194 Tallow : : ; 1180 Oak . : : ae D022 Wax . : : 2394 Cedar. ; ; re £20 Paraffine . é 4250 i ove : ; Peet S510 Lead . : : : 4653 Asha ; : PP Ls 3i4 Membranes . 2300 to 6560 Die : j SAGs Gold . ‘ : ; 7021 Walnut : ; ts 744 Paper . x . 5250 to 8860 Glass . 4 : mr LCOS 7 Silver . : : ; 8806 Steel wire . ‘ 16336 ae. : : 8 TOQOO Wrought iron and Sod 16498 The numbers for caoutchouc are of the same order of magnitude as those for the propagation of a nervous impulse, and suggest that such an EDU is transmitted by longitudinal vibrations (285) like those of sound. In the case of wood these velocities are in the directions of the fibres, and are considerably greater than across the rings or along the rings ; thus with fir the velocities are 4,382 and 2,572 for these directions respectively.’ From a recent determination of the elasticity of ice, Trowbridge and Macrae deduced the velocity of sound in it to be 9,600 feet per second, or about 9 times that of air. | 222 On Sound [238— Mallet investigated the velocity of the transmission of sound in various rocks, and found that it is as follows :—- Wet sand. j ; . 825 feet in a second Contorted, euaiined Guaere and slate TOGKs |) «lOen * Discontinuous granite : ‘ . : tk 300) * Solid granite , A ; : : * 16604 2 A direct experimental method of determining the velocity of sound in solids, gases, and vapours will be described subsequently (281). If a medium through which sound passes is heterogeneous, the waves of sound are reflected on the different surfaces, and the sound becomes rapidly enfeebled. Thus a soft earth conducts sound badly, while a hard ground which forms a compact mass conducts it well. So also we hear badly through air-spaces which are filled with porous materials, such as shavings, sawdust, cinders, and the like. 239. Reflection of sound.—So long as sound-waves are not obstructed in their motion they are propagated in the form of concentric spheres ; but when they meet with an obstacle they follow the general law of elastic bodies ; that is, they return upon themselves, forming new concentric waves, which seem to emanate from a second centre on the other side of the obstacle. This phenomenon constitutes the reflection of sound. Fig. 219 represents a series of incident waves reflected from an obstacle, PQ. Taking for example the incident wave MCDN, emitted from the centre A, the corresponding reflected wave is represented by the arc CKD of a circle whose centre a is as far behind the obstacle PQ as A is before it. If any point, C, of the reflecting surface be joined to the centre of sound, and if the perpendicular CH be let fall on the surface of this body, the angle ACH is called the angle of incidence, and the angle BCH, formed by the prolongation of aC, is the angle of reflection. The reflection of sound is subject to the two following laws :— I. The angle of reflection ts equal to the angle of incidence. —240] Echoes and Resonances 228 Il. Zhe cnctdent sonorous ray and the reflected ray are in the same plane perpendicular to the reflecting surface. From these laws it follows that the wave, which in the figure is propa- gated in the direction AC, takes the direction CB after reflection, so that an observer placed at B hears a second sound, which appears to come from C, besides the sound proceeding from the point A. The laws of the reflection of sound are the same as those for light and radiant heat, and may be demonstrated by similar experiments. One of the simplest of these is made with conjugate mirrors (see chapter on Radiant Heat) ; if in the focus of one of these mirrors, which should be rather large, a watch is placed, the ear placed in the focus of the second mirror hears the ticking very distinctly even when the mirrors are at a distance of, 12 or 13 yards. The mirrors should be large, so that the head does not prevent too large a proportion of the waves from the first mirror from falling on the other. With smaller mirrors the bell of an ear trumpet is held at the focus, and the tube end is placed in the ear, which is held on one side of the mirror. In like manner, the explosion of fulminating mercury in the focus of one mirror causes that of iodide of nitrogen placed in that of the other. 240. Echoes and resonances.—An echo is the repetition of a sound in the air, caused by its reflection from some obstacle. A very sharp quick sound can produce an echo when the reflecting surface is 55 feet distant ; but for articulate sounds at least double that distance is necessary, for it may be easily shown that no one can pronounce or hear distinctly more than five syllables in a second. Now, as the velo- city of sound at ordinary temperatures may be taken at 1,125 feet ina second, in a fifth of that time sound would travel 225 feet. If the reflecting surface is 112°5 feet distant, in going and returning sound would travel through 225 feet. The time which elapses between the articulated and the reflected sound would, therefore, be a fifth of a second, the two sounds would not interfere, and the reflected sound would be distinctly heard. A person speaking with a loud voice in front of a reflector, at a distance of 112°5 feet, can only distinguish the last reflected syllable: such an echo is said to be monosyllabic. If the reflector were at a distance of two or three times 112°5 feet, the echo would be a@syllabic, trisyllabic, and so on. When the distance of the reflecting surface is less than 1125 feet, the direct and the reflected sound are confounded. They cannot be heard separately, but the sound is strengthened. This is what is often called resonance, and is frequently observed in large rooms. Bare walls ; and par- ticularly woodwork, are very resonant ; they reflect the sound and add to it the effect of their own vibrations, so that the sound is prolonged and enforced. In a large meeting-room this may considerably aid a speaker’s voice ; too great resonance, however, hinders the distinct perception of the words. Tapestry and hangings, on the contrary, which are bad reflectors, deaden the sound. To control or eliminate the effects of resonance is a difficult problem in the acoustics of the building art. Multiple echoes are those which repeat the same sound several times ; this is the case when two opposite surfaces (for example, two parallel walls) successively reflect sound. There are echoes which repeat the same sound 224 On Sound [240- 20 or 30 times. Anecho in the chateau of Simonetta, in Italy, repeats a sound 30 times. At Woodstock there is one which repeats from 17 to 20 syllables. As the laws of reflection of sound are the same as those of light and heat, curved surfaces produce acoustic foc? like the luminous and calorific foci produced by concave reflectors. Ifa person standing under the arch of a bridge speaks with his face turned towards one of the piers, the sound is reproduced near the other pier with such distinctness that a conversation can be kept up in a low tone, which is not heard by anyone standing in the intermediate spaces. There is a square room with an elliptical ceiling on the ground floor of the Conservatoire des Arts et Métiers in Paris which presents this phenomenon in a remarkable degree to persons standing in the two foci of the ellipse. Whispering galleries are formed of smooth walls having a continuous curved form. The mouth of the speaker is presented at one point, and the ear of the hearer at another and distant point. In this case the sound is successively reflected from one. point to the other until it reaches the ear. In the whispering gallery of St. Paul’s the faintest sound is thus conveyed from one side to the other of the dome, but it is not heard at any intermediate points. Placing himself close to the upper wall of the Colosseum, a circular building 130 feet in diameter, Wheatstone found a word to be repeated a great many times. A single exclamation sounded like a peal of laughter, while the tearing of a piece of paper resembled the patter of hail. It is not merely by solid surfaces, such as walls, rocks, ships’ sails, &c., that sound is reflected. It is also reflected by clouds, and it has even been shown by direct experiment that a sound in passing from a gas of one density into another is reflected at the surface of separation as it would be against a solid surface. Now, different parts of the earth’s surface are unequally heated by the sun, owing to the shades of trees, evaporation of water, and other causes, so that in the atmosphere there are numerous ascending and descending currents of air of different density. Whenever a sound-wave passes from a medium of one density into another it undergoes partial reflec- tion, which, though not strong enough to form an echo, distinctly weakens the direct sound. This is doubtless the reason, as Humboldt remarked, why sound travels further at night than at daytime, even in the South American forests, where the animals, which are silent by day, fill the atmosphere at night with thousands of confused sounds. To this may be added that at night and in repose, when other senses are at rest, that of hearing becomes more acute. This is the case with persons who have become blind. It has generally been considered that fog in the atmosphere is a great deadener of sound ; it being a mixture of air and globules of water, at each of the innumerable surfaces of contact a portion of the vibration is lost. The evidence as to the influence of this property is conflicting ; Tyndall’s researches show that a white fog, or snow, or hail, is not an important obstacle to the transmission of sound, but that aqueous vapour is. Expe- riments made on a large scale, in order to ascertain the best form of fog signals, gave some remarkable resus On some days, which optically were quite clear, certain sounds could not 241] Refraction of Sound 225 be heard at a distance far inferior to that at which they could be heard even during a thick haze. Tyndall ascribed this result to the presence in the atmosphere of aqueous vapour, which forms in the air innumerable strize that do not interfere with its optical clearness, but render it acoustically turbid, the sound being reflected by this invisible vapour just as light is by the visible cloud. These conclusions, first drawn from observations, have been verified by laboratory experiments. Tyndall showed that a medium consisting of alternate layers of hght and heavy gas, such as coal gas and carbonic acid, deadens sound, and also that a medium consisting of alternate strata of heated and ordinary air exerts a similar influence. The same is the case with an atmosphere containing the vapours of volatile liquids. So long as the continuity of air is preserved, sound has great power of passing through the interstices of solids ; thus it will pass through twelve folds of a dry silk handkerchief, but is stopped by a single layer if it is wetted. 241. Refraction of sound.—lIt will be found afterwards (547) that ve/rac- tion is the change of direction which light and heat experience on passing from one medium to another. It has been shown by Hajech that the laws of the refraction of sound are the same as those for light and heat : he used tubes filled with various gases and liquids, and closed by membranes ; the mem- brane at one end was at right angles to the axis of the tube, while the other made an angle with it. When these tubes were placed in an aperture in the wall be- tween two rooms, a sound produced in front of the tube in one room, that of a tuning-fork for instance, was heard in directions in the other varying with the in- clination of the second mem- brane, and with the nature of the substance with which | the tube was filled. Accurate Bez: -— a measurements showed that aug the law held that the sines of the angle of incidence and of refraction are in a constant ratio, and that this ratio is equal to that of the velocity of sound in the two media. Thus the velocity of sound in water is not very different from that in hydrogen, and they produce deviations which are nearly equal. Sondhauss confirmed the analogy of the refraction of sound-waves to those of light and heat. He constructed lenses of gas by cutting equal segments out of a large collodion balloon, and fastening them on the two sides of a sheet-iron ring a foot in diameter, so as to form a double convex lens about 4 inches thick in the centre (fig. 220). This was filled with car- bonic acid, and a watch A was placed in the direction of the axis ; the point was then sought on the other side of the lens at which the sound was most Q 226 . On Sound [241— distinctly heard. It was found that when the ear was removed from the axis the sound was scarcely perceptible, but that at a certain point B on the axial line it was very distinctly heard. Consequently, the sound-waves in passing from the lens had converged towards the axis ; their direction had been changed ; in other words, they had been refracted. The refraction of sound may be easily demonstrated by means of one of the very thin india-rubber balloons used as children’s toys, inflated by carbonic acid. If, however, the balloon be filled with hydrogen, no focus is detected; it acts like a concave lens, and, the divergence of the rays is increased, instead of their being converged to the ear. A direct proof of the refraction of sound is given by the experiments of Schellbach and Bohm. The source of sound was a film of collodion stretched across a ring, ad (fig. 221), which was put in vibration by electrical sparks at 0. A disc of paper, #, sprinkled with fine charcoal powder, was suspended in the vessel BB’. When this vessel contained air, rings of dust were formed, the centre of which was at f in the direction of the propagation of the sound. But if the vessel was filled with carbonic acid the centre of the rings was found to be at 7, showing that the sound had been refracted towards the perpendicular on passing from air into the denser medium ; and measure- ments showed that the position of the point /” was in accordance with the law of refraction for light. Experiments suitably modified showed that, when hydrogen was substituted for carbonic acid, the sound was bent away from the perpendicular. It has long been known that sound is propagated in a direction against that of the wind with less velocity than with the wind. This is probably due to a refraction of sound.on a large scale. The velocity of wind along the ground is always considerably less than at a greater height ; thus, the velocity at a height of 8 feet has been observed to be double what it is at a height of one foot above the ground. Hence a wave-front (fig. 219), originally vertical, becomes tilted upwards, with the lower part forward ; and, as the direction of the wave-motion is at right angles to the front of the wave, the effect of the coalescence of a number of these rays, thus directed upwards, is to produce an increase of the sound in the higher regions. The rays which travel with the wind will, for similar reasons, be refracted downwards, and thus the sound be better heard. 242. Speaking trumpet. Ear trumpet. —These instruments depend on the reflection of sound in tubes. The speaking trumpet, as its name implies, is used to render the voice audible at great distances, more especially on board ship. It consists of a. slightly conical tin or brass tube (fig. 222), very much wider at one end (which is called the de//), and provided with a mouthpiece at the other. They are as much as 7 feet in length, the bell being 1 foot in diameter. The larger the dimensions of this instrument the greater is the distanee Fig. 221 -243] | Stethoscope 227 at which the voice is heard. Its action is usually ascribed to the successive reflections of sound-waves from the sides of the tube, by which the waves tend more and more to pass in a direction parallel to the axis of the instrument. It has, however, been objected to this explanation that the sounds emitted by the speaking trumpet are not stronger solely in the direction of the axis, but in all directions ; that the bell would not tend to produce parallelism in the sound-wave, whereas it certainly exerts consider- able influence in strengthening the sound. According to Hassenfratz, the bell acts by causing a large mass of air to be set in consonant vibration before Fig. 222 it begins to be diffused. This is probably also the reason why sound travels best in the chief direction of the sounding body ; thus the report of a cannon, the sound of a wind instrument in the line of the tube, the voice of the direction of the mouth, &c. The ear trumpet is used by persons who are hard of hearing. It is essentially an inverted speaking trumpet, and consists of a conical metallic tube, one of whose ends, terminating in a de//, receives the sound, while the other end is introduced into the ear. This instrument is the reverse of the speaking trumpet. The bell serves as a mouthpiece ; that is, it receives the sound coming from the mouth of the person who speaks. ‘These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves, which would become greatly diffused, are concentrated on the ear, and produce a far greater effect than divergent waves would have done. : iettts 243. Stethoscope.—One of the most useful applications of acoustical principles is the stethoscope. Figs. 223, 224, represent an improved form of this instrument devised by Kénig. Two sheets of caoutchouc, c and a, are fixed to the circular edge of a hollow metal hemisphere ; the edge is provided with a stopcock, so that the sheets can be jnflated, and then present the ap- pearance of a double convex lens, as represented in section in fig. 223. To Q2 228 On Sound [243— a tubulure on the hemisphere is fixed a caoutchouc tube terminated by horn or ivory, 4, which is placed in the ear (fig. 224). When the membrane c of the stethoscope is applied to the chest of a sick person, the beating of the heart and the sounds of respiration are trans- mitted to the air in the chamber a, and thence to the ear by means of the flexible tube. If several tubes are fixed to the instrument, as many observers may simultaneously auscultate the same patient. A recent application—that to the water stethoscofe—has been found of great service. It consists of a steel rod about three feet in length, with an enlargement at each end; one of these is so shaped that it fits against a water-pipe, while the other is applied to the ear. The taps having been turned off, a skilled observer can detect the slight sound due to any flow of water, which, in the circumstances, must be due to leakage. } The audiphone, invented by Mr. Rhodes, of Chicago, is of considerable service to people hard of hearing ; in its most simple form (fig. 225) it con- sists of a thin rectangular piece of fine cardboard, the square end of which Fig. 225 is held in one hand while the opposite and convex edge is pressed against the teeth of the upper jaw so that it is slightly bent: it receives the sounds which are produced in the air, and transmits them to the auditory nerves through the bones of the head. —245] Szrene 229 CHAPTER II MEASUREMENT OF THE NUMBER OF VIBRATIONS 244. Savart’s apparatus.—Savart’s toothed wheel, so called from the name of its inventor, is an apparatus by which the absolute number of vibra- tions corresponding to a given note can be determined. It consists of a solid oak frame in which are two wheels, A and B (fig. 226); the larger wheel, A, is connected with the toothed wheel by means of a strap and a multiplying wheel, thereby causing the toothed wheel to revolve with great velocity ; a card, E, is fixed on the frame, and, in revolving, the toothed wheel strikes against it and causes it to vibrate. The card, being struck by each tooth, makes as many vibrations as there are teeth. At the side of the apparatus is an indicator, H, which gives the number of revolutions of the wheel, and consequently the number of vibrations in a given time. Fig. 226 When the wheel is moved slowly, the separate shocks against the card are distinctly heard ; but if the velocity is gradually increased, the sound becomes higher and higher. Having obtained the sound whose number of vibrations is to be determined, the revolution of the wheel is continued with the same velocity for a certain number of seconds. The number of turns of the toothed wheel B is then read off on the indicator, and this multiplied by the number of teeth in the wheel gives the total number of vibrations. Dividing this by the corresponding number of seconds, the quotient gives the number of vibrations per second for the given sound. 245. Sirene.—The szvene is an apparatus which, like Savart’s wheel, is used to measure the number of vibrations of a body in a given time. The 230 On Sound [245— name ‘sirene’ was given to it by its inventor, Cagniard Latour, because it yields sounds under water. It is made entirely of brass. Fig. 227 represents it fixed on the table of a bellows, by which a continuous current of air can be sent through it. Figs. 228 and 229 show the internal details. The lower part consists of a cylin- drical box, O, closed by a fixed plate, B. On this plate a vertical rod, T, rests, to which is fixed a disc, A, moving with the rod. In the plate B there are equidistant circular holes, and in the disc A an equal number of holes of the same size,‘and at the same distance from the centre as those of the plate. These holes are not perpendicular to the disc ; they are all inclined to the same extent in the same direction in the plate, and are inclined to the same extent in the opposite direction in the disc, so that when they are opposite each other they have the appearance represented in 7m, fig. 228. Conse- quently, when a current of air from the bellows reaches the hole 7, it strikes = obliquely against the sides of the hole 7, and makes the disc A rotate in the direction 7A. For the sake of simplicity, let us first suppose that in the movable disc A there are eighteen holes, and in the fixed plate B only one, which faces one of the upper holes. The wind from the bellows striking against the sides of the latter, the movable disc begins to rotate, and the space between two of its consecutive holes closes the hole in the lower plate. But as the disc continues to turn from its acquired velocity, two holes are again opposite each other, a new impulse is produced, and so on. During a complete revolution of the disc the lower hole is eighteen times open and eighteen times closed. A series of effluxes and stoppages is thus produced, which makes the air vibrate, and ultimately produces a sound when the successive impulses are sufficiently rapid. If the fixed plate, like the moving disc, had eighteen holes, each hole would separately produce the same effect as a ~247] Limit of Perceptible Sounds 231 separate one, the sound would be eighteen times as intense, but the number of vibrations would not be increased. In order to know the number of vibrations corresponding to the sound produced, it is necessary to know the number of revolutions of the disc A in a second. For this purpose an endless screw on the rod T transmits the motion to a wheel, a, with 100 teeth. On this wheel, which moves by one tooth for every turn of the disc, there is a catch, P, which at each complete revolution moves one tooth of a second wheel, 6 (fig. 229). On the axis of these wheels there are two needles, which move round dials represented in fig. 227. One of these indices gives the number of turns of the disc A, the other the number of hundreds of turns. Ry means of two screws, D and C, the wheel @ can be uncoupled from the endless screw. Since the pitch of the sound rises in proportion to the velocity of the disc A, the wind is forced until the desired sound is produced. The same current is kept up for a certain time—two minutes, for example—and the number of turns read off. This number, multiplied by 18 and divided by 120, gives the number of vibrations in a second. For the same velocity of rotation the sirene gives the same sound in air as in water ; the same is the case with all gases ; and it appears, therefore, that any given sound depends on the number of vibrations produced, and not on the nature of the sounding body. The buzzing and humming noise of certain insects is not vocal, but is produced by very rapid flapping of the wings against the air or the body. The sirene has been ingeniously applied to count the rate per second of the undulations thus produced, which is effected by bringing it into unison with the sound. It has thus been found that the wings of a gnat flap at the rate of 1,500 times in a second. If a report is produced in a space with two parallel walls at no great distance apart, the sound is reflected from one to the other, and reaches the ear at regular and frequent intervals ; that is, the repetition of the echo acts as a note. A modification of the sirene known as Brown’s steam-horn, in which high- pressure steam is employed instead of compressed air, is used as a fog-ségnal. Its shrill and penetrating note is better adapted than an ordinary fog-horn, or even cannon, for being heard over the noise of breakers. 246. Bellows.—In acoustics a dellows is an apparatus by which wind instruments, such as the sirene and organ-pipes, are worked. Between the four legs of a table there is a pair of bellows, S (fig. 230), which is worked by means of a pedal, P. Disa reservoir of flexible leather, in which is stored the air forced in by the bellows. If this reservoir is pressed by means of weights on a rod, T, moved by the hand, the air is driven through a pipe, E, into a chest, C, fixed on thetable. In this chest there are small holes closed _ by leather valves, which can be opened by pressing on keys in front of the box. The sirene or sounding pipe is placed in one of these holes. 247. Limit of perceptible sounds.—Previous to Savart’s researches, physicists assumed that the ear could not perceive asound when the number of vibrations was below 16 for deep sounds, or above 9,000 for acute sounds. But he showed that these limits were too close, and that the faculty of per- ceiving sounds depends rather on their intensity than on their height; so that when extremely acute sounds are not heard it arises from the fact.that 232 On Sound [247— they have not been produced with sufficient intensity to affect the organ of hearing. By increasing the diameter of the toothed wheel, and consequently the amplitude and intensity of the vibrations, Savart pushed the limit of acute sounds to 24,000 vibrations in a second. For deep sounds he substituted for the toothed wheel an iron bar about two feet long, which revolved on a horizontal axis between two thin wooden plates, about 0'08 of an inch from the bar. As often as the bar passed a grave sound was produced, due to the displacement of the air. As the motion was accelerated the sound became continuous, very grave, and deafening. By this means Savart found that, with 7 to 8 vibrations in a second, the ear perceived a distinct but very deep sound. Despretz, however, who investigated the same sub- nA ii mall ject, disputed Savart’s results oe as to the limits of deep eee ZA sounds, and considers that me HN no sound is audible that is made by less than 16 vibra- tions per second. Von Helm- holtz holds that the percep- tion of a sound begins at 30 vibrations, and only has a definite musical value when the number is more than 4o. Below 30 the impression of a number of separate beats is produced. On the other hand, acute sounds are aud- ible up to those correspond- ing to 38,000 vibrations ina second. Such sounds, how- ever, are far from pleasur- able: they affect the ear as if it had been pricked with a pin or needle. The discordant results obtained by these and other observers for the limit of audibility of higher notes are no doubt due to the circumstance that different observers have different capacities for the perception of sounds. Preyer has investigated this subject by means of experimental methods of greater precision than any that have hitherto been applied for this purpose. The minimum limit for the normal ear he found to lie between 16 and 24 single vibrations in a second ; the maximum limit reached 41,000 ; but many persons with average powers of hearing were found to be absolutely deaf to notes of 16,000, 12,000, or even fewer vibrations. It appears that the limit of .audibility for any particular ear is increased with the strength of the sound. Paucher examined this by sounding a powerful sirene by steam ; he found that with steam of $ an atmosphere pres- Fig. 230 ~248] Duhamel’s Graphic Method 233 sure the upper limit was at 48,o0o vibrations, with 1} atmosphere it was 60,000, while with steam of 23} atmospheres, it had not been attained with 72,000 vibrations. 248. Duhamel’s graphic method.—When the sirene or Savart’s wheel is used to determine the exact number of vibrations corresponding to a given note, it is necessary to bring the sounds which they produce into unison with the given note, and this cannot be done exactly unless the experi- menter has a practised ear. Duhamel’s graphic method is very simple and exact, and free from this difficulty. It consists in fixing a fine point to the body emitting the note, and causing it to trace the vibrations on a properly prepared surface. The apparatus consists of a wood or metal cylinder, A (fig. 231), fixed to a vertical axis, O, and turned by a handle. The lower part of the axis is a screw working in a fixed nut, so that according as the handle is turned from left to right, or from right to left, the cylinder is raised or depressed. Round _the cylinder is rolled a sheet of paper covered with an inadhesive film of lampblack. On this film the vibrations register themselves. This is effected as follows. Suppose the body emitting the note to be a steel rod. Itis held firmly at one end, and carries at the other a fine point which grazes the sur- faces of the cylinder. If the rod is made to vibrate and the cylinder is at rest, the point would describe a short line ; but if the cylinder is turned, the point produces an wuadulating line, containing as many undulations as the point has made vibrations. Consequently, the number of vibrations can be counted. It remains only to determine the time in which the vibrations were made. 234 On Sound , [248- There are several ways of doing this. The simplest is to compare the curve traced by the vibrating rod with that traced by a tuning-fork (254), -which gives a known number of vibrations per second —for example, 500. The prong of the fork is furnished with a point, which is placed in contact with the lampblack. The fork and the rod are then set vibrating together, and each produces its own undulating trace. When the paper is unrolled, it is easy, by counting the number of vibrations each has made in the same distance, to determine the number of vibrations made per second by the elastic rod. Suppose, for instance, that the tuning-fork made 150 vibrations, while the rod made 165 vibrations. Now we already know that the tuning- fork makes one vibration in the 545 part of a second, and therefore 150 vibrations in 43° of a second. But in the same time the rod makes 165 vibrations ; therefore, it makes one vibration in the NS? 500 x 165 of a second, . 00 x 16 : and hence it makes per second 5 SE se or 550 vibrations. 150 -250] Musical Intervals 235 CHAPTER III THE PHYSICAL THEORY OF MUSIC 249. Properties of musical notes._-A simple musical note results from continuous rapid isochronous vibrations, provided the number of the vibra- tions falls within the very wide limits mentioned in the last chapter (247). Musical notes are in most cases compound. The distinction between a simple and a compound musical note will be explained later in the chapter. The tone yielded by a tuning-fork furnished with a proper resonance-box is simple ; that yielded by a wide-stopped organ pipe, or by a flute, is. zearly simple ; that yielded by a musical string 1s compound. Musical notes have three leading qualities, namely, Aztch, znfensity, and timbre or quality. i, The fztch of a musical note is determined by the number of vibrations per second yielded by the body producing the note. i. The zztenszty of the note depends on the eavent¢ of the vibrations. | It is greater when the extent is greater, and less when it is less. It is, in fact, proportional to the square of the extent, or amplitude of the vibrations which produce the note. ii. The “bre or stamp or gialzty is that peculiar property of note which distinguishes a note when sounded on one instrument from the same note when sounded on another, and which by some is called the colour. Thus when the C of the treble stave is sounded on a violin and on a flute, the two notes will have the same pitch ; that is, they are produced by the same number of vibrations per second, and they may have the same intensity, and yet the two notes will have very distinct qualities ; that is, their timbre is different. The cause of the peculiar timbre of notes will be considered later in the chapter. 250. Musical intervals.—Let us suppose that a musical note, which for the sake of future reference we will denote by the letter C, is produced by m vibrations per second ; and let us further suppose that any other musical note, X, is produced by z vibrations per second, z being greater than 7 ; then the interval from the note C to the note X is the ratio 7 : #7, the interval between two notes being obtained by azvzszon, not by subtraction. Although two or more notes may be separately musical, it by no means follows that when sounded together they produce a pleasant sensation. On the con- trary, unless they are concordant, the result is harsh, and usually unpleasing. We have, therefore, to inquire what zofes are fit to be sounded together. Now, when musical notes are compared, it is found that if they are separated by an interval of 2:1, 4:1, &c. they so closely resemble one another that they may for most purposes of music be considered as the samenote. Thus 236 On Sound [250- suppose ¢ to stand for a musical note produced by 27 vibrations per second, then C and ¢ so closely resemble each other as to be called in music by the same name. The interval from C to ¢ is called an octave, and c is said to be an octave above C, and conversely C an octave below c. If we now consider musical sounds that do not differ by an octave, it is found that if we take three notes, X, Y, and Z, resulting respectively from 7, g, and + vibrations per second, these three notes when sounded together will be con- cordant if the ratio of f:¢:7r equals 4:5:6. Three such notes form an harmonic triad, and if sounded with a fourth note, which is the octave of X, constitute what is called in music a sajor chord. Any of the notes of a chord may be altered by one or more octaves without changing its distinc- tive character ; for instance, C, E, G, and ¢ are a chord, and C, ¢, e, ¢ form the same chord. If, however, the ratiof:g:r7 equals 10:12:15, the three sounds are slightly dissonant, but not so much so as to disqualify them for producing a pleasing sensation. When these three notes and the octave to the lower are sounded together, they constitute what in music is called a wnor chord. 251. The musical scale-—The series of sounds which connects a given note C with its octave ¢c is called the dzatonic scale or gamut. The notes composing it arevindicated by the letters C) Dy) F/G, Ay Bt ihescale is then continued by taking the octaves of these notes, namely, CfA, Of Pa and again the octaves of these last, and so on. The notes are also known by names—viz. do or ut, re, mit, fa, sol, ta 34 do. The relations existing between the notes are these :—C, E, G ae a major Zvzad, G, B, d form a: major ¢riad, and F, A, c form a ee: triad. C, G, and F have, for this reason, special names, being called respectively the ¢onic, dominant, and subdominant, and the three triads the ‘onic, dominant, and subdominant triads or chords respectively. Consequently, the numerical relations between the notes of the scale will be given by the three proportions— pe Ges GPs a Sr Ga Busi erase as Bf Arede vane aaeee EG wa Ut Hence, if #z denotes the number of double vibrations corresponding to the note C, the number of vibrations corresponding to the remaining notes will be given by the following table— ado re Mite? Aa sol la St do C D E i G a B C m Sm = =2m 4770 37 Bm oS 2m The intervals between the successive notes being respectively— Cte DP eD tok Eto) We neoneree Or. tO A atc meee ees 9 10 16 9 10 9 16 8 9 15 8 9 8 1d It will be observed here that there are three kinds of intervals, 2, 4°, and i835 of these the first two are called a Zone, the last a semzttone, because it is about half as great as the interval of atone. The two tones, however, are not identical, but differ by an interval of $4, which is called a comma. Two -253] On Musical Temperament 237 notes which differ by a comma can be readily distinguished by a trained ear. The interval between the tonic and any note is denominated by the position of the latter note in the scale ; thus the interval from C to G is a fifth. The scale we have now considered is called the zajor scale, as being formed of wzajor triads. If the minor triad were substituted for the major, a scale would be formed that could be strictly called a mznor scale. As scales are usually written, however, the ascending scale is so formed that the tonic bears a minor triad, the dominant and subdominant bear major triads, while in the descending scale they all bear mzzor triads. Practically, in musical composition, the dominant triad is always major. If the ratios given above are examined, it will be found that in the major scale the interval from C to E equals 3, while in the minor scale it equals $. The former interval is called a major third, the latter a szzzor third. Hence the major third exceeds the minor third by an interval of 3%. This interval is called a semitone, though very different from the interval above called by that name. . 252. On semitones and on scales with different keynotes.—It will be seen from the last article that the term ‘semitone’ does not denote a constant interval, being in one case equivalent to $£ and in another to 33. It is found convenient for the purposes of music to introduce notes intermediate to the seven notes of the gamut ; this is done by raising or lowering these notes by an interval of 22, When a note (say C) is increased by this interval, it is said to be sharpened, and is denoted by the symbol Cf, called ‘C sharp ;’ that is, Cf +C=3%. When it is lowered by the same interval, it is said to be flattened, and is represented thus—Bb, called ‘B flat ;’ that is, B+Bb =33. If the effect of this be examined, it will be found that the number of notes in the scale from C up to ¢ has been increased from seven to twenty-one notes, all of which can be easily distinguished by the ear. Thus, reckoning C to equal I, we have--- ee Ct Db D Dt Eb E &c. I 25 $ # 8 &e. Hitherto we have made the note C the tonic or keynote. Any other of the twenty-one distinct notes above mentioned, e.g. G, or F, or Cr, &c., may be made the keynote, and a scale of notes constructed with reference to it. This will be found to give rise in each case to a series of notes, some of which are identical with those contained in the series of which C is the keynote, but most of them different. And of course the same would be true for the minor scale as well as for the major scale, and indeed for other scales which may be constructed by means of the fundamental triads. 253. On musical temperament.—The number of notes that arise from the construction of the scales described in the last article is so great as to prove quite unmanageable in the practice of music; and particularly for music designed for instruments with fixed notes, such as the pianoforte or harp. Accordingly it becomes practically important to reduce the number of notes, which is done by slightly altering their just proportions. This process is called ¢emperament, and the scale is called the tempered scale. By tempering the notes, however, more or less dissonance is introduced, and accordingly several different systems of temperament have been devised for rendering 238 On Sound [253- this dissonance as slight as possible. The system usually adopted is called the system of egwal temperament. It consists in retaining the octaves pure, and in substituting between C and c eleven notes at equal intervals, each interval being, of course, the twelfth root of 2, or 1'05946. By this means the distinction between the semitones is abolished, so that, for example, Ct and Db become the same note. The scale of twelve notes thus formed is called the chromatic scale. It follows, of course, that major triads become slightly dissonant. Thus, in the diatonic scale, if we reckon C to be 1, E is denoted by 1:25000, and G by 1°50000. On the system of equal tempera- ment, if C is denoted by 1, E is denoted by 1°25992 and G by 1°49831. If individual intervals are made pure while the errors are distributed over the others, such a system is called that of wmegual temperament. Of this class is Kzrnberger’s, in which nine of the tones are pure. Although the system of equal temperament has the advantage of afford- ing the greatest variety of tones with as small a number of notes as possible, yet it has the drawback that no chord of an equally tempered instrument, such as the piano, is perfectly pure. And as musical education mostly has its basis on the piano, even singers and instrumentalists usually give equally tempered intervals. Only in the case of string quartet players, who have freed themselves from school rules, and in that of vocal quartet singers, who sing frequently without accompaniment, does the natural pure temperament assert itself, and thus produce the highest musical effect. 254. The number of vibrations producing each note. The tuning-fork. Hitherto we have denoted the number of vibrations corresponding to the note C by wm, and have not assigned any numerical .value to that symbol. In the theory of music it is frequently assumed that the middle C corresponds to 256 double vibrations in a second. This 1s. the note which, on a pianoforte of seven octaves, is produced by the white key on the left of the two black keys close to the centre of the keyboard. This number is con- venient as being continually divisible by two, and is therefore frequently used in numerical illustrations. It is, however, arbitrary. An instrument is in tune provided the intervals between the notes are correct, when c is yielded by any number of vibrations per second not differing much from 256. Moreover, two instru- ments are in tune with each other if, being separately in tune, they have any one note, for instance C, yielded by the same number of vibra- tions.. Consequently, if two instruments have one note in common, they can then be brought into tune jointly by having their remaining notes jae separately adjusted with reference to the funda- mental note. BBOB? poe V5 508 1He Z 5508+¢ I + 5508 In this calculation, the coefficient of absolute expansion of mercury is taken, and not that of apparent expansion ; for the value H is the same as if the glass did not expand, the barometric height being independent of the diameter of the tube, and therefore of its expansion. 332. Correction of thermometric readings.—If the whole column of mercury of a thermometer is not immersed in the space whose temperature is to be determined, it is necessary to make a correction, which in the accurate determination of boiling points, for instance, is of great import- ance, in order to arrive at the true temperature which the thermometer should show. That part of the stem which projects will have a tempera- ture which must be estimated, and which may roughly be taken as some- thing over that of the surrounding air. Suppose, for instance, that the actual reading is 160° and that the whole of the part over 80° is outside the vessel, while the temperature of the surround- ing air is 15°. Wewill assume that the mean temperature of the stem is 25°, and that a length of 160°— 80° is to be heated through 160—25 = 135°; this gives 80x ae 1°66 (taking the coefficient of apparent expansion of mercury) ; so that the true reading is 161°66. 333. Force exerted by liquids in expanding.—The force which liquids exert in expanding is very great, and equal to that which would be required in order to bring the expanded liquid back to its original volume. Now we know what an enormous force is required to compress a liquid to even a very small extent (98). Thus between 0° and 10°, mercury expands by 0°0015790 of its volume at 0° ; its compressibility is 0700000295 of its volume for one atmosphere ; hence a pressure of more than 600 atmospheres would be requisite to prevent mercury expanding when it is heated from 0° to 10°. In like manner a pressure of 140 atmospheres would be required to prevent water from expanding when its temperature was raised from 4° to 14°. 312 On Feat [334— 334. Maximum density of water.—Water presents the remarkable pheno- menon that when its temperature sinks it:contracts down to 4°; but from that point, although the cooling continues, it expands to the freezing point, so that 4° represents the point of greatest contraction of water. Many methods have been used to determine the temperature of the maxi- mum density of water. Hope made the following experiment :— He took adeep vessel with two apertures in the sides, in which he fixed thermometers, and having filled the vessel with water at 0°, he placed it in a room at a tem- perature of 15°. As the layers of liquid at the sides of the vessel became heated they sank to the bottom, and the lower thermometer marked 4° while the upper one was still at zero. Hope then made the inverse experiment ; having filled the vessel with water at 15°, he placed it in a room at zero. The lower thermometer having sunk to 4° remained stationary for some time, while the upper one cooled down until it reached zero. Both these experiments prove that water is heavier at 4° than at 0°, for in both cases the water at 4° sinks to the lower part of the vessel. This last experiment may be adapted for lecture illustration by using a cylinder containing water at 15° C., partially surrounded by a jacket contain- ing bruised ice (fig. 317). Hallstr6m made a determination of the maximum density of water in the following manner :—He took a glass bulb, loaded with sand, and weighed it in water of different temperatures. Allow- ing for the expansion of glass, he found that 4°1° was the temperature at which it lost most weight, and consequently this was the temperature of the maximum density of water. Despretz arrived at the temperature 4° by another method. He took a water thermometer—that is to say, a bulbed tube containing water-—and, placing it in a bath, the temperature of which was in- dicated by an ordinary mercury thermo- meter, found that the water contracted to the greatest extent at 4°, and that this therefore is the point of greatest density. This phenomenon is of great import- ance in the economy of nature. In winter the temperature of lakes and rivers falls, from being in contact with the cold air and from other causes, such as radiation. The cold water sinks to the bottom, and a continual series of currents goes on until the whole has a temperature of °, The cooling on the surface still continues, but the cooled layers, being an lighter than those below, remain on the surface, and ultimately freeze. The ice formed thus protects the water below, the lower portions of which remain at a temperature of 4°, even in the most severe winters, a temperature at which fish and other inhabitants of the water are not destroyed. Salt dissolved in water lowers the temperature of the maximum density, 334] and sea water exhibits a maximum. According to Rosetti, this temperature is between 3°2° and 3°9° in the Adriatic. The following table of the density of pure water at various temperatures is based on several sets of observations :— Tempe- ratures Maximum Density of Water Density of water between 0° and 30°. Densities Tempe- | m OO ON DAuifHO N HO HOH 0°99988 099993 0°99997 099999 I ‘OOO00O 099999 0°99997 0°99994 099988 099982 0°99974 0°99965 NNN Go NS & Densities Ee aah Densities 0°99955 24 0°99738 0°99943 25 099714 0°99930 26 099689 O'99915 a7 0'99662 0°99900 28 0°99635 0.99884 29 0°99607 0°99870 30 0°99579 0°99847 40 - 0°99226 0°99827 50 0'98820 0.99806 60 0°98232 0°99785 70 0°97796 0'99762 80 o'9g719I 314 On Heat [335— CHARTER SIV EXPANSION AND DENSITY OF GASES 335. Gay-Lussac’s method.—Gases are the most expansible of all bodies, and at the same time the most regular in their expansion. The coefficients of expansion, too, of the several gases differ ‘only by very small quantities. The cubical expansion of gases need alone be considered. Gay-Lussac first determined the coefficient of the expansion of gases by means of the apparatus represented in fig. 318. In a rectangular metal bath, about 16 inches long, was fitted an air thermometer, which consisted of a capillary tube, AB, with a bulb, A, at one: end: "The tube) was divided into parts of equal capacity, and the contents of the bulb ascertained | in terms of these ee T parts. This was cn cay)! a aes 2 = 4b tube full of mer- ——— = (= [z= [a || ==> el cury * at) zero, and then heating slightly to expel a small quantity of mercury, which was weighed. The apparatus being again cooled down to zero, the vacant space in the tube corresponded to the weight of mercury which had overflowed ; the volume of mercury remaining in the apparatus, and consequently the volume of the bulb, was determined by calculations analogous to those made for the’piezometer (98). In order to fill the thermometer with dry air it was first filled with mercury, which was boiled in the bulb itself. A tube, C, filled with calcium chloride, was then fixed on to its end by means of a cork. A fine platinum wire having then been introduced into-:the stem AB through-the tube C, and the apparatus being slightly inclined and agitated from time to time, air entered, having been previously well dried by passing through the calcium chloride tube. The whole of the mercury was displaced, with the excep- tion of a small thread, which remained in the tube AB as an index. The air thermometer was then placed in the box filled with melting ice, the index moved towards A, and the point was. noted at which it became: Fig. 318 —336] Problems on the Expansion of Gases 315 stationary. This gave the volume of air at zero, since the capacity of the bulb was known. Water or oil was then substituted for the ice, and the bath successively heated to different temperatures. The air expanded and moved the index from A towards B. The position of the index in each case was noted, and the corresponding temperature was indicated by means of the thermometers D and E. Assuming that the atmospheric pressure did not vary during the experi- ment, and neglecting the expansion of the glass as being small in comparison with that of the air, the total expansion of the air is obtained by subtracting from its volume at a given temperature its volume at zero. Dividing this by the given temperature, and then by the number of units contained in the volume at zero, the quotient is the expansion for a single unit of volume and a single degree ; that is, the coefficient of expansion. It will be seen further on how corrections for pressure and temperature may be introduced ; by this method Gay-Lussac found that the coefficient of expansion of air was 0°00375. The two following laws hold in reference to the expansion of gases :— I. All gases have the same coefficient of expanston as atr. Il. This coefficient ts the same whatever be the pressure supported by the gas. These simple laws are not, however, rigorously exact (337); they only express the expansion of gases in an approximate manner. They were discovered independently by Dalton and by Gay-Lussac, and are usually ascribed to them. The first discoverer of the former law was, however, Charles. 336. Problems on the expansion of gases.—Many of the problems relative to the expansion of gases are similar to those on the expansion of liquids. With obvious modification, they are solved in a similar manner. In most cases the pressure of the atmosphere must be taken into account in considering the expansion of gases. The following is an example of the manner in which this correction is made :— i. The volume of a gas at ¢°, and under the pressure H, is V’: what will be the volume V of the same gas at zero, and under the normal pressure 760 millimetres ? Here there are two corrections to be made; one relative to the tempera- ture and the other to the pressure. It is quite immaterial which is taken first. If a be the coefficient of cubical expansion for a single degree, by reasoning similar to that in the case of linear expansion (317), the volume of / the gas at zero, but still under the pressure H, will be- ey . This pressure Trac is reduced to the pressure 760 in accordance with Boyle’s law (183), by peas ye VA tting Vx 760 = leben a Raa ees bi sk ad meee 760 (1 + aé) i. A volume of gas weighs P’ at 7°: what will be the-weight of an equal volume at zero? Let P be the desired weight, a the coefficient of |expansion of the gas, @ its density at 7°, and d its density at ‘zero. As the weights of equal Hi 7 volumes are proportional to the densities, we have Baie lit, besthe 316 On Fleat [336— volume of a gas at zero, its volume at ¢ will be 1+ az: but as the densities a’ I are inversely.as the’ volumes, —-=—__4 a@ i+at i I ; ; ‘ and therefore = =———_, ; whence P=P”(1 + a7). Pap dete? From this equation we get P’= K ee which gives the weight at 4, know- ing the weight at zero, and which further shows that the weight P’ is inversely as the binomial of expansion 1 + aé. 337. Regnault’s method.—Regnault used successfully four different methods for determining the expansion of gases. In some of them the pressure was constant and the volume variable, as in Gay-Lussac’s method ; in others the volume remained the same while the pressure varied. The first method will be described. It is the same as that used by Rudberg and Dulong, but is distinguished by the care with which all sources of error are avoided. The apparatus consisted of a pretty large cylindrical reservoir, B (fig. 319), terminating in a bent capillary tube. In order to fill the reservoir with ye Son eS See SS SSS dry air, it was placed in a hot-water bath, and the capillary tube connected by a caoutchouc tube with a series of drying [tubes. These tubes were joined to a small air-pump, B, by which a vacuum could be produced in the reservoir while at a temperature of 100°. The reservoir was first exhausted, and air afterwards admitted slowly ; this operation was repeated a great many times, so that the air in the reservoir became quite dry, for the mois- ture adhering to the sides passed off in vapour at 100°, and the air which entered became dry in its passage through the U tubes. The reservoir was then kept for half an hour at the temperature of boil- ing water; the air-pump having been detached, the drying tubes were then disconnected, and the end of the tube hermetically sealed, the height H of the barometer being noted. When the reservoir B was cool, it was placed 337] — Regnault’s Method aly, in the apparatus represented in fig. 320. It was there quite surrounded with ice, and the end of the tube dipped in the mercury bath, C. After the air in the reservoir B had sunk to zero, the point 6 was broken off by means of a pair of forceps ; the air in the interior became con- densed by atmospheric pressure, the mercury rising to a height 0G. In order to measure the height of this column, Go, which will be called %, a movable rod, go, was lowered until its point, 9, was flush with the surface of the mercury in the bath ; the distance between the point o and the level of the mercury G was measured by means of the cathetometer. The point & was finally closed with wax by means of the spoon a, and the barometric pressure noted at this moment. If this pressure be H’, the pressure in the reservoir is H’—4. The reservoir was now weighed to ascertain P, the weight:of the mercury which it con- tained. It was then completely filled with mer- cury at zero, in order to have the weight P’ of the mercury in the reservoir and in the tube. If 5 be the coefficient of the cubical expan- sion of glass, and D the density of mercury at zero, the coefficient a of the cubical expansion of air is determined in the following manner :— Fig. 320 The volume of the reservoir and of the tube at zero is ae from the formula P=VD (126) ; consequently, this volume is / RS osu diclall | 2k xe at the temperature 7°, assuming, as is the case, that the reservoir and tube expand as if they were solid glass (325). But from the formula P = VD, the volume of air in the reservoir at zero, and under the pressure H’—4, is P’—P At the same pressure, but at 2°, its volume would be Lt abet +at), and by Boyle’s law (183), at the pressure H, at which the tube was sealed, this volume must have been CPT) (it ad) Tae (2) time 3 —s ib) H 4 = . . . . . . . . * e —_ Now the volumes represented by these formulze (1) and (2) are each equal to the volume of the reservoir and the tube at 7°: they are therefore equal. Removing the denominators, we have P’ (1 + 64) H=(P’—P) (1 +a/) (H’—4) MEEEORIO ET from which the value of a is deduced. 318 On Heat [337- The means of a great number of experiments between zero and 100? and for pressure between 300 millimetres and 500 millimetres, gave the following numbers for the coefficients of expansion for a single degree :— AIT , : . 0°003667 Carbonic acid. 3) °O°003710 Hydrogen : . 0'003661 Nitrous oxide . . - 0°003719 ‘Nitrogen . , . 0'003661 Cyanogen . 0°003877 ‘Carbonic oxide » 0°003667 Sulphurous acid . 0°003903 ‘These numbers, with which the results obtained by Magnus closely agree, show that the coefficients of expansion of the permanent gases differ very little; but that they are somewhat greater in the case of the more easily ‘condensable gases, such as carbonic and sulphurous acids. Regnault has further found that, at the same temperature, the coefficient of expansion of any gas increases with the pressure which it supports. Thus, while the coefficient of expansion of air under a pressure of 110 mm. is 0°003648, under a pressure of 3655 mm., or nearly five atmospheres, it is 0°003709. The ‘number found by Regnault for the coefficient of the expansion of air, 0°003667, is equal to ee x+g nearly ; and if we take the coefficient of expansion at 0'0036666 . . . it may be represented by the fraction 544, which is convenient for many purposes of calculation. The small differences in the expansibility of various gases may be ascribed ‘to the circumstance that when a gas is heated the relative positions of the atoms in the molecules are thereby altered ; and a certain amount of internal work is required for this, which is different for different gases (296). 338. Air thermometer.—The azr thermometer is based on the expan- sion of air. When it is used to measure small differences of temperature, it thas the same form as the tube used by Gay-Lussac in determining the expansion of air (fig. 318), that is, a capillary tube with a bulb at the end. The reservoir being filled with dry air, an index of coloured sulphuric acid or a drop of mercury is passed into the tube ; the apparatus is then graduated in Centigrade degrees by comparing the positions of the index with the indications of a mercurial thermometer. Of course the end of the tube must remain open ; otherwise, the air above the index condensing or ex- panding at the same time as that in the bulb, the index would remain stationary. A correction must be made at each observation for the atmo- ‘spheric pressure. When considerable variations of temperature are to be measured, the tube has a form like that used in Regnault’s experiments (figs. 319 and 320). By experiments, made ‘as described invart. 933742, 1P’, H, Hand Zmmay be found, and the coefficients a and 5 being known, the temperature 7 to which the tube has been raised is readily reduced from the equation (3). Regnault found that the air and the mercury thermometer agree up to 260°, but above that point mercury expands relatively more than air. In cases where very high temperatures are to be measured, the reservoir is made of-platinum. - The use of an air thermometer is seen in Dulong and Petit’s experiment (326) ; it was by such an apparatus that Pouillet measured the temperature corresponding to the colours which metals take when heated in a fire, and found them to be as follows :— —339] Density of Gases 319 Incipient red ; 825° Cet Darkerange . : 2 Tico? G: Pullkredy +: : e700 White ™. : : . 1300 Gheétry redex a. fe) Dazzling white. . 1500 In the measurement of high temperatures Deville and Troost used with advantage the vapour of iodine instead of air, and, as platinum has been found to be permeable to gases at high temperatures, they employed porce- lain instead of that metal. The expansion of gases has been determined by Jolly by means of a form of apparatus which is also a convenient form of air thermometer (fig. 321). A quadrangular post rests on a tripod ; on one side of this post is a graduated glass scale, while in the two others are grooves in which screw-blocks A and A’ can be slid up and down and adjusted at any height. A glass bulb a is prolonged in a tube bent twice, the end of which is provided with a stopcock, not shown in the figure, and in which can be fitted a glass tube R sup- ported by the block A. This again is fitted to a flexible india-rubber tube, at the other end of which is an open glass tube R’ fixed to the block A’. This tube contains mercury. The bulb a having been filled with dry air, the stopcock is closed, the tube R fixed, and the stopcock opened. The bulb a@ is then immersed to the stem in melting ice, and when it is supposed that the temperature is stationary, the tube R’ is moved up and down until the mercury in the other limb is ata mark S. The difference between the levels of the mercury at S and at R’ is noted. If the latter is higher the difference is added to, and if lower subtracted from, the barometric height at the time, to give the pressure / in the vessel a. The bulb a is then placed in a space at any constant temperature, and the same operation repeated to get the pressure /,, From the ratio of the total pressures in the two cases we get the coefficient of expansion a from the formula £:4,=1+atf:1+at’. By means of this apparatus Jolly found 0°00366957 for the value of a. 339. Density of gases.—The relative density of a gas, or its specific gravity, is the ratio of the weight of a certain volume of the gas to that of the same volume of air ; both the gas and the air being at zero and under a pressure of 760 millimetres. In order, therefore, to find the specific gravity of a gas, it is necessary to determine the weight of a certain volume of this gas at a pressure of 760 millimetres, and a’ temperature of zero, and then the weight of the same volume of air under the same conditions. For this purpose a large globe of about two gallons capacity is used, the neck of which is provided with a stopcock, which can be screwed to the air-pump. The globe is first weighed empty, and then full of air, and afterwards full of the gas in question. The weights of the gas and of the air are obtained by subtracting the weight of the exhausted globe from the weight of the globe filled, respectively, with 320 On Heat -[389- air and gas. The quotient, obtained by dividing the latter by the former, gives the specific gravity of the gas. It is difficult to make these determina- tions at the same temperature and pressure, and therefore all the weights are reduced to zero and the normal pressure of 760 millimetres. The gases are dried by causing them to pass through drying tubes before they enter the globe, and air must also be passed over potash to free it from carbonic acid. And as even the best air-pumps never produce a perfect vacuum, it is necessary to exhaust the globe until the manometer in each case marks the same pressure. The globe having been exhausted, dried air is allowed to enter, and the process is repeated several times until the globe is perfectly dried. It is then finally exhausted until the residual pressure in millimetres is e. The weight of the exhausted globe is gZ. Air, which has been dried and purified by passing through potash and calcium chloride tubes, is then allowed to enter slowly. The weight of the globe full of airis P. If H is the barometric height in millimetres, and 2° the temperature at the time of weighing, P—/is the weight of the air in the globe at the temperature ¢, and the pressure H —e. To reduce this weight to the pressure 760 millimetres and the tempera- ture zero, let a be the coefficient of the expansion of air, and 6 the coefficient of the cubical expansion of glass. From Boyle’s law the weight, which is P—f/at 7° and a pressure of H —e, would be Gir se under the pressure —eé 760 millimetres and at the same temperature 7°. If the temperature is 0°, the capacity of the globe will diminish in the ratio 1+6¢ to 1, while the weight of the gas increases in the ratio 1 : 1+ a¢,as follows from the problems in art. 336. Consequently, the weight of the air in the globe at 0° and at the ‘pressure 760 millimetres will be (P =f) 760 (I + aZ) SEAN CHEER Tale : ; : (1) Further, let a’ be the coefficient of expansion of the gas in question ; let P’ be the weight of the globe full of gas at the temperature 7 and the pres- sure H’, and let #’ be the weight of the globe when it is exhausted to the pressure e; the weight of the gas in the salts at the pressure 760 and the temperature zero will be 760 (I sat” : (2) Ge PD oy H’—2) (1+ 62) Dividing the latter formula by the former we obtain the density bo na A ) (H —e) (1+a’Z) (1 + 62) (P —f) (H’ -e) (1 +a?) (1 + 82’) If the temperature and the pressure do not vary during the experiment, H =H’ and ¢=/; whence D= Oe ea and, if a=a’, D=~, a 340. Regnault’s method of determining the density of gases.—Regnault so modified the above method that many of the corrections may be dispensed with. The globe in which the gas is weighed is suspended from one pan of ee | -340] Method of determining the Density of Gases 321 eed a balance, and is counterpoised by means of a second globe of the same dimensions, and hermetically sealed, suspended from the other. These two globes, expanding at the same time, always displace the same quantity of air, ‘and consequently variations in the temperature and pressure of the atmo- sphere do not influence the weighing. The globe, too, is filled with air or with the gas, at the temperature of zero. This is effected by placing it ina vessel full of ice, as shown in fig. 322. It is then connected witha three-way cock, A, by which it may be put into communication either with an air-pump, or with the tubes M and N, which are connected with the reservoir of gas. The tubes M and N contain substances which by their action on the gas dry and also purify it. The stopcock A being so turned that the globe is only connected with the air-pump, a vacuum is produced ; by means of the same cock, the con- nection with the pump being cut off, but established with M and N the SSS Ea —————— BG —s = gas soon fills the globe. But, as the exhaustion could not have been com- plete, and some air must have been left, the globe is again exhausted and the gas allowed to enter, and the process is repeated until it is thought that all airis removed. The vacuum being once more produced, a differential barometer (fig. 158), connected with the apparatus by the tube E, indicates the pressure of the residual rarefied gas ¢. Closing the cock B and de- taching A, the globe is removed from the ice, and after being cleaned. is weighed. This gives the weight of the empty globe 4; it is again replaced in the ice,-the stopcock A adjusted, and the gas allowed to enter, care being taken to leave the stopcocks open long enough to allow the gas in the globe to ac- quire the pressure of the atmosphere, H, which is marked by the barometer. The stopcock A is then closed, A removed, and the globe weighed with the same precautions as before. This gives the weight P’ of the gas and globe. Y 322 On Heat [340- The same operations are then repeated on this globe with air, and two corresponding weights # and P are obtained. The only correction necessary is to reduce the weights in the two cases to the standard pressure by the method described in the preceding paragraph.- The correction for temperature is not needed, as the gas is at the temperature of melting ice. The ratio of the weight of the gas to that of the air is thus obtained by the formula je Se Vet 341. Density of gases which attack metals.—For gases which attack the ordinary metals, such as chlorine, a metal stopcock cannot be used, and vessels with ground-glass stoppers (fig. 323) are substituted. The gas is introduced by a bent glass tube, the vessel being held either upright or inverted, according as the gas is heavier or lighter than air ; when the vessel is supposed to be full, the tube is withdrawn, the stopper inserted, and the weight taken. This gives the weight of the vessel and gas. If the capacity of the vessel be measured by means of water, the weight of the air which it contains is deduced, for the density of air at 0° C. and 760 millimetres pressure is +4, that of distilled water under the same circumstances. The weight of the vessel full of air, less the weight of the contained air, gives the weight of the vessel itself. From these three data—the weight of the vessel full of the gas, the weight of the air which it contains, and the weight of the vessel alone—the specific gravity of the gas is readily deduced, the necessary corrections being made for temperature and pressure. Relative density of gases at zero and at a pressure of 760 millimetres, that of atr being taken as untty. Alted f : . 1°0000 Sulphuretted hydrogen I'1912 Hydrogen . . 0'0693 Hydrochloric acid et 2540 Ammoniacal gas. LOS 8On Protoxide of nitrogen . 1°5270 Marsh gas . 1a 035590 Carbonic acid . oP gles 2or Carbonic oxide . . 09670 Cyanogen . : . 1'8600 Nitrogen ; eO'O7.14 Sulphurous acid . 1 Basra Binoxide of nitrogen . 1°0360 Chlorine ee eye ee, Oxygen : ; » PISLOgy Hydriodic acid . ie Bn ke) Regnault made the following determinations of the weight of a litre of the most important gases at o° C. and 760 mm. :— Air. . 1°293187 grms. Nitrogen . 1°256157 grms. Oxygen . UO EEAZOGO? wats, Carbonic acid 1°977414 ,, Hydrogen’ 2 7oo8otyo = s. ~342] Fusion. lis Laws 323 CHAP TRG. CHANGES OF CONDITION. VAPOUR 342. Fusion. Its laws.—The only phenomena of heat with which we have hitherto been engaged have been those of expansion. In the case of solids it is easy to see that this expansion is limited. For in proportion as a body absorbs a larger quantity of heat, the kinetic energy of the molecules is increased, and ultimately a point is reached at which the molecular attrac- tion is not sufficient to retain the body in the solid state. A new phenomenon is then produced ; melting or fuston takes place; that is, the body passes from the solid into the liquid state. Some substances, however, such as paper, wood, wool, and certain salts, do not fuse at a high temperature, but are decomposed. Many bodies have long been considered vefractory—that is, incapable of fusion ; but, in pro- portion as it has been possible to produce higher temperatures, their number has diminished. Gaudin succeeded in fusing rock crystal by means of a lamp fed by a jet of oxygen ; and Despretz, by combining the effects of the sun, the voltaic battery, and the oxy-hydrogen blowpipe, melted alumina and magnesia, and softened carbon so as to be flexible, which is a condition near that of fusion. It has been found experimentally that the fusion of bodies is governed by the two following laws :-— I. Every substance begins to fuse at a certain temperature, which ts invariable for each substance, tf the pressure be constant. Il. Whatever be the intensity of the source of heat, from the moment fuston begins, the temperature of the body ceases to rise, and remains constant until the fusion ts complete. Melting points of certain substances. Ethylene . : .—169° Phosphorus. : ee Ae Ammonia. : . 75 Spermaceti ; : phd Mercury . é . —38°8 Potassium : : ae 55 Oil of turpentine. . —27 Margaric acid . ; bn Bromine . d ; . -12 Stearine . : : dts 00) ier ay O White wax smi hOS Nitrobenzene . ; . +3°0 Wood’s fusible metal RAO s) Formic acid . : Ose eAT CACC «4. : 7G Acetic acid. . Pea, Sodium . ; ; WO nOO Butter! 3): Htc Rose’s fusible metal. a On. Rubidium ; PERO Sulphur . : . ee! 324 On. Heat [342— Benzoic acid . 920%" NMagwiesium 2); ; Li F5or Indium. : S > BEZO Aluminium. SSO Tink: 228 Sodium chloride Anos Bismuth . ’ . 246 vers © : : . 980 Cadmium. B wUReT Gold : : : . 1060 Lead : : : iy As Copper”. : : “7068 Zinc. : ‘ : y yAze Potassium sulphate . . O73 Antimony ; ; eerie Iron. : : s . 1500 Arsenic . hw iV 590 Platinum . ; Lega Potassium iodide . ft. 023 Iridium . : : . 1950 Some substances pass from the solid to the liquid state without showing any definite melting point ; for example, glass and iron become gradually softer and softer when heated, and pass by imperceptible stages from the solidi-to the liquid condition. This inter- mediate condition is spoken of as the state of vitreous fusion. Such substances may be said to melt at the lowest temperature at which perceptible softening occurs, and to be fully melted when the further elevation of temperature does not make them more fluid ; but no precise temperature can be given as that of their melting points. The determination of the melting point of a body is a matter of considerable im- portance in fixing the identity of many chemical compounds, and is moreover of — frequent practical application in determin- ing the commercial value of tallow and other fats. It is done as follows :—A portion of the substance is melted in a watch-glass, and a small quantity of it sucked into a fine capil- lary tube, which is then placed in a bath of clear water (fig. 324) attached to a ther- mometer, and the temperature of the bath is gradually raised until the substance is completely melted, which from its small mass is very easily observed. The bath is then allowed to cool, and the solidi- fying point noted ; and the mean of the two is taken as the true melting point. 343. Influence of pressure on the melting point.—Lord Kelvin and Clausius deduced from the principles of the mechanical theory of heat that, with an increase of pressure, the melting point of a body must be raised. All bodies which expand on passing from the solid to the liquid state have to perform external work—namely, to raise the pressure of the atmosphere by the amount of this expansion. Under ordinary circumstances, the amount of external work which solids and liquids thus perform is so small that it may be neglected. But, if the external pressure be increased, the power of overcoming it can only be obtained by an increase of the kinetic Fig. 324. 4 -343] Lnfiuence of Pressure on the Melting Point 325 energy of the molecules. More external work is thereby done ; the tempera- ture of fusion and the heat of fusion are both increased. Bunsen examined the influence of pressure on the melting point by means of the apparatus represented in fig. 325, somewhat resembling in appearance a siphon barometer. The tube is closed at bothends. The part from @ to c contains mercury except at the end J, where the substance under examination is put. Air occupies the portion which is carefully calibrated. The lower part of the apparatus is placed in a water bath, the mercury being heated as well as the substance. The expansion of the mercury compresses the air, the elastic force of which reacts on the substance and exerts on it a gradually increasing pressure. It only then remains to observe the temperature at which the es TM Fig. 326. substance solidifies, and the corresponding pressure at that moment. In this way Bunsen found that spermaceti, which melts at 48° under a pressure of 1 atmosphere, melts at 51° under a pressure of 156 atmospheres. Hopkins found that spermaceti melted at 60° under a pressure of 519 atmospheres and at 80° under 792 atmospheres; the melting point of sulphur under these pressures was respectively 135° and 141° But with regard to those bodies which contract on passing from the solid to the liquid state, and of which water is the best example, the reverse is the case. Melting ice has no {external work to perform, since it has no external pressure to overcome; on the contrary, in melting, it absorbs external work, which, transformed into heat, renders a smaller quantity of heat necessary; the external work acts in the same direction as the internal heat—namely, in breaking up the crystalline aggregates. Yet these differ- ences of temperature must be but small for the molecular forces in solids 326 On Fleat [343— preponderate far over the external pressure ; the internal work is far greater than the external. Lord Kelvin found that increase of pressure lowered the melting point of ice. The apparatus consisted of a piezometer (fig. 326); a thick leaden ring divided the vessel into two compartments, the upper one of which contained water and the lower one crushed ice, which was thus prevented from rising. This also served to support a thermometer enclosed in a very stout tube, and a manometer with compressed air. The pressures were exerted by means of a screw piston V. Lord Kelvin thus found that pressures of 81 and 16°8 atmospheres lowered the melting point of ice by o-059° and o'126° respectively. These results justify the theoretical previsions of his brother, Professor J. Thomson, according to which an increase of pressure of 7 atmospheres lowers the melting point of ice by 0:00747° C.,so that a pressure of 135 atmospheres, or about 2,000 pounds to the square inch, would lower the melting point 1° C. This lowering of the melting point is also shown by the experiment of Mousson. The apparatus consists of a stout steel tube closed at one end by a screw and with a screw piston at the other (fig. 327). The tube is filled with water and a metal bullet lo ™ introduced. When the apparatus f 4 is closed it is inverted so that the f (Pi) i ul bullet rests on the piston, and | unarare placed thus in a freezing mixture ; the water freezes and presses the ball against the piston. This is then turned again, and pressure is gradually applied by turning the handle of the screw. When the lower screw is opened the copper ball falls out, and is followed by a thick cylinder of ice which must have been formed at the moment of opening. Hence the ice must, by a pressure estimated at 13,000 atmospheres, have been converted into water at about — 18° C. This influence is likewise readily demonstrated by an experiment of von Helmholtz (fig. 328). Water is boiled in a flask until all air is expelled,and it is then closed. It is afterwards placed in a freezing mixture so that some ice forms inside. This is then allowed to melt again in great part, and the flask is placed in a vessel of water containing lumps of ice. It is then found that the still unfrozen water inside the flask freezes while that of the outside is melting. 344. Alloys. Fluxes.—Alloys are generally more fusible than any of the metals of which they are composed ; for instance, an alloy of 5 parts of tin and 1 of lead fuses at 194°. The alloy known as Rose’s fusible metal, which consists of 4 parts of bismuth, 1 part of lead, and 1 of tin, melts at 94°, and Fig. 328. —-346] Solution Car: an alloy of 1 or 2 parts of cadmium with 2 parts of tin, 4 parts of lead, and 7 or 8 parts of bismuth, known as Wood's fusible Devel, melts peceea 66° and 71° C. An alloy of potassium and sodium in equivalent proportions is liquid at the ordinary temperature. Fusible alloys are of extended use in soldering and in taking casts. Steel melts at a lower temperature than iron, though it contains carbon, which is almost completely infusible. Mixtures of the fatty acids melt at lower temperatures than the pure acids. A mixture of potassium and sodium chlorides fuses at a lower temperature than either of its constituents ; this is also the case with a mixture of potassium and sodium carbonates, especially when they are mixed in the proportion of their chemical equivalents. An application of this property is met with in the case of jfwxes, which are much used in metallurgical operations. They consist of substances which, when added to an ore, partly by their chemical action, help the reduction of the substance to the metallic state, and, partly, by presenting a readily fusible medium, promote the agglomeration of the individual particles with the formation of a mass of metal or regudits. 345. Latent heat.—Since, during the passage of a body from the solid to the liquid state, the temperature remains constant until the fusion 1s com- plete, whatever be the intensity of the source of heat, it must be concluded that, in changing their condition, bodies absorb a considerable amount of heat, the only effect of which is to maintain them in the liquid state. This heat, which is not indicated by the thermometer, is called /atent heat or latent heat of fusion, an expression which, though not in strict accordance with modern ideas, is convenient from the fact of its universal recognition and employment (470). An idea of what is meant by latent heat may be obtained from the follow- ing experiment :—If a pound of water at 80° is mixed with a pound of water at zero, the temperature of the mixture is 40°. But if a pound of pounded zce at zero is mixed with a pound of water at 80°, the ice melts and two pounds of water at zero are obtained. Consequently the mere change of a pound of ice to a pound of water at the same temperature requires as much heat as will raise a pound of water through 80°. This quantity of heat represents the latent heat of the fusion of ice, or the latent heat of water. Every liquid has its own latent heat, and in the chapter on Calorimetry we shall show how this is determined. 346. Solution._-A body is said to a@ssolve when it becomes liquid in consequence of an attraction between its molecules and those of a liquid. Gum arabic, sugar, and most salts dissolve in water. The weight dissolved in a given quantity of water generally increases with the temperature, as is seen.from the following table :— Common Salt Nitre Sodium Sulphate Copper Sulphate| Zinc Sulphate ° O 35 13 32 115 20 37 21 53 42 131 100 40 247 42 203 654 Fost On Heat ‘[346- When a liquid has dissolved as much as it can at a particular tempera- ture, it is said to be saturated. The belief formerly held that the properties of a liquid were altered when a body was dissolved in it nearly in proportion to the quantity dissolved is not confirmed by the results of electrolysis. The first small quantity dis- solved produces a far greater change than a subsequent equal quantity. When a salt dissolves in water it may be supposed that the vibrations of its bounding molecules, which are in contact with the solvent, possibly owing to the attraction of the solvent, or owing to capillarity, increase their amplitude so that they get beyond the sphere of action of the other molecules of the salt, and thereby assume a progressive motion like the molecules of a gas. Like them they then exert a pressure against the sides of the containing vessel, which is called osmotic Dressure (141). During solution, as well asduring fusion, a certain quantity of heat always becomes latent, and hence it is that the solution of a substance usually produces a diminution of temperature. In certain cases, however, instead of the temperature being lowered, it actually rises, as when caustic potash is dissolved in water. This depends upon the fact that two simultaneous and contrary phenomena are produced. The first is the passage from the solid to the liquid condition, which always lowers the temperature. The second is the chemical combination of the body dissolved with the liquid, which, as in the case of all chemical combinations, produces an increase of temperature. Consequently, as the one or the other of these effects pre- dominates, or as they are equal, the temperature either rises or sinks, or remains constant. 347. Solidification — Solidification or congelation is the passage of a body from the liquid to the solid state. This phenomenon is expressed by the two following laws :— I. Every body, under the same pressure, solidifies ata fixed temperature, which ts the same as that of fusion. Il. From the commencement to the end of the solidification, the tempera- ture of a liguid remains constant. Certain bodies, more especially some of the fats, present an exception to the first law, in so far that by repeated fusions they seem to undergo a molecular change which alters their melting point. The second law is the consequence of the fact that the latent heat absorbed during fusion becomes free at the moment of solidification. The application of the very low temperatures which can now be so readily procured has lessened the number of those liquids which it was formerly thought could not be solidified. By allowing liquid ethylene (388) to boil in a vacuum, Wroblewski and Olszewski obtained a temperature of — 136°. They observed that carbon disulphide solidified at —116° and fused again at about —110°. Absolute alcohol became viscid at —129° and solidified at —130°5°. Pure ether solidifies at — 1297, Water containing a salt dissolved always solidifies below zero ; the de- pression of the freezing point is proportional to the weight of salt dissolved, at any rate for weak solutions. This is known as Blagden’s law. . If several salts which have no chemical action on each other be dis- solved in a given weight of water, the lowering of the freezing point is the —347] Solidification 329 sum of the depressions which each of them would produce separately if dissolved in the same quantity of water. When the numbers observed in any experiment of this kind do not agree with those calculated, this points to the occurrence of some chemical action between the substances dissolved, and the observation of such devia- » tions has been of use in questions of chemical statics. The elaborate researches of Raoult on the temperature of solidification of solutions of bodies in water and other solvents have led to important conclusions. The temperature at which a solution solidifies, or its freezing point, is always lower than that of the pure solvent. If P be the weight in grammes of any substance dis- solved in 100 grammes of a solvent, and C be the depression in the freez- ing point observed, then : SHAM is the depression which would be pro- duced by dissolving ove gramme of the substance in Ioo grammes of the solvent, and is known as the coefficient of depression. A comparison of the values for A for various substances and the same solvent shows that they differ considerably ; this 1s not so if we compare the depressions produced by molecular weights of the sub- stances. That is, if we multiply the value of A in the above equation by M, the molecular weight of the sub- stance dissolved, we obtain the de- pression which would be produced by dissolving one gramme-mniole- cule of a body in 100 grammes of the solvent, or the coefficient of molecular depression ; this is called T, and we have T = oe Now it is found that in a very large number of cases the value of T, for one and the same solvent, is a constant number; it has the value 19 for water, 39 for glacial acetic acid, and 49 for benzene. _ This relation is of great value ; by means of a simple determination of the freezing point of a solid we can calculate the molecular weight of substances 330 On Heat [347— which cannot be obtained in the gaseous state without being decomposed. This is conveniently effected by means of the apparatus represented in fig. 329. The solvent is contained in the vessel A, and the substance to be investigated is introduced by the lateral aperture A’. A is surrounded by a wide glass tube B containing air, and this again is placed in a wider vessel C which contains the freezing mixture ; for experiments with benzene or glacial acetic acid as a solvent, this is bruised ice, and with water a mixture of ice and salt. The liquid from these may be drawn off by a siphon placed .through 4. In A is a platinum stirrer 7, and a delicate thermometer D, indicating the +45 of a degree. C is also a Stirrer. Since C and P are known, M is determined from the formula ee where T is the constant for the particular solvent employed, which is ordinary glacial acetic acid in the majority of cases. Van ‘t Hoff has shown that the coefficient of depression ¢ may be | calculated by means of the formula ¢ = Siete @ j fusion, and T the temperature of fusion in absolute degrees (507). : In the case of such salts as potassium chloride the molecular depressions are greater than is required by the law, being nearly twice F as much as in indifferent bodies like sugar; this is probably due : to the fact that a greater or less proportion of the salt is a@ssoctated where wis heat of 40 cha into its constituents, a phenomenon analogous to the dissociation is of vapours, to which are due abnormal vapour densities (394). f 348. Crystallisation.— Generally speaking, bodies which pass [| 20 ’ i : slowly from the liquid to the solid state assume regular geometri- i cal forms, such as the cube, prism, rhombohedron, &c. ; these are Ho called crystals. Ifthe crystals are formed from a body in fusion, such as sulphur or bismuth, the crystallisation is said to take place by the dry way. The crystallisation is said to be by the moist way when it takes place owing to the slow evaporation of a solution of a salt, or when a solution saturated at a higher temperature is allowed to cool slowly. Snow, ice, and many salts present examples of crystallisation. 349. Retardation of the point of solidification.—The freezing . point of pure water can be diminished by several degrees, if the water be previously freed from air by boiling and be then kept in a perfectly still place. In fact, it may be cooled to —15° C., and even lower, without freezing. But when it is slightly agitated, the liquid at once solidifies. This may be conveniently shown by means of the apparatus represented in fig. 330, which consists of a delicate thermometer, round the bulb of which is a wider one containing some water. Before sealing at a the whole outside bulb was filled with water, which was then boiled out and sealed so that over the water the space is quite empty. This is clamped in a retort stand, and ether is dropped on it, that which has dropped off, and become colder, being used over and over again. In this way the temperature may soon be reduced to —6°, and if then the bulb be shaken, part of the water Fig 330. —349] Retardation of the Point of Solidification 331 freezes and the temperature rises to zero. The smaller the quantity of liquid, the lower is the temperature to which it can be cooled, and the greater the mechanical disturbance it supports without freezing. Fournet has observed the frequent occurrence of mists formed of particles of liquid matter sus- pended in an atmosphere whose temperature was 10° or even 15° below zero. A very rapid agitation also prevents the formation of ice. Thisis also the case with all actions which, hindering the molecules in their movements, do not permit them to arrange themselves in the conditions necessary for the solid state. Despretz was able to lower the temperature of water contained in fine capillary tubes to —20° without their solidifying. This experiment shows how it is that plants in many cases do not become frozen even during severe cold, as the sap is contained in very fine capillary vessels. If water contains salts, or other foreign bodies, its freezing point is lowered. Sea water freezes at —2°5° to —3°.C.; the ice which forms is quite pure, and a saturated solution remains. In Finland advantage is taken of this property to concentrate sea water for the purpose of extracting salt from it. If water contains alcohol, precisely analogous phenomena are observed ; the ice formed is pure, and practically all the alcohol is contained in the residue. ; Dufour has observed some very curious cases of liquids cooled out of contact with solid bodies. His mode of experimenting was to place the liquid in another of the same specific gravity but of lower melting point, in which it is insoluble. Drops of water, for instance, suspended in a mixture of chloroform and oil, usually solidified between —4° and —12°, while still smaller globules cooled down to —18° or —20°. Contact with a frag- ment of ice immediately set up congela- tion. Globules of sulphur (which solidifies at 115°) remained liquid at 40° ; and glo- bules of phosphorus (solidifying point 42°) at 20°. The superfusion of phosphorus may be illustrated by the experiment repre- sented by fig. 331. A long test tube containing phosphorus, A, and covered ‘with a layer of water, is fixed along with a thermometer T in a large flask con- taining water. This flask is raised to a temperature of about 44° at which the phosphorus fuses, and is then withdrawn from the source of heat; as its mass is considerable, it cools very slowly, and the phosphorus remains liquid even at ordinary temperatures. A glass rod may even be dipped into it without change ; but if the rod be rubbed along solid Fig. 331. phosphorus so as to detach a small par- ticle it at once brings about solidification if dipped in the melted mass. When a liquid solidifies after being cooled below its normal freezing point 332 On Heat [349— the solidification takes place very rapidly, and is accompanied by a disen- gagement of heat, which is sufficient to raise its temperature from the point at which solidification begins up to its ordinary freezing point. This is well seen in the case of sodium hyposulphite, which melts in its own water of crystallisation at 45°, and when carefully cooled will remain liquid at the ordinary temperature of the atmosphere. If it then be made to solidify by agitation, or by adding a small fragment of the solid salt, the rise of tems perature is distinctly felt by the hand. In this case the heat, which had become latent in the process of liquefaction, again becomes free, and a portion of the substance remains melted ; for it is kept hauig by the heat of solidification of that which has solidified. 350. Change of volume on solidification and liquefaction.—The rate of expansion of bodies generally increases as they approach their melting points, and is in most cases followed by a further expansion at the moment of liquefaction, so that the liquid occupies a greater volume than the solid from which it is formed. The apparatus represented in fig. 332 is well adapted for exhibiting this phenomenon. It consists of a glass tube, aé, containing water or some other suitable liquid, to which is carefully fitted a cork with a graduated glass tube c. This forms, in fact, a thermometer, and the values of the divisions on the tube ¢ are determined in terms of the capacity of the whole apparatus. A known volume of the substance is placed in the tube aa and the cork inserted ; the apparatus is then, placed in a space at a temperature very little below the melting point of the body in question, until it has acquired its temperature, and the position of the liquid in ¢ is noted. The temperature is then allowed to rise slowly, and the position noted when the melting is complete. Knowing then the difference in the two readings and the volume of the substance under experiment, and making a correction for the expansion of the liquid and of the glass, it is easy to deduce the increase due to the melting alone. Phos- phorus, for instance, increases about 3°4 per cent. on liquefaction ; that is, 100 volumes of solid phosphorus at 44° (the melting point) become 103°4 at the same temperature when melted. Sulphur expands about 5 per cent. on liquefying, and stearic acid about II per cent. Water presents a remarkable exception ; it expands at the moment of solidifying, or contracts on melting, by about Io per cent. One volume of ice at 0° gives 09178 of water at 0°, or I volume of water at 0° gives I‘102 of ice at the same temperature. In consequence of this expansion, ice floats on the surface of water. Accord- ing to Dufour, the specific gravity of ice is 0°9178; Bunsen found for ice which had been made from water freed from air by boiling the somewhat smaller number 0°91674. The increase of volume in the formation of ice is accompanied by an expansive force which sometimes produces powerful mechanical effects, of which the bursting of water-pipes and the breaking of jugs containing water are familiar examples. The splitting of stones, rocks, and the swelling up of moist ground during frost, are caused by the fact that water penetrates Fig. 332. ~851] Freezing Mixtures 333 into the pores and there becomes frozen ; in short, the great expansion of water on freezing is the most active and powerful agent of disintegration on the earth’s surface. The expansive force of ice was strikingly shown by some experiments of Major Williams in Canada. Having quite filled a 13-inch iron bomb-shell with water, he firmly closed the touch-hole with an iron plug weighing three pounds and exposed it in this state to the frost. After some time the iron plug was forced out with a loud explosion, and thrown. to a distance of 415 feet, and a cylinder of ice 8 inches long issued from the opening. In another case the shell burst before the plug was driven out, and in this case a sheet of ice spread out all round the crack (fig. 333). It is probable that under the great pressure some of the water still remained liquid (343) up to the time at which the resistance was overcome ; that it then issued from the shell in a liquid state, but at a temperature below 0°, and therefore instantly began to solidify when the pressure was removed, and thus retained the shape of the orifice whence it issued. Cast-iron, bismuth, and antimony expand on solidifying, like water, and can thus be used for casting ; but gold, silver, and copper contract, and hence coins of these metals cannot be cast, but must be stamped with a die. An iron tube filled with molten bismuth and closed by a screw, is broken as the bismuth becomes solid. This increase of volume when liquids solidify, and the correlated decrease on melting again, in the case of water and some other crystalline substances such as bismuth, are probably due to the fact that such bodies are aggregates of small crystalline masses, which are grouped in such a way that small interstices are formed. When the liquid melts these interstices fill up owing to the mobility of the molecules, and, notwithstanding the greater space which each individual group takes up, owing to expansion, there is on the whole a decrease of volume. 351. Freezing mixtures.—The absorption of heat in the passage of bodies from the solid to the liquid state has been used to produce artificial cold. This is effected by mixing together bodies which have an affinity for each other, and of which one at least is solid, such as water and a salt, ice and a salt, or an acid and a salt. Chemical affinity accelerates the fusion or solution ; the portion which melts or dissolves robs the rest of the mixture of a large quantity of sensible heat, which thus becomes latent. In many cases a very considerable diminution of temperature is produced. The following table gives the names of the substances mixed, their pro- portions, and the corresponding diminutions of temperature :— Parts Reduction of Substances by weight temperature Sodium sulphate . , , ; 8 P l + 10° to —17° Hydrochloric acid . Pounded ice or snow 5) 2) : Common salt : : F ; I} 3) 2) rlO AO =a1o Sodium sulphate Dilute nitric acid + 10° to —19° On Heat [351- 334 Parts Reduction of Substances by weight temperature Sodium sulphate . : ‘ ; 6) Ammonium nitrate 5. + 10° to — 26° Dilute nitric acid . . y, Sodium phosphate : 9) 3 ‘ Dilute nitric acid . ; 4) Tiare ae eae If the substances taken be themselves previously cooled down, a still more considerable diminution of temperature is occasioned. Freezing mixtures are frequently used in chemistry, in physics, and in domestic economy. One form of the portable ice-making machines which have come into use during the last few years consists of a cylindrical metallic vessel divided into four concentric compartments. In the central one is placed the water to be frozen; in the next there is the freezing mixture, which usually consists of sulphate of sodium and hydrochloric acid ; 6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in an hour. The third compartment also contains water, and the outside one ‘contains some badly conducting substance, such as cotton, to cut off the influence of the external temperature. The best effect is obtained when pretty large quantities (2 or 3 pounds) of the mixture are used, and when the ingredients are intimately mixed. It is also advantageous to use the machines for a succession of operations. 352. Guthrie's researches.—It appears from the experiments of the late Dr. Guthrie that what are called freezing mixtures may be divided into two classes—namely, those in which one of the constituents is liquid and those in which both are solid. The temperature indicated by the thermometer placed in a freezing mixture 1s, of course, due to the loss of heat by the thermometer in the liquefying freezing mixture, and is measured by the rate of such loss. The quantity of heat absorbed by the freezing mixture is obviously the heat required to melt the constituents, together with (+) the heat of combination of the constituents. When one constituent is liquid, as when hydrochloric acid is added to ice, then a lower temperature is got by previously cooling the hydrochloric acid. There is no advantage in cooling the ice. But when both constituents are solid, as in the case of the ice-salt freezing mixture, there is no advantage to be gained by cooling one or both constituents. Within very wide limits it is also in the latter case a matter of indifference as to the ratio between the constituents. Nor does it matter whether the ice is finely powdered as snow or in pieces as large as a pea. The different powers of various salts when used in conjunction with ice as freezing mixtures appear to have remained unexplained until Guthrie showed that, with each salt, there is always a minimum temperature below which it is impossible for an aqueous solution of any strength of that salt to exist in the liquid form ; that there is a certain strength of solution for each salt which resists solidification the longest, that is, to the lowest temperature. Weaker solutions give up ice on being cooled, stronger solutions give up the salt either in the anhydrous state or in Sombuiation built water. A solution of such a strength as to resist solidification to the lowest temperature, was called by Guthrie a cryohydrate. It is of such a strength that when cooled ~355] Elastic Force of Vapour 335 below o° C. it solidifies as a whole; that is, the ice and the salt solidify together and form crystals of constant composition and constant melting and the same solidifying temperatures. The liquid portion of a freezing mixture, as long as the temperature is at its lowest, is, indeed, a melted cryohydrate. The slightest depression of temperature below this causes solidification of the cryohydrate, and hence the temperature can never sink below the solidifying temperature of the cryohydrate. Guthrie also showed that colloid bodies, such as gum and gelatine, neither raise the boiling point of water nor depress the solidifying point, nor can they act as elements in freezing mixtures. VAPOURS. MEASUREMENT OF THEIR PRESSURE. 353. Vapours.—We have already seen (155) that vapours are the aériform fluids into which volatile substances, such as ether, alcohol, water, and mercury, are changed by the absorption of heat. Volatile liguids are those which thus possess the property of passing into the aériform state, and fixed liguids are those which do not form vapour at any temperature without undergoing chemical decomposition, such as the fatty oils. Ice and snow volatilise in closed spaces, forming crystals on the cooled parts. The forma- tion of vapour is thus not restricted to the liquid state, and in some bodies, such as arsenic, the boiling point is below the freezing point. As the boiling point is raised by pressure it is possible to liquefy such bodies also, by applying sufficient pressure. Iodine melts at 104° and boils at 175° under ordi- nary pressure. It therefore evaporates after melting ; | but at a pressure of 250 mm. its boiling point is below its melting point, and it then evaporates without melt- ing. Even at ordinary temperatures a considerable quantity volatilises without melting. Vapours are transparent, like gases, and generally colourless ; there are only a few coloured liquids which also give coloured vapours. 354. Vaporisation.—The passage of a liquid into the gaseous state is designated by the general term vaporisation; the term evaporation especially refers to the slow production of vapour at the free surface of a liquid, and doz/ig to its rapid pro- duction in the mass of the lquid itself. We shall presently see (367) that at the ordinary atmospheric pressure, ebullition, like fusion, takes place at a definite temperature. This is not the case with evaporation, which occurs even with the same liquid at very different temperatures, although the formation of a vapour seems to cease below a certain point. Mercury, for example, is stated to give no vapour below — 10°, nor sulphuric acid below 30°. 355. Elastic force of vapour.—Like gases, vapours have a certain elastic force, in virtue of which they exert pressures on the sides of vessels in which they are contained. The elastic force of vapour may be demonstrated 336 On Heat | (355- by the following experiment :—A quantity of mercury is placed in a bent glass tube (fig. 334), the shorter leg of which is closed; a few drops of ether are then passed into the closed leg and the tube is immersed in a water bath at a temperature of about 45°. The mercury then sinks slowly in the short branch, and the space aé is filled with a gas which has all the appearance of air, and whose elastic force counterbalances the pressure of the column of mercury cd, and the atmospheric pressure on @. This gas is the vapour of ether. If the water be cooled, or if the tube be removed from the bath, the vapour which fills the space aé disappears, and the drop of ttt i AO fe ‘4 ether is reproduced. If, on the contrary, the bath be heated still higher, the level of the mercury descends below 4, indicating an increase in the elastic force of the vapour. 356. Formation of vapour in a vacuum.—The change from liquid to vapour takes place very slowly when the liquid is freely exposed to the air. The atmosphere is an obstacle to the vaporisation. In a vacuum there is no resistance, and the formation of vapour is instantaneous, as is seen in the following experiment :—Four barometer tubes, filled with mercury, are im- mersed in the same trough, fig. 335. One of them, A, serves as a barometer, ~358] Unsaturated Vapours 337 and a few drops of water, alcohol, and ether are respectively introduced into the tubes B, C, D. When the liquids reach the vacuum, a depression of the mercury is at once produced. And as this depression cannot be caused by the weight of the liquid, which is an extremely small fraction of the weight of the displaced mercury, it must be due to the formation of some vapour whose elastic force has depressed the column of mercury. The experiment also shows that the depression is not the same in all the tubes ; it is greater in the case of alcohol than of water, and greater again with ether than with alcohol. We consequently obtain the two following laws of the formation of vapours :— I. In a vacuum all volatile liguids are instantaneously converted into vapour. Il. Ad the same temperature the vapours of different liquids have different pressures. For example, at 20° the pressure of ether vapour is 25 times as great as that of aqueous vapour. 357. Saturated vapour. Maximum of pressure.—When a very small quantity of a volatile liquid, such as ether, is introduced into a barometer tube, it is at once completely vaporised, and the column of mercury is not ‘depressed to its full extent; for if some more ether be introduced -the depression increases. The ether, if still more be added, finally ceases to vaporise, and remains in the liquid state. There is, therefore, for a certain temperature, a limit to the quantity of vapour which can be formed in a given space. This space is accordingly said to be saturated. Further, when the vaporisation of the ether ceases, the depression of the mercurial column stops. And hence there is a limit to the pressure of the vapour, a limit which, as we shall presently see (358), varies with the temperature. To show that, in a closed space, saturated with vapour and containing liquid 27 excess, the temperature remaining constant, there is a maximum of pressure which the vapour cannot exceed, a barometric tube is used which dips in a deep bath (fig. 336). This tube is filled with mercury, and then so much ether is added as to be in excess after the Torricellian vacuum is saturated. The height of the column of mercury is next noted by means of the scale graduated on the tube itself. Now, whether the tube be depressed, which tends to compress the vapour, or whether it be raised, which tends to expand it, the height of the column of mercury is constant. The pressure of the vapour remains constant in the two cases, for the depression neither increases nor diminishes it. Hence it is concluded that when the saturated vapour is compressed, a portion returns to the liquid state ; that when, on the other hand, the pressure is diminished, a portion of the excess of liquid vaporises, and the space occupied by the vapour is again saturated ; but in both cases the pressure and the density of the vapour remain constant. 358. Unsaturated vapours.—It will be seen from what has been said, that vapours present two very different states, according as they are saturated or not. In the first case, where they are saturated and in contact with the liquid, they differ completely from gases, since for a given temperature they can neither be compressed nor expanded ; their elastic force and their density remain constant. In the second case, on the contrary, where they are not saturated, they z 338 On Heat [358-- exactly resemble gases. For if the experiments (fig. 336) be repeated, only a small quantity of ether being introduced, so that the vapour is not saturated, and if the tube be then slightly raised, the level of the mercury is seen to rise, which shows that the elastic force of the vapour has diminished. Similarly, by immersing the tube still more, the level of the mercury sinks. The vapour consequently behaves just as a gas would do, its pressure diminishing when the volume increases, and vice versa ; and as in both cases the volume of the vapour is inversely as the pressure, it is concluded that umsaturated vapours obey Boyle's law. When an unsaturated vapour is heated, its volume increases like that of a gas ; and the number 000367, which is the coefficient of the expansion of air, may be taken for that of unsaturated vapours. Hence we see that the physical properties of unsaturated vapours are comparable with those of gases, and that the formulz for the compressibility and expansibility of gases (184 and 336) also apply to unsaturated vapours. 359. Pressure of aqueous vapour below zero.—In order to measure the elastic force of aqueous vapour below zero, Gay-Lussac used two baro- meter tubes filled with mercury, and placed in the same reservoir (fig. 337). The straight tube, A, serves as a barometer ; the other, C, is bent, so that part of the Torricellian vacuum can be surrounded by a freezing mixture, B (351). When a little water is admitted into the bent tube, the level of the mercury sinks below that in the tube A, to an extent which varies with the temperature of the freezing mixture. At o° the depression is . 4°54 millimetres 9 ee ” ” » 4°25 ” 2). ee ” ” : 3°63 ” ey Oe 5° ” 2a oh) » ZI ” 2) ee Tie ” ” 2 2°67 ” 3) gaa! 10° ” ” . 2°08 ” ” 310" ” ” 2 0°84 ” ” = 307 ” ” : 0°36 ” These depressions, which must be due to the pressure of aqueous vapour in the space BC, show that even at very low temperatures there is always some aqueous vapour in the atmo- sphere. Although in the above experiment the part B and the part C are not both immersed in the freezing mixture, we shall presently see that when two communicating vessels are at different temperatures, the tension of the vapour is the same in both, and always corresponds to that of the lower temperature. That water evaporates even below zero follows from the fact that wet linen exposed to the air during frost becomes first stiff and then dry, showing that the particles of water evaporate even after the latter has been converted into ice. ~360] Pressure of Aqueous Vapour 339 360. Pressure of aqueous vapour between zero and one hundred degrees.—i. Dalton’s method. Dalton measured the elastic force of aqueous vapour between o° and 100° by means of the apparatus represented in fig. 338. Two barometer tubes, A and B, are filled with mercury, and inverted in an iron bath full of mercury, which is placed on a furnace. The tube A contains a small quantity of water. The tubes are supported in a cylindrical vessel, open top and bottom and full of water, the temperature of which is indicated by the thermometer. The bath being gradually heated, the water in the cylinder becomes heated too; the water which is in the tube A : Ls Ra mH nl WAT = l yy TTT TT = == ZA \" z: | | ih ie||/>s oe ———e Fig. 338. vaporises, and in proportion as the pressure of its vapour increases, the mercury sinks. The depressions of the mercury corresponding to each degree of the thermometer are indicated on the scale E, and in this manner a table of the elastic forces between zero and 100° has been constructed. ii. Regnaul’s method.—Dalton’s method is wanting in precision, for the temperature of the liquid in the cylinder is not everywhere the same, and consequently the exact temperature of the aqueous vapour is not shown. Regnault’s apparatus is a modification of that of Dalton. The cylindrical glass vessel is replaced by a large cylindrical zinc drum, MN (fig. 339), in the Z2 340 On Heat [3860- bottom of which are two tubulures. The tubes A and B pass through these tubulures, and are fixed by caoutchouc collars. The tube containing vapour, B, is connected with a flask, a, by means of a brass three-way tube, O. The third limb of this tube is connected with a drying tube, D, containing pumice charged with sulphuric acid, which is connected with the air-pump. When the flask @ contains some water, a small portion is distilled into B by gently heating the flask. Exhausting, then, by means of the air-pump, the water distils continuously from the flask and from the barometric tube towards D, which condenses the vapour. After having vaporised some quantity of water, and when it is thought that the air in the tube is with- drawn, the capillary tube which connects B with the three-way tube is sealed. The tube B being thus closed, it is experimented with asin Dalton’s method. The drum, MN, being filled with water, is heated by a spirit lamp, i} i! | YAWN yyy, pen which is screened from the tubes by a wooden board. By means of a stirrer, K, all parts of the liquid are kept at the same temperature. In the side of the drum is a glass window, through which the height of the mercury in the tubes can be read off by means of a cathetometer ; from the difference in these heights, reduced to zero, the tension of vapour is deduced. By means of this apparatus, the elastic force of vapour between o° and 50° has been determined with accuracy. ) 361. Pressure of aqueous vapour above 100° C.—Two methods have principally been employed for determining the pressure of aqueous vapour at temperatures above 100° ; the one by Dulong and Arago in 1830, and the other by Regnault in 1844. Fig. 338 represents a vertical section of the apparatus used by Dulong and Arago. It consisted of a copper boiler, 4, with very thick sides, and of about 20 gallons’ capacity. Two gun-barrels, a, of which only one is seen in —-362] Pressure of Aqueous Vapour 341 ‘ the drawing, were firmly fixed in the sides of the boiler, and plunged in the water. The gun-barrels were closed below, and contained mercury, in which were placed thermometers, 7, indicating the temperature of the water and of the vapour. The pressure of the vapour was measured by means of a mano- meter with compressed air, 7, previously graduated (187) and fitted into an iron vessel, @, filled with mercury. In order to see the height of the mercury in the vessel, it was connected above and below with a glass tube, z, in which the level was always the same as in the bath. A copper tube, z, connected the upper part of the vessel, ¢, with a vertical tube, ¢, fitted in the boiler. The tube z and the upper part of the bath d@ were filled with water, which was kept cool by means of a current of cold water flowing from a reservoir, and circulating through the tube 4. The vapour which was disengaged from the tube ¢ exerted a pressure on the water of the tube z; this pressure was transmitted to the water and to the mercury in thé bath d@, and the mercury rose in the manometer. By noting on the manometer the pressures corresponding to each degree of the thermometer, Dulong and Arago were able to make a direct measurement of the pressure up to 24 atmospheres, and the pressure to 50 atmospheres was determined by calculation. 362. Pressure of vapour below and above 100° C.—Regnault devised a method by which the Heese of vapour may be measured at temperatures either below or above 100° It depends on the principle that when a liquid boils, the pressure of the vapour is equal to the pressure the liquid sup- ports:(367).. (lf therefore, the temperature and the corresponding pressure 342 On Feat [362— are known, the question is solved, and the method merely consists in causing * water to boil in a vessel under a given pressure, and measuring the corre- sponding temperature. The apparatus consists of a copper retort, C (fig. 341), hermetically closed and about two-thirds full of water. In the cover are four thermometers, two of which just dip into the water, and two descend almost to the bottom. By means of a tube, AB, the retort C is connected with a glass globe, M, of about 6 gallons’ capacity, and full of air. The tube AB passes through a metal cylinder, D, through which a current of cold water is constantly flowing from the reservoir E. To the upper part of the globe a tube with two branches is attached, one of which is connected with a manometer, O ; the other tube, HH’, which is of lead, can be attached to either an exhaust- ing or a condensing air-pump, according as the air in the globe is to be rare- fied or condensed. ‘The reservoir K, in which is the globe, contains water at the temperature of the surrounding air. If the elastic force of aqueous vapour below 100° is to be measured, the end H’ of the lead pipe is connected with the plate of the air-pump, and the air in the globe M, and consequently that in the retort C, is rarefied. The retort being gently heated, the water begins to boil at a temperature below 100°, in consequence of the diminished pressure. And since the vapour is condensed in the tube AB, which is always cool, the pressure originally indicated by the manometer does not increase, and therefore the pressure of the vapour during ebullition remains equal to the pressure on the liquid. A little air is then allowed to enter; this alters the pressure, and the liquid boils at a new temperature ; both these are read off, and the experi- ment repeated as often as desired up to 100°. In order to measure the pressure above I00°, the tube H’ is connected Pressures of aqueous vapour from —i0° to 104° C. Tempe-| Pressure in | Tempe-| Pressure in Tempe. Pressure in Terps | Pressure in | ratures | millimetres | ratures | millimetres |) ratures | millimetres || ratures millimetres Se Wa eer 2) | alae DS aR) Sean 1 — 10° 2°078 | 12° 10°457 29° 29782. |e OO" 1 ak 25 oie 8 2250 ga els I1°062 30 315450 1) Ol a e545 7omm 6 2890 || 14 11-906 a1 33405 || 92 | 560°76 | 4 3387, || 15 | 12°699 32 35°359 || 93 | 588-41 | 2 31985 Otte a3 33 37°410 . || 94 | 610°74 | fe) 4°600 ||P 17 | 14421 34 39°565 || 95 | 633°78 ee 49940 | 18 | 15°357 35 41°827 || 96 | 657°54 z 5°302 || «19 16°346 40 54°906 || 97 .| 682°03 Br Gr W75'087.-) Boll ahi asOn 45 | 71391 || 98 | 707°26 4 G:i007.) (iil) 21g yeas 50 | 91982 || 985; 720715 Soin 25345. in i22.u) pekOiORe 55 \1 117479 | 99:0). 733791 6 6:998 23. |) 420°886 60 | 148791 | 99°5, 746°50 7 7-492 ||. 24 22°184 65 | 186.945 | 100°0 760'00 8 BOL7 sai 26 | 237550) a0 2330034 OOS me vaao7. 5 9 eS 7 ae NiueeG 24°998 75 288°517 Iolo, 787°63 fe) S105 27 Fess 80 354°643 102°0| 816°17 II O17921 ier e8') | 28-TOD 85 43341 | 10470) 875°69 -364] Pressure of Aqueous Vapour 343 with a condensing pump, by means of which the air in the globe M and that in the vessel C are exposed to successive pressures, higher than the atmo- sphere. The ebullition is retarded (371), and it is only necessary to observe the difference in the height of the mercury in the two tubes of the mano- meter O, and the corresponding temperature, in order to obtain the pressure for a given temperature. The table on the preceding page by Regnault gives the pressure of aqueous vapour from — 10° to 104°. In the following table the numbers were obtained by direct observation up to 24 atmospheres ; the others were calculated by the aid of a formula of interpolation. This table and the one next following show that the elastic force increases much more rapidly than the temperature. It has been attempted to express the relation between them by formule, but none of the formulze seems to have the simplicity which characterises a true law. Pressures in atmospheres from 100° to 230°9° | | i 7 | | || Number Number'| Number Number | Temperatures | ofatmo- Temperatures of atmo-| Temperatures of atmo- | Temperatures of atmo- | spheres spheres | spheres | spheres RO eet | | NPS Nee Ns Z| | | | 100'0° ie eae FRO ve he 1 sTepedre aan hielo ay = a7 Ou 22 | by 2 eeees te Id polienk'75:8 Oi 2019 16 29079 23 | 120°6 he 180°3 10 204°9 17 22275 Pyne | 133'9 6 184°5 LI 207°7 18 224°7 25 | | 144°0 Ae ERT OS AL oll) 12 210°4 19 226°8 20:4 BN ih oad all an 07 8 13 27 3:00 20 228°'9 oY a | T59'21 Gs) 4 mirg dss 14 QT SiSMnniy "aT 230°9 28 | 15 tame 97 | | 363. Pressure of the vapours of different liquids.—Regnault deter- mined the elastic force, at various temperatures, of the vapours of a certain number of liquids which are given in the following table : ea leiae | Tempe- Pressures in | Polat Tempe- Pressures in | Liquids | eee cre Liquids ratures millimetres if | 0° 0°02 (| —20° GS ie Mercury . Se eail-fe) Ort in tian O Too «| | r a LOOusa| o'74 | Uae 60 1728 | fe) U3 ot 100 | 4950 | Alcohol | BO. | 220 | — 20 Azo e | : x | Sulphurou | too | : . —181°4° Butyric acid . . UT eOe Nitrous oxide : - —-92 Turpentine. : ei hy; Carbonic acid ; f, 00, Aniline > : yh key Ammonia A - —39 #.Methylene ‘eilae: : Selo Methyl chloride . pee) tien LOCINGmay : ; 12200 Cyanogen . : . -—20 +x.Naphthaline . ; Bae 7 Sulphurous acid . . -—I10 Diphenyl / ; ue ie Ethyl] chloride : Pees Dii benzOlc acicume: ‘ se ee Aldehyde. : : 21 Phosphorus. : eer 200: Ether ‘ : 370) Wiphenyiaminem aa ae STO Carbon Becenide : 47 Strong sulphuricacid . 318 Acetone. : ; : 56 Phenanthrene : g4O Bromine : : : 58 Mercury : Me cht Methylic alcohol . ; 66 Phenyl Bhocenate ; gy vio Alcohol . : : - 78 ASSORICY a ‘ aay Benzole. s : é SI Sulphur . : 444 Distilled water . . 100 Phosphorus pentasulphide 530 Acetic acid . : ne Sd Ry: Selenium . ‘ 665 Amylic alcohol . Pedic Cadmium ‘ : eat a0 Propionic acid ; ByiA bev ehie : : : png Oia) Kopp pointed out that in homologous chemical compounds the same difference in chemical composition frequently involves the same difference of boiling points; and he showed that in an extensive series of com- 348 On Heat [367— pounds, the fatty acids for instance, the difference of CH, is attended by a difference of 19° C. in the boiling point. In other series of homologous compounds, the corresponding difference in the boiling point is 30°, and in others again 24°. 368. Theoretical explanation of evaporation and ebullition.— From what has been said about the nature of the motion of the molecules in liquids (296), it may readily be conceived that in the great variety of these motions, the case occurs in which, by a fortuitous concurrence of the progressive, vibratory, and rotatory motions, a molecule is projected from the surface of the liquid with such force that it overleaps the sphere of the action of its cir- cumjacent molecules, before, by their attraction, it has lost its initial velocity ; and that it then flies into the space above the liquid. Let us first suppose this space limited and originally vacuous ; it gradu- ally fills with the propelled molecules, which act like a gas and in their motion are driven against the sides of the envelope. One of these sides, however, is the surface of the liquid itself, and a molecule when it strikes against this surface will not in general be repelled, but will be retained by the attraction which the adjacent ones exert. Equilibrium will be established when as many molecules are dispersed in the surrounding space as, on the average, impinge against the surface and are retained by it in the unit of time. This state of equilibrium is not, however, one of rest, in which eva- poration has ceased, but a condition in which evaporation and condensation, which are equally strong, continually compensate each other. ° The density of a vapour depends on the number of molecules which are repelled in a given time, and this manifestly depends on the motion of the molecules in the liquid, and therefore on the temperature. What has been said respecting the surface of the liquid clearly applies to the other sides of the vessel within which the vapour is formed ; some vapour is condensed, this 1s subject to evaporation, and a condition ultimately occurs in which evaporation and condensation are equal. The quantity of vapour necessary for this depends on the density of vapour in the closed space, on the temperature of the vapour and of the sides of the vessel, and on the force with which this attracts the molecules. The maximum will be reached when the sides are covered with a layer of liquid, which then acts like the free surface of a liquid. In the interior of a liquid it may happen that the molecules repel each other with such force as momentarily to destroy the coherence of the mass. The small vacuous space which is thereby formed is entirely surrounded by a medium which does not allow of the passage of the repelled molecules. Hence it cannot increase and maintain itself as a bubble of vapour, unless so many molecules are projected from the inner sides that the internal pressure which thereby results can balance the external pressure which tends to condense the bubble. The expansive force of the enclosed vapour must therefore be so much the greater, the higher the external pressure on the liquid, and we can thus understand the influence of pressure on the tempera- ture of boiling. 369. Influence of substances in solution on the boiling point.—The ebullition of a liquid is the more retarded the greater the quantity of any substance it may contain in solution, provided that the substance be not -369] Influence of Substances 349 volatile, or, at all events, be less volatile than the liquid itself. Water, which boils at 100° when pure, boils at the following temperatures when saturated with different salts :— Water saturated with common salt ‘ : boils at 102° oh potassium nitrate : aL io " + potassium carbonate . 5 135 _ be calcium chloride : Hee cia) Acids in solution present analogous results; but substances merely mechanically suspended, such as earthy matters, bran, wooden shavings, &c., do not affect the boiling point. Absorbed air exerts a very marked influence on the boiling point of water. Deluc first observed that water freed from air by ebullition, and placed in a flask with a long neck, could be raised to 112° without boiling. Donny examined this phenomenon by means of the apparatus depicted in figure 345. It consists of a glass tube CAB, bent at one end and closed at C, while the other is blown into a pear-shaped bulb, B, drawn out to a point. The tube contains water which is boiled until all air is expelled, and the open end is hermetically sealed. By inclining the tube the water passes into the bent end CA ; this end being placed in a bath of chloride of calcium, the temperature may be raised to 130° without any signs of boiling. At 238° the liquid is suddenly converted into steam, and the water is thrown over into the bulb, which is smashed if it is not sufficiently strong. Boiled-out water, covered with a layer of oil, may be raised to 120° with- out boiling, but above this temperature it suddenly begins to boil, and with almost explosive violence. When a liquid is suspended in another of the same specific gravity, but of higher boiling point, with which it does not mix, it may be raised far be- yond its boiling point without the formation of a trace of vapour. Dufour made a number of valuable experiments on this subject ; he used in the case of water a mixture of oil of cloves and linseed oil, and placed in it globules of water, and then gradually heated the oil ; in this way ebullition rarely set in below 110° or 115°; globules of to millimetres’ diameter very commonly reached a temperature of 120° or 130°, while very small globules of 1 to 3 millimetres reached the temperature of 175°, a temperature at which the pressure of vapour on a free surface is 8 or 9 atmospheres. At these high temperatures the contact of a solid body, or the production of gas bubbles in the liquid, occasioned a sudden vaporisation of the globule, accompanied by a sound like the hissing of a hot iron in water. Saturated aqueous solutions of copper sulphate, sodium chloride, &c., remain liquid at a temperature far beyond their boiling point, when immersed in melted stearic acid. In like manner, globules of chloroform 350 On Heat [369- (which boils at 61°), suspended in a solution of chloride of zinc, could be heated to 97° or 98° without boiling. It is a disputed question as to what is the temperature of the vapour from boiling saturated saline solutions. It has been stated by Rudberg to be that of pure water boiling under the same pressure. The experiments of Magnus seem to show, however, that this is not the case, but that the vapour of boiling solutions is hotter than that of pure water ; and that the temperature rises as the solutions become more concentrated, and therefore boil at higher temperatures. Nevertheless, the vapour was always found somewhat cooler than the mass of the boiling solution, and the difference was greater at high than at low temperatures. The boiling point of a liquid is usually lowered when it is mixed with a more volatile liquid than itself, but raised when it contains one which is less volatile. Thus a mixture of two parts alcohol and one of water boils at 83°, a mixture of two parts of carbon bisulphide and one part of ether boils at 38°. In some cases the boiling point of a mixture is lower than that of either of its constituents. A mixture of water and bisulphide boils at 43°, the boiling point of the latter being 46°. On this depends the following curious experiment. If water and carbon bisulphide, both at the tempe- rature 45°, are mixed together, the mixture at once begins to boil briskly. 370. Influence of the nature of the vessel on the boiling point.— Gay-Lussac observed that water in a glass vessel required a higher tempera- ture for ebullition than in a metal one. Taking the temperature of boiling water in a copper vessel at 100%, its boiling point in a glass vessel was found to be ro1°; and if the glass vessel had been previously cleaned by means of sulphuric acid and of potash, the temperature would rise to 105° or even to 106°, before ebullition commenced. A piece of metal placed in the bottom of the vessel was always sufficient to lower the temperature to 100°, and at the same time to prevent the violent concussions which accom- pany the ebullition of saline or acid solutions in glass vessels. Whatever be the boiling point of water, the temperature of its vapour is uninfluenced by the substance of the vessels. 371. Influence of pressure on the boiling point.—We see from the table of pressures (362) that at 100°, the temperature at which water boils under a pressure of 760 millimetres, which is that of the atmosphere, aqueous vapour has a pressure exactly equal to this pressure. This principle is general, and may be thus enunciated : A Uiguid boils when the pressure of its vapour ts equal to the pressure tt supports. Consequently, as the superin- cumbent pressure increases or diminishes, the pressure of the vapour, and therefore the temperature necessary for ebullition, must increase or diminish. Hence a liquid has, strictly speaking, an indefinite number of boiling points. In order to show that the boiling point is lower under diminished pres- sure, a small dish containing water at 30° is placed under the receiver of an air-pump, which is then exhausted. The liquid soon begins to boil, the vapour formed being pumped out as rapidly as it is generated. A paradoxical but very simple experiment also well illustrates the de- pendence of the boiling point on the pressure. In a glass flask, water is boiled for some time, and when all air has been expelled by the steam, the flask is closed by a cork and inverted, as shown in fig. 346. Ifthe bottom —373] Measurement of Heights 351 is then cocled by a stream of cold water from a sponge, the water begins to boil again. This arises from the condensation of the steam above the surface of the water, by whicha partial vacuum is produced. It is in consequence of this dimi- nution of pressure that liquids boil on high mountains at lower temperatures. On Mont Blanc, for example, water boils at 84°, and at Quito at go°. On the more rapid evaporation of water under feeble pressures is based the use of the air-pump in concentrat- ing those solutions which either cannot bear a high temperature, or which can be more cheaply evaporated in an exhaustedspace. Howard madea most important and useful application of this principle in the manufacture of sugar. The syrup, in his method, is enclosed in an air-tight vessel, which is exhausted by a steam-engine. The evaporation consequently goes on at a lower temperature, which secures the syrup from injury. The same plan is adopted in evaporating the juice of certain plants used in preparing medicinal extracts. On the other hand, boiling is retarded by increasing the pressure ; under the pressure of two atmospheres, for example, water only boils at 1297°6. 372. Franklin’s experiment.— The influence of pressure on boiling raay further be illustrated by means of an experiment originally made by Franklin. The apparatus con- sists of a bulb, a, and a tube, J, joined by a tube of smaller dimen- Sionse e804 7).6 el Demtube (2) 1s drawn out, and the apparatus filled with water, which is then in part boiled away by means of a spirit lamp. When it has been boiled sufficiently long to expel all the air, the tube J is sealed. There is then a vacuum in the apparatus, or rather there is a pressure due to the elastic force of aqueous vapour, which at ordinary temperatures is very small. Consequently, if the bulb, a, be placed in the hand, the heat is sufficient to produce a pres- sure which drives the water into the tube, 4, and causes a brisk ebullition. 373. Measurement of heights by the boiling point.— From the connection between the boiling point of water and the pressure, the heights of mountains may be measured by the thermometer instead of by the baro- meter. Suppose, for example, it is found that water boils on the summit: 352 On Heat [373- of amountain at 90°, and at its base at 98° ; at these temperatures the elastic force of the vapour is equal to the pressure on the liquid ; that is, to the pressure of the atmosphere at the two places respectively. Now, the pressures of aqueous vapour for various temperatures have been determined, and accord- ingly the pressures corresponding to the above temperatures are sought in the tables. These numbers represent the atmospheric pressures at the two places ; in other words, they give the barometric heights, and from these the height of the mountain may be calculated by the method already given (181). An ascent of about 1‘o80 feet produces a diminution of 1°C. in the boiling point. The instruments used for this purpose are called thermo-barometers or hypsometers, and were first supplied by Wollaston. They consist essentially of a small metallic vessel for boiling water (fig. 348), fitted with very delicate thermo- meters, which are only graduated from 80° to 100° ; so that, as each degree occupies a con- siderable space on the scale, the roths, and even the rooths, of a degree may be estimated, and thus it is possible to determine the height of a place by means of the boiling point to within about Io feet. 374. Formation of vapour in closed tubes.— We have hitherto considered vapours as being produced in an indefinite space, or where they could expand freely, and it is only under this condition that boiling can take place. In a closed vessel, the vapours pro- duced finding no issue, their pressure and their density increase with the tem- perature, but that rapid disengagement of vapour which constitutes boiling is impossible. Hence, while the temperature of a liquid in an open vessel can never exceed that of boiling, in a closed vessel it may be much higher. The liquid state has, nevertheless, a limit ; for, according to experiments by ‘Cagniard-Latour and others, if either water, alcohol, or ether be placed in strong glass tubes, which are hermetically sealed after the air has been ex- pelled by boiling, and if then these tubes are exposed to a sufficiently high temperature, a moment is reached at which the liquid suddenly disappears, and is converted into vapour. With ether this occurs at 200° ; the vapour then occupies a space less than double its volume in the liquid state, its pressure being then 38 atmospheres. Alcohol which half fills a tube is converted into vapour at 207° C. If a glass tube about half filled with water, in which some carbonate of soda has been dissolved, to diminish the action of the water on the glass, be heated, it is completely vaporised at about the temperature of melting zinc. When ethyl chloride is heated in a stout sealed tube, the upper surface ceases to be distinct at 170°, and is replaced by an ill-defined —374] Formation of Vapour in Closed Tubes 353 nebulous zone. As the temperafure rises this zone increases in width in both directions, becoming at the same time more transparent ; after a time the liquid is completely vaporised, and the tube becomes transparent and seemingly empty. On cooling, the phenomena are reproduced in opposite order. Similar appearances are observed on heating ether in a sealed tube at OOo, Andrews made a series of observations on the behaviour of condensed gases at different tem- peratures, by means of an apparatus the principal features of which are represented in fig. 349. The pure and dry gas is contained in a tube g, which is sealed at one end, and the gas is shut in by a thread of mercury. The tube is inserted in a brass end-piece, E, which is firmly screwed on a strong copper tube, R. At the other end is a similar piece, in which a steel screw works, perfect tightness being ensured by good packing. The tube is full of water, so that by turning this screw the pressure on the enclosed gas can be increased up to 500 atmospheres. In some cases the projecting capillary tube is bent downwards, so that it can be placed in a freezing mixture. Andrews found on raising liquid carbonic acid in such a tube to a temperature of 31° C. that the surface of demarcation between the liquid.and the gas became fainter, lost its curvature, and gradually disappeared. The space was then occupied by a homogeneous fluid, which, when the pressure was suddenly diminished, or the temperature slightly lowered, exhibited a peculiar appearance of moving or flickering striz throughout its whole mass. Above 31° no apparent liquefaction of carbonic anhydride, or separation into two distinct forms of matter, could be effected, not even when the pres- sure of 400 atmospheres was applied. From similar observations made with other substances it seems that there exists for every liquid a temperature, the critical point or critical tem- perature. While below this critical point a sudden transition from gas to liquid is accompanied by a sudden diminution of volume, and liquid and gas are separated by a sharp line of demarcation, above this critical point the change is connected with a gradual diminution of volume, and is quite imperceptible. The condensation can, indeed, only be recognised by a sudden ebullition when the pressure is lessened. Hence, ordinary condensa- tion is only possible at a temperature below the critical point, and it is not surprising, therefore, that mere pressure, however great, should have failed to liquefy many of the gases. These relations are shown in the case of carbonic acid by fig 351, in which the horizontal lines, the abscissze, represent volumes, and the vertical AA Fig. 350 354 ) On Heat | [374- lines, the ordinates, pressures in atmospheres. Suppose now at the particular temperature 13°1° a given volume of gas is subjected to gradually increasing pressure : the volume diminishes until it reaches 48 atmospheres, the gas begins to liquefy, and the continued application of this pressure completes the liquefaction (this state is repre- sented by the line AB), after which any further increase of pressure only diminishes the volume to much the same extent as any other liquid (98). At a higher temperature, 21°5°, the same general results are obtained, ex- cept that a pressure of 61 atmospheres is required for the liquefaction, the line A’B’ is shorter. On continuing the ex-. periments it is found that at a tem- perature of 30°9° there is no horizontal part, the lines merge into each other, and at no higher temperature is there a separation into liquid and gas. This is the critical temperature, and the higher the temperature the more nearly does the curve show the behaviour of a perfect gas. The phenomenon of the critical temperature may be conveniently illus- trated by the following arrangement (fig. 350), which is also well adapted for projection on a screen by means of a magic-lantern for lecture purposes. A stout glass tube about 2°5™™ wide and 4o™™ long, contains liquid sulphurous acid, and is supported, with the drawn-out end downwards, in a test-tube by means of a wire frame. Pure melted paraffin is added to about 10°" above the inner tube. The whole arrangement is suspended in a retort-holder, and heat applied with a spirit lamp. With careful manipulation there is no danger, and the course of the phenomenon is readily seen through the clear paraffin. The boiling point of a body may be defined as the temperature above which a body passes into the state of gas, not only on the surface but in the body of the liquid ; this temperature is therefore different for different pres- sures, and is accordingly a velatzve magnitude. The absolute boiling point is the temperature at which a body is converted into gas, whatever be the pressure ; it is identical with the critical temperature. Mendelejeff found that a relation existed between the absolute temperature and the capillarity of liquids. Increase of temperature diminishes the cohesion, and therefore the elevation of a liquid in a capillary tube. The elevation ultimately vanishes, and the temperature at which this takes place is the absolute boiling point. For some it is very low ; in the case of air, for instance, it is iba The critical pressure is that at which condensation takes place at the critical temperature, and the volume of the saturated vapour at the critical temperature, and under the critical pressure, is called the critical volunte. A vapour may be defined as being a gas at any temperature below its Fig. 351 —376] Papin’s Digester—Latent Heat of Vapour 355 critical point. Hence a vapour can be converted into a liquid by pressure alone, and can therefore exist at the pressure of its own liquid, while a. gas requires cooling as well as pressure to , convert it into a liquid ; that is, to alter its arrangement in such a manner that a liquid can be seen to be separated from a gas by a distinctly bounded surface. 375. Papin’s digester.— Papin appears to have been the first to investigate the effects of the production of jvapour ,jin closed vessels. The apparatus* which bears his name consists of a cylindrical iron vessel M (fig. 352) provided with a cover, which is firmly fastened down by the screw B. In order to close the vessel hermetically, sheet lead is placed between the edges of the cover and the vessel. A cylindrical channel through the cover is closed by a valve to which a rod wz is attached.’ This rod presses against a lever ab, movable at a, and the pressure may be regulated by means of a weight f movable on this lever. The lever is so weighted that when the pressure in the interior is equal to six atmospheres, for example, the valve rises and the vapour escapes. The destruction of the apparatus is thus avoided, and this mechanism has hence received the name of safety-valve. The digester is filled about two-thirds with water, and is heated on a furnace. The water may thus be raised to a temperature far above 100°, and the pressure of the vapour increased to several atmospheres, according to the weight on the lever. | We have seen that water boils at much lower temperatures on high mountains (371) ; the temperature‘of water boiling in open vessels in such localities is not sufficient to soften animal fibre completely and extract the nutriment, and hence Papin’s digester is used in the preparation of food. It is also used in extracting gelatine. When bones are digested in this apparatus they are softened, so that the gelatine which they contain is dissolved: the part through which the screw B passes is made of such elasticity that it yields, and the lid opens when the pressure of the vapour becomes dangerous. e 376. Latent heat of vapour.—As the temperature of a liquid remains constant during boiling, whatever be the source of heat (367), it follows that a considerable quantity of heat becomes absorbed in boiling, the only effect of which is to transform the body from the liquid to the gaseous con- dition. And, conversely, when a saturated vapour passes into the state of liquid, it gives out a definite amount of heat. . These phenomena were first observed by Black, and he described them by saying that during vaporisation a quantity of sensible heat became latent, -and that the latent heat again became free during condensation. The AA2 356 On Heat [376— quantity of heat which a liquid must absorb in passing from the liquid to the gaseous state, and which it gives out in passing from the state of vapour to that of liquid, is spoken of as the latent heat of evaporation. The analogy of these phenomena to those of fusion will be at once seen ; the modes of determining them will be described in the chapter on Calori- metry ; but the following results, which have been obtained for the latent heats of evaporation at 0°, may be here given :— Water : , ROOT, Carbon bisulphide . «! OO Alcohol . : : = 230 Turpentine : : Nive Benzole. : : Le 109 Chloroform . : sy Oy Acetic acid : nlo2 Bromine . tee. 249 Ether ; : ‘ aod Iodine. : : et The meaning of these numbers 1s, in the case of water, for instance, that it requires as much heat to convert a pound of water from the state of liquid at o° C. to that of vapour at the same temperature, as would raise a pound of water through 607 degrees, or 607 pounds of water through one degree ; or that the conversion of one pound of vapour of alcohol at o° into liquid alcohol of the same temperature would heat 236 pounds of water through one degree. Watt, who investigated the subject, held that the whole quantity of heat necessary to raise a given weight of water from zero to any temperature, and then to evaporate it entirely, or what is called the heat of evaporation, is a constant quantity. His experiments showed that this quantity is 640. Hence the lower the temperature the greater the latent heat, and, on the other hand, the higher the temperature the less the latent heat. The latent heat of the vapour of water evaporated at 100° would be 540, while at 50° it would be 590. At higher temperatures the latent heat of aqueous vapour would go on diminishing. Water evaporated under a pressure of 15 atmospheres at a temperature of 200° would have a latent heat of 440, and if it could be evaporated at 640° it would have no latent heat at all. Regnault, who examined this question with great care, found that the total quantity of heat necessary for the evaporation of water increases with the temperature, and is not constant, as Watt had supposed. It is repre- sented by the formula Q = 606'5 + 0°305/, in which Q is the total quantity of heat, and ¢ the temperature of the water during evaporation, while the numbers are constant quantities. The total quantity of heat necessary to evaporate water at 100° is 606°5 + (0°305 x 100) = 6373 at 120° it 15,643 ; at.150° it is 651 ;,and at 180° 1t/1s 66%. The total heat of the evaporation of ether is expressed by a formula similar to that of water, namely, Q=94+0'045/; and that for chloroform Q =67 + 013752. The heat which is expended simply in evaporating a liquid, and which is spoken of as the latent heat, produces no rise of temperature, and only appears as doing the work of a change of state. One portion of this work is expended in overcoming the cohesion of the particles in the liquid state, —377] Cold due to Evaporation. Mercury Frozen '357 and enabling them to assume the gaseous form—this is the zzéermal work, and is by much the greater ; the other, the external work, is expended ‘in overcoming the external pressure on the vapour formed. Knowing the increase of volume, and the pressure, the external work may be readily calculated ; for if the volumes of unit weight of the substance in the state of liquid and of vapour are respectively s and o, and the pressure for unit surface is #, then the external work is Ap (o —s), A being the mechanical equivalent of heat. So that, if ~ is the total heat of evaporation, r=p+Ap (a—s) in which p is the internal work. From the values of ~ and of AD (a —S), it is easy to deduce that of p, and it is found that this value decreases as the temperature increases. Thus for the temperatures 0°, 50°, 100°, and 150° the values are 576, 536, 496, and 457 respectively ; that is, that when water at o° is converted into vapour, a greater in- ternal work is required to overcome the cohe- sion, than at 100° for instance. 377. Cold due to evaporation. Mercury frozen.—Whatever be the temperature at which a vapour is pro- duced, an absorption | of heat always takes TT 2 MRACUPRUEDAMUPOR RCP RRRERS 1) | place. If, therefore, a i i ai liquid evaporates, and IN does not receive from Fig. 353 Fig. 354 without a quantity of heat equal to that which is expended in producing the vapour, its tempera- ture sinks, and the cooling is greater in proportion as the evaporation is more rapid, : Leslie succeeded in freezing water by means of its own rapid evaporation. Under the receiver of the air-pump is placed a vessel containing strong sulphuric acid, and above it a thin metal capsule, A (fig. 353), containing a small quantity of water. By exhausting the receiver the water begins to boil (367), and since the vapour is absorbed by the sulphuric acid as fast as it is formed, a rapid evaporation is produced, which quickly effects the freezing of the water. This experiment is best performed by using, instead of a thin metal dish, a watch-glass coated with lampblack and resting on acork. The advantage of this is twofold: firstly, the lampblack is a very bad conductor ; and, secondly, it is not moistened by the liquid, which remains in the form of a globule not in contact with the glass. A small porous dish may also ad- vantageously be used, The same result is obtained by means of Wollaston’s cryophorus (fig. 354), 358 On Feat [377— which consists of a bent glass tube provided with a bulb at each end. The apparatus is prepared by introducing a small quantity of water, which is then boiled so as to expel all air. It is then hermetically sealed, so that on-cooling it contains only water and the vapour of water. The water being passed into the bulb A by tilting the apparatus, the other bulb is immersed in a freezing mixture. The vapour in the tube is thus condensed ; the water in A rapidly yields more. But this rapid production of vapour requires a large amount of heat, which is abstracted from the water in A, and its tem- perature is so much reduced that it freezes. By using liquids more volatile than water, more particularly liquid sul- phurous acid, which boils at — 10°, or, still better, methyl chloride, which is now prepared industrially in large quantities, a degree of cold is obtained sufficiently low to freeze mercury. This experiment may be made on a small scale by covering the bulb of a thermometer with cotton wool, and, after having moistened it with the liquid in question, placing it under the receiver of the air-pump. When a vacuum is produced the mercury is quickly frozen. By passing a current of air, previously cooled, through liquid methyl chloride, temperatures of from —23° to —70° C. may be maintained with great constancy for several hours. Thilorier, by directing a jet of liquid carbonic acid on the bulb of an alcohol thermometer, obtained a tempera- ture of — 100° without freezing the alcohol (347). By means of the evaporation of carbon bisulphide the formation of ice may be illustrated without the aid of an air-pump. A little water is dropped on a board, and a capsule of thin copper foil, containing carbon bisulphide, is placed on the water. The evaporation of the bisulphide is accelerated by means of a pair of bellows, and after a few minutes the water freezes round the capsule so that the latter adheres to the wood. In like manner, if some water be placed in a test-tube, which is then dipped in a glass containing some ether, and a current of air be blown through the ether by means of a glass tube fitted to the nozzle of a pair of bellows, the rapid evaporation of the ether very soon freezes the water in the tube. Richardson’s apparatus for producing local anesthesia also de- pends on the cold produced by the evaporation of ether. The cold produced by evaporation is used in hot climates to cool water by means of alcarrazas. These are porous earthen vessels, through which water percolates, so that on the outside there is a continual evaporation, which is accelerated when the vessels are placed in a current of air. For the same reason wine is cooled by wrapping the bottles in wet cloths and placing them in a draught. In Harrison’s method of making ice artificially, a steam-engine is used to work an air-pump which produces a rapid evaporation of some ether, in which is immersed the vessel containing the water to be frozen. The apparatus is so constructed that the vaporised ether can be condensed and used again. _ The cooling effect produced by a wind or draught does not necessarily arise from the wind being cooler, for it may, as shown by the thermometer, be actually warmer, but arises from the rapid evaporation it causes from the surface of the skin. We have the feeling of oppression even at moderate —378] Carré’s Apparatus for Freesing Water 359 temperatures, when we are in an atmosphere saturated by moisture, in which no evaporation takes place. 378. Carré’s apparatus for freezing water.—We have already seen that when any liquid is converted into vapour it absorbs a considerable quantity of sensible heat ; this furnishes a source of cold which is more abundant the more volatile the liquid, and the greater its heat of vaporisa- tion. This property of liquids has been utilised by Carré, in freezing water by the distillation of ammonia. The apparatus consists of a cylindrical boiler C (figs. 355, 356), and of a slightly conical vessel A, which is the freezer. These two vessels are connected by a tube, 7z, and a brace, 7, binds them firmly. They are made of strong galvanised iron plate, and can resist a pressure of seven atmospheres. a Fig. 355 Fig. 356 The boiler C, which holds about two gallons, is three parts filled with a strong solution of ammonia. In a tubulure in the upper part of the boiler ‘some oil is placed, and in this a thermometer 4 The freezer A consists of two concentric envelopes, in such a manner that, its centre being hollow, a metal vessel, G, containing the water to be frozen, can be placed in this space. Hence only the annular space between the sides of the freezer is in communication with the boiler by means of the tube.7z. In the upper part of the freezer there is a small tubulure which can be closed by a metal stopper, and by which the solution of ammonia is introduced. The formation of ice comprises two distinct operations. In the first, the boiler is placed in a furnace F, and the freezer in a bath of cold water of about 12°. The boiler being heated to 130°, the ammoniacal gas dissolved in the water of the boiler is disengaged, and, in virtue of its own pressure, is liquefied in the freezer A, along with about a tenth of its weight of water. This 360 | On feat . [378- distillation of C towards A lasts about an hour and a quarter, and when it is finished the second operation commences ; this consists in placing the boiler in the cold-water bath (fig. 356), and the freezer A out- side, care being taken to surround it with dry flannel. The vessel G, about three-quarters full of water, is placed in the freezer. As the boiler cools, the ammoniacal gas with which it is filled is again dis- solved ; the pressure thus being di- minished, the am- monia which has been liquefied in the freezer is con- verted into the gaseous form, and now distils from A towards C, to re- dissolve in the water which has remained in the boiler. During this distillation the ammonia which is gasified absorbs a great quantity of heat, which is withdrawn from the vessel G and the water it contains. Hence it is that this water freezes. In order to have better contact between the sides of the vessel G and the freezer, alcohol is poured between them. In about an hour and a quarter a perfectly compact cylin- drical block of ice can be taken from the vessel G. This apparatus gives about four pounds of ice in an hour, at a price of about a farthing per pound; large continuously working apparatus have, however, been constructed, which produce as much as 800 pounds of ice in an hour. Carré constructed an ice-making machine which is an industrial appli- cation of Leslie’s experiment (377), and by which considerable quantities of water may be frozen in a short time. It consists of a cylinder, R, about 15 inches long by 4 in diameter, made of an alloy of lead and antimony (fig. 357). At one end is a funnel E, by which strong sulphuric acid can be in- troduced ; at the other is a tubulure 7, to which is screwed a dome d that supports a series of obstacles intended to prevent any sulphuric acid from spirting into # and 6. There are, moreover, on the receiver a wide tube, z, closed by a thick glass disc O, and a long tube 4, to the top of which is fitted the bottle C containing water to be frozen. The dome d, the disc O, and the stopper z of the funnel E are all sealed with wax. —880] Liquefaction of Vapours 361 On the side of the receiver is an air-pump P, connected with it bya tube 6, and worked bya handle M. To this handle is attached a rod 4, which, by the mechanism represented on the left of the figure, works a stirrer A in the sulphuric acid. A lever x connected with a horizontal axis which traverses a small stuffing-box , transmits its backward and forward motion to the rod e and to the stirrer. This and the stuffing-box z are fitted in a tubulure on the side of the tubulure zz. The smallest size which Carré makes contains 2°5 kilogrammes of sul- phuric acid, and the water-bottle about 400 grammes, when it is one-third full. After about 70 strokes of the piston the water begins to boil ; the acid being in continued agitation, the vapour is rapidly absorbed by it, and the pump is worked until freezing begins. For this purpose it is merely necessary to give a few strokes every five minutes. The rate of freezing depends on the strength of the acid ; when this gets very dilute it requires renewal ; but 12 water-bottles can be frozen with the same quantity of acid. LIQUEFACTION OF VAPOURS AND GASES 379. Liquefaction of vapours.-—The “guwefaction or condensation of vapours is their passage from the aériform to the liquid state. Condensa- tion may be due to three causes—cooling, compression, or chemical action. For the first two causes the vapours must be saturated (357), while the latter produces the liquefaction of the most rarefied vapours. Thus, a large number of salts absorb and condense the aqueous vapours in the atmo- sphere, however small its quantity. When vapours are condensed, their latent heat becomes free ; that is, it affects the thermometer. This is readily seen when a current of steam at 100° is passed into a vessel of water at {the ordinary temperature. The liquid becomes rapidly heated, and soon reaches 100°. The quantity of heat given up in liquefaction is equal to the quantity absorbed in producing the vapour. 380. Distillation. Stills.—D¢zstillation is an operation by which a volatile liquid| may be separated from substances which it holds in solution, or by which two liquids o. different volatilities may be separated. The operation depends on!}the transformation of liquids .nto vapour by the action of heat, and on the condensation ot this vapour by cooling. The apparatus used in distillation is called a s¢/Z. Its form may vary * greatly, but it consists essentially of three parts: rst, the dody, A (fig. 358), a copper vessel containing the liquid, the lower part of which fits in the furnace ; 2nd, the head, B, which fits on the body, and from which a lateral tube, C, leads to ; 3rd, the worm, S, a long spiral tin or copper tube placed in a cistern kept constantly full of cold water. The object of the worm is to condense the vapour by exposing a greater extent of cold surface. To free ordinary water from the many impurities which it contains, it is placed in a still and heated. The vapours disengaged are condensed in the worm, and the distilled water arising from the condensation is collected in the receiver D. The vapours in condensing rapidly heat the water in the cistern, which must therefore be constantly renewed. For this purpose a 362 On Feat , [380—. continual supply of cold water passes into the bottom of the'cistern, while the lighter heated water rises to the surface and escapes by a tube in the top of the cistern. Fig. 358 381. Liebig’s Condenser.—In distilling smaller quantities of liquids, the: apparatus known as Lzebig’s Condenser ts extremely useful. It consists of a glass tube, ¢¢ (fig. 359), about thirty inches long, fitted in a copper or tin eat ines megan" Fig. 359 tube by means of perforated corks. A constant supply of cold water from the vessel a passes into the space between the two tubes, being conveyed to: —383] Apparatus for determining Alcoholic Value of Wines 363 the lower part of the condenser by a funnel and tube g, flowing out from the upper part of the tube £ The liquid to be distilled is contained: in a retort, the neck of which is placed in the tube ; the condensed liquid drops quite cold into a vessel placed to receive it at the other end of the condensing tube. 382. Apparatus for determining the alcoholic value of wines.—One of the forms of this apparatus consists of a glass flask resting on a tripod, and heated bya spirit lamp (fig. 360). By means of a caoutchouc tube this is con- nected with a worm placed in a copper vessel filled with cold water, below which is a test glass for collect- © ing the distillate. On this are three divisions, one a, which measures the quantity of wine taken ; the two others indi- cating one-half and one-third of this volume. The test glass is filled with the wine up to a; this is then poured into the flask, which having been connected with the worm, the distillation is commenced. The liquid which distils overis a mixture of alcohol and water ; for ordinary wines, such as clarets and hocks, about one-third is distilled over, and for wines richer in spirit, such as sherries and ports, one-half must be distilled ; experiment has shown that in these circumstances practically all the alcohol passes over in the distillate. The measure is then filled up with distilled water to a ; this gives the mixture of alcohol and water of the same volume as the wine taken, free from all solid matters, such as sugar, colouring matter, and acid, but containing all the alcohol. The specific gravity of this distillate is then taken by means of an alcoholometer (129), and the number thus obtained corresponds to a certain strength of alcohol as indicated by the tables. 383. Safety-tube.—In preparing gases and collecting them over mercury or water, it occasionally happens that these liquids rush back into the generating vessel, and destroy the operation. This arises from an excess of atmospheric pressure over the elastic force in the vessel. Ifa gas—sulphurous acid for example—be generated in the flask 7 (fig. 361), and be passed into water in the vessel A, as long as the gas is given off freely, its elastic force exceeds the atmospheric pressure, and the weight of the column of water, on, so that the water in the vessel cannot rise in the tube, and absorption is impossible. But if the tension decreases, either through the flask becoming Fig. 360 304 On Heat [383— cooled or the gas being disengaged too slowly, the external pressure pre- vails, and when it exceeds the internal pressure by more than the weight of the column of water co, the water rises into the flask, and the operation is spoiled. This accident is prevented by means of safety-tubes. These are tubes which prevent absorption by allowing the air to enter in proportion as the internal pressure decreases. The simplest is a tube C (fig. 362), passing through the cork which closes the flask M, in which the gas is generated, and dipping in the liquid. When the pressure of the Fig 362 gas diminishes in M, the atmospheric pressure on the water in the bath E causes it to rise to a certain height in the tube DA ; but this pressure, acting also on the liquid in the tube C, depresses it to the same depth, assuming that the liquid has the same density as the water in E. Now, as this depth is less than the height DH, air enters by the aperture, before the water in the bath can rise to A, and no absorption takes place. 384. Liquefaction of gases.—We have already seen that a saturated vapour, the temperature of which is constant, is liquefied by decreasing the volume, and that, the volume remaining constant, it is brought into the liquid state by diminishing the temperature. Unsaturated vapours behave in all respects hke gases. For the gaseous form is accidental, and is not inherent in the nature of the substance. At ordinary temperatures sulphurous anhydride is a vapour, while in countries near the poles it is a liquid ; in temperate climates ether is a liquid, at a tropical heat it is a vapour. And just as unsaturated vapours may be brought to the state of saturation, and then liquefied, by suitably diminishing the tempe- rature or increasing the pressure, so by the same means gases may be liquefied. But as they are mostly very far removed from this state of satura- tion, great cold and pressure are required. Some of them may indeed be liquefied either by cold or by pressure ; for the majority, however, both agencies must be simultaneously employed. Recent researches have shown that the distinction fermanent gas no longer exists, now that all have been liquefied. We have seen that there is for each gas a critical temperature (374), so that no pressure, however great, can liquefy a gas which is above this tempe- rature. If a gas is below this point, then the nearer it is to it the greater is —385] Apparatus to Liguefy and Solidify Gases 365 the pressure required ; conversely, if the temperature is very low, the pressure required to liquefy it may be low too. Faraday was the first to liquefy some of the gases. His method con- sists in enclosing in a bent glass tube (fig. 363) substances by whose chemical action the gas to be liquefied is produced, and then sealing the shorter leg. In proportion as the gas is dis- engaged its pressure increases, and it ultimately liquefies and collects in the shorter leg, more especially if its condensation is assisted by placing the shorter leg in a freezing mixture. A small manometer may be placed in the appa- ratus to indicate the pressure. Cyanogen gas is readily liquefied by heating cyanide of mercury in a bent tube of this de- scription ; other gases have been condensed by & taking advantage of special reactions, the con- Fig. 363 sideration of which belongs rather to chemistry than to physics. For example, silver chloride absorbs about 200 times its volume of ammonia; when the compound thus formed is placed in the long leg of a bent tube and gently heated, while the shorter leg is immersed in a freezing mixture, a quantity of liquid ammonia speedily collects in the shorter leg. 385. Apparatus to liquefy and solidify gases.—Thilorier first constructed an apparatus by which considerable quantities of carbonic acid could be liquefied. Its principle is the same as that used by Faraday in working with glass tubes ; the gas is generated in an iron cylinder, and passes through a metal tube into another similar cylinder, where it condenses. The use of this apparatus is not free from danger; many accidents have already happened with it, and it has been superseded by an apparatus constructed by Natterer, of Vienna, which is both convenient and safe. A perspective view of the apparatus, as modified by Bianchi, is repre- sented in fig. 365, and a section on a larger scale in fig. 364. It consists of a wrought-iron reservoir A, of something less than a quart capacity, which can resist a pressure of more than 600 atmospheres. A small force-pump is screwed on the lower part of this reservoir. The piston rod ¢is moved by the crank-rod E, which is worked by the handle M. As the compression of the gas and the friction of the piston produce a considerable disengagement of heat, the reservoir A is surrounded by a copper vessel, in which ice or a freezing mixture is placed. The water arising from the melting of the ice passes by a tube 77 into a cylindrical copper case C, which surrounds the force-pump, whence it escapes through the tube z and the stopcock 0. The whole arrangement rests on an iron frame, PQ. The gas to be liquefied is previously collected in airtight bags R,. whence it passes into a bottle V, containing some suitable drying substance ; it then passes into the condensing pump through the vulcanised indiarubber tube H. After the apparatus has been worked for some time the reservoir A can be unscrewed from the pump without any escape of the liquid, for it is. closed below by a valve S (fig. 364). In order to collect some of the liquid gas, the reservoir is inverted, and on turning the stopcock 7 the liquid escapes, by a small tubulure x. The specific gravity of liquid CO, is 0°88. 366 : On teat [385- When carbonic acid has been liquefied and is allowed to escape into the air, a portion only of the liquid volatilises ; in consequence of the ‘heat ab- sorbed by this evaporation, the rest is so much cooled as to solidify'in white flakes like snow or anhydrous phosphoric acid. This may be collected by placing a stout woollen bag like a tobacco pouch over a pipe attached to the tube x; if the porous mass is compressed or hammered in stout wooden cylinders, sticks of solid carbonic acid are obtained, very lke chalk in appearance. Its specific gravity is 1:2. We ZZ Solid carbonic acid evaporates very slowly. By means ot an alcohol thermometer its temperature has been found to be about —90° C. A small quantity placed on the hand does not produce the sensation of such great cold as might be expected. This,arises from the imperfect contact. But if the solid be mixed with ether the cold produced is so intense that when a little is placed on the skin all the effects of a severe burn are produced. A mixture of these two substances solidifies four times its weight of mercury in 386] Cailletet’s Researches 367 a few minutes. When a tube containing liquid carbonic acid is placed in this mixture, the liquid becomes solid and looks like a transparent piece of ice. The most remarkable liquefaction obtained by this apparatus is that of nitrous oxide. The gas once liquefied only evaporates slowly, and produces a temperature of —88° C. Mercury placed in it in small quantities instantly solidifies. The same is the case with water ; it must be added drop by drop, otherwise, its latent heat being much greater than that of mercury, the heat given up by the water in solidifying would be sufficient to cause an explosion of the nitrous oxide. Nitrous oxide is readily decomposed by heat, and has the property of supporting the combustion of bodies with almost as much brilliancy as oxygen ; and even at low temperatures it preserves this property. When a piece of incandescent charcoal is thrown on liquid nitrous oxide, it continues to burn with a brillant light. The cold produced by the evaporation of ether (377) has been used by Loir and Drion in the liquefaction of gases on a small scale. By passing a current of air from a blowpipe bellows through several tubes into a few ounces of ether,.a temperature of — 34° C. can be reached in five or six minutes, and may be kept up for fifteen or twenty minutes. By evaporating liquid sulphurous acid in the same manner a great degree of cold, -— 50° C. is obtained. At this temperature ammonia may be liquefied. By rapidly evaporating liquid ammonia under the air-pump, in the presence of sulphuric acid, a temperature of — 87° is attained, which is found sufficient to liquefy carbonic acid under the ordinary pressure of the atmosphere. 386. Cailletet’s researches.—Cailletet and Pictet, working independently, but simultaneously, have effaced the old distinction between permanent and non-permanent gases, by effecting the liquefaction of oxygen, and other gases which it was supposed could not be condensed. This has been accomplished by means of powerful material appliances directed with great skill and ingenuity. The critical temperature of these gases is mostly below — 100°, while their critical pressure is somewhat less than that of carbonic acid, excepting in the case of hydrogen, which is over 100 atmospheres. The essential parts of Cailletet’s apparatus are represented in fig. 366. BB’ is a strong wrought-iron bath containing mercury ; in this is placed the tube TO, the upper part of which is capillary and contains the gas to be liquefied. ‘This tube is supported bya screw z, in which it is fixed by marine glue. In the side of BB’ is a second screw, through which passes a tube 4, giving passage to the water forced by the pump. The valves of this, one for suction and one for compression, are placed under the screws S and S’. A screw plunger worked by the wheel X-serves to force the pressure, while by a stopcock worked by a wheel X’ the compressed gas can be suddenly allowed to expand. A manometer. zz fixed on the case indicates the pressure. To fill the tube TO it is placed horizontally, the capillary end being still open, and pure well-dried gas is admitted at the other end (fig. 367) by a caoutchouc tube. When all air is expelled, the end O is sealed, the tube held vertically so that a drop of mercury @ previously introduced closes the tube. It is then placed.in the bath BB’, z being firmly screwed. On this is fixed the 368 On Heat [386— plate Q, to which is attached a cylinder M, which can be filled with water from 7 or a freezing mixture. This is surrounded by a safety bell-jar, C. By working the force pump a pressure of 400 atmospheres can be pro- duced, which can be increased to 2,500 atmospheres by means of the screw Ss W SS AZ. LA, Fig. 366 piston. When a suitable pressure has been applied, and after waiting until the heat due to the compression has disappeared, if the screw worked by the wheel X is suddenly opened, the pressure being diminished to one Fig. 367 atmosphere, the cold produced by the sudden expansion of the gas in the tube TP is so great as to liquefy a portion of it, as is shown by the produc- tion of a mist. This observation was first made with nitric oxide, but similar results have been obtained with marsh gas, carbonic acid, and oxygen. ~387] Pictet’s Method 369 387. Pictet’s method.—The principle of Pictet’s method is that of liberating the gas under great pressure, combined with the application of a very low temperature. The essential parts of the apparatus are the following :—Two double-acting pumps, A and B (fig. 368), are so ‘coupled together that they cause the evaporation of liquid sulphurous acid contained in the annular receiver C. By the action of the pumps the gas thus evaporated is forced into the receiver D, where it is cooled by a current of water, and again liquefied under a pressure of three atmospheres. Thence it passes again by the narrow tube d to the receiver C, to replace that which is evaporated. In this way the temperature of the liquid sulphurous acid is reduced to —65°. Its function is to produce a sufficient quantity of liquid carbonic acid, which is then sub- mitted to a perfect- ly analogous pro- cess of rarefaction and condensation. This is effected by means of two simi- lar pumps, E and Pb. > The, carbonic acid gas, perfectly pure and dry, is drawn from a reser- voir through a tube not represented in the figure, and is forced into the con- denser K, which is cooled by the liquid ssulphurous acid to eo a temperature of -— 65°, and is there ==" liquefied. S D Miss astube.of ae v ig. 368 stout copper con- nected with the condenser K by anarrow tube &. Whena sufficient quantity of carbonic acid has been liquefied, the connection with the gasholder is cut off, and by working the pumps E and F a vacuum is created over the liquid carbonic acid in H, which produces so great a cold as to solidify it. L is a stout wrought-iron retort capable of standing a pressure of 1,500 atmospheres. In it are placed the substances by whose chemical actions the gas is produced: potassium chlorate in the case of oxygen. The retort is connected with a strong copper tube in which the actual condensation is effected. This tube, the pressure in which is indicated by a specially con- structed manometer R, is closed by a stopcock N, When the four pumps are set in action, for which a steam-engine of 15 horse-power is required, heat is applied to the retort. Oxygen is liberated in a calculated quantity, the temperature of the retort being about 485°. Towards the close of the decomposition the manometer indicates a pressure BB 370 On Fleat [387— of 500 atmospheres, and then sinks to 320. This diminution is due to the condensation of gas, and at this stage the tube contains liquefied oxygen If the cock N is opened, the liquid issues with violence, having the appear- ance of a dazzling white pencil. This lasts three or four seconds. On closing the stopcock the pressure, which had diminished to 400 atmospheres, now rises, and again becomes stationary, proving that the gas is once more being condensed. The phenomena presented by the jet of oxygen when viewed by the electric light showed that the light it emits was partially polarised, indicating a probable transient crystallisation of the liquid. The following table, given by Olszewski (January 1895), exhibits some of the physical properties of substances, gaseous at ordinary teniperatures, when reduced to very low temperatures :— Boiling Critical | ‘point at Petene Density of the Name tempera- | atmo- | dices: liquid at the Colour of liquid ture spheric ie boiling point pressure fo) | fo) ° Hydrogen . —235 .|-244 | — a Colourless Nitrogen . |-146'°0 | —194 —214'0 | 0°885 . Carbonic oxide . |—139°5 | -—190 | —207°0 (?) i Argon —I12I‘0 | --187. | —190 I°5 (about) 5 Oxygen —1188 }»-183 £4x— ried Bluish Nitric oxide —93°5 | -154 —167°0 ~ Colourless Methane —81°8 —164 — 186 O45 ‘ 388. Later researches.—Wroblewski and Olszewski made use of the apparatus represented in fig. 369. The gas to be liquefied is contained in the tube gv, and is compressed by means of a sort of Cailletet pump coupled up with 4. Liquid ethylene is contained in the reservoir x, which is surrounded by a freezing mixture of ice and salt ; it passes thence through the tube 6’, which is surrounded by a paste of solid carbonic acid and ether, and then reaches s, cooled down to a temperature of — 100°. By means of an air-pump to which is connected the lead tube vw this. cooled liquid can be caused to evaporate under a pressure of 25 mm., so that the temperature as indicated by the hydrogen thermometer ¢ is -136°. The vessel in which this is effected contains calcium chloride y, the object of which is to prevent any deposition of dew on the tube. At a temperature of — 136° oxygen at once liquefies under a pressure of 20 atmospheres. By still further reducing the pressure so that ethylene evapo- rates at a pressure of I mm. the temperature sinks to—152° C., and now nitro- gen and carbonic oxide can be directly condensed. If again the space above these lige is rarefied, carbonic oxide becomes. solid at -190°, and nitrogen at — 203°. Dewar has carried out extensive researches on the liquefaction of gases, and has liquefied and even solidified air. The methods adopted do not differ in principle from those which have been mentioned ; the cold is pro- duced by the evaporation of liquid ethylene. -388] Later Researches 371 He has introduced an important improvement in surrounding the vessel in which the liquefied gas is contained by a single or double vacuum jacket, that is, a space from which the air is exhausted ; in this way liquid air may be kept and manipulated in open vessels, or, in other words, at the ordinary atmospheric pressure. o&~ JACQUET Fig. 369 Fig. 370 Fig. 370 illustrates an arrangement by which liquid air may be kept in an open glass vessel virtually without evaporation. The smaller tube is a glass one surrounded by a second one, from which the air has been exhausted ; this tube contains liquid air, and, after the insertion of a glass tube and stopper, it is immersed in liquid air contained in a similar outer vacuum tube ; A is connected with the inner and B with the outer tube. As the latter receives all the radiant and conducted heat, air is continuously boiling off from the outer tube ; but as no heat reaches the inner tube there is no escape from A. By connecting B with an air-pump so as to reduce the pressure to about Io mm., and simultaneously connecting A with an air- pump which is worked, the temperature of the liquid air is so reduced that it solidifies to a jelly-like mass. These experiments have made it possible to examine physical properties of various substances at temperatures which approach absolute zero. It is impossible here to give an account of the results obtained, but some of the most important will be mentioned in their places. One interesting experi- BB2 372 On Feat [388— ment may be mentioned. Ifa barometer is prepared in the usual way, and a sponge dipped in liquid air is applied to a portion of the outer surface of the Torricellian vacuum space, a mirror of metallic mercury is immediately deposited on the inside. Linde has constructed an apparatus for the liquefaction of gases, which works continuously and depends essentially on the cooling produced when a gas expands ; it may be looked upon as the reverse of a regenerative furnace. The main features of this apparatus are represented in fig. 371. Consider, in the first case, a single round of operations. Air supplied through the intake z, at the pressure Z, and temperature 7,, is brought by the compressor F to the pressure #,, say of 50 atmospheres, thereby becoming heated, but by passing through the cooler K is restored to the temperature z,; from this it passes through the inner tube of C, which is the character- istic feature of the apparatus ; meeting there a current of cooled gas pro- Ry Fig. 371 ceeding in the opposite direction through the annular space of C, its temperature is lowered to ¢,. If the throttle valve v is opened for a moment the gas suddenly expands, its pressure is reduced to J,, and its temperature falls to Z,. With this latter temperature it passes through the annular space of C, and so back to the compressor F’, cooling, as already stated, the current passing in the opposite direction through the inner tube and itself becoming raised to the tempe- rature Z,. The gas thus reduced to this latter temperature, and at the original pressure 7, again goes through the same round of operations, again experi- encing a further reduction of temperature until liquefaction sets in. The operations are, in fact, continuous, and with a large apparatus of this kind several litres of liquid air have been prepared in an hour. -389] Mixture of Gases and Vapours 373 MIXTURE OF GASES AND VAPOURS 389. Laws of the mixture of gases and vapours.—Every mixture of a gas and a vapour obeys the two following laws :— I. The pressure, and, consequently, the quantity, of vapour which saturates a given space are the same for the same temperature, whether this space con- tains a gas or ts a vacuum. Il. Zhe pressure of the mixture of a gas and a vapour ts equal to the sum of the pressures which each would exert tf tt occupied the same space alone. These are known as Dalton’s laws, from their discoverer, and are de- monstrated by the following apparatus, which was invented by Gay-Lussac :— It consists of a glass tube A (fig. 372), to which two stopcocks, 4 and d@, are cemented. The lower stopcock is provided with a tubulure which connects the tube A with a tube B of smaller diameter. A scale between the two tubes serves to measure the heights of the mercurial columns in these tubes. The tube A is filled with mercury, and the stopcocks 6 and dare closed. A glass globe M, filled with dry air or any other gas, is screwed on by means of a stopcock in the place of the funnel C. All three stopcocks are then opened, and a little mercury is allowed to escape, which is replaced by the dry air of the globe. The stopcocks are then closed, and as the air in the tube expands on leaving the globe, the pressure on it is less than that of the atmosphere. Mer- cury is accordingly poured into the tube B until it is at the same level in bothtubes. The globe is then removed, and replaced by the funnel C, provided with a stopcock a@ of a peculiar con- struction. It is not perforated, but has a small cavity, as represented in 7, on the left of the figure. Some of the liquid to be vaporised is poured into C, and the height of the mercury & having been noted, the stopcock 6 is opened, and a@ turned so that its cavity becomes filled with. liquid ; being again turned, the liquid enters the space A and vaporises. The liquid nie: 272 is allowed to fall drop by drop until the air in the tube is saturated, which is the case when the level £ of the mercury ceases to sink (357). As the pressure of the vapour produced in the space A is added to that of the air already present, the total volume of gas is increased. It may easily be restored to its original volume by pouring mercury into B. When the mercury in the large tube has been raised to the level 4, there is a difference Bo in the level of the mercury in the two tubes which obviously 374 On Heat [389- represents the pressure of the vapour ; for as the air has resumed its original volume, its pressure has not changed. Now, if a few drops of the same liquid be passed into the vacuum of a barometric tube, a depression exactly equal to Bo is produced, which proves that, for the same temperature, the pressure of a saturated vapour is the same in a gas as in a vacuum; from which it is concluded that at the same temperature the quantity of vapour is also the same. The second law is likewise proved by this experiment, for, when the mercury has regained its level, the mixture supports the atmospheric pressure on the top of the column B, in addition to the weight of the column of mer- cury Bo. But of these two pressures, one represents that of the dry air, and the other that of the vapour. The second law is, moreover, a necessary consequence of the first. Experiments can only be made with this apparatus at ordinary tempera- tures ; but Regnault, by means of an apparatus which can be used at different temperatures, investigated the pressures of the vapours of water, ether, bisulphide of carbon, and benzole, both in a vacuum and in air. He found that the pressure in air is less than it is in a vacuum, but the differences are so small as not to invalidate Dalton’s law. Regnault was even inclined to consider this law as theoretically true, attributing the differences which he observed to the hygroscopic properties of the sides of the tubes. 390. Problems on mixtures of gases and vapours.—i. A volume of dry air V, at the pressure H, being given, what will be its volume V’, when it is saturated with vapour, the temperature and the pressure remaining the same? If F be the elastic force of the vapour which saturates the air, the latter, in the mixture, only supports a pressure equal to H — F (356). But by Boyle’s law the volumes V and V’ are inversely as their pressures, consequently Vv = ashe whence V’/= te ii. Let V be a given volume of saturated air at the pressure H and the temperature ¢; what will be its volume V’, also saturated, at the pressure H’ and the temperature 7? If f be the maximum pressure of aqueous vapour at 2°, and /” its maximum pressure at 2’°, the air alone in each of the mixtures V and V’ will be respec- tively under the pressures H—f and H’~—/’; consequently, assuming first that the temperature is constant, we obtain Meoaties 7. Wi H’ —f But as the volumes V’ and V of air, at the temperatures / and 4, are in the . ratio of 1 +a?’ to 1+a¢, a being the coefficient of the expansion of air, the equation becomes W Hf 1+ at’ Vie WEL? eal az iil. What is the weight P of a volume of air V saturated with aqueous vapour at the temperature ¢ and pressure H ? If F be the maximum pressure of the vapour at 7°, the pressure of the air alone will be H-F, and the problem reduces itself to finding: Ist, —891] © Spheroidal State 375 the weight of V cubic inches of dry air at ¢ and under the pressure H-F ; and 2nd, the weight of V cubic inches of saturated vapour at 7° under the pressure F. To solve the first part of the problem, we know that a cubic inch of dry air at o° and the pressure 760 millimetres weighs 0°31 grain, and that at 7°, and the pressure H - F, it weighs > ay vee (335) ; consequently V cubic inches of dry air weigh 031 (H-F) V (1 A at) 760 ° . 4 ° ° : (1) To obtain the weight of the vapour, the weight of the same volume of dry air at the same temperature and pressure must be sought, and this is to be multiplied by the relative density of the vapour. Now,as V cubic inches O3U 4 ie (14 + at) 760° aqueous vapour, whose density is 3 that of air (339), weigh of dry air at 7°, and the pressure F, weigh V cubic inches of ci a ae : : ; ; aria (2) (1+ at) 760 8 and as the weight P is equal to the sum of the weights (1) and (2) we have Prog nN og te VE) 5 OBR ea / (H —2 F). (1 + at) 760 (1+at) 760 8 (1+ fi Suu Wun ii ) “a (| ———SSSSSS—aaaaaaasasasaeE SS = Sins i —— Fig. 389 400 On Feat [416— layer as metals have ; but certainly when they are restrained in their motion their conductivity is very small. All substances, for instance, between whose particles air remains stationary, offer great resistance to the propagation of heat. This is well seen in straw, eider-down, and furs. The propagation of heat in a gaseous mass is effected by means of the ascending and descending currents formed in it, as is the case with liquids. The following experiment, a modification of one originally devised by the late Sir W. Grove, is considered to prove that gases have a certain conductivity. A glass tube, fig. 390, with two lateral tubes @ and e opening into it at one end, is closed in the middle by a cork, J, through which a stout copper wire passes. This is connected by thin platinum wires with similar stout copper wires passing through the corks a and c. Whena sufficiently strong electric current is passed through the wires, both platinums are equally incandescent. If, now, one half of the tube is filled with hydrogen by con- necting one of the small tubes with a supply of that gas, and the current is again passed, the wire in the hydrogen is scarcely luminous, while that in air is still brightly incandescent. This greater chilling of the wire in hydrogen than in air was considered by Magnus to be an effect of conduction ; while Tyndall ascribed it to the greater mobility of the particles of hydrogen. Stefan found the value of & for air to be 070000558 in CGS units, so that its conductivity is only ;545,5 that of copper, and 3,5; that of iron. He also found that hydrogen conducts seven times as well as air, and that difference of density seems to have no influence on the conductivity. Maxwell deduced from purely theoretical considerations, based on the kinetic theory of gases, that the conductivity of air must be 5:4, that of iron. 417. Applications.—The greater or less conductivity of bodies meets with numerous applications. Ifa liquid is to be kept warm for a long time, it is placed in a vessel and packed round with non-conducting substances, such as shavings, straw, or bruised charcoal. For this purpose water-pipes and pumps are wrapped in straw at the approach of frost. The same means are used to hinder a body from becoming heated. Ice is transported in summer by packing it in bran or folding it in flannel. Double walls constructed of thick planks having between them any finely divided materials, such as shavings, sawdust, dry leaves, &c., retain heat extremely well ; and are likewise advantageous in hot countries, for they prevent its access. Pure silica in the state of rock crystal is a better con- ductor than lead, but in a state of powder it conducts very badly. If a layer of asbestos is placed on the hand, a red-hot iron ball can be held without inconvenience. Red-hot cannon-balls can be wheeled to the gun’s mouth in —417] Applications 401 wooden barrows partially filled with sand. Lava has been known to flow over a layer of ashes underneath which was a bed of ice, and the non- conducting power of the ashes has prevented the ice from melting. The clothes which we wear are not warm in themselves; they only hinder the body from losing heat, in consequence of their spongy texture and the air they enclose. The warmth of bed-covers and of counterpanes is explained in a similar manner. Double windows are frequently used in cold climates to keep a room warm—they do this by the non-conducting layer of air interposed between them. It is for the same reason that two shirts are warmer than one of the same material but of double the thickness. Hence, too, the warmth of furs, eider-down, &c. The small conducting power of felt is used in the North of Europe in the construction of the Morwegian stove, which consists merely of a wooden ‘box with a thick lining of felt on the inside. In the centre is a cavity in which can be placed a stew-pan provided with a cover. On the top of this is a lid, also made of felt, so that the pan is surrounded by a very badly conducting envelope. Meat, with water and suitable additions, is placed in the pan, and the contents are then raised to boiling point. The whole is then enclosed in the box and left to itself; the cooking will go on without fire, and after the lapse of several hours it will be quite finished. The cooling down is very slow, owing to the bad conducting power of the lining ; at the end of three hours the temperature is usually not found to have sunk more than from 10° to 15°. That water boils more rapidly in a metallic vessel than in one of porcelain of the same thickness ; that a burning piece of wood can be held close to the burning part with the naked hand, while a piece of iron heated at one end can only be held at a great distance, are easily explained by reference to their various conductivities. The sensation of heat or cold which we feel when in contact with certain bodies is materially influenced by their conductivity. If their temperature is lower than ours, they appear colder than they really are, because from their conductivity heat passes away from us. If, onthe contrary, their temperature is higher than that of our body, they appear warmer from the heat which they give up at different parts of their mass. Hence it is clear why carpets, for example, are warmer than wooden floors, and why the latter again are warmer than stone floors. The closer the contact of the hand with a substance, the greater is the difference of temperature felt. With smooth surfaces there are more points of contact than with rough ones. A hot glass rod feels hotter than a piece of rusted iron of the same temperature, although the latter is a better con- ‘ductor. The closer the substance is pressed, the more intimate the contact ; an ignited piece of charcoal can be lifted by the fingers if it is not closely pressed. AOSi) |)” On Feat [418— CHAPTERS VAT! RADIATION OF HEAT 418. Radiant heat.—It has been already stated (410) that heat can be transmitted from one body to another without altering the temperature of the intervening medium. If we stand in front of a fire we experience a sensation of warmth which is not due to the temperature of the air, for if a screen be interposed the sensation immediately disappears, which would not be the case if the surrounding air had a high temperature. Hence bodies can send out rays which excite heat, and which penetrate through the air without heating it, as rays of light through transparent bodies. Heat thus propagated is said to be radiated ; and we shall use the terms ray of heat, or thermad, or calorific ray, in a similar sense to that in which we use the term vay of light, or luminous ray. We shall find that the property of radiating heat is not confined to luminous bodies, such as a fire or a red-hot ball, but that bodies of all tem- peratures radiate heat. It will be convenient to make a distinction between luminous and obscure rays of heat. 419. Detection and measurement of radiant heat.—In demonstrating the phenomena of radiant heat, very delicate thermometers are required, and the thermo-electrical multiplier of Melloni is used for this purpose with great advantage ; for it not only indicates minute differences of temperature, but it also measures them with accuracy. This instrument cannot be properly understood without a knowledge of the principles of thermo-electricity, for which Book X. must be consulted. It may, however, be stated here that when two different metals A and B are soldered together at one end (figs. 391, 392), the free ends being joined by a wire, when the soldering C is heated, a current of electricity circulates through the system; if, on.'+ they jcontraryagorhe soldering be cooled, a current is also produced, Bivesor Rivteoe but it circulates in exactly the opposite direction. This is called a thermo-electric couple or pair. If a number of such pairs be alternately soldered together, as represented in fig. 392, the strength of the current produced by heating the ends is increased ; or, what amounts to the same thing, a smaller quantity of heat will produce the same effect. Such an. —420] Laws of Radiation 403 arrangement of a number of thermo-electric pairs is called a ¢thermo-electric battery or pile. Melloni’s thermomultiplier consists of a thermo-electric pile connected with a delicate galvanometer. The thermo-electric pile is constructed of a number of thin bars of bismuth and antimony soldered together alternately, though kept insulated from each other, and contained in a rectangular box P (fig. 393). The terminal bars are connected with two binding screws m and 7, which in turn are connected with the galvanometer G by means of the wires a and 6. The galvanometer consists of a quantity of fine insulated copper wire coiled round a frame, in the centre of which a delicate magnetic needle is suspended by means of a silk thread. When an electric current is passed through this coil, the needle is deflected through an angle which depends on the strength of the current. The angle is measured ona dial by an index connected with the needle. It may then be sufficient to state that the thermo-electric pile being con- nected with the galvanometer by means of the wires a and J, an excess of Fig. 393 temperature at one end of the pile causes the needle to be deflected through an angle which depends on the extent of this excess ; and similarly if the temperature is depressed below that of the other end, a corresponding deflection is produced in the opposite direction. With an instrument of this kind Melloni was able to measure differences of temperature of sj4oth of a degree. The object of the cone C is to concentrate the thermal rays on the face of the pile. 420. Laws of radiation.—The radiation of heat is represented by three laws :— . | I. Radiation takes place tn all directions from a body. \f a thermometer be placed in different positions round a heated body, it indicates everywhere a rise in temperature. Il. J a homogeneous medium radiation takes place in a right line. For, if a screen be placed in the right line which joins the source of heat and the thermometer, the latter is not affected. DD2 404 On Feat [420- But in passing obliquely from one medium into another, as from air into glass, thermal like luminous rays become deviated, an effect known as refraction. The laws of this phenomenon are the same for heat as for light, and they will be more fully discussed under the latter subject. Ill. Radiant heat ts propagated in vacuo as well as in aiy. This is demonstrated by the following experiment :— In the bottom of a glass flask a thermometer is fixed in such a manner that its bulb occupies the centre of the flask (fig. 394). The neck of the flask is carefully narrowed by means of the blowpipe, and then the apparatus having been suitably attached to an air-pump, a vacuum is produced in the interior. This having been done, the tube is sealed at the narrow part. On immersing this apparatus in hot water, or on bringing near it some hot charcoal, the thermometer is at once seen to rise. This could only be due to radiation through the vacuum in the interior, for glass is so bad a conductor that the heat could not travel with this rapidity through the sides of the flask and the stem of the ther- mometer. 421. Causes which modify the intensity of radiant heat.—By the zx/enszty of radiant heat is understood the quantity of heat received on the unit of surface. Three causes are found to modify this intensity : the temperature of the source of heat, its distance, and the obliquity of the calorific rays in reference to the surface which emits them. The laws which regulate these modifications may be thus stated :— I. Zhe intensity of radiant heat ts proportional to the temperature of the source. Il. Zhe intensity ts inversely as the square of the distance. Ill. Zhe intenstty ts less, the greater the obliquity of the rays with respect to the radiating surface. The first law is demonstrated by placing a metal box containing water at 10°, 20°, or 30° successively at equal distances from the bulb of a differen- tial thermometer. The temperatures indicated by the latter are then found to be in the same ratio as those of the box: for instance, if the temperature of that corresponding to the box at 10° be 2°, those of others will be 4° and 6° re- spectively. The truth of the second law follows from the geometrical principle that the surface of a sphere increases as the square of its radius. Suppose a hollow sphere aé (fig. 395) of any given radius and a source of heat, C, in its centre ; each unit of surface in the interior receives a certain quan- tity of heat. Nowa sphere, ef, of double the radius will present a surface four times as great ; its internal surface contains, therefore, four times as many units of surface, and as the quantity of heat emitted is the same, each unit must receive one-fourth the quantity. To demonstrate the same law experimentally, a narrow tin-plate box is Fig. 304 Fig. 395 —421] Causes which modify the Intensity of Radiant Heat 405 taken (fig. 396), filled with hot water, and coated on one side with lampblack. The thermopile with its conical cap, which in this experiment is lined with black paper to absorb any radiation that falls upon it, is placed so that its face is at a certain definite distance, co, say 9 inches, from this box, and the cover having been lowered, the needle of the galvanometer is observed to be deflected, through 80° for example. —— sil - Sa SS Fig. 396 If now the pile is removed to a distance, CO (fig. 397), double that of co, the deflection of the galvanometer remains the same, which shows that the pile receives the same amount of heat; the same is the case if the pile is removed to three or four times the distance. This result, though a ‘| Fig. 397 apparently in opposition to the second law, really confirms it. For at first the pile only receives heat from the circular portion ad of the side of the box, while, in the second case, the circular portion AB radiates towards it: But, as the two cones ACB and acé are similar, and the height of ACB is double that of acé, the diameter AB is double that of ad, and therefore the 406 On Feat [421- area AB is four times as great as that of ad, for the areas of circles are pro- portional to the squares of the radii. But since the radiating surface increases as the square of the distance, while the galvanometer remains stationary, the heat received by the battery must be inversely as this same square. The third law is demonstrated by means of the following experiment, which is a modification of one originally devised by Leslie (fig. 398) :—P represents the thermomultiplier which is connected with its galvanometer, and A a metal cube full of hot water. The cube being first placed in such Fig. 398 a position, A, that its front face, ac, is vertical, the deflection of the galvano- meter is noted. Supposing it amounts to 45°, this represents the radiation from ac. If this now be turned in the direction represented by A’, the galvanometer is still found to mark 45°. The second surface is larger than the first, and it therefore sends more rays to the mirror. But as the action on the thermometer is no greater than in the first case, it follows that in the second case, where the rays are oblique, the intensity is less than in the first case, where they are per- pendicular. In order to express this in a formula, let z be the intensity of the rays emitted perpendicularly to the surface, and z’ that of the oblique rays. These intensities are necessarily inversely as the surfaces ac and a’c’, for the effect is the same in both cases, and therefore z’ x surface a’c’ =z x surface ac ; surf, .@¢_ 4, ac SUti7 aa of oblique rays ts proportional to the cosine of the anglewhich these rays form wzth the normal to the surface ; for this angle is equal to the angle aoa’. This law is known as the law of the cosine ; it is, however, not general ; Desains and De la Provostaye have shown that it is only true within very narrow limits ; that is, only with bodies which, like lampblack, are entirely destitute of reflecting power (430). 422. Mobile equilibrium. Theory of exchanges.—Prévost of Geneva suggested the following hypothesis in reference to radiant heat, known as Prévost’s theory of exchanges, which is now universally admitted. All bodies, whatever their temperatures, constantly radiate heat in all directions. If we imagine two bodies at different temperatures placed near each other, the one at a higher temperature will experience a loss of heat, its temperature will sink, because the radiation it emits is greater than that which it receives ; the colder body, on the contrary, will rise in temperature, because it receives more radiation than it emits. Ultimately the temperature of both bodies becomes the same, but heat is still exchanged between them, only hence z’=2z =7 cos. aoa’; which signifies that the znzensity —424] Reflection of Heat 407 each receives as much as it emits, and the temperature remains constant. This state is called the modzle eguzlibrium of temperature. 423. Newton’s law of cooling.—A body placed in a vacuum is only cooled or heated by radiation. In the atmosphere it becomes cooled or heated by its contact with the air, according as the latter is colder or hotter than the radiating body. In both cases the velocity of cooling or of heating —that is, the guantity of heat lost or gained in a second—is greater accord- ing as the difference of temperature is greater. Newton enunciated the following law in reference to the cooling or heating of a body :— The quantity of heat lost or gained by a body in a second zs proportional to the difference between tts temperature and that of the sur- rounding medium. Dulong and Petit have proved that this law is not so general as Newton supposed, and only applies where the differences of temperature do not exceed 15° to 20°. Beyond that, the quantity of heat lost or gained is greater than what is required by this law. Two consequences follow from Newton’s law :— I. When a body is exposed to a constant source of heat, its temperature does not increase indefinitely, for the quantity which it receives in the same time is always the same ; while that which it loses increases with the excess of its temperature over that of the surrounding medium. Consequently a point is reached at which the quantity of heat emitted is equal to that ab- sorbed, and the temperature then remains stationary. II. Newton’s law, as applied to the differential thermometer, shows that its indications are proportional to the quantities of heat which it receives. If one of the bulbs of a differential thermometer receives rays of heat from a constant source, the instrument exhibits, first, increasing temperature, but afterwards becomes stationary. In this case, the quantity of heat which it receives is equal to that which it emits. But the latter is proportional to the excess of the temperature of the bulb above that of the surrounding atmo- sphere—that is, to the number of degrees indicated by the thermometer : consequently, the temperature indicated by the differential thermometer is proportional to the quantity of heat it receives. REFLECTION OF HEAT. 424. Laws of reflection.— When thermal rays fall upon a body they are, speaking generally, divided into two portions, one of which penetrates the body while the other rebounds as if repelled from the surface like an elastic ball. This is D said to be reflected. If 7m be a plane reflecting surface (fig. 399), CB an zucident ray, DB a line perpendicular to the surface called the zormal, and BA the ,re- flected ray, the angle CBD is called the angle of incidence, and DBA the angle of reflection. The reflection of heat, like that of lhght, is Fig. 399 governed by the two following laws :— I. The angle of reflection ts equal to the angle of incidence. Il. Both the incident and the reflected ray are in the same plane with the perpendicular to the reflecting surface. 408 On Feat [425— 425. Experimental demonstration of the laws of reflection of heat.— This may be effected by means of Melloni’s thermopile and also by the con- jugate mirrors (427). Fig. 400 represents the arrangement adopted in the former case. MN isa horizontal bar, about a metre in length, graduated in millimetres, on which slide various parts, which can be clamped by means of screws. The source of heat, S,isa platinum spiral, kept at a white heat in a spiritlamp. A screen K, when raised, cuts off the radiation from the source ; a second screen, F, with an aperture in the centre, cuts off all rays except a pencil which falls upon the mirror 7. At the other end is an upright rod, I, with a graduated dial, the zero of which is in the direction of MN, and therefore parallel to the pencil S7z. In the centre of the dial is an aperture, in which turns an axis that supports a metallic mirror 7. About this axis turns an arm, R, on which is fixed the thermopile, P, in connection with the galvanometer G ; H is a screen, the object of which is to cut off any direct radiation from the source of heat towards the pile. In order not to mask the pile, it is not represented in the position it occupies in the experiment. Fig. 400 By lowering the screen K, a pencil of parallel rays, passing through the aperture F, falls upon the mirror 7z, and is there reflected. If the arm R is not in the direction of the reflected pencil, this latter does not fall on the pile, and the needle of the galvanometer remains stationary ; but by slowly turning the arm R, a position is found at which the galvanometer attains its greatest deviation, which is the case when the pile receives the reflected pencil perpendicularly to its surface. Reading off then on the dial the position of a small needle perpendicular to the mirror, we observe that this bisects the angle formed by the incident and the reflected pencils, which demonstrates the first law. 7F The second law is also proved by the same experiment, for the various pieces of the apparatus are arranged so that the incident and reflected rays are in the same horizontal plane, and therefore at right angles to the reflect- ing surface, which is vertical. ~427] Verification of the Laws of Reflection 409 426. Reflection from concave mirrors.—Concave mirrors ox reflectors are polished spherical or parabolic surfaces of metal or of glass, which are used to concentrate luminous or calorific rays in the same point. We shall only consider the case of spherical mirrors. Fig. 402 represents two of these mirrors; fig. 401 gives a medial section, which is called the principal section. The, centre C of M the sphere to whichthemirror belongsis called Miso the centre ofcur- , jes See vature;thepoint , Coma ene A, the middleof \4-~ the refiector, 1s LNG Mere en Oy the petra, Ae Fig. 401 straight line AB | passing through these points, is the principal axis of the mirror. In order to apply to spherical mirrors the laws of reflection from plane surfaces, they are considered to be composed of an infinite number of in- finitely small plane surfaces, each belonging to the corresponding tangent plane; the normals to these small surfaces are all radii of the same sphere, and therefore meet at its centre, the centre of curvature of the mirror. Suppose now, on the axis AB of the mirror MN, a source of heat so distant that the rays EK, PH . . . . which start from it may be considered as parallel. From the hypothesis that the mirror 1s composed of an infini- tude of small planes, the ray EK is reflected from the plane K just as from a plane mirror ; that is to say, CK being the normal to this plane, the reflected ray takes a direction such that the angle CKF is equal to the angle CKE. ‘The other rays, PH, GI... . are reflected in the same manner, and all converge approximately towards the same point F, on the line AC. There is then a concentration of the rays in this point, and conse- quently a higher temperature than at any other point. This point is called the focus, and the distance from the focus to the mirror at A is the focal distance. In the above figure the heat is propagated along the lines EKF, LDF, in the direction of the arrows ; but, conversely, if the heated body be placed at _F, the heat is propagated along the lines FKE, FDL, so that the rays emitted from the focus are nearly parallel after reflection. 427. Verification of the laws of reflection.—The following experiment, which was made for the first time by Pictet and Saussure, and which is known as the experiment of the conjugate mirrors, demonstrates not only the existence of the foci, but also the laws of reflection. Two reflectors, M and N (fig. 402), are arranged at a distance of 4 to 5 yards, and so that their axes coincide. In the focus of one of them, A, is placed a small wire basket containing a red-hot iron ball. In the focus of the other is placed B, an easily inflammable body, such as gun-cotton or phosphorus. The rays emitted from the focus A are first reflected from the mirror M, in a direction parallel to the axis (426), and falling on the other mirror, N, are reflected Eaw&n B&B 410 On Fleat [427- so that they coincide in the focus B. That this is so, is proved by the fact that the gun-cotton at this point takes fire, which is not the case if it is above or below it. The experiment also serves to show that light and heat are reflected in the same manner. For this purpose a lighted candle is placed in the focus of A, and a ground-glass screen in the focus of B, when a luminous focus is seen on it exactly in the spot where the gun-cotton ignites. Hence the luminous and the calorific foci are produced at the same point, and the reflection takes place in both cases according to the same laws, for it will be afterwards shown that for light, the angle of reflection is equal to the angle of incidence, and that both the incident and the reflected rays are in the same plane perpendicular to the plane reflecting surface. From the high temperature produced in the foci of concave mirrors they have been called durning mirrors. It is stated that Archimedes burnt the Roman vessels before Syracuse by means of such mirrors. | Buffon constructed burning mirrors of such power as to prove that the feat attributed to Archimedes was not impossible. The mirrors were made up of a number of silver plane mirrors about 8 inches long by 5 broad. They could be turned independently of each other in such a manner that the rays reflected from each coincided in the same point. With 128 mirrors anda hot summer’s sun Buffon ignited a plank of tarred wood at a distance of 70 yards. 428. Reflection in a vacuum.—Heat is reflected in a vacuum asjwell as in air, as is seen from the following experiment (fig. 403), due to Sir Hum- phry Davy. Two small concave reflectors were placed opposite each other under the receiver of an air pump. In the focus of one was placed a delicate —430] Reflecting Power 4LI thermometer, and in the focus of the other a platinum wire made incandescent by means of a galvanic current. The thermometer was immediately seen to rise several degrees, which could only be due to reflected heat, for the ther- mometer did not show any increase of temperature if it were not exactly in the focus of the second reflector. 429. Apparent reflection of cold.— If two mirrors are arranged as repre- sented in fig. 400, and a piece of ice is placed in one of the foci instead of the red-hot ball, the surrounding tempera- ture being greater than zero, a differ- ential thermometer placed in the focus of the second reflector would exhibit a decrease in temperature of several de- grees. This appears at first to be caused by the emission of /rigorific rays from ice. It is, however, easily explained A I NE from what has been said about the ii iii Heat Hh Fig. 403 mobile equilibrium of temperature (422). There is still an interchange of tempera- ture, but here the thermometer is the warmer body. As the radiation from the thermometer is greater than that emitted by the ice, the former gives out more heat than it receives, and hence its temperature sinks. The sensation of cold experienced when we stand near a plaster or stone wall whose temperature is lower than that of our body, or when we stand in front of a wall of ice, is explained in the same way. 430. Reflecting power.—The veflecting power of a substance is its pro- perty of throwing off a greater or less proportion of incident heat. This power varies in different substances. In order to study this power in different bodies without having recourse to as many reflectors, Leslie arranged his experiment as shown in fig. 404. The source of heat is a cubical canister, M, now known as Leséze’s cube, filled with hot water. A plate, a, of the substance to be experimented upon is placed on the axis of a reflecting mirror between the focus and the mirror. In this manner the rays emitted by the source are first reflected from the mirror and impinge on the plate a, where they are again reflected and converge to the focus between the plate and the mirror, at which point a differential thermometer is placed. The reflector and the thermometer are always in the same position, and the water of the cube is always kept at 100°, but it is found that the temperature indicated by the thermometer varies with the nature of the plate. This method gives a means of determining, not the absolute reflecting power of a body, but its power relatively to that of some body taken‘ as a standard of comparison. For from whatjhas been said on the application of Newton’s law to the differential thermometer (423), the temperatures which this instrument indicates are proportional to the quantities of heat which it receives. Hence, if in the above experiment a plate of glass causes the temperature to rise 1° and a plate of lead 6°, it follows that the quantity of heat reflected by the 412 On Fleat [430- latter is six times as great as that reflected by the former. For the heat emitted by the source remains the same, the concave reflector receives the same portion, and the difference can only arise from the reflecting power of the plate a. By this method Leslie determined the reflecting powers of the following substances, relatively to that of brass, taken as Ioo :— Polished brass . , 4-100 Indian ink : 2 ae Silver ; : ; fiot9o Glass , ; : “BIO Steel , ; SO Oiled glass. , Se Lead ; . ‘ + NGO Lampblack ; 91, FHD The numbers only represent the relative reflecting powers. Their absolute power is the relation of the quantity of heat reflected to the guantity of heat received. Desains and De la Provostaye obtained the following results for the absolute reflecting power by means of Melloni’s thermomultiplier (419), the heat being reflected at an angle of 50° :— Silver plate. : LOO? Steel : 1 Loge Gold : ¢ FOROS Zinc : ; OSE Brass: *; : , EQOA Iron ; : MIO g a Platinum + FO'S3 Cast iron ; i Ok 431. Absorbing power.—The absorbing power of a body is its property of allowing a greater or less quantity of the heat which falls upon it to pass. into its mass. Its absolute value is the ratio of the quantity of heat absorbed to the quantity of heat received. The absorbing power of a body is always inversely as its reflecting power : a body which is a good absorbent is a bad reflector, and vice versd.. —432] Radiating Power 413 It was formerly supposed that the two powers were exactly complementary, that the sum of the reflected and absorbed heat was equal to the total quan- tity of incident heat. This is not the case; it is always less: the incident heat is divided into three parts—tIst, one which is absorbed ; 2nd, another which is reflected regularly—that is, according to laws previously demon- strated (424); and a third, which is irregularly reflected in all directions, and which is called scattered or diffused heat. In order to determine the absorbing power of bodies, Leslie used the apparatus which he employed in determining the reflecting powers (430). But he suppressed the plate a, and placed the bulb of the thermometer in the focus of the reflector. This bulb being then covered successively with lampblack, or varnish, or with gold, silver, or copper foil, &c., the thermo- meter exhibited a higher temperature under the influence of the source of heat, M, according as the substance with which the bulb was covered absorbed more heat. Leslie found in this way that the absorbing power of a body is greater the less its reflecting power. In these experiments, how- ever, the relation of the absorbing powers cannot be deduced from that of the temperatures indicated by the thermometer, for Newton’s law is not exactly applicable in this case, as it only prevails for bodies whose substance does not vary, and here the covering of the bulb varied with each observa- tion. But we shall presently show (433) how the comparative absorbing powers may be deduced from the ratios of the emissive powers. Taking, as a source of heat, a canister filled with water at 100°, Melloni found, by means of the thermomultiplier, the following relative absorbing powers :-— Lampblack . , . 100 Indian ink . ; es White lead . EL OO Shellac : é ie Isinglass : : eet Metals : : ; le 432. Radiating power.—The vadiating or emisstve power of a body is its capability of emitting, at the same temperature, and with the same extent ‘of surface, greater or less quantities of heat. The apparatus represented in fig. 405 was also used by Leslie in deter- mining the radiating power of bodies. For this purpose the bulb of the thermometer was placed in the focus of the reflector, and the faces of the canister M were formed of different metals, or covered with different substances such as lampblack, paper, &c. The cube being filled with hot water, at 100°, and all other conditions remaining the same, Leslie turned each face of the cube successively towards the reflectors, and noted the temperature each time. That face which was coated with lampblack caused the greatest elevation of temperature, and the metal faces the least. Applying Newton’s law, Leslie found the following table of radiating powers :— Lampblack . Sis Tarnished lead . PAs White lead, : TOS Mercury . : . che? 15) Paper 98 Polished lead. ’ Sass Ordinary white glass . 90 Polished iron. 15 Isinglass : : 224880 Tin, gold, silver, copper, &c. 12 414 On Heat [432- It will be seen that, in this table, the order of the bodies is exactly the reverse of that in the tables of reflecting powers. The radiating powers of several substances were determined by Desains and De la Provostaye, who used the thermomultiplier. They found, in this manner, the following numbers compared with lampblack as 1oo :— Platinum foil . ; : . 10°80 Burnished platinum ‘ s ghOrRgO Silver deposited chemically. . . : 2 5936 Copper foil Wi . ; : ; free A10G Gold leaf F : , : ‘ : : -=RAZS Pure silver laminated ; : : : ir 13°08 r, deposited chemically and burnished - 2°25 The radiating power found by Leslie for the metals is thus too large. 433. Identity of the absorbing and radiating powers.—The absorbing power of a body cannot be accurately deduced from its reflecting power, because the two are not exactly complementary. But the absorbing power would be determined if it could be shown that in the same body it is equal to the radiating power. This conclusion has been drawn by Dulong and Petit from the following experiments :—In a large glass globe, blackened on the inside, was placed a thermometer at a certain temperature, 15° for ex- ample; the globe was kept at zero by surrounding it with ice, and having been exhausted by means of atubulure connected with an air-pump, the time was noted which elapsed while the thermometer fell through 5°. The experi- ment was then made in the contrary direction ; that is, the sides of the globe were heated to 15°, while the thermometer was cooled to zero ; the time was then observed which the thermometer occupied in rising through 5°. It was found that this time was exactly the same as that which the thermometer had taken in sinking through 5°, and it was thence concluded that the radiating power is equal to the absorbing power for the same body, and for the same difference between its temperature and the temperature of the sure rounding medium, because the quantities of heat emitted or absorbed in the same time are equal. This point may also be demonstrated by means of the following apparatus devised by Ritchie. Fig. 405 represents what is virtually a differential thermometer, the two glass bulbs of which are replaced by two cylindrical reservoirs B and C, of metal, and full of air. Between them is a third and larger one A, which can be filled with hot water by means of a tubulure, The ends of B and of A, which face the right, are coated with lampblack ; those of C and of A, which face the left, are either painted white, or are coated with silver foil. Thus one of the two faces opposite each other is black, and the other white ; hence when the cylinder A is filled with hot water, its white face radiates towards the black face of B, and its black face towards the white face of C. In these circumstances the liquid in the stem does not move, indicating that the two reservoirs are at the same temperature. On the one hand, the greater emissive power of the black face of A is compensated by the smaller absorptive power of the white face —434] Causes which modify the different Powers 415 of C ; while, on the other hand, the feebler radiating power of the white face of A is compensated by the greater absorbing power of the black face of B. The experiment .may be varied by re- fA, placing the two white faces by discs of paper, = = glass, porcelain, &c. 434. Causes which modify the reflecting, absorbing, and radiating powers.—As the radiating and absorbing powers are equal, any cause which affects the one affects the other also. And as the reflecting power varies in an inverse manner, whatever in- creases it diminishes the radiating and absorbing powers, and vice versa. It has been already stated that these dif- ferent powers vary with different bodies, and that metals have the greatest reflecting power, and lampblack the least. In the same body these powers are modified by the degree of polish, the density, the thickness of the radiating substance, the obliquity of the incident or emitted rays, and, lastly, by the j nature of the source of heat. ie 4s It has been usually assumed that the reflecting power increases with the polish of the surface, and that the other powers diminish therewith. But Melloni showed that by scratching a polished metallic surface its reflecting power was sometimes diminished and sometimes increased. This pheno- menon he attributed to the greater or less density of the reflecting surface. If the plate had been originally hammered, its homogeneity would be destroyed by this process, the molecules would be closer together on the surface than in the interior, and the reflecting power would be increased. But if the surface is scratched, the interior and less dense mass becomes exposed, and the reflecting power diminished. On the contrary, in a plate which has not been hammered, and which is homogeneous, the reflecting power is increased when the plate is scratched, because the density at the surface is increased by the scratches. Melloni found that when the faces of a cube filled with water at a constant temperature were varnished, the emissive power increased with the number of layers up to 16 layers, while above that point it remained constant, what- ever the number. The thickness of the 16 layers was calculated to be o70o4 mm. With reference to metals, gold leaves of 0.008, o’004, and 0-002 of a millimetre in thickness, having been successfully applied on the sides of a cube of glass, the diminution of radiant heat was the same in each case. It appears, therefore, that, beyond certain limits, the thickness of the radiating layer of metal is without influence. The absorbing power is greatest when the rays are at right angles to the surface, and it diminishes in proportion as the incident rays deviate from the normal. This is one reason why the sun is hotter in summer than in winter, because, in the former case, the sun’s rays are less oblique. The radiating power of gaseous bodies in a state of combustion is very Mt —— ila Mt 416 On Heat [434— weak, as is seen by bringing the bulb of a thermometer near a hydrogen flame, the temperature of which is very high. But if a platinum spiral be placed in this flame, it assumes the temperature of the flame, and radiates a great amount of heat, as is shown by the thermometer. For a similar reason the flames of oil and of gas lamps radiate more than a hydrogen flame in consequence of the excess of carbon which they contain, and which, not being entirely burned, becomes incandescent in the flame. 435. Melloni’s researches on radiant heat._-For our knowledge of the phenomena of the reflection, emission, and absorption of heat which have up to now been de- scribed, science is indebted mainly to Leslie. But since his time the dis- covery of other and far more delicate modes of detecting and measuring heat th has not only — extended and Mi ll corrected our previous know- ledge, but has led to the discovery of other phenomena of radiant heat, which ‘without such improved means must have remained unknown. This advance in science is due to an Italian philosopher, Melloni, who first applied the thermo-electric pile, invented by Nobili, to the measurement of very small differences of temperature ; a method of which a preliminary account has already been given (419). In his experiments Melloni used five sources of heat—trst, a Locatelli’s lamp—one, that is, without a glass chimney, but provided with a reflector (fig. 406) ; 2nd, an Argand lamp, that is, one with a chimney and a double draught ; 3rd, a platinum spiral, kept red-hot by a spirit lamp (fig. 407) ; 4th, a blackened copper plate, kept at a temperature of about 400° by a spirit lamp (fig. 408) ; 5th, a copper tube, blackened on the outside and filled with water at 100° (fig. 409). 436. Dynamical theory of heat.—Before describing the results arrived ‘at by Melloni and others, it will be convenient to explain here the view now generally taken as to the mode in which heat is propagated. For additional information the chapter on the Mechanical Theory of Heat and the book on Light should be read. According to what has already been stated (296), a hot body is nothing more than one whose particles are ina state of vibration. The higher the temperature of the body, the more rapid are these vibrations, and a diminution in temperature is but a diminished rapidity of vibration of the particles. The propagation of heat through a bar is due to a gradual communication of this vibratory motion from the heated part to the rest of the bar. A good conductor is one which readily takes up and transmits the vibratory motion from particle to particle, while a bad conductor is one which mk UTI PANASEY Fig. 409 —436] Dynamical Theory of Heat 417 takes up and transmits the motion with difficulty. But even through the best conductors the propagation of this motion is comparatively slow. How then are we to explain the instantaneous perception of heat experienced when a screen is removed from a fire, or when a cloud drifts from the face of the sun? In this case the heat passes from one body to another without affect- ing the temperature of the space through which it passes. In order to ex- plain these phenomena, it is imagined that all space, the interplanetary spaces as well as the interstices in the hardest crystal or the heaviest metal—in short, matter of any kind—is permeated by a medium having the properties of a fluid of infinite tenuity, called eter (511). The particles of a heated body, being in a state of intensely rapid vibration, communicate their motion to the ether around them, throwing it into a system of waves which travel through space and pass from one body to another with the velocity of light. When the undulations of the ether reach a given body, the motion is again delivered up to the particles of that body, which in turn begin to vibrate: that is, the body becomes heated. This process of motion through the hypothetical ether is termed radiation, and what is called a ‘ ray of heat’ is merely a series of waves moving in a certain direction. It will facilitate the understanding of this to consider the analogous mode in which sound is produced and propagated. A sounding body is one whose entire mass is in a state of vibration (228) ; the more rapid the rate of vibra- tion, the more acute the sound ; the slower the rate of vibration, the deeper thesound. This vibratory motion is communicated to the surrounding air, by means of which the vibrations reach the auditory nerve, and there produce the sensation of sound. If a metal ball be heated, say, to the temperature of boiling water, we can ascertain that it radiates heat, although we cannot see any luminosity; and if its temperature be gradually raised, we see it becomes successively of a dull red, bright red, and dazzling white. At each particular temperature the heated body emits waves of a definite length ; in other words, its particles vibrate in a certain period. As its temperature rises it sends out other and more rapid vibrations, which coexist, however, with all those which it had previously emitted. Thus the motion at each successive temperature is compounded of all preceding ones. It has been seen that vibrations of the air below and above a certain rate do not affect the auditory nerve (247) ; it can only take up and transmit to the brain vibrations of a certain periodicity. So too with the vibrations which produce light. The optic nerve is insensible to a large number of wave- lengths. It can apprehend only those waves that form the visible spectrum. If the rate of undulation be slower than the red or faster than the violet, though intense motion may pass through the humours of the eye and fall upon the retina, yet we shall be utterly unconscious of the fact, for the optic nerve cannot take up and respond to the rate of vibrations which exist beyond the visible spectrum in both directions. Hence, these are termed inuistble or obscure rays. A vast quantity of these obscure rays is emitted by flames which, though intensely hot, are yet almost non-luminous, such as the oxy-hydrogen flame, or that of a Bunsen’s burner ; for the vibra- tions which these emit, though capable in part of penetrating the media of the eye, are incapable of exciting in the optic nerve the sensation of light. EE 418 On Ffeat [437— 437. Thermal analysis of sunlight.—When a beam of sunlight (fig. 410), admitted through an aperture in a dark room, is concentrated on a prism of rock salt by means of a lens of the same material, and then, after emerging from the prism, is received on a screen, it will be found to present a band of colours in the following order: red, orange, yellow, green, blue, and violet. This is called the sfectrum (576). If now a narrow and delicate thermopile be placed successively on the space occupied by each of the colours, it will be scarcely affected on the violet, but in passing over the other colours it will indicate a gradual rise of temperature, which is greatest at the red. Painters, thus guided by a cor- rect but unconscious feeling, always speak of blue and green colours as cold, and of red and orange as warm tones. If the pile be now moved in the same direction beyond the limits of the luminous spectrum, the temperature will gradually rise up to CP, at which it attains its maximum. From this point the pile indicates a decrease of temperature until it reaches a point, O, where it ceases to be affected. This point is about as distant from R as the latter is from V ; that is, there is a region in which thermal effects are pro- Riba Fig. 410 duced extending as far beyond the red end of the spectrum in one direction as the entire length of the visible spectrum in the other. In accordance with what we have stated, the sun’s light consists of rays of different rates of vibration. By their passage through the prism they are unequally broken or refracted ; those of greatest wave-length or slowest vibrating period are least bent aside, or are said to be the least refrangible, while those with shorter wave-lengths are the most refrangible. These non-luminous rays outside the red are called the ultra-red rays, or sometimes the Werschelian rays, from Sir W. Herschel, who first discovered their existence. If, in the above case, prisms of other materials than rock salt be used, the position of the maximum heat will be found to vary with the nature of the prism, a fact first noticed by Seebeck. Thus with a prism of water it is in the yellow, with one of crown glass in the middle of the red, and so on. These changes are due to the circumstance that prisms of different materials absorb rays of different refrangibility to unequal extents. But rock salt practically allows heat of all kinds to pass with equal facility, and thus gives a normal spectrum. —438 | Lyndalls Researches 419 438. Tyndall’s researches.—Tyndall investigated the spectrum pro- duced by the electric light, by the following method :—The beam of electric light, rendered parallel by a rock-salt lens, was caused to pass through a narrow slit, and then through a second lens of rock salt ; the slices of white light thus obtained being decomposed by a prism of the same material. To investigate the thermal conditions of the spectrum a “near thermo-electric pile was used ; that is, one consisting of a number of ele- ments arranged ‘B in a line, in front of which was a slit that could be nar- rowed to any extent mnie ite strument was c \ mounted on a movable bar connected with » D a fine screw, so that by turning a handle the pile could be ‘ moved through the smallest space. On placing this apparatus successively in each part of the spectrum of the electric light, the heating effected at various points near each other was determined by a delicate galvanometer. As in the case of the solar spectrum, the heating effect gradually increased from the violet end towards the red, and was greatest in the dark space beyond the red. The position of the greatest heat was about as far from the limit of the visible red as the latter was from the green, and the total extent of the invisible spectrum was found to be twice that of the visible. The increase of temperature in the dark space is very considerable. If thermal intensities are represented by perpendicular lines of proportionate length, erected at those parts of the spectrum to which they correspond, on passing beyond the red end these lines increase rapidly and greatly in length, reach a maximum, and then fall somewhat more suddenly. If these lines are connected, they form a curve (fig. 411), which beyond the red represents a peak, quite dwarfing that of the visible spectrum. In fig. 410, the dark parts at the end represent the obscure radiation. The curve is based, in the manner above stated, on the results obtained by Tyndall with the electric light. The upper curve in fig.\412 represents the spectrum of sunlight with a rock-salt prism, while the lower curve represents the results obtained with a flint-glass prism, which is thus seen to absorb some of the ultra-red radiation. By interposing various substances, more especially water, in certain thicknesses, in the path of the electric hight, the ultra-red radiation was greatly diminished. Now aqueous vapour, like water, absorbs the obscure rays. And probably the reason why the obscure part of the spectrum of sunlight is not so intense as in the case of the electric light is that the EB 2 Fig, 411 420 On Heat [438- obscure rays have been already partially absorbed by the aqueous vapour of the atmosphere. If a solar spectrum could be produced outside the atmo- sphere, it would probably give a spectrum more like that of the electric light, which is unaffected by the atmospheric absorption. This has been confirmed in other ways. Melloni observed that the position of the maximum in the solar spectrum differs on different days ; which is probably due to the varying absorption of the atmosphere, in con- sequence of its varying hygrometric state. Secchi, in Kome, found the red than in sum- same shifting of a i the maximum to mer, when the aqueous vapour in the air is most abundant. Cooke.jfound that the faint occur in the dif- black lines in the selar spectrum attributed to the absorption of light by our ferent seasons atmosphere (see book on Optics) are chiefly caused by the presence of of the year ; for in winter, when © aqueous vapour. there is least moisture in the atmosphere, the maximum is far- ther from the Fig. 412 | Use 1 1 n Aa —— oma i HbDCA | i i ui OY ivisiic: 1% 2h 5 Zea ae ar i] ‘ t : Fig. 413 439. Langley’s observations.—The most accurate and complete investiga- tions of the heat spectrum of the sun have been those made by Langley ; he —440] Luminous and Obscure Radiation 421 used for this purpose a Rowland’s grating (666) so as to avoid effects due to absorption, and the heat in the various parts in the spectrum thus produced was measured by a dolometer which showed differences in temperature of o‘oooo1°® F. He obtained in this way a spectrum invisible to the eye extending beyond the red to 20 times the length of the visible spectrum. Fig. 413 represents about two-thirds of this length, extending to a wave length of 54=0'005 mm. The thermal action begins just outside the violet at a wave length of about 0°25 uw, and is at a maximum between yellow and orange at a wave length of 0°65 ». The depressions in the curve represent the dark lines, or what are called Fraunhofers lines (585). For details of the experiments and interpretation of the results the student should consult the original paper, Phil. Mag. [v] vol. 26, p. 505. 440. Luminous and obscure radiation.—The radiation from a luminous object, a gas flame, for example, is of a composite character ; a portion con- sists of what we term light, but a far greater part consists of heat rays, which are insensible to our eyes, being unable to affect the optic nerve. When this mixed radiation falls upon the blackened face of a thermo-electric pile, the whole of it is taken to be absorbed, the light by this act being converted into heat, and affecting the instrument proportionally with the purely calorific rays. The total radiation of a luminous source, expressed in units of heat, can thus be measured. By introducing into the path of the rays a body capable of stopping either the luminous or the obscure radiation, we can ascertain by the comparative action on the pile the relative quanti- ties of heat and hght radiated from the source. Melloni sought to do this by passing a luminous beam through a layer of water containing alum in solution, a liquid which he found in previous experiments absorbed all the radiation from bodies heated under incandescence. Comparing the transmission through this liquid—which allowed the luminous but not the obscure part of the beam to pass—with the transmission through a plate of rock salt—which affected neither the luminous nor the obscure radiation, but gave the loss due to reflection—Melloni found that 90 per cent. of the radiation from an oil flame and 99 per cent. of the radiation from an alcohol flame consist of invisible calorific rays. Tyndall employed a solution of iodine in carbon bisulphide, which he found to be impervious to the brightest light, but very pervious to radiant heat; only a slight absorption being effected by the bisulphide. By comparing the transmission through the transparent bisulphide, and that through the same liquid rendered opaque by iodine, the value of the luminous radiation from various sources was found to be as follows :— Source Luminous Obscure Red-hot spiral ; ; : EO 100 Hydrogen flame . : ; ORK: 100 Oil flame mike 97 Gas flame : : : : ; cet 96 White-hot spiral ; : Seacliae, 95°4 Electric ight . . : . ; Jnl, go Here by direct experiment the ratio of luminous to obscure rays in the electric light is found to be ro per cent. of the total radiation. By prismatic 422 On Fleat [440- analysis, the curve shown in fig. 411 was obtained, graphically representing the proportion of luminous to obscure rays in the electric light ; by calculating the areas of the two spaces in the diagram, the obscure portion, DCBA, is found to be nearly to times as large as the luminous one, DCE. 441. Transmutation of obscure rays.—We shall find, in speaking of the luminous spectrum (575), that beyond the violet there are rays which are in- visible to the eye, but which are distinguished by their chemical action, and are spoken of as the actinic or chemical rays ; they are also known as the Ritteric rays, from the philosopher who first discovered their existence. Stokes, as we shall afterwards see in the book on Optics, succeeded in converting these rays into visible rays of lower refrangibility ; so Tyndall effected the corresponding but inverse change, and increasing the refrangi- bility of the ultra-red rays, rendered them visible. The charcoal points of the electric light were placed in front of a concave silvered glass mirror so that the rays after reflection were concentrated to a focus about 6 inches distant. On the path of the beam was interposed a cell full of a solution of iodine in carbon bisulphide, which (440) has the power of completely stopping all luminous radiation, but gives free passage to the non-luminous rays. A piece of platinum placed in the focus of the beam, thus sifted, was raised to incandescence by the perfectly invisible rays. In like manner a piece of charcoal zz vacuo was heated to red- ness. By a proper arrangement of the charcoal points a metal may be raised to whiteness, and the light now emitted by the metal yields on prismatic analysis a brilliant luminous spectrum, which is thus entirely derived from the invisible rays beyond the red. This transmutation of non-luminous into luminous heat Tyndall called calorescence. When the eye was cautiously placed in the focus, guarded by a small hole pierced in a metal screen, so that the converged rays should only enter the pupil and not affect the surrounding part of the eye, no impression of light was produced, and there was scarcely any sensation of heat. A con- siderable portion was absorbed by the humours of the eye, but yet a power- ful beam undoubtedly reached the retina; for, as Tyndall showed by a separate experiment, about 18 per cent. of the obscure radiation from the electric light passed through the humours of an ox’s eye. 442. Transmission of thermal rays.—Melloni examined the absorption of heat by solids and liquids by;the apparatus represented in fig. 414, where AB is the thermo-electric pile ; a is a support for the source of heat, in this case a Locatelli’s lamp ; F and E are screens, and C is a support ; while 7z is the pile, and D the galvanometer. To express the power which bodies have of transmitting heat, Melloni used the term diathermancy: diathermancy bears the same relation to radiant heat that transparency does to light ; and in like manner the power of stopping radiant heat is called athermancy, which thus corresponds to opacity for ight. In experimenting on the diathermancy of liquids, Melloni used glass troughs with parallel sides, the thickness of the liquid layer being 0°36 in. The radiant heat of an Argand lamp was first allowed to fall directly on the face of the pile, and the deflection produced in the galvanometer taken as measuring the total radiation 7’, the substance under examination was then —442] Transmission of Thermal Rays 4.23 interposed, and the deflection noted. This corresponded to the quantity of heat, ¢, which is transmitted by the substance. Hence POUT TOO" a the percentage of rays transmitted. Thus calling the total radiation 100, Melloni found that Carbon bisulphide transmitted : : : ; who xs Olive oil Be : ‘ ; : ; » Xe Ether . : : : : : tea Sulphuric acid a : “ ; : ; 2 flys Alcohol -* : : : 5 ; Jets Solution of alum or sugar @ ; : ; : : yA: Distilled water 9 ; : J : : eats In experimenting with solids they were cut into plates o‘1 inch in thick- ness, and it was found that of every Ioo rays there was transmitted by Rock salt ws , : =e 92 Selenite : A220 Smoky quartz } : m7, Adore : . Vek? Transparent lead carbonate . 52 Copper sulphate . 2 ke. The transmission of heat through liquids was re-examined by Tyndall, who used a cell consisting of parallel plates of rock salt separated by a ring of brass with an aperture on the top through which the liquid could be poured. As this ring could be changed at will, liquid layers of various thicknesses were easily obtainable, the apparatus being merely screwed together and made liquid-tight by paper washers. The instrument was mounted on a support before an opening in a brass screen placed in front of the pile. The source of heat employed was a spiral of platinum wire raised to incandescence by an electric current, the spiral being enclosed ina small glass globe with an aperture in front, through which the radiation 424 On Heat [442— passed unchanged in its character, a point of essential importance overlooked by Melloni. The following table contains the results of experiments made with liquids in the various thicknesses indicated, the numbers expressing the absorption per cent. of the total radiation. The ¢vansmisston per cent. can be found in each case by subtracting the absorption from too. Thus a layer of water o'2 inch thick absorbs 80°7 and transmits 19°3 per cent. of the radiation from a red-hot spiral. Absorption of heat by liquids | Thickness of liquids in parts of an inch Liquid | 0°02 | 0°04 0°07 : O'14 0°27 -Carbon bisulphide . OE seg Gin lll Se BIS eee | 1632 bie eee Chloroform . ‘ Al TO Gr ine 2570 35:0 the doro: (aia asones Methyl iodide . ; SPROUT ee 84035 cag 65°20) [aes G iebenzolé.. ‘ HiRAS A; ABS. 55 7A ots 715 nee | Amylene . ; . ch S'S ee heOSr eu shth7s0 TI Fh, AROOBES | Ether : ; : veh te 3" 3 Mew 73 Sie sh GO the ehieaeu lee tama | Alcohol . : ; O7 Bent 0 Om on ro Te Se Lela Phot | Water. ; ch. 80°77. W ASO at boo Oo. nO UO salsa tear It thus appears that there is no connection between diathermancy and transparency. Liquids, except olive oil, are all colourless and transparent; and yet vary as much as 75 per cent. in the amount of heat transmitted. Smoky quartz, which is nearly opaque to light, transmits heat very well ; while alum, which is perfectly transparent, cuts off 88 per cent. of heat rays. As there are different degrees of transparency, so there are different degrees of diathermancy ; and the one cannot be predicated from the other. By studying the transmission of heat from different parts of the spec- trum separately, the connection between light and heat becomes manifest. With this view Masson and Jamin received the spectrum of the solar light given by a prism of rock salt on a movable screen provided with an aperture, so that by raising or lowering the screen the action of any given part of the spectrum on different plates could be investigated. They thus found— That glass, rock crystal, ice, and generally substances transparent for light, are also diathermanous for all kinds of /umznous heat ; That a coloured glass, red, for instance, which only transmits the red rays of the spectrum, and extinguishes the others, also extinguishes every kind of luminous heat, excepting that of the red rays ; That glass and rock crystal, which are diathermanous for luminous heat, also transmit the obscure heat near the red—that is, the most refrangible of the ultra-red rays—but extinguish the extreme obscure rays, or those which are the least deflected by the prism. Alum extinguishes a still greater pro- portion of the obscure spectrum, and ice stops it altogether. Knoblauch has shown that very thin layers of gold, silver, and platinum, which are known to transmit luminous rays of a definite colour, also allow —443] Jnfluence of the Nature of the Source of Heat 425 rays of heat to pass ; so that these substances are diathermanous, though in a small degree. This is also the case with thin sheets of ebonite. 443. Influence of the nature of the source of heat.—The diathermanous power differs greatly with the radiation from different sources, as is seen from the following table, in which the numbers express what proportion of every Ioo rays from the different sources of heat incident on the plates is trans- mitted :— | Locatelli’s | lamp sae | Copper at 400° | Copper at 100° | | | Rock salt . ; hy 92 92 92 92 | Fluor spar : a 78 69 42 a | | Plate glass ma 39 24 6 ) | Black glass : i 26 55 I2 O | Selenite .. 14 5 O O ' Alum : ; Aa 9 | 3 re) O iv Leer: pa SAe A 6 | O'5 | fe) fe) | These different sources of heat correspond to light from different sources. ‘Rock salt is here stated to transmit all kinds of heat with equal facility, and to be the only substance which does so. It is analogous to white glass, which is transparent for light from all sources. Fluor spar transmits 78 per cent. of the rays from a lamp, but only 33 of those from a blackened surface at 100°. A piece of plate glass only one-tenth of an inch thick, and perfectly transparent to light, is opaque to all the radiation from a source of 100°, transmits only 6 per cent. of the heat from a source at 400°, and but 39 of the radiation from the lamp. Black glass, on the contrary, though it cuts off all heat from a source at 100°, allows 12 per cent. of the heat at 400° ta pass, and is equally transparent to the heat from the spiral, but on account of its blackness is more opaque to the heat from the lamp. As we have already seen, every luminous ray is a heat ray ; now as several of the sub- stances in this table are pervious to all the luminous rays, and yet, as in the case of ice, transmit about 6 per cent. of luminous heat, we have an apparent anomaly ; which, however, is only a confirmation of the remarkably small ratio which the luminous rays of a lamp bear to the obscure. From these experiments Melloni concluded that as the temperature of the source rose, more heat was transmitted. This was confirmed by Tyndall. The platinum lamp (438) was used as the source, the temperature of which could be varied from a dark to a brilliant white heat, by a gradual augmentation of the strength of the electric current which heated the platinum spiral. Instead of liquids, vapours were examined in a manner to be de- scribed subsequently ; the results of experiments are given in the table on next page. The percentage of rays absorbed is here seen to diminish in each case as the temperature of the source rises. Mere rise of temperature does not, however, invariably produce a high penetrative power in the rays emitted : the rays from sources of far higher temperature than any of the foregoing are more largely absorbed by certain substances than are the rays 426 On Fleat [443— Absorption of heat by vapour Source, platinum spiral Name of vapour 5 a Barely visible | Bright red White hot Near fusion | Carbon bisulphide 6°5 4°7 2°9 2% Chloroform . g'l 6°3 Si, 3°9 Methyl iodide . i2°5 ) 9°6 7°8 Benzole 26.4 20°6 165 Ether 43°4 314 25°9 237 Formic ether 45°2 31°9 FA 21-3 Acetic ether 49°6 34°65 27o emitted from any one of the sources as yet mentioned. Thus, the radia- tion from a hydrogen flame was completely intercepted by a layer of water only 0:27 of.an inch thick, the same layer transmitting 9 per cent. of the radiation from the red-hot spiral, a source of much lower temperature. The explanation of this is, that those rays which heated water emits (and water the product of combustion is the main radiant in a hydrogen flame) are the very ones which this substance most largely absorbs. This statement, which will become clearer after considering the analogous phenomena in the case of light, was exemplified by the powerful absorption of the heat from a carbonic oxide flame by carbonic acid gas. It will be seen presently (446) that of the rays from a heated plate of copper, ethylene absorbs Io times the quantity intercepted by carbonic acid, whilst of the rays from a carbonic oxide flame Tyndall found carbonic acid absorbed twice as much as ethylene. Carbonic acid, at a pressure of a tenth of an atmosphere, enclosed in a tube 4 feet long, absorbs 60 per cent. of the radiation from a carbonic oxide flame. Radiant heat of this character can thus be used as a delicate test for the presence of carbonic acid, the amount of which may even be accurately measured by the same means. Prof.: Barrett made in this way a physical analysis of the human breath. In one experiment, the carbonic acid con- tained in breath physically analysed was found to be 4°65 per cent., whilst the same breath chemically analysed gave 4°66 per cent. 444. Influence of the thickness and nature of screens.—It will pee seen from the table (443) that of every 100 rays rock salt transmits 92. The other 8 may either have been absorbed or reflected from the surface of the plate. According to Melloni, the latter is the case ; for if, instead of on one plate, heat be allowed to fall on two or more plates whose total thickness does not exceed that of the one, the quantity of heat arrested will be propor- tional to the number of reflecting surfaces. He therefore concluded that rock salt was quite diathermanous. Later experiments show that this con- clusion is not strictly correct ; rock salt does absorb a very small proportion of obscure rays. The quantity of heat transmitted through rock salt is practically the same, whether the plate be 1, 2, or 4 millimetres thick. But with other bodies absorption increases with the thickness, although by no means in direct proportion. This is seen to be the case in the table of absorption by liquids —445] Influence of the Thickness and Nature OF Screens A427 at different thicknesses. The following table tells what proportion of 1,000 rays from a Locatelli’s lamp pass through a glass plate of the given thickness :— MDickness Intiiinmerces. 0,5 ff 2 @ueetemse O75)! S Rays transmitted . - 775 733 682 653 634 620 609 600 592 The absorption takes place in the first layers ; the rays which have passed these possess the property of passing through other layers ina higher degree, so that beyond the first layers the heat transmitted approaches a certain constant value. If a thin glass plate be placed behind another glass plate a centimetre thick, the former diminishes the transmission by little more than the reflection from its surface. But if a plate of alum were placed behind the glass plate, the result would be different, for the latter is opaque for much of the heat transmitted by glass. Heat, therefore, which has traversed a glass plate traverses another plate of the same material with very slight loss, but is very greatly diminished by a plate of alum. Of I00 rays which had passed through green glass or tourmaline, only 5 and 7 were respectively transmitted by a similar plate of - alum. A plate of blackened rock salt only transmits obscure rays, while alum extinguishes them. Consequently, when these two substances are superposed, a system impervious to light and heat is obtained. These phenomena find their exact analogies in the case of hight. The different sources of heat correspond to flames of different colours, and the screens of various materials to glasses of different colours. A red flame looked at through a red glass appears quite bright, but through a green glass it appears dim or is scarcely visible. So in like manner heat which has traversed a red glass passes through another red glass with little diminu- tion, but it is almost completely stopped by a green glass. Rock salt at 150° emits only one kind of heat ; it is »zonothermadl, just as sodium vapour is monochromatic. Different luminous rays being distinguished by their colours, Melloni gave the name of ‘¢hermocrose or heat coloration to these different obscure calorific rays. The invisible portion of the spectrum is accordingly mapped out into a series of spaces, each possessing its own peculiar feature corre- sponding to the coloured spaces which are seen in that portion of the spec- trum visible to our eyes. Besides thickness and colour, the polish of a substance influences the transmission. Glass plates of the same size and thickness transmit more heat as their surface is more polished. Bodies which transmit heat of any kind very readily are not heated. Thus a window pane is not much heated by the strongest sun’s heat ; but a glass screen held before a common fire stops most of the heat, and is itself heated thereby. The reason of this is that by far the greater part of the heat from a fire is obscure, and glass is opaque to this kind of heat. | 445. Diffusion of heat.—When}a ray of light falls upon an unpolished surface in a definite direction, it is decomposed into a variety of rays which are reflected from the surface in all directions. This irregular reflection is called afuston, and it is in virtue of it that bodies are visible when light falls up6n them. A further peculiarity is, that all solar rays are not equally 428 On Heat : [445- diffused from the surface of bodies. Certain bodies diffuse certain rays and absorb others, and accordingly appear coloured. The red colour of a gera- nium is caused by its absorbing all the rays, excepting the red, which are irregularly reflected. Just as is the case with transmitted light in transparent bodies, so with diffused hight in opaque ones ; for if a red body is illuminated by red light it appears of a bright red colour, but if green light fall upon it it is almost black. We shall now see that here again analogous phenomena prevail with heat. Various substances diffuse different thermal rays to a different extent ; each possesses a peculiar thermocrose. Melloni placed a number of strips of brass foil between the source of heat and the thermopile. They were coated on the side opposite to the pile with lampblack, and on the other side with the substances to be investigated. Representing the quantity of heat absorbed by the lampblack by too, the absorption of the other bodies was as follows :— arisen eal | Copper at 400° | Copper at 100° | | | Lampblack : : : i 100 | 100 100 White lead : . : 56 | 89 100 | Isinglass . ; 54 | 64 gI | Indian ink : ‘ : ae 95 | 87 85 | | Shellac . : F : ~ 47 70 D | | Polished metal | Tas peer 13 3 Hence white lead absorbs far less of the heat radiated from incandescent platinum than lampblack, but it absorbs the obscure rays from copper at 100° as completely as lampblack. Indian ink is the reverse of this; it absorbs obscure rays less completely than luminous rays. Lampblack absorbs the heat from all sources in equal quantities, and very nearly com- pletely. In consequence of this property all thermoscopes which are used for investigating radiant heat are covered with lampblack, as it is the best- known absorbent of heat. The behaviour of metals is the reverse of that of lampblack. They reflect the heat of different sources in the same degree. They are to heat what wz¢e bodies are to light. As coloured light is altered by diffusion from several bodies, so Knoblauch has shown that the different kinds of heat are altered by reflection from dif- ferent surfaces. The heat of an Argand lamp diffused from white paper passes more easily through calcspar than when it has been diffused from black paper. The rays of heat, like the rays of light, are susceptible of polarisation and double refraction. These properties will be better understood after the subject of light has been treated. 446. Relation of gases and vapours to radiant heat.—This subject was investigated by Tyndall ; the apparatus he used is represented in the adja- cent figure, the arrangement being looked upon from above. A (fig. 415) is a cylinder about 4 feet in length and 24 inches in diameter, placed horizontally, the ends of which can be closed with rock salt plates ; —446] Relation of Gases and Vapours to Radiant Heat 429 by means of a lateral tube at 7 it can be connected with an air-pump and exhausted ; while at ¢ is another tube which serves for the introduction of gases and vapours. T is a sensitive thermopile connected with an extremely delicate galvanometer, M. The deflections of this galvanometer were proportional to the differences of temperature of the faces of the thermopile up to about 30° ; beyond this point the proportionality no longer held good, and accordingly, for greater differences, a table was empirically constructed, in which the value of the higher deflections was expressed in units; the unit being the difference of temperature necessary to move the needle through one of the lower degrees. C was a source of heat, which usually was either a Leslie’s cube filled with boiling water, or else a sheet of blackened copper heated by gas. Now, when the source of heat was permitted to radiate through the exhausted ube, the needle made a great deflection ; and in this position a very con- siderable degree of absorption would have been needed to produce an alteration of 1° of the galvanometer. Andif to lessen this deflection a source of heat of lower temperature had been used, the fraction absorbed would be correspondingly less, and might well have been insensible. Hence Tyndall adopted the following device, by which he was enabled to use a powerful flux of heat, and at the same time to discover small variations in the quantity falling on the pile. Cc ey) Fig. 415 The source of heat at C was allowed to radiate through the tube at the end of which the pile was placed ; a deflection was produced of, say, 70° ; a second source of heat, D, was then placed near the other face of the pile, the amount of heat falling on the pile from this compensating cube being regulated by means of a movable screen S. Since the strength of the thermo- electric current, and therefore the deflection of the galvanometer needle, depends upon the difference of temperature of the two faces.of the thermo- pile, it is clear that when the compensation by D is perfect there will be no deflection, however high may be the temperature on both sides. In the arrangement just described, by means of the screen S, the radiation from the compensating cube was caused to neutralise exactly the radiation from the source C ; the needle consequently was brought down from 70° to zero, and remained there so long as both sources were equal. If now a gas or vapour be admitted into the exhausted tube, any power of absorption it may possess will be indicated by the destruction of this equilibrium, and pre- ponderance of the radiation from the compensating cube by an amount corresponding to the heat cut off by the gas. Examined in this way, air, hydrogen, and nitrogen, when dried by passing through sulphuric acid, were found to exert an almost inappreciable effect; their presence as regards 430 On Fleat [446- radiant heat being but little different fromavacuum. But with ethylene and other complex gases the case was entirely different. Representing by the number 1 the quantity of radiant heat absorbed by air, ethylene absorbs g70 times, and ammoniacal gas 1,195 times, this amount. In the following table is given the absorption of obscure heat by various gases, referred to air as unity :— Absorption |! Absorption Name of gas ‘under 30 inches|| Name of gas ‘under 30 inches i of pressure | of pressure Air I | Carbonic acid . a go | Oxygen I || Nitrous oxide. os Nitrogen I | Marsh gas . ‘ 403 Hydrogen , I | Sulphurous acid . . 710 . Chlorine ; é fe 39 |) Ethylene. ~. ; . 970 Hydrochloric acid a 62 | Ammonia . : VINE SiO5 If, instead of comparing the gases at a common pressure of one atmo- sphere, they are compared at a common pressure of an inch, their differences in absorption are still more strikingly seen. Thus, assuming the absorption by 1 inch of dry air to be 1, the absorption by 1 inch of ethylene is 7,950, and by the same amount of sulphurous acid 8,800. 447. Influence of pressure and thickness on the absorption of heat by gases.—The absorption of heat by gases varies with the pressure; this variation is best seen in the case of those gases which have considerable absorptive power. Taking the total absorption by atmospheric air under ordinary pressure at unity, the numbers of ethylene under a pressure of 1, 3, 5, 7, and ro inches of mercury are respectively 90, 142, 168, 182, and 193. Thus ethylene, at a pressure of one-thirtieth of an atmosphere, exerts go times the absorption of air at ordinary pressure. And the absorption, it is seen, increases with the density, though not in a direct ratio. Tyndall showed, however, by special experiments, that for very low pressures the absorption does increase with the density. Employing as unit volume of the gas a quantity which measured only »4 of a cubic inch, and admitting succes- sive measures of ethylene into the experimental tube, it was found that up to 15 measures the absorption was directly proportionate to the density in each case. In these experiments the length of the experimental tube remained the same, whilst the pressure of the gas within it was caused to vary ; in subse- quent experiments the pressure of the gas was kept constant, whilst the length of the tube was, by suitable means, varied from o:o! of an inch up to so inches. The source was a heated plate of copper ; of the total radiation from this nearly 2 per cent. was absorbed by a film of ethylene -o1 of an inch thick, upwards of 9 per cent. by a layer of the same gas ol of an inch thick, 33 per cent. by a layer 2 inches thick, 68 per cent. by a column 20 inches long, and 77 per cent. by a column rather more than 4 feet long. 448. Absorptive power of vapours.—The absorptive power of ethy- lene is exceeded by that of-several vapours. The liquid from which the —448] Absorptive Power of Vapours 431 vapours were to be produced was enclosed in a small flask, which could be attached with a stop-cock to the exhausted experimental tube. The absorp- tion was then determined after admitting the vapours into the tube in quantities measured by the pressure of the barometer gauge attached to the air-pump. The following table shows the absorption of vapours under pressures varying from o'l to 4 inch of mercury :— Absorption under pressure in inches of mercury Name of vapours | o'r | ou T‘o | Carbon bisulphide. 15 47 | 62 Benzole : : : Saul 66 182 | 267 | Chloroform . ! ; 28 85 182 | 236 ieEther =! f é 2 300 710 | 870 | Alcohol . , ‘ . hy 325 622 | Acetic ether . ; : : 590 986 ie MEIOS These numbers refer to the absorption of a whole atmosphere of dry air as their unit, and it is thus seen that a quantity of carbon bisulphide vapour, the feeblest absorbent yet examined, which only exerts a pressure of the 34, of an atmosphere, gave fifteen times the absorption of an entire atmosphere of air ; and acetic ether, under the same conditions, 590 times as much. Comparing air at a pressure of o'r with acetic ether of the same pressure, the absorption of the latter would be more than 17,500 times as great as that of the former. Odours from the essential oils exercised a marked influence on radiant heat. Dry air was allowed to pass through a tube containing dried paper impregnated with various essential oils, and then admitted into the experi- mental tube. Taking the absorption of dry air as unity, the following were the numbers respectively obtained for air scented with various oils :— Patchouli 31, otto of roses 37, lavender 60, thyme 68, rosemary 74, cassia 109, aniseed 372. Thus the perfume of a flower-bed absorbs a large percentage of the heat of low refrangibility emitted from it. Ozone prepared by electrolysing water was also found to have a remark- able absorptive effect. The small quantity of ozone present in electrolytic oxygen was found in one experiment to exercise 136 times the absorption of the entire mass of the oxygen itself. But the most important results are those which follow from Tyndall’s experiments on the behaviour of aqueous vapour to radiant heat. The experi- mental tube was filled with perfectly dry air, and the absorption was found to be one unit. Exhausting the tube, and admitting the ordinary undried, but not specially moist, air from the laboratory, the absorption now rose to 72 units. The ‘difference between dried and undried air can only be ascribed to the aqueous vapour the latter contains. Thus on a day of average humidity the absorption due to the transparent aqueous vapour present in the atmosphere is 72 times as great as that of the air itself, though in quantity the latter is about 200 times greater than the former. Analogous results were obtained 432 On Heat [448— on different days, and with specimens of air taken from various localities. When air which had been specially purified and dried was allowed to pass through a tube filled with fragments of moistened glass and examined, it was found to exert an absorption 90 times that of dry air. In other experi- ments Tyndall suppressed the use of rock salt plates in his experimental tube, and even the tube itself, and yet in every case the results were such as to show the great power which aqueous vapour possesy2s as an absorbent of radiant heat. The absorptive action which the aqueous vapour in the atmosphere exerts on the sun’s heat has been established by a series of actinometrical observa- tions made by Soret at Genevaand on the summit of Mont Blanc ; he found that the intensity of the solar heat on the top of Mont Blanc is £ of that at Geneva; in other words, that of the heat which is radiated at the height of Mont Blanc, about 4 is absorbed in passing through a vertical layer of the atmosphere 14,436 feet in thickness. The same observer has found that with the sun at heights which are virtually equal there is the smallest trans- mission of heat on those days on which the pressure of aqueous vapour is greatest ; that is, when there is most moisture in the atmosphere. 449. Radiating power of gases.—Tyndall also examined the radiating power of gases. A red-hot copper ball was placed so that the current of heated air which rose from it acted on one face of a thermopile ; this action was compensated by a cube of hot water placed in front of the opposite face. On then allowing a current of dry ethylene from a gasholder to stream through a ring burner over the heated ball and thus supplant the ascending current of hot air, it was found that the gas radiated energetically. By com- paring in this manner the action of many gases it was discovered that, as is the case with solids, those gases which are the best absorbers are also those which radiate most freely. 450. Dynamic radiation and absorption.—A gas when permitted to enter an exhausted tube is heated in consequence of the collision of its par- ticles against the sides of the vessel ; it thus becomes a source of heat, which is perfectly capable of being measured. Tyndall calls this dynamic heating. In like manner, when a tube full of gas or vapour is rapidly exhausted, a chilling takes place owing to the loss of heat in the production of motion ; this he calls dynamic chilling or absorption. He could thus determine the radiation or absorption of a gas without any source of heat external to the gas itself. An experimental tube was taken, one end of which was closed with a polished metal plate, and the other with a plate of rock salt ; in front of the latter was the face of the pile. The needle being at zero, and the tube exhausted, a gas was allowed quickly to enter until the tube was full, the effect on the galvanometer being noted. This being only a transitory effect, the needle soon returned to zero; the tube was then rapidly pumped out, by which a sudden chilling was produced, and the needle exhibited a deflection in the opposite direction. Comparing in this way the dynamic heating and chilling of various gases, those gases which are the best absorbers were also found to be the best radiators. Polished metallic surfaces are, as we have seen (432), bad radiators, but radiate freely when covered with varnish. Tyndall made the curious experiment of varnishing a metallic surface by a film of gas.. A Leslie’s —451] Relation of Absorption to Molecular State 433 cube was placed with its polished metal side in front of the pile, and its effect neutralised by a second cube placed before the other face of the pile. On allowing a stream of ethylene or of coal gas to flow over the metal face of the first cube, a copious radiation from that side was produced as long as the flow of gas continued. Acting on the principle indicated in the fore- going experiment, Tyndall determined the dynamic radiation and absorp- tion of vapours. The experimental tube containing a vapour under a small known pressure, air was allowed to enter until the pressure inside the tube was the same as that of the atmosphere. In this way the enter- ing air, by its impact against the tube, became heated ; and its particles mixing with those of the minute quantity of vapour present, each of them became, so to speak, coated with a layer of the vapour. The entering air was in this case a source of heat, just as in the above experiments the Leslie’s cube was. Here, however, one gas varnished another ; the radia- tion and subsequently the absorption of various vapours could thus be determined. Vapours were found to differ very materially in their power of radiating under these circumstances ; of those tried carbon bisulphide was the worst and boracic ether the best radiator. In all cases the best absorbents were also the best radiators. 451. Relation of absorption to molecular state.—After examining the absorption of heat by vapours, Tyndall tried the same substances in a liquid form in the same conditions of experiment. Thesource of heat was a spiral of platinum heated to redness by an electric current of known strength ; and plates of rock salt were invariably employed in the case of both vapours and liquids. Finally, the absorption by the vapours was re-measured ; in this case by introducing into the experimental tube, not, as before, equal quanti- ties of vapour, but amounts proportional to the density of the liquid. When this last condition had been attained, it was found that the order of absorp- tion by a series of liquids, and by the same series when turned into vapour, was precisely the same. Thus the substances tried stood in the following order as liquid and as vapour, beginning with the feeblest absorbent, and ending with the most powerful :— Liquids Vapours Carbon bisulphide . . Carbon bisulphide. Chloroform . : : ; : . Chloroform. Ethyl iodide. ¢ : : ; . Ethyl iodide. Benzole ; J : ‘ 5 . Benzole. Ether ©. ; : . 4 L/P Ether Alcohol : : : : é . Alcohol. Water A direct determination of aqueous vapour could not be made, on account of its small elastic force and the hygroscopic nature of the rock salt. But the undeviating regularity of the absorption by all the other substances in the list, both as liquids and vapour, establishes the fact, which is corroborated by the experiments already mentioned, that aqueous vapour is one of the most energetic absorbents of heat. In this table it will be noticed that those substances which have the ¥ F 434 On Feat [451— simplest chemical constitution stand first in the list, with one anomalous exception, namely, that of water. Inthe absorption of heat by gases, Tyndall found that the elementary gases were the feeblest absorbents, while the gases of most complex constitution were the most powerful absorbents. Thus it may be inferred that absorption is mainly dependent on chemical consti- tution; that is to say, that absorption and radiation are molecular acts independent of the physical condition of the body. Tyndall discovered that the radiation of powders is similar to that of the solids from which they were derived, and therefore differs greatly zzfer se. The absorbent power of powders was also found to correspond with their radiative power—which, as we have shown, is the case with solids and gases, and is doubtless also true for liquids. The powders were attached to the tin surfaces of a Leslie’s cube, in such a manner that radiation took place from the surface of the powder alone. The following table gives the radiation in units from some of the powders examined by Tyndall; the metal surface of the cube giving a deflection of 15 units :— Radiation from powders. Rock salt 2 : ges Calcium sulphate. nitager Mercury biniodide. sor, Red oxide of iron . LSA Sulphur . i yoo Hydrated zinc oxide . 804 Calcium carbonate wo? Iron sulphide . f on fey Dead ‘oxide. : ne we. Lampblack . ; BAO These substances are of various colours. Some are white, such as rock salt, calcium carbonate and sulphate, and hydrated zinc oxide; some are red, such as mercury biniodide and lead oxide; whilst others are black, as iron sulphide and lampblack. The colours, therefore, have no influence on the radiating power: rock salt, for example, is the feeblest of radiators, and hydrated zinc oxide one of the most powerful. Nearly a century ago Franklin made experiments on coloured pieces of cloth, and found their absorption, indicated by their sinking into snow on which they were placed, to increase with the darkness of the colour. But all the cloths were equally powerful absorbents of obscure heat, and the effects noticed were only produced by their relative absorptions of light. In fact, the conclusions to be drawn from Franklin’s experiments only hold good for luminous heat, especially sunlight such as he employed. 452. Applications.—The properties which bodies possess of absorbing, emitting, and reflecting heat meet with numerous applications in domestic economy and in the arts. Leshe stated in a general manner that white bodies reflect heat very well, and absorb very little, and the contrary is the case with black substances. As we have seen, this principle is not generally true, as Leslie supposed ; for example, white lead has as great an absorbing power for non-luminous rays as lampblack (445). Leslie’s principle applies to powerful absorbents like cloth, cotton, wool, and other organic substances when exposed to luminous heat. Accordingly, the most suitable coloured clothing for summer is just that which experience has taught us to use, namely, white, for it absorbs less of the sun’s rays than black clothing, and hence feels cooler. ~453] } Applications 435 The polished fire-irons before a fire are cold, whilst the black fender is often unbearably hot. If, on the contrary, a liquid is to be kept hot as long as possible, it must be placed in a brightly polished metallic vessel, for then, the emissive power being less, the cooling is slower. Hence it is advantageous that the steam pipes, &c., of locomotives should be kept bright. In the Alps, the mountaineers accelerate the fusion of the snow by covering it with earth, which increases the absorbing power. ‘In our dwellings, the outside of stoves and of hot-water apparatus ought to be black, and the insides of fireplaces ought to be lined with firebrick, in order to increase the radiating power towards the apartment. It is owing to the great diathermancy of dry atmospheric air that the higher regions of the atmosphere are so cold, notwithstanding the great heat which traverses them; whilst the intense heat of the sun’s rays on high mountains is probably due to the comparative absence of aqueous vapour at these elevations. As nearly all the luminous rays of the sun pass through water, and the sun’s radiation as we receive it on the surface of the earth consists of a large proportion of luminous rays, accidents have often arisen from the con- vergence of these luminous rays by bottles of water which act as lenses. In _ this way gunpowder could be fired by the heat of the sun’s rays concen- trated by a water lens; and the drops of water on leaves in greenhouses have been found to act as lenses, and burn the leaves on which they Tesh. Certain bodies can be used (440) to separate the heat and light radiated from the same source. Rock salt coated with lampblack, or still better with iodine, transmits heat, but completely stops light. On the other hand, alum, either as a plate or in solution, or a thin layer of water, is permeable to light, but stops all the heat from obscure sources. This property is made use of in apparatus illuminated by the sun’s rays, in order to sift the rays of their heating power; a vessel full of water or a solution of alum is used with the electric light when it is desirable to avoid too intense a heat. In gardens, the use of shades to protect plants depends partly on the diathermancy of glass for heat from luminous rays and its athermancy for obscure rays. The heat which radiates from the sun is largely of the former quality, but by contact with the earth it is changed into obscure heat, which, as such, cannot retraverse the glass. This explains the manner in which greenhouses accumulate their warmth, and also the great heat experienced in summer in rooms having glass roofs, for the glass in both cases acts, as it were, as a valve which effectually entraps the solar rays. On the same principle plates of glass are frequently used as screens to protect us from the heat of a fire ; the glass allows us to see the cheerful light of the fire, but intercepts the larger part of the heat radiated from the fire. Though the screens thus become warm by the heat they have absorbed, yet, as they radiate this heat in all directions towards the fire as well as towards us, we finally receive less heat when they are interposed. 453. Attraction and repulsion arising from radiation.—Crookes dis- covered a highly remarkable class of phenomena which are due to the radiant action of heated and of luminous bodies. These phenomena are FF 2 436 On Feat [453— most conveniently illustrated by means of an instrument which he has devised, and which is called the ~adtometer, the construction of which 1s as follows :—A glass tube (fig. 416), with a bulb blown on it, is fused at the bottom to a glass tube which at one end serves to rest the whole apparatus in a wooden support. In the other end is fused a fine steel point. On this rests a small vane or fly, consisting of four arms of aluminium wire fixed at one end to a small cap, while at the others are fixed small discs or lozenges of thin mica, coated on one side with lampblack. The weight of the fly is not more than two grains. In order to keep the fly on the pivot a tube is fused in the upper part of the bulb which reaches down to and just sur- rounds the top of the cap, without, how- ever, touching it; the other end of this tube is drawn out and connected with an arrangement for exhausting the air by the Sprengel pump (208) or by chemical means : when the desired degree of ex- haustion has been attained this can be sealed. By keeping the apparatus during exhaustion in a hot-air bath at a tempera- ture of 300°, the gases occluded on the inner surface of the glass, and by the vanes, are got rid of. If a source of light or of heat, a candle for instance, is brought near the fly, it is attracted, and the fly rotates slowly in a direction showing that the blackened side moves towards the light ; this movement, indicating an attraction, depends on a certain state of rarefaction. If, however, the apparatus be connected with an arrangement which allows the pressure to be varied, this rotation gradu- ally diminishes in rapidity as the air = within is further rarefied, until a certain Fig. 416 ) point is reached at which it ceases. If now the rarefaction is pushed further, the highly remarkable phenomenon is observed that repulsion succeeds to attraction, and that the fly now rotates in the direction away from the source of heat. In a double radiometer, in which two flies are pivoted indepen- dently one over the other, having their blackened sides opposite each other, the flies rotate in opposite directions on the approach of a lighted candle. When a cold body, such as a piece of ice, is brought near, instead of a hot one, exactly the opposite effects are observed; when the vessel contains air a pith ball svspended at one end of a light arm is repelled, the —453] dia iv; Z, RS SSSA GAA AAAS SS SS SSN SS SSS SNS SN SSS NS SSS SITS SN ISS INSISTENT SNWH FS RE BSRIAWSG ¥ NISRA SSS SSS SIS SSISSISS SSIS SS SS SS SSSI SSSI INSS SSN SAQAA,/ Fig. 433 encircling the boiler with flues it is endeavoured to get all the heat possible from the gases before they are allowed to pass away up the chimney. The principal f¢tings or mountings of the boiler are indicated in the figures, and are as follows : G is a dome on which stands the s¢op-valve N through which the steam is carried to the engine. The object of the dome is to take the steam from a point far away from the water line, so that it may be as dry as possible. P is a safety valve, held down on its seat by the action of a weighted lever, and so ad- justed that as soon as the pressure of steam reaches its intended maximum and tends to rise beyond it, the valve is lifted and the steam : rushes away into the air. Q isa man-hole Edy door by which access is had to the interior : of the boiler, when it is empty and out of use, for cleaning and repair. Ris a pressure gauge or indicator, standing in front of the shell, showing, by a hand working in front ofa dial plate, the ‘ boiler pressure’ or amount by which the pressure of steam inside the boiler exceeds that of the atmosphere surrounding it. S is a water gauge, a glass tube connected at top and bottom to the boiler, its upper end to the steam space, and the lower end to the water space. The water stands in the glass tube at the same level as in the boiler, and the fireman can see at a glance whether it is at the right height. This matter is of great importance, because an accidental fall of water-level is a frequent cause of boiler explo- sions. If, for instance, the water fell so low as to leave the top of the furnace B uncovered, the plates would get red-hot and soften so much as to collapse Ss SSSGEVN Fig. 434 477] Cornish Engine 465 under the action of the steam pressure, with consequences that might be most serious. : In marine boilers, when it is of the greatest importance to get as much heating surface as possible into a small space, and similarly in the locomotive boiler to be presently described, the hot gases after leaving the furnace are made to pass through a number of small tubes instead of one large one as in fig. 433. Such boilers are called szzltitubular botlers. Of late years the shells of large boilers have frequently been made of “mild steel,’ produced by the Bessemer or Siemens- Martin processes, rather than of wrought iron. In locomotive boilers, where the combustion is very rapid and intense, the fire-boxes are frequen made of copper, a mnych better conductor a heat than either iron or steel. 477. Cornish engine.—Fig. 435 shows the oldest of all the types of engines still in use, the Cornish pumping engine, which is worth examina- Spear SSB == Oe 2) SOOAD AS w \\ AA A a ~~ mr i | I | | NX pe Seba pa i M ie it mt | l Tee Hl IN a ul) le le ECC ll. ao \~ \ Be : ~ SAR Xr CS 9 WR Fig. 435 tion both for its historical interest and on account of the special way in which it works. (In the figure all details except those absolutely necessary to illustrate the action of the engine are omitted.) The engine has a vertical cylinder A (often of very great size, and with as much as Io or I! ft. stroke), in which works a piston P, whose rod is connected by a chain to a sector on the end of a beam B. Beside the cylinder is a chamber C containing the valves for admitting and discharging steam, whose mode of working will be presently described. At the further end of the beam a second sector is HH 466 On Feat [477— connected with the pump-rod, at the upper end of which is placed a heavy counterweight Q. Below the cylinder a pipe M leads to a chamber N called the condenser, into which a jet of water from the tank in which it stands continually plays. The condenser in its turn is connected with a pump called an air-pump, worked from the beam by the rod E, and fitted with suction and discharge valves, and valves in its piston in the usual way. We can follow the working of the engine easily by supposing the piston to start at the top of its stroke. The valves are then in the position shown, uz open, 7 and o closed. Steam passes from the boiler through the pipe T to the top of the piston, and forces it down against the small pressure of the steam below it, this steam escaping into the condenser through the valve o and the pipe M. The pump-rods or fzt work, and the weight Q, are thus lifted to the top of their stroke. When the piston arrives at the bottom of its stroke the valves #7 and o are shut and wz is opened. This allows free communication between the two sides of the piston, and so puts it into equilibrium. The counter-weight Q, together with the pump-rods, is made somewhat heavier than the piston and rod plus the whole weight of the column of water to be lifted. It therefore falls slowly (the whole affair thus becoming an Atwood’s machine (78) on an enormous scale), and forces up the water through the pumps. As soon as the piston has once more got to the top of its stroke, by which time of course all the steam has been transferred to its under side, the position of the valves is again reversed, and the piston once more begins to fall. The steam below the piston is suddenly put into communication with the condenser N, into which a jet of cold water is always playing. It is therefore reduced in temperature almost instantaneously, much of it is condensed into water, and the rest, which still fills the space below the piston, is necessarily reduced to a pressure of only about 3 pounds per square inch or about 4 of an atmosphere. As the pres- sure of the steam coming direct from the boiler in such engines is often 50 pounds per square inch above that of the atmosphere, it follows that the differ- ence of pressure on the two sides of the piston in such a case is 50+ 15 —3 =62 pounds per square inch, and it is this difference of pressure which compels the piston to move downwards and lift all the weight at the other end of the beam. The condensed steam and the condensing water fall together at the bottom of the condenser, and are continually removed (along with the uncondensed steam and any air that may be present) by the azr pump, which is a simple lift pump with a valve in its piston (220). In all modern Cornish engines the beams are of iron and the sector and chains are replaced by an arrangement of iron links forming a parallel motion which it is not necessary here to describe. The simple arrangement for working the valves, shown in outline in the figure, is also replaced by a much more complicated apparatus in which, by means of cataracts, any required length of pause can be made between the strokes of the engine, a matter which is sometimes of importance in heavy pumping work. It will be noticed that by the peculiar single-acting method of working adopted in the Cornish engine, the velocity of the down stroke (also called the steamer stroke, or the zndoor stroke) depends—other things being equal—upon the steam pressure, but the velocity of the up stroke (eguzl¢brium or outdoor stroke) depends solely on the overplus weight put on the outer end of the —479] Distribution of Steam. Slide Valves 467 beam. In this way a slow and quiet upward motion can be given to the water, no matter how quickly the steam may move the piston. 478. Ordinary horizontal engine.—The engines now most largely used in factories for driving machinery differ altogether in their action from the Cornish engine. In them the cylinder is generally horizontal, and the crank is driven through a connecting rod only, without the intervention of any beam. Such an engine is shown in fig. 436. Here A is the steam cylinder, B the valve chest, or chamber in which works the valve whose mode of action is described in the next article. D is the main shaft, on the inner end of which is the crank driven by the connecting rod E. C is an eccentric (fig. 438), which works the valve by the rod N._ F is a governor controlling the admission of steam to the cylinder by the valve H. M 1s the dedplate or frame of the engine, and L the flywheel. A few words are necessary about the governor. This apparatus, an invention of James Watt’s, consists of two weighted arms hinged at the top, iN ( oo = mn [iw i i i eT nl Tm i il il TT me which fly outward when the speed of rotation is increased and drop together when it is reduced. The outward or inward motion of the arms is caused by a simple arrangement to turn the spindle G and so to close or open the valve H, which admits steam through K to the cylinder. In this way the engine automatically controls its own speed (480). 479. Distribution of steam. Slide valves.—Figs. 437 and 438 show details as to the working of the valve and the distribution of the steam in the engine just described. The former is a longitudinal section of the cylinder shown in fig. 436. A is the cylinder itself, B the piston, C the piston-rod, D the stuffing box through which the piston passes steam-tight. It will be seen that a fort or passage L communicates between each end of the cylinder and the surface on which the valve works, or valve face. On this face, and between the two steam-ports, comes a third point M, communi- cating directly with the atmosphere or with a condenser as the case may be. The valve G is shaped in section something like an irregular D, and is often. H H 2 468 On Feat [479- called a ‘D’ valve in consequence. It is moved continuously backwards and forwards upon the valve face by the valve rod H working in the stuffing- box K. When in the position, shown in the figure, the steam enters by F, and passes into the left-hand end of the cylinder (past the edge of the valve) and pushes the piston from left to right. The steam at present in the cylinder (as shown by the arrows) passes out at L, and through the under part of the valve G to the exhaust port M. As the piston moves on, the valve at first moves in the same direction, opening the port a little wider, then gradually moves back again and closes the admission port altogether. The point at which this occurs is called the point of cut of Nomore steam is allowed to enter the cylinder for that stroke, the piston being pushed forward by the pressure of the elastic steam expanding behind it. By the time the piston has got to the end of its stroke, the position of the valve is just reversed from that in which it is shown, and steam passes into the cylinder through the right-hand port, driving the piston from right to left, while the steam which has already done duty in the left-hand end of the cylinder passes away, in its turn, through the exhaust. BN bs AN WHETEEEEEHEEELEpLLfltli~ Up YM MM LM/; WH Fig. 437 Fig. 438 The eccentric from which the valve receives its motion (lettered C in fig. 437) is shown in detail in fig. 438. Here D is the crankshaft and A a disc (solid or ribbed) fixed eccentrically on it so asto revolve with it. Encircling this disc (which is the eccentric) is a strap or ring B (made in two pieces for the sake of getting on and off), rigidly connected with a rod C, which is coupled by a pin to the valve-rod E. .In each revolution of the eccentric the valve-rod is moved backwards and forwards through a space equal to twice the eccentricity of the eccentric, or distance between the centres of D and of A. The eccentric is thus equivalent exactly to a crank having a radius equal to its eccentricity. It is used instead of a crank because it does not require any gap to be left in the shaft, as a crank would do, but allows it to be carried continuously on. In locomotive or marine engines two eccentrics are commonly used, one so placed as to give the valve the right motion when the shaft rotates in one direction, and one rightly placed for the other. By apparatus called reversing gear either one or the other can be caused to move the valve, so that the engine can be made, at pleasure, to turn the shaft in one or the other direction. —480] Locomotives 409 480. Locomotives.—Locomotive engines, or simply locomotives, are steam engines which, mounted on a carriage, propel themselves by trans- mitting their motion to wheels. The whole machine, fig. 439, boiler and engine, is fixed to a wrought-iron /yvame, which, therefore, is made strong Fig. 439 enough to carry the whole weight, and which in turn transmits that weight to the axle-boxes (or bearings in which the ax/es turn), by means of springs, and thence through the wheels to the rails. The doz/er is of a special type, adopted in order to get the greatest possible heating surface in a very limited 470 On Heat [480- space. It consists of three parts—the five-dox, barrel, and smoke-box. The fire-box, in the left of the engraving, is generally a more or less rectangular box, with a flat top, placed inside a second box of somewhat similar shape, but with a semi-cylindrical, or, as in the figure, domed top. In the inner fire-box are the fire-bars, on which the fuel is placed through a door in front. The space between the inner and outer boxes is filled with water to a height considerably over the top of the inner one, and communicates freely with a long cylindrical darre/, closed at the other end by the soke-box. This barrel, which forms the main bulk of the boiler, is filled with water to within nine or ten inches of its upper side. It is traversed from end to end by a great number of small tubes (about 14 inch in diameter) which communicate with the inner fire-box at the one end, and with the smoke-box at the other. They, therefore, are entirely immersed in the water from end to end. The gases of combustion, formed in the inner fire-box, pass through these tubes to the smoke-box, and thence up the chimney, and impart most of their heat to the water as they pass along. There are two steam cylinders, one on each side of the frame, each one with its piston and connecting rod, etc., being simply an ordinary high-pressure horizontal engine. Their exhaust steam is discharged through a d/ast pipe into a nozzle inside the chimney near its base, and this serves to excite the fierce draught which is required in order that the necessary heat may be developed by the very small furnace. The two cylinders work cranks at right angles to each other, so that one may be in full action when the other is'at its dead point. A locomotive such as that shown in the figure is called an outside cylinder engine, on account of the position of its cylinders. In England many engines have cylinders placed inside the frames, which are then called inside cylinder locomotives. In express ‘engines the cylinders frequently drive only one very large pair of wheels, as is shown in the figure. These are called driving wheels, those on the front axle being leading wheels, and on the rear axle ¢razling wheels. In the case of goods engines, however (as well as in many other instances), when less speed but a greater pull is re- quired, two or more pairs of wheels of the same diameter are connected together by coupling rods, so that two or more axles may be directly or indirectly actually driven by the engine. Such engines are called coupled engines. The action of the engine upon the wheels may cause them either to slip round on the rails (in which case the engine, of course, does not move onwards) or to roll on themin the usual way. To prevent slipping occurring it is necessary to make the friction between the wheels and the rails as great as possible. This is done by making as large a proportion of the whole weight as possible rest on the driving or the coupled wheels, and also—when bad weather causes the rails to be greasy or otherwise unusually slippery— by increasing the coefficient of friction (47) between the wheels and the rails by pouring sand on the latter. All locomotives are furnished with a sand- box for this purpose. The steam pressure in locomotives is greater than that commonly used in any other engines, being often 120 to 130 Ibs. per square inch above the atmosphere. In marine engines 70 to 80 Ibs. 1s often used, in stationary engines seldom quite so much. —481] Vartous Kinds of Steam Engine 471 The following is an explanation of the reference letters in fig. 439 :—A, the main steam-pipe, conveying steam to the cylinder F, in which works a piston P, driving the crank M through the connecting-rod K, rv are the piston-rod guides, V the stuffing-box. The ‘exhaust steam is discharged through the pipe E. (It will be remembered that the cylinder and all this gear are duplicated on the other side of the engine.) DZ is the outer fire- box and X the barrel of the boiler, both covered with felt and wood or sheet iron to prevent loss of heat by radiation. The small tubes are seen at a, Y is the smoke-box, and Q the chimney or funnel. TT are the springs which transmit the weight of the frame to the axle-boxes. Of the smaller details, GI is the arrangement for closing or opening the steam-admission valve, BéC the reversing gear, RR feed-water pipes, N coupling rod for attaching tender and rest of train, ez safety valves, 2 whistle, #z steps, 72 water gauge, ¢ cocks for blowing water out of cylinders, H cock for blowing out boiler when necessary. It is perhaps hardly necessary to explain that the breaking away of part of the fire-box, cylinder, etc., is done in the drawing only for the sake of showing clearly the internal construction. 481. Various kinds of steam engine.—Three types of steam engine have been described: the Cornish engine, the ordinary horizontal engine, and the locomotive engine. Others ought to be mentioned, although they cannot be here described in detail. Compound engines are those in which the steam is first used in the ordinary way in one cylinder and then trans- ferred—of course at a comparatively low pressure—to another cylinder and used in it before being sent away to the condenser. This type is practically universal for marine purposes, and is very common for stationary engines. Its main advantage is a thermodynamic one. In an ordinary engine the cylinder walls are exposed alternately to the hot steam from the boiler and the cool vapour passing to the condenser. The latter so reduces the temperature of the iron, that when the first rush of fresh steam comes into the cylinder, much of it is immediately condensed on the cool metal, and an enormous quantity of heat is thereby lost. By passing the steam through an intermediate, or low-pressure, cylinder on its way to the condenser, the sides of the first or A¢gh-pressure cylinder are never exposed to condenser temperature, but only to that of the steam as it passes to the low-pressure cylinder ; they therefore are not so much cooled, and the loss of steam by condensation on them is very much reduced. There is no mechanical gain, as has sometimes been stated, in the use of two cylinders instead of one. Sometimes the cylinder of an engine is enclosed ina second, slightly larger, cylinder, and fresh steam at boiler pressure admitted to the annular space so formed outside the working cylinder. The object of this is to re- duce still further the condensation in the cylinder just alluded to. Such an engine is said to be steam-jacketed. A surface-condensing engine is one in which the steam is condensed by contact with the surface of a number of small tubes through which cold water is kept continually circulating without being itself actually mixed with the condensing water. By this arrangement the condensed steam is kept by itself, and being distilled water it can be used very advantageously to feed the boiler again. Compound marine engines are almost invariably surface. 472 On Ffeat [481— condensing. In this case the air-pump only takes away the condensed steam, a separate pump, called a c¢vculating pump, being used to force the condensing water through the tubes. Engines without any condenser, like that shown in fig. 439, in which the steam is exhausted directly into the atmosphere after it has done its work, are often called high-pressure engines, but high pressures (of 80 to 90 pounds. per square inch) are now frequently used in condensing engines, so that the name may be somewhat misleading. In such an engine as is shown in fig. 439 we have seen that the governor keeps the speed constant, by closing or opening an exterior valve through which the steam passes on its way to the main valve. An artificial resist- ance is in this way opposed to the passage of the steam, by increasing which the pressure can be reduced, and therefore the work done by the steam, so that the engine will not run too fast if the resistance to its motion be diminished (as by disconnecting some of the machines it is driving, etc.). The actual weight of steam passing into the cylinder at each stroke remains unchanged, but the amount of wsefu/ work the steam can do is. diminished anincely by giving it some wseless work to do in addition, in forcing its way through a constricted passage. This is now known to Se a wasteful way of controlling speed. In modern engines, therefore, the governor is frequently made to act by regulating the quantity of steam ad- mitted by each stroke, and thus making the consumption of steam as nearly as possible proportional to the work done. Engines so arranged, of which the Corliss engine is one of the best known examples, are said to be fitted with automatic cut-off gear. There is a popular misconception, that somehow or other work is lost in an engine of the ordinary type between the piston and the crank, the latter receiving less work than is done on the former in consequence of the nature of the mechanism connecting them. It is probably unnecessary to point out here the fallacy of this notion, but it has received sufficient acceptance to lead to the invention of a host of vofavry engines, in which it is endeavoured to obtain the desired rotary motion in a somewhat more direct fashion. Reuleaux has shown that in almost every case the mechanisms used in the rotary engines are the same as those of ordinary engines, although disguised in form, so that the idea of mechanical advantage is doubly a mistake, while in almost every case the rotary engines possess such grave mechanical defects that none of them have practically come into use. 482. Work of an engine. Horse-power.—The unit of work by which the performance of an engine is measured is in this country always the foot- pound. The number of foot-pounds of work done by the engine in any given time is equal to the average effective pressure upon its piston during that time, multiplied by the total distance through which the piston has moved under that pressure. By average effective pressure is meant the average value of the difference between the pressures on its two sides. Taking the time as one minute, this quantity of work in foot-pounds is equal to :— Area of piston x mean intensity of pressure on piston x length of stroke x number of strokes per minute. The stroke must be taken in feet. If the area is in square feet, the 483] Indicator. Brake 473 pressure must be in pounds per square foot ; if the area is in square inches, the pressure must be in pounds per square inch. If the strokes are doudble strokes, each corresponding, that is, to one whole revolution of the shaft, the length of stroke must be multiplied by 2. To find, for example, the work done in one minute by an engine with cylinder 16 inches diameter and 24 inches stroke, making 50 (double) strokes per minute with a mean pressure of 52 pounds per square inch, we have (GISCRLIALO) x5 2: x (Chke 2) x 50 = 2,091,000 ft.-lbs. The rate at which an engine does work is often measured in horse-fower of 33,000 ft.-Ilbs. per minute, an arbitrary unit supposed to represent the maxi- mum rate at which work could actually be done by a horse. In the case supposed the horse-power would be 2107000 = 63°4. 33,000 On the Continent the unit of work is a kilogrammetre, which is very closely equal to 77 {ft.-lbs. The horse-power used abroad, of 75 kilo- grammetres per second, is nearly 2 per cent. smaller than that in use in this country. 483. Indicator. Brake.—By the expression work done by an engine we may mean either of two things, viz.—the Zofa/ work done by the engine, or what is called its useful, or effective, work. The total work is the actual work done by the steam on the piston and obtained by calculation, as described in the last paragraph. The useful work is what remains of this total after deduction has been made of the work necessary to drive the engine itself against its own frictional resistances. The total work of an engine is mea- sured by means of an apparatus called an zwzdtcator, invented by Watt, of which fig. 440 shows one of the most recent forms (Richard’s), omitting a number of constructional details. The steam-engine indicator consists of a small cylinder A, half a square inch in area, in which works a piston B, the under side of which can be put into full communication with the cylinder of the engine by opening the cock C. Between the top side of the piston and the under side of the cylinder-cover is a spiral spring. The motion of the piston-rod is transferred to a parallel motion DD, and so causes a point E to move in a straight line up and down, its stroke being about four times as great as that of the small piston. The indicator is fixed on to the cylinder of the steam-engine near one end, so that when the cock C is opened, there is the same pressure of steam on the indicator piston as on the engine piston. This pressure forces up the piston, and the amount of com- pression of the spring so caused is proportionate to the pressure causing it. The upward motion of E, therefore, is proportional to the steam pressure. In front of E is a vertical drum F, on which a strip of paper can be fixed, and this drum is caused to rotate about its axis by attaching the cord G to any suitable part of the engine. The paper thus moves horizontally under the pencil, with a motion proportional to the stroke of the engine, while the pencil moves up and down on the paper with a motion proportional to the steam pressure on the piston. The two motions occurring simul- taneously, the pencil traces on the paper a curve whose horizontal and vertical ordinates are proportional to the two quantities just named, and 474 On Heat [483- whose area is therefore proportional to the product of these quantities, or, which is the same thing, to the work done by the piston as defined in the last paragraph. The curve is called an indicator card, or zzditcator diagram, and while its avea shows the whole work done by the steam, its fori shows the engineer what is happening within the cylinder at each point of the stroke, which he may often require to know. Figs. 441 and 442 show two forms of indicator diagram. The curves themselves, as drawn by the indicators, are lettered ABCD. Beside them a scale of pressure in atmospheres is placed. In fig. 441 the steam is ex- panded about seven times, and the back pressure is about 4 of an atmo- sphere, the pressure during admission being five atmospheres. The engine is a condensing one, and the diagram is fairly good. Fig. 442 is for a non- condensing engine, the back pressure being above that of the atmosphere. Ce eo oH A: 3: Ze U7 SZ = — i} i} INQ 4 bea ) I: Gini; Ti 7 i i‘ i i Pressure tin Albmospheres Fig. 441 Pressure tn Atmospheres Fig. 440 Fig. 442 The steam is cut off (at B) only at about 3 of the stroke, so that it is not working economically, and from the roundness of its corners the diagram would be considered a poor one. The wseful work of an engine is measured by an entirely different piece of apparatus, called a dynamometer. This is used in many forms, but fig. 443 shows the principle upon which the majority act. The apparatus shown in the figure is known as a Prony’s friction brake. A is the shaft, the usual work transmitted by which we require to find. Upon the shaft is a fixed pulley B, embraced by two blocks B, and B,, which can be tightened up by the screws at C, and C,. ‘To the lower block is fixed a lever D, from which hangs a weight, and which has at its extremity a small pointer work- ing against a short scale F. If such an apparatus be set in motion by turning the shaft A, one of two things must happen: either the pulley must —484] Efficiency of Heat Engines 475 slip round in the blocks, or it must so grip them as to carry both them and the lever D round its own axis. The moment of resistance to the former is x F, if ~ be the radius of the pulley and F the frictional resistance at its p Fig. 443 periphery ; that of the latter is RW, where R is the radius of the weight and W the weight itself. In practice the screw C, is loosened just suffi- ciently to keep the weight just lifted from the ground, while the pulley is always turning round in the blocks, so that, therefore, 7 = RW. The work done at the brake per minute is equal to the frictional resistance multiplied by the distance through which it is overcome in the same time, or, if 2 be the number of revolutions per minute, = 2nrFu=27rRW2. It is therefore just the same as if a resistance = W were continually being overcome at the periphery of a wheel of radius R, making z turns per minute. As the values of all the quantities in the expression 27RWz7 are very readily determined, it will be seen that this brake affords a very simple way of measuring the net work transmitted through the shaft of an engine. The ratio ane mae gone shOw mapa Re , is called the efi- total work’ work shown by indicator ciency of the engine as a machine, or its mechanical efficiency. It is often as much as 0°85, and sometimes even higher than o-9 or go per cent., being generally greatest in large engines. 484. Efficiency of heat engines.—There is another ratio of efficiency connected with the steam-engine, namely the ratio Total work done by engine Total heat expended - what is called the effictency of the engine as a heat engine or its thermo- dynamic efficiency. lf T, and T, be respectively the absolute temperatures (508) of the steam and the feed water in any engine, then it can be shown 476 On Heat [484— that such an engine, if working quite perfectly, could transform no more than(“1—*2) of the heat which it receives into work. This fraction in the t case of a steam engine is seldom more than about 0°25. The value of the actual efficiency of the engine is often from o'lo to o'14; while, therefore, an ordinary steam engine, with such an efficiency, turns into work only from z5 to 4 of the whole heat it receives, yet it may be turning into work 4 or more of the whole heat which it could possibly transform into work if it were perfect. To increase the economy of steam engines we require to make the value ot (222 larger. This is done either by raising T, or by lowering T,, or 1 both. The chief difficulty is that we cannot raise T, without increasing the steam pressure, which it is often not convenient to do, while we cannot lower T, below such a temperature, 50° to 60° F., as can readily be obtained naturally at all seasons of the year. 485. Hot-air engines.—The difficulty as to T, just mentioned is got over by the use of some fluid whose pressure is not a function of its temperature, and naturally azv is the most convenient fluid for the purpose. Many ‘hot- air’ engines have been designed, and some have found a considerable measure of success commercially, as Rider’s, Hock’s, and Lehmann’s. In all cases the engines consist essentially of one (or two) chambers placed so that one end can be heated by a furnace and the other cooled by a refrige- rator. The air is compelled to move from the cold space to the hot and back again continually. When hot it is allowed to expand and push forward a piston, when cold it is compressed by pushing back the piston again to its original position. The difference between these two quantities of work is the whole work done by the engine. By making T, avery high temperature, the theoretical efficiency( “17 ny of an air engine may be made much 1 higher than that of a steam engine. But it is so much more difficult to attain the theoretical efficiency in the air than in the steam engine, that its actual efficiency is generally much lower than that of a steam engine. There are constructive difficulties connected with the hot-air chambers, and with the regulation of the speed, and these, as well as with the large bulk of most air engines in proportion to their power, have stood greatly in the: way of their development. No doubt, however, much more improvement would have taken place in these engines had not gas engines come into prominence of late years and proved much more convenient. 486. Gas engines.—Gas engines, like steam engines and air engines, are heat engines, but in them the working fluid is ordinary coal gas mixed with air, in«the proportion of about 1 to 11 by volume. The principle of action is very simple :—The explosive mixture after being drawn into the cylinder is set light to, the heat generated by the very rapid combustion, which we call an explosion, causes the mixed gases to expand and drive forward the piston. The great difficulty for many years was that the explosion was so rapid that the comparatively slow-going piston could not keep up with it, and the greater part of the energy of the explosion was lost by radiation and conduction. In the more modern gas engines, however (Otto’s and Clerk’s. —486] Gas Engines 477 and others), this difficulty is got over by compressing the charge before igniting it, a treatment which is found to decrease very much the rapidity of the explosion and so greatly increase the actual efficiency of the engine. Fig. 444 shows the principal parts of an Otto ‘ Silent’ gas engine, as now made. A is the cylinder, open at front and single-acting, in which works a deep piston F, driving a crank in the usual manner. The cylinder is surrounded by a water jacket, to prevent it from getting too hot. At the back of the cylinder is a slide valve B, worked by a cam, not shown in drawing, on the lay shaft G. The valve B is kept up against its face by spiral springs E. D is a chamber in which a small jet of gas for igniting the mixture is con- tinually burning. C, is the cock for admission of gas, and C, an india- rubber bag to equalise the gas pressure. The working of the engine is as follows :—the piston moves from left to right and draws into the cylinder the explosive mixture. On the return stroke it compresses the mixture to about 3 atmospheres. The igniting flame is then allowed to come for an instant ll TE il — = mi) Fig. 444 into contact with the compressed mixture, which burns very rapidly (or explodes slowly, whichever expression be preferred) and pushes the piston forward again, the pressure rising to Io or 12 atmospheres. On the next return stroke the burnt gases are pushed out through the opening shown in the drawing, and the process begins again once more. There are many ingenious arrangements about this type of engine which our space will not allow us to mention in detail. It must suffice to say that the engine has proved distinctly economical, and has such very great conveniences as may fairly account for the rapid way in which its use (and that of other gas engines) has extended. In conclusion, it is as well to point out that, as long as they work between the same temperatures, there is no difference between steam, air, and gas engines as to theoretical economy. The last two gain by the possibility of using higher limits of temperature than can be employed in a steam engine, but, so far, have lost by constructive and mechanical difficulties which pre- vent their theoretical efficiency from being attained. 478 On Ffeat [487 . CHAT TTGRT TA! SOURCES OF HEAT AND COLD 487. Different sources of heat.—The following different sources of heat may be distinguished: i. the szechantcal sources, comprising friction, percussion, and pressure ; ii. the Pxystcal sources—that is, solar radiation, terrestrial heat, molecular actions, change of conditions, and electricity ; iii. the chemical sources, or molecular combinations, and more especially combustion. In what follows it will be seen that heat may be produced by reversing its effects ; as, for instance, when a liquid is solidified or a gas compressed (489) ; though it does not necessarily follow that in all cases the reversal of its effects causes heat to be produced—uinstead of it, an equivalent of some other form of energy may be generated. In like manner heat may be forced to disappear, or cold be produced when a change such as heat can produce is brought about by other means, as when a liquid is vaporised or a solid liquefied by solution ; though here also the disappearance of heat is not always a necessary consequence of the production, by other means, of changes such as might be effected by heat. MECHANICAL SOURCES 488. Heat due to friction.—The friction of two bodies, one against the other, produces heat, which is greater the greater the pressure and the more rapid the motion. For example, the axles of carriage wheels, by their fric- tion against the boxes, often become so strongly heated as to take fire. By rubbing together two pieces of ice in a vacuum below zero, Sir H. Davy partially melted them. In boring a brass cannon Rumford found that the heat developed in the course of 2} hours was sufficient to raise 263} pounds of water from zero to 100°, which represents 2,650 thermal units (456). Mayer raised water from 12° to 13° by shaking it. At the Paris Exhibition, in 1855, Beaumont and Mayer exhibited an apparatus, which consisted of a wooden cone covered with hemp, and moving with a velocity of 400 revolutions in a minute, in a hollow copper cone, which was fixed and immersed in the water of an hermetically closed boiler. The surfaces were kept covered with oil. By means of this apparatus 88 gallons of water were raised from Io to 130 degrees in the course of a few hours. In the case of flint and steel, the friction of the flint against the steel raises the temperature of the metallic particles, which fly off, heated to such an extent that they take fire in the air. -489] Hleat due to Pressure and Percussion 479 The luminosity of aerolites is considered to be due to their friction against the air, and to their condensation of the air in front of them (489), their velocity attaining as much as I50 miles in a second. Tyndall devised an experiment by which the great heat developed by friction is illustrated in a striking manner. A small brass tube closed at one end (fig. 445) is fixed on a small wheel. The tube, three parts full of water, is closed by a cork, and is pressed between a wooden clamp, while the wheel is rotated with some rapidity. The water rapidly becomes heated by the friction, and its temperature soon exceeding the boiling-point, the cork is projected to a height of several yards by the elastic force of the steam. 489. Heat due to pressure and percussion.—If a body be so com- pressed that its density is increased, its temperature rises according as the volume diminishes. Joule verified this in the case of water and of oil, which were exposed to pressures of 15 to 25 atmospheres. In the case of water at 1'2° C., increase of pressure caused lowering of temperature—a result which agrees with the fact that water contracts by heat at this temperature. Similarly, when weights are laid on metal pillars, heat is evolved, and absorbed when they are removed. So in like manner the stretching of a metal wire is attended with a diminution of temperature. The production of heat by the compression of gases is easily shown by means of the pueumatic syringe (fig. 446). This consists of a glass tube with thick sides, closed hermetically by a leather piston. At the bottom of this there is a cavity in which a small piece of cotton, moistened with ether or bisulphide of carbon, is placed. The tube being full of air, the piston is suddenly plunged downwards ; the air thus compressed disengages so much heat as to ignite the cotton, which is seen to burn when the piston is rapidly withdrawn. ‘The ignition of the cotton in this experiment indicates a temperature of at least 300°. The rise of temperature produced by the compression in the above 480 On Fleat [489 - experiment is sufficient to effect the combination, and therefore the detonation, of a mixture of hydrogen and oxygen. A curious application of the principle of the pneumatic syringe is met with in the American powder ram for pile-driving. On the pile to be driven is fixed a powder mortar, above which is suspended at a suitable distance an iron rammer, shaped like a gigantic stopper, which just fits in the mortar. Gunpowder is placed in the mortar, and when the rammer is detached it falls into the mortar, compresses the air, producing so much heat that the powder is exploded. The force of the gases projects the rammer into its original position, where it is caught by a suitable arrangement ; at the same time the reaction of the mortar on the pile drives this in with far greater force than the fall of the rammer. After adding a fresh charge of powder, the rammer is again allowed to fall, again produces heat, explosion, and so forth, so that the driving is effected in a surprisingly short time. Percussion is also a source of heat. In firing shot at an iron target, a sheet of flame is frequently seen at the moment of impact ; and Sir J. Whit- worth used iron shells which are exploded by the concussion on striking an iron target. A small piece of iron hammered on the anvil becomes very hot. Fig. 446 The heat due to the impact of bodies is not difficult to calculate. When- ever a body moving with a velocity v is suddenly arrested in its motion, its kinetic energy is converted into heat.. This holds equally whatever be the cause to which the motion is due: whether it be that acquired bya stone falling from a height, by a bullet fired from a gun, or the rotation of a copper disc by means of a turning table. The energy of any moving body is expressed by ““”" or in foot-pounds by Pv", where p is the weight in 2 2 pounds, zv the velocity in feet per second, and g¢ is about 32 (29) ; and if the whole of this be converted into heat, its equivalent in thermal units will be 2 Be 2: Suppose, for instance, a lead ball weighing a pound be fired from a gun, and strike against a target, what amount of heat will it produce? We may assume that its velocity will be about 1,600 feet per second ; then its kinetic energy will be ~~ - 1600° =o on 40,000 foot-pounds. Some of this will . have been consumed in producing the vibrations which represent the sound of the shock, some of it also in its change of shape ; but neglecting these two as being small, and assuming that the heat is equally divided between the ball —490] Solar Radiation 481 and the target, then, since 40,000 foot-pounds is the equivalent of 28:7 thermal units, the share of the ball will be 14:3 thermal units ; and if, for simplicity’s sake, we assume that its initial temperature is zero, then, taking its specific heat at 0'0314, we shall have Weoo3t4x7=14'3 or £= 457 = which is a temperature considerably above that of the melting point of lead (342). . By allowing a lead ball to fall from various heights on an iron plate, both experience an increase of temperature which may be measured by the thermopile ; and from these increases it may be easily shown that the heat is directly proportional to the height of fall, and therefore to the square of the velocity. By similar methods Mayer calculated that if the motion of the earth were suddenly arrested the temperature produced would be sufficient.to melt and even volatilise it ; while, if it fell into the sun, as much heat would be produced as results from the combustion of 5,000 spheres of carbon the size of our globe. PHYSICAL SOURCES 490. Solar radiation..-The most intense of all sources of heat is the sun. Pouillet made the first accurate measurements of the heat of the sun by means of an instrument called the pyroheliometer. The form represented in fig. 447 consists of a flat cylindrical metal box 3 inches in diameter and $ an inch deep, containing a known weight of water. To it is fitted a metal tube which contains the stem of a deli- cate thermometer, the bulb of which dips in the liquid of the box, being fitted by means of acork. The tube works in two collars, so that by means of a milled head it can be turned, and with it the vessel, and the liquid thus be uniformly mixed. The face of the vessel is coated with lampblack, and is so adjusted that the sun’s rays fall perpendicularly upon it. This can be ascertained by observing when the shadow exactly covers the lower disc which is fitted to the same axis. The instrument was exposed for five minutes at a time to the sun’s rays ; knowing the weight of the water, and the rise of temperature, we may easily calculate the heat absorbed by it. Corrections were necessary for the heat reflected by the lampblack, and also for the heat absorbed by the air. The solar constant Q is the quantity of heat in gramme degrees which a im 482 . On Feat [490- square centimetre of a perfect absorbent would receive in a minute from the vertical sun’s rays at the limit of the atmosphere. On the surface of the earth the value Q is less, but by determining it at various heights and combining the observations, the absorption by the atmosphere can be deter- mined and Q ascertained. The most trustworthy experiments give for this value 3 gramme calories. When the sun is in the zenith about one-third is absorbed and two-thirds reach the earth. Of older data, Pouillet calculated from the results of experiments with his apparatus that if the total quantity of heat which the earth receives from the sun in the course of a year were employed to melt ice, it would be capable of melting a layer of ice all round the earth of 35 yards in thickness. Another statement is that the heat emitted by the sun is equal to that produced by the combustion of 1,500 pounds of coal in an hour on each square foot of its surface. But from the surface which the earth exposes to the sun’s radia- tion, and from the distance which separates the earth from the sun, the quantity of heat which the earth receives can only be esau of the heat emitted by the sun. Violle calculated the thickness of ice melted by the sun’s heat at the equator, apart from absorption by the atmosphere, at 55 metres in thickness ; and, deducting this absorption, at 37 metres. Faraday calculated that the average amount of heat radiated in a day on each acre of ground in the latitude of London is equal to that which would be produced by the combustion of sixty sacks of coal. The heat of the sun cannot be due to combustion, for even if the sun consisted of hydrogen, which of all substances gives the most heat in com- bining with oxygen, it can be calculated that the heat thus produced would not last more than 3,000 years. Another supposition is that originally put forth by Mayer, according to which the heat which the sun loses by radiation is replaced by the fall of aerolites against its surface. One class of these is what we know as shooting stars, which often appear in the heavens with great brilliancy, especially on August 14 and November 15 ; the term seteoric stone or aerolite being properly restricted to the bodies which fall on the earth. They are often of considerable size, and are even met with in the form of dust. Although some of the sun’s heat may be restored by the impact of such bodies against the sun, the amount must be very small, for Lord Kelvin has proved that a fall of o°3 gramme of matter in a second on each square metre of surface would be necessary for this purpose. The effect of this would.be that the mass of the sun would increase, and the velocity of the earth’s rotation about the sun would be accelerated to an extent which would be detected by astronomical observa- tions. Helmholtz considers that the heat of the sun was produced originally by the condensation of a nebulous mass, and is kept up by a continuance of this contraction. A sudden contraction of the primitive nebular mass of the sun to its present volume would produce a temperature of 28 millions ot degrees Centigrade ; and a contraction of z;5}5p of its mass would be sufficient to supply the heat radiated by the sun in 2,000 years. This amount of contraction could not be detected even by the most refined astronomical methods. 492] Heat produced by Absorption and Imbtbition 483 491. Terrestrial heat.—Our globe possesses heat peculiar to it, which is called terrestrial heat. ‘The heat from the sun penetrates slowly by conduc- tion into the interior, and accordingly the maximum temperature will be at different depths at different times. Thus with four thermometers sunk at depths of 3, 6, 12 and 25°5 feet in the porphyry rock of the Calton Hill, Edin- burgh, the registered maximum temperatures were on August 19,September 8, October 19, and January 4 respectively. But some of the heat is retained in each layer and raises the temperature so that the yearly variations diminish with the depth. For the above thermometers these were 8°2°, 5°6°, 2°7°, and o'7°._ From observations of this kind it is concluded that the solar heat does not penetrate below a certain internal layer, which is called the /ayer of constant annual temperature ; its depth below the earth’s external surface varies, of course, in different parts of the globe ; at Paris, itis about 30 yards, and the temperature is constant at 11°8° C. Below the layer of constant temperature, the temperature is observed to increase, on the average, 1° C. for every 90 feet. The most rapid increase is at Irkutsk in Siberia, where it is 1° for 20 feet, and the slowest in the mines at Mansfield, where it is about 1° C. for 330 feet. This increase has been verified in mines and artesian wells. According to this at a depth of 3,000 yards, the teniperature of a corresponding layer would be I00°, and at a depth of 20 to 30 miles there would be a temperature sufficient to melt all substances which exist on the surface. Hot springs and volcanoes confirm the existence of this central heat. Various hypotheses have been proposed to account for the existence of this central heat. The one usually admitted by physicists is that the earth was originally in a liquid state in consequence of the high temperature, and that by radiation the surface has gradually solidified, so as to form a solid crust. The cooling must be very slow, owing to the small conductivity of the crust. For the same reason the central heat does not appear to raise the temperature of the surface more than 34 of a degree. Fourier calculated that the heat given off by the earth in 100 years would be sufficient to melt a layer of ice 3 metres in thickness, which therefore is only zg455 Of that received by the sun in the same time. 492. Heat produced by absorption and imbibi- tion.— Molecular phenomena, such as imbibition, absorption, capillary actions, are usually accom- panied by disengagement of heat. Pouillet found = 2 Se that whenever a liquid is poured on a finely divided —— solid, an increase of temperature is produced which Fig. 448 varies with the nature of the substances. With in- organic substances, such as metal, the oxides, the earths, the increase is 345 of a degree ; but with organic substances, such as sponge, flour, starch roots, dried membranes, the increase varies from I to 10 degrees. The absorption of gases by solid bodies presents the same phenomena. W1i2 Cie > ; 4“ Ui! == 484 On Heat | [492-- Débereiner found that when platinum, in the fine state of division known as platinum black, is placed in oxygen, it absorbs many hundred times its volume, and that the gas is then in such a state of density, and the tempera- ture so high, as to give rise to strong combustion. Spongy platinum pro- duces the same effect. A jet of hydrogen directed on it takes fire. The apparatus known as Dodereiner’s Lamp depends on this property of finely divided platinum. It consists of two glass vessels (fig. 448). The first, A, fits in the lower vessel by means of a tubulure which closes it hermetically. At the end of the tubulure is a lump of zinc, Z, immersed in dilute sulphuric acid. By the chemical action of the zinc on the dilute acid hydrogen gas is generated, which, finding no issue, forces the liquid out of the vessel B into the vessel A, so that the zinc is not in contact with the liquid. The stopper of the upper vessel is raised to give exit to the air in proportion as the water rises. Ona copper tube, H, fixed in the side of the vessel B, there is a small cone, a, perforated by an orifice ; above this there is some spongy platinum in the capsule, c. As soon now as the cock, which closes the tube H, is opened, the hydrogen escapes, and, coming in contact with the spongy platinum, is ignited. The condensation of vapours by solids often produces an appreciable rise of temperature. This is particularly the case with humus, which, to the benefit of plants, is warmer in moist air than the air itself. Favre found that when a gas is absorbed by charcoal the amount of heat produced by the absorption of a given weight of sulphurous acid, or of nitrous oxide, greatly exceeds that which is disengaged in the lique- faction of the same weight of gas ; for carbonic acid, the heat produced by absorption exceeds even the heat which would be disengaged by the solidi- fication of the gas. The heat produced by the absorption of these gases cannot, therefore, be explained by assuming that the gas is liquefied, or even solidified in the pores of the charcoal. It is probable that it is in part due to that produced by the liquefaction of the gas, and in part to the heat due to the imbibition in the charcoal of the liquid so produced. CHEMICAL SOURCES 493. Chemical combination. Combustion.—-Chemical combinations are usually accompanied by a rise of temperature. When these combinations take place slowly, as when iron oxidises in the air, the heat produced is im- perceptible ; but if they take place rapidly, the disengagement of heat is very intense. The same quantity of heat is produced in both cases, but when evolved slowly it is dissipated as fast as formed. Combustion is chemical combination attended with the evolution i light and heat. In ordinary combustion in lamps, fires, candles, the carbon and hydrogen of the coal, or of the oil, etc., combine au the oxygen of the air. But combustion does not necessarily involve the presence of oxygen. If either powdered antimony or a fragment of phosphorus be placed in a vessel of chlorine, it unites with chlorine, producing thereby heat and flame. Many combustibles burn with flame. A flame is a gas or vapour raised to a high temperature by combustion. Its illuminating power varies with the nature of the product formed. The presence of a solid body in the fame —494] feat disengaged during Chemical Action 485 increases the illuminating power. The flames of hydrogen, carbonic oxide, and alcohol are pale, because they only contain gaseous products of com- bustion. But the flames of candles, lamps, coal gas, havea high illuminating power. They owe this to the fact that the high temperature produced de- composes certain of the gases, with the production of carbon, which, not being perfectly burnt, becomes incandescent in the flame. Coal-gas, when burnt in an arrangemerft by which it obtains an adequate supply of air, such as a Bunsen’s burner, is almost entirely devoid of luminosity. A non-lumi- nous flame may be made luminous by placing in it platinum wire or asbestos. The temperature of a flame does not depend on its illuminating power. A hydrogen flame, which is the palest of all flames, is the hottest. Chemical decomposition, in which the attraction of heterogeneous mole- cules for each other is overcome, and they are moved further apart, is an operation requiring an expenditure of work or an equivalent consumption of heat ; and conversely, in chemical combination, motion is transformed into heat. When bodies attract each other chemically their molecules move towards each other with gradually increasing velocity, and when impact has taken place the progressive motion of the molecules ceases, and is converted into a rotating, vibrating, or progressive motion of the molecules of the new body. The heat produced by chemical combination of two elements may be compared to that due to the impact of bodies against each other. Thus the action of the atoms of oxygen, which in virtue of their progressive motion, and of chemical attraction, rush against ignited carbon, has been lhkened by Tyndall to the action of meteorites which fall into the sun. 494. Heat disengaged during chemical action.— Many physicists, more especially Lavoisier, Rum- -| sean | lords Dulong, Despretz)* Hess, 2 a Favre and Silbermann, Berthelot, = Thomsen, and Andrews, have in- vestigated the quantity of heat dis- engaged by various bodies in chemical actions. —— Lavoisier used in his experi- Sage ES | ; ments the ice calorimeter already a Oe described. Rumford used a calori- meter known by his name, which consists of a rectangular copper Joe Eee canister filled with water. In this RAIA III canister there is a worm which passes through the bottom of the box, and terminates below in an inverted funnel. Under this funnel is burnt the substance experimented upon. The products of combustion, in passing through the worm, heat the water of the canister. and from the increase of Fig. 449 486 ? On Feat [494- its temperature the quantity of heat evolved is calculated. Despretz and Dulong successively modified Rumford’s calorimeter by allowing the com- bustion to take place, not outside the canister, but in a chamber placed in the liquid itself; the oxygen necessary for the combustion entered by a tube in the lower part of the chamber, and the products of combustion escaped by another tube placed at the upper part and twisted in a ser- pentine form in the mass of the liquid to be heated. * Favre and Silbermann improved this calorimeter very greatly (473), not only by avoiding or taking account of all possible sources of error, but by arranging it for the deter- mination of the heat evolved in such chemical actions as take place between gases and vapours. The gases enter by tubes BB’ and CC’, fig. 448, into a metal chamber A, where the reaction takes place, the course of which can be watched through a glass plate which closes a wider tube FK. The gaseous products before passing into the air traverse a long serpentine tube H, at the lower end of which is a small box G which receives the liquids arising from the condensation of the vapours. The cylinder A and the serpentine are contained in a known mass of water contained in a calori- meter, and from the rise in temperature of this water the heat developed can be calculated. To avoid any loss of heat this is placed within a metal case, MM, containing swan’s down. The whole is contained in a vessel of water NN in which is a thermometer, to eliminate the influence of changes in the temperature of the air. The experiments of Favre and Silbermann are the most trustworthy, as having been executed with the greatest care. They agree very closely with those of Dulong. Taking as thermal unit the heat necessary to raise the temperature of a pound of water through ove degree Centigrade, the following table gives the thermal units in round numbers disengaged by a pound of each of the substances while burning in oxygen :— Hydrogen . s 134,402 Diamond : ; n4t%, 778 Marsh gas . ; wr El 3,003 Absolute alcohol . Weak oo Ethylenea a : 1 t,055 Cokeay : ‘ pe TZ000 Petroleum . : . 1,000 Phosphorus . ; 53750 Oil of turpentine PalO, 652 Coal gas ; : , ) 5,600 Olive oil : yt O,d00 Wood, dried at-120° t7.. 3,619 Ether . : : re O30 Carbon bisulphide . .- 3,401 Anthracite . ; eet 0,400 Wood, ordinary . ub 23750 Charcoal ; Se OOO Carbonic oxide ; -, 2,400 Oodle : : HO, G00. Sulphur . : : sH12,220 Tallow : . . «8,000 Zinc : ; ; s+ 1g300 Graphite . : ti Bray Se Iron ¢ ; f P ahehod Bunsen’s calorimeter (460) has been used with advantage for studying the heat produced in chemical reactions, in cases in which only very small quantities are available. For experiments on the heat of neutralisation of acids and bases the apparatus represented in fig. 450 may be used. Wis a large vessel of water of constant temperature ; the beaker glass, B, which is the calorimeter, rests on a cork in the outer one, A. On the wooden lid, H, are two weights, S, —496] Berthelot’'s Calorimetrical Bomb 487 and S,, to keep A down in the water; c and dare tubes placed in holes in the lid, and contain weighed quantities of the two liquids; 4 is a delicate thermometer. After the tubes c and d@ have acquired the temperature of the water ¢, their contents are poured into B through an aperture in the lid for this purpose. When the reaction is complete, the temperature indicated by the thermometer, which reaches to the middle of B, rises to ¢,, so that, when we know the weight of the substances, and the rise of temperature z,—7 the quantity of heat produced in the reaction is easily determined. mT Fig. 451 495. Berthelot’s calorimetrical bomb.—This apparatus, represented in section in fig. 451, is small enough to be inserted in the water of a calori- meter. It consists of a steel reservoir C lined with platinum, which can be hermetically closed by a screwed cover B. At thecentre is a cylinder in which a tube can be turned, serving to admit the gases to be worked with. Near this is a carefully insulated platinum wire, which ends near the side of the apparatus ; when an electric spark is passed it sets up the chemical reaction, the heat due to which is to be measured. For this purpose the bomb before the experiment is placed in a calorimeter, and from the rise in temperature of the known weight of water the quantity of heat can be deduced. If a solid is to be burned it is placed in a platinum capsule, and the combustion set up by passing a current through a very fine platinum wire in contact with it. 496. Endothermic and exothermic actions.—All chemical actions whether 458 On Heat [496— of combination or of decomposition, are attended by a disturbance of the thermal equilibrium ; and the quantity of heat disengaged is a measure of the physical and chemical work. In most cases the act of chemical combination is attended by a rise of temperature, and the quantity of heat is a measure of the energy developed in the reaction. Thus in the formation of one szolecule of water there are: liberated 68,924 thermal units, which may be written thus, H, +O=H,0 + 68,924. Those reactions which take place with disengagement of heat are said to: be exothermic ; there are, however, cases where bodies do not directly com- bine without the intervention of extraneous heat—for instance, iodine and hydrogen to form hydriodic acid ; the equation for this is I+H+6,000=I1H. Such reactions are called endothermic. Those bodies are most stable in the formation of which most heat is. developed ; thus the iron and zinc oxides, in the formation of which 1,181 and 1,300 units are respectively developed, are much more stable than silver oxide, in the formation of which only 27 units are developed. The heat of decomposition is the reciprocal of that of combination ; those bodies which develop most heat in their formation require conversely an equivalent quantity to decompose them; decompositions which require an expenditure of heat to produce them are called endothermic. Those com- pounds, on the contrary, which absorb heat in their formation, develop an equivalent quantity in being decomposed, and the reactions are exothermic ; they often take place with explosive violence, as in the case of the nitrogen chlorides and iodide. An exothermic reaction gives rise to an endothermic compound ; and, conversely, an endothermic reaction forms an exothermic compound. The oxidising compounds in ‘most ordinary explosives, potassium chlorate and nitrate, are endothermic, evolving heat during decomposition which thus helps the reactions. If there be any system of bodies which act on each other without the supply of extraneous energy, then that body or set of bodies results, in the formation of which most heat is produced. This is called the principle of greatest chemical action. The heat developed in any chemical reaction depends on the relation between the initial and the final products, and is independent of the nature and succession of the intermediate stages. It is equal to the sum of the quantities of heat produced in each stage, regard being had to the negative quantities due to such processes as solution and gasification. Thus a unit weight of carbon in burning to carbonic acid produces 8,080 units. If the same weight of carbon burns so as to form carbonic oxide, it forms 2,473 ; and the combustion of the carbonic oxide resulting from this reaction yields 5,607, making together 8,080. Potassium combines directly with chlorine to form potassium chloride, the heat of formation of which is 15,000 and is equal to that produced by the same weight of salt, whether this be forméd by the direct union of hydro- 497] Animal Heat 489 chloric acid and potash, or whether it be produced by the action of potassium on aqueous solution of hydrochloric acid. . The heat of combustion of a compound is not always equal to the sum of that of each of its constituents. The heat of combustion of carbon bisulphide iS 3,401, while that calculated from its constituents is 3,145 ; the compound accordingly possesses more energy than its constituents, and its formation is due to an endothermic reaction. Metameric bodies are those which contain the same number of elements but in different groupings ; thus acetic acid and methylic formate have each the composition C,H,O,; but the heat of combustion of the latter 1s 4,157, and that of the former 3,505 ; from this it is to be inferred that the grouping of the atoms to form acetic acid has been attended with the expendi- ture of more energy than in the case of methylic formate. Polymeric bodies are those which have the same elements and the same percentage composition but differ in the number-of atoms which form a molecule. Thus the more complex the molecule the smaller is the quantity of heat. That of amylene, for instance, C,H,,, is 11,401, and that of metamylene, C,,H,,, 1s 10,908. Many chemical elements, such as carbon, sulphur, and phosphorus, exist in modifications which are essentially different from each other in their physical properties, but which form, when they enter into combination with other elements, identical chemical products. Such bodies are said to have graphite or different allotropic forms which have different thermal values. The heat lberated when one allotropic form is changed into another, for instance, when charcoal is converted into diamond, cannot be directly deter- mined, but must be arrived at by indirect methods. A given weight of carbon, whether it be charcoal or diamond, produces exactly the same weight of carbonic acid, though the heat of combustion is different. Thus, when a gramme each of charcoal, graphite, and diamond are severally burnt in oxygen in the calorimetric bomb, the heats produced are respectively 8,137, 7,900, and 7,860 thermal units ; hence 237, the differ- ence between the two former values, represents the heat developed in the transformation of one gramme of charcoal into graphite, and 4o, the corre- sponding number, in the change from graphite to diamond. The temperature of combustion, or, in the case of gases, the temperature of the flame, is the upper limit of the temperature which can be attained by the combustion of a body. This can be deduced from the heat of combus- tion, and from the specific heats of the bodies produced. The theoretical temperature of combustion of hydrogen in oxygen is calculated at 6,715° ; this, however, is never even approximately reached, for at much lower tem- peratures aqueous vapour is dissociated (395) into its constituents, and the combustion cannot exceed a certain limit of temperature. 497. Animal heat.—In all the organs of the human body, as well as those of all animals, processes of oxidation are continually goingon. Oxygen passes through the lungs into the blood, and so into all parts of the body. In like manner the oxidisable bodies, which are principally hydrocarbons, pass by the process of digestion into the blood, and likewise into all parts of the body, while the products of oxidation, carbonic acid and water, are eliminated by the skin, the lungs, etc. Oxidation in the muscle produces motions of the 490 On Heat [497— molecules, which are changed into contraction of the muscular fibres ; all other oxidations produce heat directly. When the body is at rest, all its functions, even involuntary motions, are transformed into heat. When the body is at work, the more vigorous oxidations of the working parts are transferred to the others. Moreover, a great part of the muscular work is changed into heat, by friction of the muscles and of the sinews in their sheaths, and of the bones in their sockets. Hence the heat produced by the body when at work is greater than when at rest. The blood distributes heat uniformly through the body, which in the normal condition has a temperature of 37° C.=98°6° F. The blood of mammalia has the same temperature, that of birds is somewhat higher. In feyer the temperature rises to 42° to 43°, and in cholera, or when near death, sinks as low as 35°. The function of producing work in the animal organism was formerly con- sidered as separate from that of the production of heat. The latter was held to be specially due to the oxidation of the hydrocarbons of the fat, while the work was ascribed to the chemical activity of the nitrogenous matter. This view has now been generally abandoned ; for it has been found that during work there is no increase in the secretion of urea, which is the result of the oxidation of nitrogenous matter ; moreover, the organism while at rest produces less carbonic acid, and requires less oxygen than when it is at work ; and the muscle itself, both in the living organism and also when removed from it and artificially stimulated, requires more oxygen in a state of activity than when at rest. For these reasons the production of work is ascribed to the oxidation of the organic matter generally. The process of vegetation in the living plant is not in general connected with any oxidation. On the contrary, under the influence of the sun’s rays, the green parts of plants decompose the carbonic acid of the atmosphere into free oxygen gas and into carbon, which, uniting with the elements of water, form cellulose, starch, sugar, and so forth. In order to effect this, an expenditure of heat is required which is stored up in the plant, and which reappears during the combustion of the wood, or of the coal arising from its decomposition. At the time of blossoming a process of oxidation goes on, which, as in the case of the blossoming of the Victoria regia, is attended with an appre- ciable rise of temperature. HEATING 498. Different kinds of heating.—//eading is the art of utilising for domestic and industrial purposes the sources of heat which nature offers to us. Our principal source of artificial heat is the combustion of coal, coke, turf, wood, and charcoal. 499. Fireplaces.—Fireplaces are open hearths built against a wall under a chimney, through which the’products of combustion escape. However much they may be improved, fireplaces will always remain the most imperfect and costly mode of heating, for they only render available 13 per cent. of the total heat yielded by coal or coke, and 6 per cent. of that by wood. ‘This enormous loss of heat arises from the fact that the current of air necessary for combustion always carries with it a large quantity of the heat produced, which is dissipated in the atmosphere. Hence Franklin said ‘fireplaces should be adopted in cases where the smallest quantity of heat -500] Draught of Fireplaces 491 was to be obtained from a given quantity of fuel.’ Notwithstanding their want of economy, however, they will always be preferred as the healthiest and pleasantest mode of heating, on account of the cheerful light which they emit, and the ventilation which they ensure. 500. Draught of fireplaces.—The draught of a fire is the upward cur- rent in the chimney caused by the ascent of the products of combustion ; when the current is rapid and continuous, the chimney is said to draw well. The draught is caused by the difference between the temperature of the inside and that on the outside of the chimney ; for, in consequence of this difference, the gaseous bodies which fill the chimney are lighter than the air of the room, and consequently equilibrium is impossible. The weight of the column of gas CD, fig. 452, in the chimney being less than that of the external column of air AB of the same height, there is a pressure from the outside to the inside which causes the products of combustion to ascend the more rapidly in proportion as the difference in weight of the two gaseous masses is greater. The velocity of the draught of a chimney may be deter- mined theoretically by the formula y= /2ga(t’ — th, in which g is the acceleration of gravity, a the coefficient of the expansion of air, 2 the height of the chimney, z’ the mean temperature of the air inside the chimney, and ¢ the temperature of the surrounding air. The currents caused by the difference in temperature of two communi- cating gaseous masses may be demonstrated by placing a candle near the top and near the bottom of the partially opened door of a warm room. At the top, A the flame will be turned from the room to- \ wards the outside, while the contrary effect will be produced when the candle is placed on the ground. The two effects are caused by the current of heated air which issues by the top of the door, while the cold air which replaces it enters at the bottom. In order to have a good draught, a chimney ought to satisfy the following con- ditions :— i. The section of the chimney ought not to be larger than is necessary to allow an exit for the products of combustion ; other- pola wise ascending and descending currents are Dy EE ae as produced in the chimney, which cause it to CZ. — smoke. It is advantageous to place on the Fig. 452 top of the chimney a conical pot narrower than the chimney, so that the smoke may escape with sufficient velocity to resist the action of the wind. ii. The chimney ought to be sufficiently high, for, as the draught is caused by the excess of the external over the internal pressure, this excess is greater in proportion as the column of heated air is longer. iii, The external air ought to pass into the chamber with sufficient L a oe ys 8 “¢ WSS aS ~ S YY, 7, Bi 492 On Heat [500~ rapidity to supply the wants of the fire. In an hermetically closed room combustibles would not burn, or descending currents would be formed which would drive the smoke into the room. Usually air enters in sufficient quantity by the crevices of the doors and windows. iv. Two chimneys should not communicate, for if one draws better than the other, a descending current of air is produced in the latter, which carries smoke with it. For the strong fires required by steam-boilers and the like, very high chimneys are needed ; of course the increase in height would lose its effect if the hot column above became cooled down. Hence chimneys are often made with hollow walls—that is, of separate concentric layers of masonry or brickwork—the space between them containing air. 501. Stoves.—Sfoves are apparatus for heating with a detached fire, placed in a room to be heated, so that heat radiates in all directions round the stove. At the lower part is the draught-hole by which the air necessary for combustion enters. The products of combustion escape by means of iron chimney-pipes. This mode of heating is one of the most economical, but it is by no means so healthy as that by open fireplaces, for the ventilation is very bad, more especially where the stoves are fed from the outside of the room. These stoves also emit a bad smell, arising in part from the decomposition of organic substances which are always present in the air by their contact with the heated sides of the chimney-pipes ; or possibly, as Deville and Troost’s researches seem to show, from the diffusion of gases through the heated sides of the stove. The heating is very rapid with blackened metal stoves, but they also cool very rapidly. Stoves constructed of polished earthenware, which are common on the Continent, tion, and this property is used in heating baths, public buildings, hothouses, &c. For this purpose steam is generated in boilers lke those used for steam engines, UD YMA \\ \\ heat more slowly, but more Ss y : \\ ISN pleasantly, and they retain NN M IN the heat longer. WS IN : VIB x 502. Heating by steam.— Nie Wl SS Steam, in condensing, gives. Ni Teter aN Hl S : ‘ Ni ct tj NS up its latent heat of vaporisa- \ SS = ae Ss Ss SMGGV SSS Tis 7 4, and is then made to circulate a , Lk in pipes placed in the room te : Sy] LW SW to be heated. The steam SN MW \ ~ SAS VC condenses, and in doing so ee ES SS ZS 4 imparts £6: the pipes its latent VW) WW Wi a heat, whi which becomes free, Fig. 453 and thus heats the surround- ing air. 503. Heating by hot air.—Heating by hot air consists in heating the air in the lower part of a building, whence it rises to the higher parts in 504] Fleating by Hot Water 493 virtue of its lessened density. The apparatus is arranged as represented in fig. 453. A series of tubes, AB, only one of which is shown in the figure, is placed in a furnace F, in the cellar. The air passes into the tubes through the lower end, A, where it becomes heated, and, rising in the direction of the arrows, reaches the room M by a higher aperture, B. The various rooms to be heated are provided with one or more of these apertures, which are placed as low in the room as possible. The conduit O is an ordinary chim- ney. These apparatus are more economical than open fireplaces, but they are less healthy, unless special provision is made for ventilation. 504. Heating by hot water.—This consists of a continuous circulation of water, which, having been heated in a boiler, rises through a series of tubes, and then, after becoming cool, passes into the boiler again by a similar series. Fig. 454 represents an apparatus for heating a building of several] stories. The heating apparatus, which is in the basement, con- sists of a bell-shaped boiler, 0 0, with an in- ternal flue, F. A long pipe, ein stsiinythe upper part of the boiler, and also in the reservoir Q, placed in the upper part of the building to be heated. At the top of this re- servoir there is a safety valve, s, by which the pressure of the vapour ~~“ in the interior can be SS ed LELLLLLLL LLL L Lb MQ aes rd ROSS) NANA RQ MA AAA S regulated. Y WZ The boiler, the pipe Y j 1a LI M, andaportionof the =v Ura ELT fy reservoir Q, being Y 1 Y ] pe. WEAN filled with water, as it Y\ WZ | WY : becomes heated in the GR Y sad Y et | ZZ mrbteed | 77 Ls ; : A 5 7. GY NE WS Ue LEAL TELE DAE PEALE LE TBE \ 4 \ SS SUNS SESE TEES \ N oP SS ARS S ‘ = S SSS current of hot water rises to the reservoir Q, while at the same time descending currents of colder and denser water pass from the lower part of the reservoir Q into receivers 4, d, f, filled with water. The water from these passes again through pipes into other receivers, a, ¢, é, and ultimately reaches the lower part of the boiler. During this circulation the hot water heats the pipes and the receivers, which thus become true water-stoves. The number and the dimensions of these parts are determined from the fact that a cubic foot of water in falling through a temperature of one degree can theoretically impart the same in- crease of temperature to 3,200 cubic feet of air (469). In the interior of the Fig. 454 494 On Ffeat [504— receivers, @, 4, ¢, d, e, f, there are cast-iron tubes which communicate with the outside by pipes, P, placed underneath the flooring. The air becomes heated in these tubes, and issues at the upper part of the receiver. The principal advantage of this mode of heating is that of giving a temperature which is constant for a long time, for the mass of water only cools slowly. It is much used in hot-houses, baths, artificial incubation, drying rooms, and generally wherever a uniform temperature is desired. SOURCES OF COLD 505. Various sources of cold.—Besides the cold caused by the passage of a body from a solid to the liquid state, of which we have already spoken, cold is produced by the expansion of gases, by radiation in general, and more especially by radiation at night. 506. Cold produced by the expansion of gases. Ice machines.—We have seen that when a gas is compressed the temperature rises (489). The re- verse of this is also the case : when a gas is rarefied, a reduction of temperature ensues, because a quantity of sensible heat disappears when the gas becomes increased to a larger volume. This may be shown by placing a delicate Breguet’s thermometer under the receiver of an air-pump, and exhausting ; at each stroke of the piston the needle moves in the direction of zero, and regains its original position when air is admitted. The production of cold when a gas is expanded has been extensively applied in machines for artificial refrigeration on a large scale. By Wind- hausen’s ice machine, from 15,000 to 150,000 feet of air can be cooled in an hour, through 40 to 100 degrees in temperature, by means of a steam-engine of from 6 to 20 horse-power. The essential parts of this machine are repre- sented in fig. 455. The piston B in the cylinder A is worked to the right by | zs : = ——— 4\ \ ————— ee Fig. 455 a steam-engine and to the left by a steam-engine and by the compressed air. As it moves towards the right the valve a opens, and air under the ordinary atmospheric pressure enters the space A,. When this is full the piston moves towards the left, the air in A is compressed to about 2 atmospheres, the valve a is closed, the valve 4 opens, and air passes in the direction of the —508] Cold produced by Radiation at Night 4Q5 arrows into the cooler, C. By its compression it has become strongly heated, and the necessary cooling is effected by means of pipes through which cold water circulates, entering at 5 and emerging at 6. The air, thus compressed and cooled, passes out through the valve c, which is automatically worked by the machine, into the space A,, where, in conjunction with the steam-engine, it moves the piston to the left, and compresses the air in A, ; for at a certain position of the piston the valve c is closed, the compressed air in the cylinder A, expands, and thereby is cooled far below the freezing point. As the piston moves again to the right, the valve dis opened by the working of the machine, and the cooled air emerges through the tube 4 to its destination. Ifit passes into an ordinary room, by condensing the moisture it fills it with snowflakes. Machines of this kind are extensively employed in the arts ; in breweries, oil refineries, in the artificial production of ice, and in cooling rooms on board ship for the transport of dead meat, &c., which has become an industry of the greatest importance. In the Linde machine the material used is ammonia gas, which is liquefied by compression and surface condensation. This liquid ammonia being allowed to evaporate takes the heat for this change of state from the surrounding bodies, which are thereby cooled. The ammonia vapour thus formed is again liquefied, and flowing back to the refrigerator is again evaporated, so that a small quantity of ammonia is always passing through the same cycle of operations. A machine of this kind worked by a steam-engine of half a horse-power can cool in an hour 3,400 cubic yards of air from 10° to 5° C., or 1,400 cubic yards from 6° to — 4° C.; or it will produce I cwt. of ice in the same time. The larger machines are relatively more advantageous. 507. Cold produced by radiation at night.—During the day the ground receives from the sun more heat than it radiates into space, and the. temperature rises. The reverse is the case during night. The heat which the earth loses by radiation is no longer compensated, and consequently a fall of temperature takes place, which is greater according as the sky is. clearer, for clouds send towards the earth rays of greater intensity than those which come from the celestial spaces. In some winters it has been found that rivers have not frozen, the sky having been cloudy, although the thermometer had been for several days below — 4°; while in other less severé winters the rivers freeze when the sky is clear. The emissive power: exercises a great influence on the cold produced by UA oy the greater it is, the greater is the cold. In Bengal, the cooling by night is used in manufacturing ice. Large. flat vessels containing water are placed on non-conducting substances, such as straw or dry leaves. In consequence of the radiation the water freezes, even when the temperature of the air is 10° C. The same method can be applied in all cases with a clear sky. The, Peruvians, in order to preserve the shoots of young plants from freezing, light great fires in their neighbourhood, the smoke of which, pro- ducing an artificial cloud, hinders the cooling produced by radiation. 508. Absolute zero it temperature. es a gas is increased 4, of its volume for each degree Centigrade, it follows that at a temperature Ole aan C. the volume of any gas measured at zero is doubled, supposing the pressure: 496 On feat [508— to remain constant. In like manner, assuming the gaseous laws to continue to hold, we should have at 273° below zero, PV =o (183) ; that is, either the gas would shrink into nothing or it would be subjected to no pressure. We are not, however, driven to either of these conclusions, since we know that all gases are liquefied before a temperature of —273° is reached. Nevertheless, this temperature — 273° C. is a very important one, and is called the absolute zero of temperature. Thermodynamical considerations, apart from the behaviour of any particular gas, point to the conclusion that at this temperature all substances entirely lose their molecular motion, z.e. are entirely deprived of heat. Absolute temperatures are obtained by adding 273 to the temperature on the Centigrade scale. Thus — 35° C. is 238° on the absolute scale of temperature, and + 15° C. is 288°. —509] Mechanical Equivalent of Heat 497 GCiAP Ditkh sock MECHANICAL EQUIVALENT OF HEAT 509. Mechanical equivalent of heat.—If the various instances of the production of heat by motion be examined, it will be found that in all cases mechanical energy is expended. Thus in rubbing two bodies against each other motion is apparently destroyed by friction ; it is not, however, lost, but appears in the form of a motion of the particles of the body ; the motion of the mass 1s transformed into a motion of the molecules. Again, if a body be allowed to fall from a height, it strikes against the ground with a certain velocity. According to older views, its motion is destroyed, vzs viva is lost. This, however, is not the case ; the vzs viva of the body or its £zmetic energy appears as energy of its molecules. In the case, too, of chemical action, the most productive artificial source of heat, it is not difficult to conceive that there is, in the act of combining, an impact of the dissimilar molecules against each other, an effect analogous to the production of heat by the impact of masses of matter against each other (489). In like manner, heat may be made to produce motion, as in the case of the steam-engine, and the propulsion of shot from a gun. Traces of a view that there is a connection between heat and motion are to be met with in the older writers, Bacon for example ; and. Locke says, ‘ Heat is a very brisk agitation of the insensible parts of the object, which produces in us that sensation from whence we denominate the object hot ; so that what in our sensation is heat, in the object is nothing but motion.’ Rumford, in explaining his great experiment of the production of heat by friction, was unable to assign any other cause for the heat produced than motion ; and Davy, in the explanation of his experiment of melting ice by friction 2% vacuo, expressed similar views. Carnot, in a work on the steam- engine published in 1824, also indicated a connection between heat and work. The views, however, which had been stated by isolated writers had little or no influence on the progress of scientific investigation, and it is in the year 1842 that the modern theories may be said to have had their origin. In that year Dr. Mayer, a physician in Heilbronn, formally stated that there exists a connection of simple proportionality between heat and work ; and he it was who first introduced into science the expression ‘ mechanical equt- valent of heat” Mayer also gave a method by which this equivalent could be calculated ; the particular results, however, are of no value, as the method, though correct on principle, was founded on incorrect data. In the same year too, Colding of Copenhagen published experiments on KK 498 On Heat [509- the production of heat by friction, from which he concluded that the evolu- tion of heat was proportional to the mechanical energy expended. About the same time as Mayer, but quite independently of him, Joule commenced a series of experimental investigations on the relation between heat and work. These first drew the attention of scientific men to the subject, and were admitted as a proof that the transformation of heat into mechanical energy, or of mechanical energy into heat, always takes place in a definite numerical ratio. Subsequently to Mayer and Joule, several physicists, by their theoretical and experimental investigations, have contributed to establish the mechanical theory of heat: namely, in this country, Lord Kelvin and Rankine; in Germany, Von Helmholtz, Clausius, and Holtzmann; and in France, Clapeyron and Regnault. The following are some of the most important and satisfactory of Joule’s experiments. A copper vessel, B (fig. 456), was provided with a brass paddle-wheel (indicated by the dotted lines), which could be made to rotate about a vertical axis. Two weights, E and F, were attached to cords which passed over the pulleys C and D, and were connected with the axis A. These weights in falling caused the wheel to rotate. The height of the fall, which in Joule’s experiments was about 63 feet, was indicated on the scales G and H. The roller A was so constructed that by detaching a pin the weights could be raised without moving the wheel. The vessel B was filled with water and placed on a stand, and the weights allowed to sink. When they had reached the ground, the roller was detached from the axis, and the weights again raised, the same operations being repeated twenty times The heat produced was measured by ordinary calorimetric methods (456). The work expended is measured by the product of the weight into the height through which it falls, or A, less the work lost by the friction of the various parts of the apparatus. This is diminished as far as possible by the use of friction wheels (78), and its amount is determined by connecting C -509] ~ Mechanical Equivalent of Heat 499 and D without causing them to pass over A, and then determining the weight necessary to communicate to them a uniform motion. In this way it has been found that a thermal unit—that is, the quantity of heat by which a pound of water is raised through 1° C.—is generated by the expenditure of the same amount of work as would be required to raise 1,392 pounds through 1 foot, or 1 pound through 1,392 feet. This is expressed by saying that the mechanical equivalent of the thermal unit is 1,392 foot- pounds. The friction of an iron paddle-wheel in mercury gave 1,397 foot-pounds, and that of the friction of two iron plates gave 1,395 foot-pounds, as the mechanical equivalent of one thermal unit. In another series of experiments, the air in a receiver was compressed by means of a force-pump, both being immersed in a known weight of water at a known temperature. After 300 strokes of the piston the heat, C, was measured which the water had gained. This heat was due to the compres- ‘sion of the air and to the friction of the piston. To eliminate the latter in- fluence, the experiment was made under the same conditions, but leaving the receiver open. The air was not compressed, and 300 strokes of the piston developed C’ thermal units. Hence C—C’ is the heat produced by the com- pression of the gas. Representing the foot-pounds expended in producing this heat by W, we have for the value of the mechanical equivalent. WwW C-—C’ By this method Joule obtained the number 1,442. The mean number which Joule adopted for the mechanical equivalent of one thermal unit on the Centigrade scale is 1,390 foot-pounds ; on the Fahrenheit scale it is 772 foot-pounds. The number is called /ozle’s egut- valent, and is usually designated by the symbol J. On the metrical system 424 metres are usually taken as the height through which a kilogramme of water must fall to raise its temperature 1 degree Centigrade. This is equal to 42,400,000 ergs or 4°24 x Io’ grammes raised through a height of a centimetre. | Professor Rowland of Baltimore has recently made a very careful and complete determination of the mechanical equivalent of heat, by Joule’s method, in which he has examined and allowed for all possible sources of error. His results give 4:269 x 10’ grammes centimetre or 1,401 foot-pounds as the mean value of this constant for the latitude of Baltimore ; and this value is in close agreement with a still more recent determination by Mr. E. H. Griffiths, who found, by an electrical method, 4°2788 x 10’ grammes cen- timetre or 1,403°6 foot-pounds for the latitude of Greenwich (¢=981'17), and ‘by Micalescu, who found 4:267 x to’ for the latitude of Paris (= 980°96). Hirn made the following determination of the mechanical equivalent by means of the heat produced by the compression of lead. A large block of sandstone, CD (fig. 457), is suspended vertically by cords ; its weight is P. E is a piece of lead, fashioned so that its temperature may be determined by the introduction of a thermometer. The weight of this is I, and its specific heat c. AB is a cylinder of cast iron, whose weight is Z. If this be raised to A’B’, a height of %, and allowed to fall again, it compresses the lead, E, against the anvil, CD. It remains to measure on the one hand the work -spent, and on the other the heat gained. KK2 500 On Fleat [509— The hammer AB being raised to a height 4, the work of its fall is Dh ; but as, by its elasticity, it rises again to a height 4, the work is ~ (A-Z,). The anvil CD, on the other hand, has been raised through a height H to C’D’, and has required in so doing PH units of work. The work, W,. definitely absorbed by the lead is # (A—Z,) —-PH. On the other hand, the lead has been heated by 6, it has gained IIc@ thermal units, c being the specific heat of lead, and the mechanical equivalent J is equal to the quotient ai A series of six experiments gave 1,394 for the mechanical equivalent as thus obtained. QQ MQW, ©HHWd, AQ] DF.” tw - -_—" —— ‘GANT ign _f ie = au 1c | vl at ele El The experiments of Cantoniand Gerosa in this direction are the simplest. They allowed mercury to fall from a funnel through a narrow tube into a vessel below, when its temperature was measured. In this way the number Fig. 457 1,390 was obtained. Experiments in the opposite direction have also been made, in which the work produced by one thermal unit was determined. This was done on a large scale by Hirn by means of a steam-engine of one hundred horse-power. He determined the quantity of heat contained in the steam before its action, and then the amount contained in the water after its condensation. This was less, for some had been expended in work ; and this work as measured by the dynamometer was equivalent to that which had disappeared, the number 390'7 being thus obtained. The following is the method which originally Mayer employed in calcu- lating the mechanical equivalent of heat. It is taken, with slight modifica- tions, from Tyndall’s work on Heat, who, while strictly following Mayer’s reasoning, has corrected his data. Let us suppose that a rectangular vessel with a section of a square foot contains at o° a cubic foot of air under the ordinary atmospheric pressure ; and let us suppose that it is inclosed by a piston without weight. Suppose now that the cubic foot of air is heated until its volume is: doubled ; from the coefficient of expansion of air we know that this is the case at 273° C. The gas in doubling its volume will have raised the piston through a foot in height ; it will have lifted the atmospheric pressure through this distance. But the atmospheric pressure on a square foot is in round —509] Mechanical Equivalent of Heat 501 numbers 15 x 144=2,160 pounds. Hence a cubic foot of air in doubling its volume has lifted a weight of 2,160 pounds through a height of a foot. Now a cubic foot of air at zero weighs 1°29 ounce, and the specific heat of air under constant pressure—that is, when it can expand freely—as com- pared with that of an equal weight of water, is 0:24; so that the quantity of heat which will raise 1:29 ounce of air through 273° will only raise 0°24 x 1°29 = 0°31 oz. of water through the same temperature ; but 0°31 oz. of water raised through 273° is equal to 5:29 pounds of water raised through 1° C. That is, the quantity of heat which will double the volume of a cubic foot of air, and in so doing will lift 2,160 pounds through a height of a foot, is 5'29 thermal units. Now in the above case the gas has been heated under constant pressure, that is, when it could expand freely. If, however, it had been heated under. constant volume, its specific heat would have been less in the ratio 1:1°414 (469), so that the quantity of heat required under these circumstances to raise the temperature of a cubic foot of air would be 5°29 x= 374, Deducting this from 5:29, the difference 1°55 represents the weight of water which would have been raised 1° C. by the excess of heat imparted to the air when it could expand freely. But this excess has been consumed in the work of raising 2,160 pounds through a foot. Dividing this by 1°55 we have 1,393. Hence the heat which will raise a pound of water through 1° C. will raise a weight of 1,393 pounds through a height of a foot ; a numerical value of the mechanical equivalent of heat agreeing as closely as can be expected with that which Joule adopted as the most certain of his experimental results. Fig. 458 The law of the relation of heat to mechanical energy may be thus stated :— Heat and mechanical energy are mutually convertible ; and heat requires for its production, and produces by its disappearance, mechanical energy tn the ratio of 1,390 foot-pounds for every thermal unit. 502 On Feat [509-— A variety of experiments may in like manner be adduced to show that whenever heat disappears work is produced. For example, suppose that the air in a reservoir immersed in water be compressed to the extent of Io atmospheres, and that, when the compressed air has acquired the tempera- ture of the water, it be allowed to act upon a piston loaded by a weight, the result is that the weight is raised. At the same time the water becomes cooler, showing that a certain quantity of heat had disappeared in producing the mechanical effort of raising the weight. This may also be illustrated by the following experiment (fig. 458), due to Tyndall :-— A strong metal box is taken, provided with a stopcock, on which can be screwed a small condensing pump. Having compressed the air since it becomes heated by this process, the box is allowed to stand for some time, until it has acquired the temperature of the surrounding medium. On opening the stopcock the air rushes out ; it is expelled by the expansive force of the internal air: in short, the air drives itself out. Work is there- fore done by the air against external pressure, and there should bea dis- appearance of heat ; andif the jet be allowed to strike against the thermopile, the galvanometer is deflected, and the direction of its deflection indicates a cooling (fig. 456). A similar effect is observed when, on opening a bottle of soda water, the carbonic acid gas which escapes is allowed to strike against the thermopile. If, on the contrary, the experiment is made with an ordinary pair of bellows, and the current of air is allowed to strike against the pile, the deflection of the galvanometer is in the opposite direction, indicating an increase of temperature (fig. 459). In this case the hand of the experimenter performs the work, which is converted into heat. Joule placed in a calorimeter two equal copper reservoirs, which could Fig. 459 be connected by a tube. One of these contained air at 22 atmospheres, the other was exhausted. When they were connected, they came into equi- librium under a pressure of I1 atmospheres; but as the gas in expanding had done no work, there was no alteration in temperature. When, however, -510] Dissipation of Energy 503 the second reservoir was full of water, the air in entering was obliged to expel it and thus perform work, and the temperature sank, owing to an absorption of heat. For further information the student of this subject is referred to the following works :—Tyndall on Heat as a Mode of Motion, Maxwell on feat, Wormell’s Thermodynamics (Longmans), and Tait on Thermodynamics (Edmondston & Douglas). A condensed, though complete and systematic, account of the dynamical theory of heat is met with in Professor Foster’s articles on ‘Heat’ in Watts Dictionary of Chemistry. 510. Dissipation of energy.—Rankine made the following interesting observations on a remarkable consequence of the mutual convertibility which has been shown to exist between heat and other forms of energy :—Lord Kelvin has pointed out the fact that there exists, at least in the present state of the known world, a predominating tendency to the conversion of all other forms of physical energy into heat, and to the uniform diffusion of heat throughout all matter. The form in which we generally find energy originally collected is that of a store of chemical power consisting of uncom- bined elements. The combination of these elements produces energy in the form known by the name of electrical currents, part only of which can be employed in electrolysing chemical compounds, and thus reconverted into a store of chemical power; the remainder is necessarily converted into heat ; and again, only a part of this heat can be employed in electrolysing compounds or in reproducing electric currents. If the remainder of the heat be employed in expanding an elastic substance, it may be converted entirely into visible motion, or into a store of visible mechanical power (by raising weights, for example), provided the elastic substance is enabled to expand until its temperature falls to the point which corresponds to the absolute privation of heat ; but unless this condition is fulfilled a certain proportion only of the heat, depending on the range of temperature through which the elastic body works, can be converted, the rest remaining in the state of heat. On the other hand, all visible motion is of necessity ultimately converted into heat by the agency of friction. There is, then, in the present state of the known world, a tendency towards the conversion of all physical energy into the sole form of heat. Heat, moreover, tends to diffuse itself uniformly by conduction and radia- tion, until all matter shall have acquired the same temperature. There is consequently, so far as we understand the present condition of the universe, a tendency towards a state in which all physical energy will be in the state of heat, and that heat so diffused that all matter will be at the same temperature ; so that there will be an end of all physical phenomena. Vast as this speculation may seem, it appears to be soundly based on experimental data, and to truly represent the present condition of the uni- verse as far as we know it. 504 On Light [511— BOO Kaa tl ON LIGHT CHAP thee TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT 511. Theories of light.—ZzgA¢ is the agent which, by its action on the retina, excites in us the sensation of vision. That part of physics which deals with the properties of light is known as oféics. In order to explain the origin and transmission of light, various hypo- theses have been made, the most important of which are the evzzsszon or corpuscular theory, and the undulatory theory. On the emzsstzon theory it is assumed that luminous bodies emit, in all directions, an imponderable substance, which consists of molecules of an extreme degree of tenuity : these are propagated in right lines with an almost infinite velocity. Penetrating into the eye they act on the retina, and deter- mine the sensation which constitutes vision. On the undulatory theory, all bodies, as well as the celestial spaces, are filled by an extremely subtle elastic medium, which is called the /umindferous ether. The luminosity of a body is due to an infinitely rapid vibratory motion of its molecules, which, when communicated to the ether, is propagated in all directions in the form of spherical waves, and this vibratory motion, being thus transmitted to the retina, calls forth the sensation of vision. The vibrations of the ether take place not in the direction in which the wave is travelling, but in a plane at right angles to it. An idea of these may be formed by shaking a rope at one end. The vibrations, or to and fro move- ments, of the particles of the rope, are at right angles to the length of the rope, but the onward motion of the wave’s form is in the directien of the length. On the emission theory the propagation of light is affected by a motion or translation of particles of light thrown out from the luminous body, as a bullet is discharged from a gun; on the undulatory theory there is no pro- gressive motion of the particles themselves, but only of the state of disturb- ance which was communicated by the luminous body ; and this is transmitted by the vibratory motion of the particles of the luminiferous ether. The luminiferous ether penetrates all bodies, but on account of its extreme tenuity it is uninfluenced by gravitation ; it occupies space, and although it presents no appreciable resistance to the motion of the denser bodies, it is possible that it hinders the motion of the smaller comets. It has —514] | Luminous Ray and Pencil 505 been found, for example, that Encke’s comet, whose period of revolution is about 34 years, has its period diminished by about o-11 of a day at each successive rotation, and this diminution is ascribed by some to the resistance of the ether. Graetz has calculated that the density of ether is 9 x 107'° that of water. From a formula of Lord Kelvin it is calculated to be greater than Io! ; it may accordingly be admitted to be 107!7. While the air over a square metre weighs 10,000 kilogrammes, the ether in it, taking the height of the atmosphere at 30 miles, would weigh only o-0022 milligramme. Kelvin concludes that if the density of the air followed Boyle’s law, and the tem- perature were constant, at a height equal to that of the earth’s radius it would be only 10°**® that of water. The ether is therefore far more dense than air so rarefied. He calculated that a volume equal to that of the earth cannot contain less than 2,775 pounds of ether. The fundamental principles of the undulatory theory were enunciated by Huyghens, and subsequently by Euler. The emission theory, principally owing to Newton’s powerful support, was for long the prevalent scientific creed. The undulatory theory was adopted and advocated by Young, who showed how a large number of optical phenomena, particularly those of diffraction, were to be explained by that theory. Subsequently, too, though independently of Young, Fresnel showed that the phenomena of diffraction, and also those of polarisation, are explicable on the same theory, which since his time has been generally accepted. The undulatory theory not only explains the phenomena of light, but reveals an intimate connection between these phenomena and those of heat (436) ; 1t shows, also, how completely analogous the phenomena of light are to those of sound, regard being had to the differences of the media in which these two classes of phenomena take place. 512. Luminous, transparent, translucent, and opaque bodies.—Lwzuz- nous bodies are those which emit light, such as the sun and ignited bodies. Transparent or adtaphanous bodies are those which readily transmit light, and through which objects can be distinguished ; water, gases, polished glass are of this kind. Zvanslucent bodies transmit light, but objects cannot be distinguished through them: ground glass, oiled paper, &c., belong to this class. Ofague bodies do not transmit light ; for example, wood, metals, &c. No bodies are quite opaque ; they are all more or less translucent when cut in sufficiently thin leaves. Foucault showed that when the object-glass of a telescope is thinly silvered, the layer is so transparent that the sun can be viewed through it without danger to the eyes, since the metallic surface reflects the greater part of the heat and light. 513. Luminous ray and pencil.—A luminous ray is the direction of the line in which light is propagated ; a /umznous pencil is a collection of rays from the same source; it is said to be parallel when it is composed of parallel rays, divergent when the rays separate from each other, and com- vergent when they tend towards the same point. Every luminous body emits divergent rectilinear rays from all its points, and in all directions. 514. Propagation of light in a homogeneous medium.—A medium is any space or substance which light can traverse such as a vacuum, air, water, 506 On Light [514— glass, &c. A medium is said to be homogeneous when its chemical com- position and density are the same in all parts. In every homogeneous medium light ts propagated in a right line. For, if an opaque body is placed in the right line which joins the eye and the luminous body, the light is intercepted. The light which passes into a dark room by a small aperture is visible from the light falling on the particles of dust suspended in the atmosphere. Light changes its direction on meeting an object which it cannot pene- trate, or when it passes from one medium to another. These phenomena will be described under the heads reflection and refraction. 515. Shadow, penumbra.—When light falls upon an opaque body it cannot penetrate into the space immediately behind it, and this space is called the shadow. Fig. 460 In determining the extent and the shape of a shadow projected by a body, two cases are to be distinguished: that in which the source of light is a single point, and that in which it is a body of any given extent. In the first case, let S (fig. 460) be the luminous point, and M a spherical body, which causes the shadow. If an infinitely long straight line, SG, Fig. 46r move round the sphere M tangentially, always passing through the point S, this line will trace a conical surface, which, beyond the sphere, separates that portion of space which is in shadow from that which is illuminated. In the present case, on placing a screen, PQ, behind the opaque body the limit —515] Shadow, Penumbra 507 of the shadow HG will be sharply defined. This is not, however, usually the case, for luminous bodies have always a certain magnitude, and are not merely luminous points. Suppose that the luminous and illuminated bodies are two spheres, SL and MN (fig. 461). If an infinite straight line, AG, moves tangentially to both spheres, always cutting the line of centres in the point A, it will pro- duce a conical surface with this point for a summit, and which traces behind the sphere MN a perfectly dark space MGHN. Ifa second right line, LD, which cuts the line of centres in B, moves tangentially to the two spheres, so as to produce a new conical surface, BDC, it will be seen that all the space outside this surface is illuminated, but that the part between the two conical surfaces is neither quite dark nor quite light. So that if a screen, PO,\is placed behind the opaque body, the portion cGdH of the screen is quite in the shadow, while the space aé receives light from certain parts of the lumi- nous body, and not from others. It is brighter than the true shadow, and not so bright as the rest of the screen, and it is accordingly called the penumobra. Shadows such as these are geometrical shadows; physical shadows, or those which are really seen, are by no means so Sharply defined. A certain quantity of light passes into the shadow, even when the source of light is a mere point, and con- versely the shadow influ- £ ences the _ illuminated | part. This phenomenon, which will be afterwards described, is known by the name of adffraction (660). The explanation of the phenomena of eclzfses follows directly from the theory of shadows. When the opaque disc of the moon comes, according to the conditions, between the sun and the earth, the shadow cast by the moon causes a more or less complete solar eclipse on those parts of the earth which it meets. Let S be the sun, T the earth, and L the moon placed in a position favourable for an eclipse (fig. 462). If we can suppose the three bodies represented with their ve/ative magnitudes and distances, we need only repeat the graphical construction of this figure to determine the dimensions of the cone of the shadow, and of the penumbra of the moon. The length LI of the cone of the shadow varies between 57 and 59 terrestrial radii, accord- ing to the relative positions of the earth and its satellite ; the distance of the two planets varies between 55 and 62 such radii; hence, under favour- able conditions the cone of the shadow may reach the earth, and in those points of the earth thus touched, 7, there is a total eclipse of the sun. As this area has relatively a small extent, an eclipse which is visible by the inhabitants of this area is not seen by those in the neighbourhood. After the lapse of a time which never exceeds 3 min. 13 sec. the cone will have left the place #z and will pass to wz’, which is not necessarily on the same oS Sos> PRS Fig. 462 508 On Light [515— parallel of latitude. It will thus sweep over the surface of the earth, in virtue of the special motion of the two heavenly bodies, along a line which astronomers can determine beforehand. On all points along this line (fig- 463) there will successively be a total eclipse ; for adjacent ones, which are within the cone of the penumbra, the eclipse will be fartzal. If the cone of the shadow does not reach the earth, there will nowhere be a total eclipse ; but on a point m’ (fig. 464) there will be no light from the Fig. 463 central part of the sun; this willthen appear like a black circle surrounded by a bright ring (fig. 465), and forms what is called an axnular eclipse. Total or partial eclipses of the moon are produced by the total or partial immersion of the moon in the cone of the shadow cast by the earth ; for an observer on the moon they would constitute total or partial eclipses of the sun ; total at those parts of the moon in the shadow, fartza/ at those in the penumbra. The ¢vanszts of Venus or of Mercury over the sun are phenomena of the same kind as eclipses, being produced by the projection on the earth of the Fig. 465 penumbral cones of shadow of those planets. The eclipses of the satellites of certain planets such as Jupiter are identical with the eclipses of the moon. The shadow of a body, a sphere for instance, in sunlight is about 110 times as long as the body is broad. This follows from the proportion Distance of the sun _ Diameter of the sun Length of the shadow _ Diameter of the sphere’ 516. Images produced by small apertures.—When rays of light which pass into a dark chamber through a sa// aperture are received upon a -516] lmages produced by Small Apertures 509 screen, they form images of external objects. These images are inverted ; their shape is always that of the external objects, and is independent of the shape of the aperture. The inversion of the images arises from the fact that the luminous rays proceeding from external objects, and penetrating into the chamber, cross one another in passing the aperture, as shown in fig. 466. Continuing in a straight line, the rays from the higher parts meet the screen at the lower parts ; and conversely, those which come from the lower parts meet the Fig. 466 higher parts of the screen. Hence the inversion of the image. In the article Camera Obscura (613) it will be seen that the brightness and precision of these images are increased by means of lenses. In order to show that the shape of the image is independent of that of the aperture, when the latter is sufficiently small and the screen at an ade- quate distance, imagine a triangular aperture, O (fig. 467), made in the door of a dark chamber, and let ad be a screen on which is received the image of a flame, AB. A divergent pencil from each point of the flame passes through the aperture, and forms on the screen a triangular image resembling the Fig. 467 aperture. But the union of all these partial images produces a total image of the same form as the luminous object. For if we conceive that an infinite straight line moves round the aperture, with the condition that it is always tangential to the luminous object AB, and that the aperture is very small, the straight line describes two cones, the apex of which is the aperture, while one of the bases is the luminous object and the other the luminous object on the screen—that is, the image. Hence, if the screen is per- pendicular to the right line joining the centre of the aperture and the centre of the luminous body, the image is similar to the body ; but if the screen is 510 On Light [516— oblique, the image is elongated in the direction of its obliquity. This is what is seen in the patches of light on the ground when solar light falls upon foliage ; the rays of the sun passing through the minute interstices between the leaves produce images of the sun, which are either round or elliptical, according as the ground is perpendicular or oblique to the solar rays ; arid this is the case whatever be the shape of the aperture through which the light passes. 517. Velocity of Light.—Light moves with such a velocity that at the surface of the earth there is, to ordinary observation, no appreciable interval between the occurrence of any luminous phenomenon and its perception by the eye. And, accordingly, this velocity was first determined by means of astronomical observations. Rdmer, a Danish astronomer, in 1675, first deduced the velocity of light from observations of the eclipses of Jupiter’s first satellite. Jupiter is a planet, round which four satellites revolve, as the moon does round the earth. This first satellite, E (fig. 468), suffers occuwltation— that is, passes into Jupiter’s shadow—at equal intervals of time, which are 42h..28m. 36s. While the earth moves in that part of its orbit, ad, nearest Jupiter its distance from that planet does not materially alter, and the intervals between two successive occultations of the satellite are approximately the same; but, in proportion as the earth moves away in its revolution round the sun, S, the interval between two occultations increases, and when, at the end of six months, the earth has passed from the position T to the position T’, a total retardation of 16m. 36s.is observed between the time at which the phe- nomenon is seen and that at which it is calculated to take place. But when the earth was in the position T, the sun’s light reflected from the satellite E had to traverse the distance ET, while in the second position the light had to traverse the distance ET. This distance exceeds the first by the quantity TT’, for, from the great dis- tance of the satellite E, the rays ET and ET’ may be considered parallel. Consequently, light requires 16m. 36s. to travel the diameter TT’ of the terrestrial orbit, or twice the distance of the earth from the sun, which gives for its velocity 190,000 miles in a second. The stars nearest the earth are separated from it by at least 206,265 times the distance of the sun. Consequently, the light which they send requires more than 3 years to reach us. Those stars which are only visible by means of the telescope are possibly at such a distance that thousands of years would be required for their light to reach our planetary system. They might have been extinguished for ages without our knowing it. 518. Foucault’s apparatus for determining the velocity of light.—Not- withstanding the prodigious velocity of light, Foucault succeeded in deter- Fig. 468 -518] Apparatus for determining the Velocity of Light 511 mining it experimentally by the aid of an ingenious apparatus, based on the use of the rotating mirror, which was adopted by Wheatstone in measuring the velocity of electricity. In the description of this apparatus, a knowledge of the principal pro- perties of mirrors and of lenses is presupposed. Fig. 469 represents the chief parts of Foucault’s arrangement. The window shutter, K, of a dark chamber is perforated by a rectangular slit, behind which the platinum wire 9 is stretched vertically. A beam of sunlight reflected from the out- side upon a mirror enters the dark room by the slit, meets the platinum wire, and then traverses an achromatic lens, L, with a long focus placed at a distance from the platinum wire less than double the principal focal distance. The image of the platinum wire, more or less magnified, would thus be formed on the axis of the lens; but the pencil of light, having traversed the lens, impinges on a plane mirror, m, rotating with great velocity ; it is reflected from this, and forms in space an image of the Fig. 469 Fig. 470 platinum wire, which is displaced with an angular velocity double that of the mirror (532). This image is reflected by a concave mirror, M, whose centre of curvature coincides with the axis of rotation of the mirror 7, and with its centre of figure. The pencil reflected from the mirror M returns upon itself, is again reflected from the mirror m, traverses the lens a second time, and forms an image of the platinum wire, which appears on the wire itself so long as the mirror 7 is at rest or turns slowly. In order to see this image without hiding the pencil of light which enters by the aperture in K, a plane parallel mirror of unsilvered glass, V, is placed between the lens and the wire, and is inclined so that the reflected rays fall upon a powerful eyepiece, P. The apparatus being arranged, if the mirror 7 is at rest, the pencil after meeting M is reflected to 7, and thence returns along its former path, till it meets the glass plate V in a, and being partially reflected, forms at d— the distance ad being equal to ao—an image of the wire, which the eye is 512 On Light ~ [518- enabled to observe by means of the eyepiece, P. If the mirror, instead of being fixed, is moving slowly round—its axis being at right angles to the plane of the paper—there will be no sensible change in the position of the mirror # during the brief interval elapsing while light travels from # to M and back again, but the image will alternately disappear and reappear. If now the velocity of M is increased to upwards of 30 turns per second, the interval between the disappearance and reappearance ‘is so short that the impression on the eye is persistent, and the image appears perfectly steady. Lastly, if the mirror turns with sufficient velocity, there is an appreciable change in its position during the time which the light takes in making the double journey from #z to M, and from M to mm: the return ray, after its reflection from the mirror #, takes the direction 7d, and forms its image at z; that is, the image has undergone a total deviation a. Speaking pre- cisely, there is a deviation as soon as the mirror turns, even slowly ; but it is only appreciable when it has acquired a certain magnitude, which is the case when the velocity of rotation is sufficiently rapid, or the distance Mv suffi- ciently great, for the deviation necessarily increases with the time which the light takes in returning on its own path. In Foucault’s experiment the dis- tance Mw was only 134 feet ; when the mirror rotated with a velocity of 600 to 800 turns in a second, deviations of 0°2 to 0°3 mm. were obtained. Taking Mma=/, La=J’, oL=rs, and representing by # the number of turns in a second, by 6 the absolute deviation dz, and by V the velocity of light, Foucault arrived at the formula | 8rlPar 8047) from which the velocity of light is calculated at 185,157 miles in a second ; this number agrees remarkably well with the value deduced from newer determinations of the value of the solar parallax. The mechanism by which the mirror was turned consisted of a small steam turbine, bearing a sort of resemblance to the siren, and, like that instrument, giving « higher sound as the rotation is more rapid: in fact, it is by the pitch of the note that the velocity of the rotation is determined. In this apparatus liquids can be experimented upon. For that purpose a tube, AB, ro feet long, and filled with distilled water, is placed between the turning mirror #, and a concave mirror M’, identical with the mirror M. The luminous rays reflected by the rotating mirror, in the direction 72M’, traverse the column of water AB twice before returning to V. But the return ray then becomes reflected at c, and forms its image at #: the deviation is consequently greater for rays which have traversed water than for those which have passed through air alone ; hence the velocity of light is less in , water than in air. . This is the most important part of these experiments. It is a necessary consequence of the undulatory theory that the velocity of light must be less in the more highly refracting medium (652), while the opposite is a necessary consequence of the emission theory. Hence Foucault’s result may be regarded as a crucial test of the validity of the undulatory theory. 519. Experiments of Fizeau.—In 1849 Fizeau measured directly the velocity of light, by ascertaining the time it took to travel from Suresnes to ~520] Laws of the Intensity of Light 513 Montmartre and back again. Theapparatus employed was a toothed wheel, capable of being turned more or less quickly, and with a velocity that could be exactly ascertained. The teeth were made of precisely the same width as the intervals between them. The apparatus being placed at Suresnes, a pencil of rays was transmitted through an interval between two teeth to a mirror placed at Montmartre. The pencil, directed by a properly arranged system of lenses, returned to the wheel. As long as the apparatus was at rest the pencil returned exactly through the same interval as that through which it first set out. But when the wheel was turned sufficiently fast, a tooth was made to take the place of an interval, and the ray was intercepted. As the wheel was turned still more rapidly, the light reappeared when the in- terval between the next two teeth had taken the place of the former tooth at the instant of the return of the pencil. The distance between the two stations was 28,334 feet. Froma knowledge of this distance, the dimensions of the wheel, its velocity of rotation, &c., Fizeau found the velocity of light to be 196,000 miles per second—a result agreeing with that given by astronomical observation as closely as can be expected in a determination of this kind. Cornu recently investigated the velocity of light by Fizeau’s method, but with improvements so that the probable error did not exceed ;4, of the total amount ; the two stations, which were 6:4 miles apart, were a pavilion of the Ecole Polytechnique and a room in the barracks of Mont Valérien. By means of electro-magnetic arrangements the rotation of the toothed disc, and the times of obscuration and illumination, were registered on a blackened cylinder, on the principle of the method described in art. 248. Cornu thus obtained the number 185,420 miles—a result closely agreeing with that of Foucault, and supported by calculations based on the results of astronomical observations of the transit of Venus in 1874. Newcomb improved Foucault’s method by using a slightly concave mirror instead of a plane one, by which the image of the slit was brighter; it was observed by a telescope through a distance of 4,000 metres. The rotations also were reversed, by which the angle between the two positions of the telescope was observed with greater accuracy ; he thus obtained the number 186,364 miles, while Michelson repeated a former determination and found 186,354, a difference of only about 10 miles. 520. Laws of the intensity of light.—The zzzenszty of illumination is the quantity of light re- ceived on the unit of sur- face ; 1t is subject to the following laws :— I. The intensity of tllu- mination on a given sur- face ts inversely as the sguare of tts distance from the source of light. Il. The intensity of Fig. 471 tllumination which ts re- ceived obliquely ts proportional to the cosine of the angle which the luminous rays make with the normal to the illuminated surface. LL S14 On Light [520- In order to demonstrate the first law, let there be two circular screens, CD and AB (fig. 472), one placed at a certain distance from a source of light, L, regarded as a point, and the other at double this distance, and let s and S be the areas of the two screens. If @ be the total quantity of light which is emitted by the source in the direction of the cone ALB, the intensity of the light on the screen CD—that is, the quantity which falls on the unit of surface—is < and the intensitv on the screen AB is x Now as the triangles ALB and CLD are similar, the diameter of AB is double that of CD ; and as the surfaces of circles are as the squares of their diameters, the surface S is four times s, consequently the intensity = is one- fourth that of “. S Fig. 472 shows that it is owing to the divergence of the luminous rays emitted from the same source that the intensity of light is inversely as the square of the distance ; the illumination of a surface placed in a beam of parallel luminous rays is the same at all distances in a vacuum. In air and in other transparent media the intensity of light decreases, in consequence of absorption, more rapidly than the square of the distance. The second law of intensity corresponds to the law which we have found to prevail for heat: it may be theoretically deduced as follows :—Let DA, EB (fig. 472) be a pencil of parallel rays falling obliquely on a surface, AB, and let ov be the normal to this surface. If S is the section of the pencil, a the total quantity of light which falls on the surface AB, and I that which falls on the unit of surface—that is, the intensity of Fig. 472 illumination—we have I= ae But as S is only the projection of AB on a plane perpendicular to the pencil, we Ss ; This know from trigonometry that S=AB cos a, from which AB= cos a value substituted in the above equation gives I =% cos @; a formula which demonstrates the law of the cosine, for as a and S are constant quantities, I is proportional to cos a. The law of the cosine applies also to rays emitted obliquely by a luminous surface ; that is, the rays are less intense in proportion as they are more inclined to the surface which emits them. In this respect they correspond to the third law of the intensity of radiant heat. 521. Photometers.—A fhotfometer is an apparatus for measuring the relative intensities of different sources of light. Rumford s photometer.—This consists of a ground-glass screen, in front of which is fixed an opaque rod (fig. 473) ; the lights to be compared—for instance, a lamp and a candle—are placed at a certain distance in such a manner that each projects on the screen a shadow of the rod, Theshadows -§21] Photometers 515 thus projected are at first of unequal intensity, but by altering the position of the lamp it may be so placed that the intensity of the two shadows is the same. Then, since the shadow thrown by the lamp is illuminated by the candle, and that thrown by the candle is illuminated by the lamp, the illu- mination of the screen due to each light is the same. The intensities of the two lights—that is, the illuminations which they would give at equal dis- tances—are then directly proportional to the squares of their distances from the shadows ; that is to say, if the lamp is three times the distance of the candle, its illuminating power is nine times as great. For if z and z’ are the intensities of the lamp and the candle at the unit of distance, and d@ and @’ their distances from the shadows, it follows, from the first law of the intensity of light, that the intensity of the lamp at the distance d is, and that of the eandlea at the distance a’. On the screen these two intensities are equal ; hence — ia =—., which was to be z = 2 proved. Bunsen’s photometer—When a grease-spot is made on a piece of bibu- lous paper, the part appears translucent. If the paper be illuminated by a light placed in front, the spot appears darker than the surrounding space ; if, on the contrary, it be illuminated from behind, the spot appears light on a dark ground. If the greased part and the rest appear unchanged, the intensity of illumination on both sides is the same. Bunsen’s photometer depends on an application of this principle. Its essential features are repre- sented in fig. 474. A circular spot is made on a paper screen by means of a solution of spermaceti in naphtha : on one side of this is placed a light of a certain intensity, which serves as a standard ; in London it isa sperm candle 4 of an inch in diameter, and burning 120 grains in an hour. The light to be tested, a petroleum lamp or a gas burner consuming a certain volume of gas in a given time, is then moved in a right line to such a distance on the other side of the screen that there is no difference in brightness between the greased part and the rest of the screen. By measuring the distances of Ela 516 On Light [521- the lights from the screen by means of the scale, their relative illuminating powers are respectively as the squares of their distances from the screen. The difficulty of getting more carefully constructed candles to give a light sufficiently uniform for standard purposes has led Harcourt to adopt as unit the light formed by burning a mixture of 7 volumes of pentane gas and 20 volumes of air, at the rate of half a cubic foot in an hour, in a specially constructed burner so as to produce a flame of a definite height. This has been found to answer well in practice. By this kind of determination the Fig. 474 degree of accuracy which can be attained is not so great as in many physical determinations, more especially when the lights to be compared are of dif- ferent colours ; one, for instance, being yellow, and the other of a bluish tint. It gives, however, results which are sufficiently accurate for practical purposes, and is almost universally employed for determining the il- luminating power of coal gas and of other artificial lights. In” *Germany “ithe” ffve777e Alteneck lamp is much used as standard ; the combustible is amylic acetate or artificial pear oil, and a flame of constant height is produced in a burner of special con- struction. The absolute unit of light adopted by the International Congress of Electricians, proposed by M. Violle, is that emitted by a square centimetre of melted platinum at the moment of its solidification. It is equal to about fifteen standard candles. Wheatstone’s photomeier.—The principal part of this instrument is a steel bead P (fig. 475), fixed on the edge of a disc, which rotates on a pinion, 0, working in a larger toothed wheel. The wheel fits in a cylindrical brass box which is held in one hand, while the other works a handle, A which turns a central axis, the motion of which is transmitted by a spoke, a, to the pinion 9. In this way the latter turns on itself, and at the same time revolves round the circumference of the box; the bead shares the double motion and consequently describes a curve in the form of a rose (fig. 476). Fig. 476 —522] Relative Intensities of various Sources of Light 517 Now, let M and N be the two lights whose intensities are to be com- pared ; the photometer is placed between them and rapidly rotated. The brilliant points produced by the reflection of the light on the two opposite sides of the beads give rise to two luminous bands, arranged as represented in fig. 476. If one of them is more brilliant than the other—that which pro- ceeds from the light M, for instance—the instrument is brought nearer the other light until the two bands exhibit the same brightness. The distance of the photometer from each of the two lights being then measured, their intensities are proportional to the squares of the distances. 522. Relative intensities of various sources of light.—The light of the sun is 600,000 times as powerful as that of the moon ; and 16,000,000,000 times as powerful as that of a Centauri, the third in brightness of all the stars. The moon is thus 27,000 times as bright as this star ; the sun is 5,500 million times as bright as Jupiter, and 80 billion times as bright as Neptune. Its light is estimated to be equal to 670,000 times that of a wax candle at a distance of 1 foot. According to Fizeau and Foucault the electric light produced by 50 Bunsen’s cells is about 4 as strong as sunlight. The relative luminosities of the following stars are as compared with Vega=1: Pole Star o13, Aldebaran o°30, Saturn 047, Arcturus 0°79, Mars 2°93, Sirius 4°291, Jupiter 8:24, Venus 38°9. A difference in the strength of light or shadow is perceived when the duller light is 2 of the brightness of the other, and both are near together, especially when the shadow is moved about. Our requirements as regards illumination are constantly on the increase ; thus for public receptions of a state character in recent times in Paris, a number of lamps was used corresponding to over 13 candles per square yard, which is 6 times as much as was used on the occasion of the marriage of the Dauphin in 1745; the former, however, is still far removed from perfect illumination, that of daylight, which is estimated at about 180 candles per square yard. 518 On Light [523— CHAPTER! REFLECTION OF LIGHT. MIRRORS 523. Laws of the reflection of light.—When a ray of light meets a polished surface, it is reflected according to the two following laws, which, as we have seen, also hold for heat. I. The angle of reflection ts equal to the angle of incidence. Il. Zhe incident and the reflected ray are both in the same plane, which zs perpendicular to the reflecting surface. The words are here used in the same sense as in article 424, and need no further explanation. first proofi—The two laws may be demonstrated by the apparatus represented in fig. 477. It consists of a graduated circle in a vertical plane. Two brass slides move round the cir- cumference ; on one of them there is a piece of ground glass, P, and on the other an opaque screen, N, in the centre of which is a small aperture. Fixed to the latter slide there is also a mirror, M, which can be more or less inclined, but always remains in a plane perpendicular to the plane of the gra- duated circle. Lastly, there is a small polished metallic mirror, 7, placed horizontally in the centre of the circle. In making the experiment, a pencil of solar or any suitable artificial light, S, is caused to fall on the mirror M, which is so inclined that the reflected light passes through the aperture in N, and falls on the centre of the mirror, =| SSS Se m. The luminous pencil then experi- Fig. 477 ences a second reflection in a direction mP, which is ascertained by moving P until an image of the aperture is found in its centre. The number of degrees comprised in the arc AN is then read off, and likewise that in AP ; these being equal, it follows that the angle of reflection AzzP is equal to the angle of incidence AmM. The second law follows from the arrangement of the apparatus, the plane of the rays Mzz and mP being parallel to the plane of the graduated circle, and consequently perpendicular to the mirror z. Second proof.—The law of the reflection of light may also be demon- —525| Reflection of Light from Plane Surfaces 519 strated by the following experiment, which is susceptible of greater accuracy than that just described :— In the centre of a graduated circle, M (fig. 478), placed in a vertical position, there is a small telescope movable in a plane parallel to the limb ; ata suitable distance there is a vessel D full of mercury, which forms a perfectly horizontal plane mirror. Some particular star of the first or second magnitude is viewed through the telescope in the direc- tion AE, and the telescope is then inclined so as to receive the ray AD coming from the star after being reflected from the brilliant surface of the mercury. Fig. 478 In this way the two angles formed by the rays EA and DA, with the hori- zontal AH, are found to be equal, from which it may easily be shown that the angle of incidence E’DE is equal to the angle of reflection EDA. For if DE is the normal to the surface of the mercury, it is perpendicular to AH, and AED, ADE are the complements of the equal angles EAH, DAH ; therefore AED, ADE are equal ; but the two rays AE and DE’ may be considered parallel, in consequence of the great distance of the star, and therefore the angles EDE’ and DEA are equal, for they are alternate angles and consequently the angle E’DE is equal to the angle EDA. REFLECTION OF LIGHT FROM PLANE SURFACES 524. Mirrors. Images.—J/rrors are bodies with polished surfaces which show by reflection objects presented to them. According to their shape, mirrors are divided into plane, concave, convex, spherical, parabolic, conical, &c. Rays of light diverging from any point of the object and falling upon a mirror, are caused by reflection either to converge to, or to appear to diverge from, a second point. In either case the second point is called an image of the first point. 525. Formation of images by plane mirrors.—The determination of the position and size of images resolves itself into investigating the images of a series of points. And first, the case of a single point, A, placed in front of a plane mirror, MN (fig. 479) will be considered. ey, ray, AB, incident from this point on the mirror is reflected in the direction BO, making the angle of reflection DBO equal to the angle of incidence DBA. 520 On Light [525— If now a perpendicular, AN, be let fall from the point A on the mirror, and if the ray OB be prolonged below the mirror until it meets this perpen- dicular in the point a, two triangles are formed, ABN and BNa, which are equal, for they have the side BN common to both, and the angles ANB, ABN, equal to the angles aNB, aBN ; for the angles ANB and @NB are right angles, and the angles ABN and @BN are each equal to the angle OBM. From the equality of these triangles, it follows that aN is equal to AN ; that is, that any ray, AB, takes such a direction after being reflected, that its prolongation below the mirror cuts the perpendicular Aa in the point a, which is at the same distance fromthe mirror as the point A. This applies also to the case of any other ray from the point A ; AC, for example. Fig. 479 Fig. 480 From this the important consequence follows, that all rays from the point A, reflected from the mirror, follow, after reflection, the same dtrection as if they had all proceeded from the point a. The eye is deceived, and sees a reproduction of the point A at a, as if it were really situated at a. Hence in plane mirrors ¢he tmage of any point ts formed behind the mirror at a distance equal to that of the given point, and on the perpendicular let fall from this point on the mtrror. It is manifest that the image of any object will be obtained by construct- ing, according to this rule, the image of each of its points, or, at least, of those which are sufficient to determine its form. Fig. 480 shows how the image @é of any object, AB, is formed. It follows from this construction that in plane mirrors ¢he zmage zs of the same size as the object ; for if the trapezium ABCD be applied to the trape- zium DCaé, they are seen to coincide, and the object AB agrees with its image. A further consequence is, that in plane mirrors the image is sym- metrical in reference to the object, and not inverted. 526. Virtual and real images.—There are two cases relative to the direction of rays reflected by mirrors according as the rays after reflection are convergent or divergent. In the latter case the reflected rays do not meet, but if they are supposed to be produced on the other side of the mirror, their prolongations meet in the same point, as shown in figs. 479 and 48o. The eye is then affected just as if the rays proceeded from this point, and it sees an image. But the image has no rea! existence, the luminous rays do not come from the other side of the mirror: this appearance is called the virtual tmage. The images of real objects produced by plane mirrors are of this kind. 528] Multiple Images from two Plane Mirrors 521 In the second case, where the reflected rays converge, as we shall soon see in concave mirrors, the rays meet at a point in front of the mirror and on the same side as the object. They form there an image called the real image, for it can be received on a screen. The distinction may be ex- pressed by saying that veal zmages are those formed by the reflected rays themselves, and virtual tmages those formed by their prolongations. 527. Multiple images formed by glass mirrors.—Metal mirrors which have but one reflecting surface give only one image; glass mirrors give rise to several images, which are readily observed | when the image of a candle is looked at obliquely in a looking-glass. A very feeble image is first seen, and then a very distinct one; behind this there are several others, whose intensities gra- dually decrease until they disappear. This phenomenon arises from the looking-glass having two reflecting surfaces. When the-rays from the point A meet the surface, fig. 481, a partis reflected and forms an image, a, of the point A, on the prolongation of the ray dE, reflected by this surface ; the other part passes into the glass (548), and is reflected at c from the layer of metal which covers the hinder surface of the glass, and reaching the eye in the direction dH, gives the image a’. This image is distant from the first by double the thickness of the glass. It is brighter, because metal reflects better than glass. In regard to other images it will be remarked that whenever light is trans- mitted from one medium to another—for instance, from glass to air—(548), only some of the rays get through ; the remainder are reflected at the surface which bounds the two media. Consequently when the pencil cd, reflected from ¢c, attempts to leave the glass at @, most of the rays composing it pass into the air, but some are reflected at d@, and continue within the glass. These are again reflected by the metallic surface, and form a third image of A; after this reflection they come to MN, when many emerge and render the third image visible ; but some are again reflected within the glass, and in a similar manner give rise to a fourth, fifth, &c., image, thereby complet- ‘ing the’ series above described. It is manifest from the above explanation that each image must be much feebler than the one preceding it, and con- sequently only a small number are visible—ordinarily not more than eight or ten in all. This multiplicity of images is objectionable in observations, and, accord- ingly, metal mirrors are to be preferred in optical instruments. 528. Multiple images from two plane mirrors.—When an object is placed between two plane mirrors, which form an angle with each other, either right or acute, images of the object are formed, the number of which increases with the inclination of the mirrors. If they are at right angles to each other, three images are seen, arranged as represented in fig. 482. The rays OC and OD from the point O, after a single reflection, give the one an image O’, and the other an image O”, while the ray OA, which has under- gone two reflections at A and B, gives the third image O’’”. When the angle of the mirrors is 60°, five images are produced, and seven if it is 45°. Fig. 481 522 On Light [528— The number of images continues to increase in proportion as the angle diminishes, and when it is zero—that is, when the murrors are parallel—the number of images is theoretically infinite. In general, if two mirrors are inclined to each other at an angle which is an exact submultiple of 180° (e.g. 30°, 45°, 60°, 90°), the number of images they produce —counting for this purpose the object as one image—is equal to the number of times the angle between them is contained in 360. The alezdoscofe, invented by Sir D. Brewster, depends on this property of inclined mirrors. It consists of a tube, in which are three mirrors inclined at 60° ; one end of the tube is closed by a piece of ground glass, and the other by a cap pro- Rig. 484 vided with an aperture. Small irregular pieces of coloured glass are placed at one end between the ground glass and another glass disc, and when looked at through the aperture, the other end being held towards the light, the objects and their images are 'seen arranged in beautiful symmetrical forms ; by turning the tube, an almost endless variety of these shapes is obtained. 529. Multiple images in two plane parallel mirrors.—In this case the number of images of an object placed between them is theoretically infinite. Physically the number is limited, for as the incident light is never totally reflected, some of it being always absorbed, the images gradually become fainter, and are ultimately quite extinguished. Fig. 483 shows how the pencil La reflected once from M gives at I the: image of the object L at a distance mI =mL; then the pencil L@ reflected once from the mirror M, and once from N, furnishes the image I’ at a distance zI’=~lI ; in like manner the pencil Le, after two reflec- tions on M, and one on N, forms the image I” at a distance #1” =mlI’, and so on for an in- Fig. 483 finite series. The images’ z, 2’, 2’’, are forned in the same manner iby rays of light waich,,. emitted by the object L, fall first on the mirror N. 530. Irregular reflection. Diffused light.—The reflection from the surfaces of polished bodies, the laws of which have been just stated, is called the regular or specular reflection ; but the quantity thus reflected 1s less. -532] Intensity of Reflected Light 523 than that of the incident light. The light incident on an opaque body separates, in fact, into three parts: one is reflected vegularly ; another trregularly—that is, in all directions; while a third is extinguished, or absorbed by the reflecting body. If light falls on a transparent body, a considerable portion is transmitted with regularity. The irregularly reflected light is called scattered light: it is that which makes bodies visible (514). The light which is reflected regularly does not give us the image of the reflecting surface, but that of the body from which the light proceeds. If, for example, a beam of sunlight be incident on a well-polished mirror in a dark room, the more perfectly the light is reflected the less visible is the mirror in the different parts of the room. The eye does not perceive the image of the mirror, but that of the sun. If the reflect- ing power of the mirror be diminished by sprinkling on it a light powder, the sun’s image becomes feebler, and the mirror is visible from all parts of the room. Perfectly smooth, polished reflecting surfaces, if such there were, would be invisible. The beam of light itself is only seen in the room owing to irregular reflections from the particles of dust, and the like, which are floating in the air. Tyndall showed that when this floating matter in the air in an enclosed space is completely removed, the beam of sunlight or the electric light is quite invisible. The atmosphere diffuses the light which falls on it from the sun in all directions, so that it is light in places which do not receive the direct rays of the sun. Thus, the upper layers of the air diffuse the light which they receive before sunrise and after sunset, and ac- cordingly give rise to the phenomena of fw2/ight. 531. Intensity of reflected light.—The intensity of the light reflected is always less than that of the incident light, for some of the original vibrations are converted into vibrations of the reflecting surfaces. The intensity increases with the obliquity of the incident ray. For instance, if a sheet of white paper be placed before a candle, and be looked at very obliquely, an image of the flame is seen by reflection, which is not the case if the eye receives less oblique rays. The quantity of the reflected light varies with different bodies, even when the degree of polish and the angle of incidence are the same. Thus with perpendicular incidence, the light reflected from a metal mirror is 2 of the incident light, $ from mercury, 34 from glass, and »4 from water. It also varies with the nature of the medium which the ray is traversing before and after reflection. Polished glass immersed in water loses a great part of its reflecting power. In the case of scattered reflection the actual lustre or brightness of a luminous surface is only a fraction of the light which falls upon it, and depends on the nature of the surface. If we call the incident light 100, we have for the brightness of freshly fallen snow 78, white paper 70, white sandstone 24, porphyry 11, and ordinary earth 8. 532. Reflection of a ray of light in a rotating mirror.—When a hori- zontal ray of light falls on a plane mirror which can rotate about an axis, if the mirror is turned through an angle a, the reflected ray is turned through double the angle. Let 2m (fig. 484) be the first position of the mirror, 77’ its position after it has been turned through the angle a; and let OD be the fixed incident 524 On Light [532 ray. If from the centre of rotation C, with any radius we describe the cir- cumference Ova, and from the point O, where it cuts the incident ray, chords OO’ and OO” are drawn perpendicular respectively to mn and m’n’ ; the pons O’ and O” are the i images of the point O in the two posi- tions of the mirror, and if C is joined to each of the points O, O’ and O” it will be seen that the angles CO’D, CO”D’ are equal to each other, since each is equal to the angle COD. Hence the chords AO’, A’O” are equal, and therefore the, arciAAis.equal.to the are OlO7. ihe rotations of the reflected ray and of the mirror are thus measured by the two arcs O’O” and mm’ respectively. Now, the two angles O’OO” and mCvz’ are equal, for they have their sides perpendicular Pig-i¢°4 each to each; but the angle O’OO”, which is an angle at the circumference, is measured by half the arc O’O”, and the angle #zCm/’ by the whole arc m7’ ; hence O’O” is the double of #7’, which shows that when the mirror has turned through an angle a, the reflected ray has turned through 2a. 533. The sextant.—This instrument is used to measure the angular distance of any two distant objects ; its principle is as follows. Suppose A (fig. 485) is a small mirror half silvered, so that the eye at E, can see through the free part. Bis a second mirror which can turn about an axis at right angles to the plane of the figure. When its plane is parallel to that of A, the ray EB of a distant object, which we will call L, is reflected from RB to A, so that the eye sees simultaneously the image of L reflected from the silvered part of the mirror, and directly the object L, through the unsilvered part in the direction OE,, L being assumed to be so distant that EyvB wand EB vare sparallel elie pais, non parallel to A, but in the position repre- sented by the shading, the ray EB is not reflected to the eye, but the image of some other object F in the direction BF. Fig. 486 represents one form of sextant which derives its name from the fact that only one sixth of the divided circle is used. Fig. 485 It consists of a graduated metal sector AA, on which plays the index arm F; this is provided with a vernier and a micrometer screw by which the index may be accurately adjusted and also clamped ; G is a lens for more accurate reading. The mirror B, which is called the zadex glass, is rigidly fixed to the arm BF and moves with it. The telescope DE is fixed to one arm as shown, and on the other arm opposite is the horizon glass C, also rigidly -534] Measurement of Angles by Reflection from Mirrors 525 fixed, the lower half of which is silvered. The axis of the telescope just traverses the boundary of the silvered and unsilvered part of the mirror. K and L are dark glasses for shading off the sun’s light. In making an ob- servation the sextant is held vertically by the handle, H, so that its plane .passes through both the objects whose angular distance is to be measured. The index arm being at the zero of the graduation, the two mirrors are parallel. One of the objects, the horizon for instance, is viewed through the telescope and the unsilvered part of the mirror C. The index arm is then moved until the eye sees simultaneously Fig. 486 with this the image of another body, the sun or a star for example, which reaches the eye after successive reflections from the mirror B, and from the silvered part of the mirror C. The angle which the two mirrors now form is measured by the graduation of the sector, and is half the angular distance (532) between the horizon and the sun. A great advantage of this instrument is that a slight agitation does not affect the measurement of the angle; it can accordingly be used on ship- board, is indispensable for use at sea, and in travelling where the use of a stand is ob- jectionable. 534. Measurement of small angles by re- flection from a mirror. An important applica- tion of the laws of re- flection in measuring small angles of deflec- tion in magnetic and other observations was Fig. 487 first made by Gauss. The principle of this method will be understood from fig. 487, in which AO: represents a telescope, underneath which, and at right angles to its axis, 526 On Light [534- is fixed a graduated scale ss; the centre of which, the zero, corresponds to the axis of the telescope. Let NS be the object whose angular deflection is to be measured, a magnet for instance, and let sm represent a small plane mirror fixed at right angles to the axis of the magnet. If now, at the beginning of the observation, the telescope is adjusted so that the image of the zero appears behind the cross wires, its axis is perpendicular to the mirror. Now when the mirror is turned, by whatever cause, through an angle a, the eye will see, through the telescope, the image of another division of the scale, a for instance, the ray proceeding from which makes with the line cOA the angle 2a. From the distance of this division Oa from the zero of the scale and the Oa distance Oc from the mirror we have tan 2a = (on Thus, for instance, if Oa C is 12 millimetres and Oc 5,000 millimetres, then tan 2a= —, from which : } 2a=8’ 15’. Asa practised eye can easily read +4, of a millimetre, it 1s pos- sible by such an arrangement to read off an angular deflection of two seconds. 535. Mance’s heliograph.—The reflection of light from mirrors has been applied by Sir H. Mance in signalling at great distances by means of the sun’s light. The apparatus consists essentially of a mirror about 4 inches in diameter mounted on a tripod, and provided with suitable adjustments, so that the sun’s light can be received upon it and reflected to a distant station. An observer then can see through a telescope the reflection of the sun’s rays as a spot of light. The mirror has an adjustment by which it can be made to follow the sun in its apparent motion. There is also a lever key by which the signaller can deflect the mirror through a very small angle either to the right or left, and thus the observer at the distant station sees corresponding flashes to the right or left. Under the subject of Telegraphy it will be seen how these alternate motions can be used to form an alphabet. The heliograph proved of essential service in the campaigns in Africa and Afghanistan. Instead of any special form of apparatus, an ordinary shaving mirror or handglass is frequently used ; and the proper inclination having been given so as to send the sun’s rays to the distant station, which is very easily effected, the signals are produced by obscuring the mirror by sliding a piece of paper over it for varying lengths of time. In this way longer or shorter flashes of light are produced, which, properly combined, form the alphabet. Of course this mode of signalling can only be used where the sun’s light is available, but it has the advantage of being cheap, simple, and portable. Signals have been sent at the rate of 12 words a minute, through distances, in very fine weather, of 4o miles. -537] Reflection from a Spherical Concave Mirror Bor, REFLECTION OF LIGHT FROM CURVED SURFACES 536. Spherical mirrors.—It has been already stated (524) that there are several kinds of curved mirrors ; those most frequently employed are spherical and parabolic mirrors. Spherical mirrors are those whose curvature is that of a sphere ; their surface may be supposed to be formed by the revolution of an arc MN (fig. 488) about the radius CA, which unites the middle of the arc to the centre of the circle of which it is a part. According as the reflection takes place from its internal or from - its external face, the mirror is said to be coz- cave or convex. C, the centre of the hollowsphere of which the mirror forms part, is called the centre of curvature, or geometrical centre: the point A is the centre of the mirror. The infinite right line AL, which passes through A and C, is the principal axis of the mirror; any right line which simply passes through the centre C, and not through the point A, is a secondary axis. The angle MCN, formed by joining the centre and extremities of the mirror, is the aperture. A principal section is the section made by a plane through its principal axis. In speaking of mirrors those lines alone will be considered which lie in the same principal section. The theory of the reflection of light from curved mirrors is easily deduced from the laws of reflection from plane mirrors, by considering the surface of the former as made up of an infinitude of extremely small plane surfaces, which are its e/ements. The normal to the curved surface at a given point is the perpendicular to the corresponding element, or, what is the same thing, to its correspondent tangent plane. It is shown in geometry that in spheres all the normals pass through the centre of curvature, so that the normal may readily be drawn to any point of a spherical mirror. 537. Reflection from a spherical concave mirror.—In a curved mirror the focus of a point isa point in which the reflected rays meet or tend to meet, if produced either backwards or forwards ; there may be either a veal focus or a virtual focus corresponding to an incident pencil. Real focus.—We shall first consider the case in which the rays of light are parallel to the principal axis, which presupposes that the luminous body is at an infinite distance. Let GD (fig. 488) be such a ray. From the hypothesis that curved mirrors are composed of a number of infinitely small plane elements, this ray would be reflected from the element corresponding to the point D, according to the laws of the reflection from plane mirrors (525); that is, that CD being the normal at the point of incidence D, the angle of reflection CDF is equal to the angle of incidence GDC, and is in the same plane. It follows from this, that the point F, where the reflected ray cuts the principal axis, divides the radius of curvature AC very nearly into two equal parts. For in the triangle DFC the angle DCF Fig. 488 528 On Light | [537— is equal to the angle CDG, for they are alternate angles ; likewise the angle CDF is equal to the angle CDG, from the laws of reflection ; therefore the angle FDC is equal to the angle FCD, and the sides FC and FD are equal as being opposite to equal angles. Now the smaller the arc AD, the more nearly does DF equal AF ; and when the arc is only a small number of degrees, the right lines AF and FC may be taken as approximately equal, and the point F may be taken as the middle of AC. So long as the aperture of the mirror does not exceed 8 to 10 degrees, any other ray HB will, after reflection, pass very nearly through the point F. Hence, for practical pur- poses, we may say that when a pencil of rays parallel to the axis falls on a concave mirror the rays intersect after reflection in the same point, which is. at an equal distance from the centre of curvature and from the mirror. This point is called the Arzucipfal focus of the mirror, and the distance AF is the principal focal distance, or the focal length of the mirror. All rays parallel to the axis meet in the point F ; and, conversely, if a luminous point be placed at F, the rays emitted by this point will after reflection take! the direc- ' tions} DG, BH, ‘parallel to the principal axis; for in this case the angles of in- cidence and reflection have changed places ; but these angles always remain equal. The case is now to be considered in which the rays are emitted from a luminous point, L (fig. 489), placed on the principal axis, but at such a distance that they are not parallel, but divergent. The angle LKC, which the incident ray LK forms with the normal KC, is smaller than the angle SKC, which the ray SK, parallel to the axis, forms with the same normal ; and, conse- quently, the angle of reflection corresponding to the ray LK must be smaller than the angle CKF, corresponding to the ray SK. And therefore the ray LK will meet the axis after reflection in the point /, between the centre C and the principal focus F. So long as the aperture of the mirror does not exceed a small number of degrees, all the rays from the point L will inter- sect after reflection in the point 7. This point is called the conjugate focus of the point L; for there is this connection between the points L and /, that if the luminous point were transferred to /, its conjugate focus would be at L, ZK being the incident and KL the reflected ray. On considering the figure 489 it will be seen that when the point L is brought near to or removed from the centre C, its conjugate focus approaches or recedes in a corresponding manner, for the angles of incidence and re- flection increase or decrease together. If the point L coincides with the centre C, the angle of incidence is null, and as the angle of reflection must be the same, the ray is reflected on itself and the focus coincides with the luminous point. When the luminous point is between the centre C and the principal focus, the conjugate focus in turn is on the other side of the centre, and is further from the centre accord- ing as the luminous point is nearer the principal focus. If the luminous point Fig. 489 —538] Reflectton from Convex Mirrors 529 coincides with the principal focus, the reflected rays, being parallel to the axis, will not meet, and there is, consequently, no focus. Virtual focus.—There is, lastly, the case in which the luminous point is at some point, L, between the principal focus and the mirror (fig. 490). Any ray LM, from the point L, makes with the normal CM an angle of in- cidence LMC, greater than FMC; the angle of reflection must be greater than CMS, and therefore the reflected ray ME diverges from the axis AK. Fig. 490 Fig. 491 This is also the case with all rays from the point L, and hence these rays do not intersect, and, consequently, form no conjugate focus; but if they are conceived to be prolonged on the other side of the mirror, their prolongations will intersect in the same point, /, on the axis, and an eye looking in the direction KA experiences the same impression as if the rays were directly emitted from the point 7. Hence a wzrtwal focus is formed quite analogous to those formed by plane mirrors (525). Hitherto the luminous point has always been supposed to be placed on the principal axis itself, and then its focus is formed on this axis. In the case in which the luminous point is situate on a secondary axis, LB (fig. 491), by applying to this axis the same reasoning as in the preceding case, it will be seen that the focus of the point L is formed at a point 7 on the secondary axis, and that, according to the distance of the point L, the focus may be either principal, conjugate, or virtual. 538. Reflection from convex mirrors.—In convex mirrors there are only virtual foci. Let SI, TK .. . (fig. 492) be rays parallel to the principal axis Of Fae T Cornvex mirror.’ “Thesé rays, after reflec- tion, take the diverging direc- tions IM, KH, which, . when continued, meet in Waliipomt ob; which is the principal vir- Fig. 492 tual focus of the mirror. By means of the triangle CKF, it may be shown, in the same manner as with concave mirrors, that the point F is approximately the centre of the radius of curvature, CA. If the incident luminous rays, instead of being parallel to the axis, M M 530 On Light [538- proceed from a point L, situated on the axis at a finite distance, it is at once seen that a virtual focus will be formed at a point /, between the principal focus F and the mirror. 539. Determination of the principal focus of a mirror.—In the appli- cations of concave and convex mirrors it is often necessary to know the radius of curvature. This is tantamount to finding the principal focus ; for being situated at the middle of the radius, it is simply necessary to double the focal distance. Be To find this focus with a concave mirror, it is exposed to the sun’s rays, so that its principal axis is parallel to them, and then with a small screen of ground glass the point is sought at which the image is formed with the greatest dis- tinctness ; this is the princi- pal focus. The radius of the mirror is double this distance. If the mirror is convex, it is covered with paper ; but two small portions, H Fig. 493 and I, are left exposed at equal distances from the centre of the figure A, and on the same principal section (fig. 493). A screen MN, in the centre of which is an opening larger than the distance HI, is placed before the mirror. If a pencil of the sun’s rays, SH, S’I, parallel to the axis, falls on the mirror, the light is reflected at H and I, on the parts where the mirror is left exposed, and forms on the screen two bright images at # and z. By moving the screen MN nearer to or farther from the mirror, a position is found at which the distance Az is double that of HI. The distance AD from the screen to the mirror then equals the principal focal distance. For the arc HAI does not sensibly differ from its chord ; and because the triangles FHI and F/AZz are similar, a = a but HI is half of Zz, and therefore also FA is the half of FD, and therefore AD is equal to AF. Further, FA is the principal focal distance ; for the rays SH and S’I are parallel to the axis : consequently also twice the distance AD equals the radius of curvature of the mirror. 540. Formation of images in concave mirrors.—It has hitherto been supposed that the luminous or illuminated object placed in front of the mirror was sim- ply a point ; but if this object has a certain magni- tude we can con- ceive a second- ary axis drawn through each of its points, and thus a series of real or virtual foci could be determined, the collection of which composes the image of the object. By the aid of the constructions which have Fig. 494 —340] Formation of Images in Concave Mirrors 531 served for determining the foci, we shall investigate the position and magnitude of these images in concave and in convex mirrors. Real tmage.—We shall first take the case in which the mirror is concave, and the object AB (fig. 494) is on the other side of the centre. To obtain the image or the focus of any point A, a secondary axis, AE, is drawn from this point, and then drawing from the point A an incident ray AD, the normal to this point, CD, is taken, and the angle of reflection CDa is made ‘equal to the angle of incidence ADC. The point a, where the reflected ray cuts the secondary axis AE, is the conjugate focus of the point A, because every other ray drawn from this point passes through a. Similarly if a ‘secondary axis, BI, be drawn from the point B, the rays from this point meet after reflection in 6, and form the conjugate focus of B. .And as the images of all the points of the object are formed between a and 4, ad is the complete image of AB. From what has been said about foci (537), it follows that ths zmage zs real, inverted, smaller than the object, and placed between the centre of curvature and the principal focus. This image may be seen in two ways: by placing the eye in the continuation of the reflected rays, and then it is an aérial image which is seen ; or the rays -are collected on a screen, on which the image appears to be depicted. If the luminous or illuminated object is placed at ad, between the prin- ‘cipal focus and the centre, its image is formed at AB. It is then a real but inverted image; it is larger than the object, avd the larger as the object, ab, is nearer the focus. If the object is placed in the principal focus itself, no image is produced ; for then the rays emitted from each point form, after reflection, as many pencils respectively parallel to the secondary axis, which is drawn through the point from which they are emitted (536), and hence neither foci nor images are formed. When all points of the object AB are above the principal axis, it is readily seen, by repeating the preced- ing construction (fig. 495), that the image of.the object is formed at ad. Virtual tmage.—The case remains in which the object is placed between the principal focus and the mirror. Let AB be this object (fig. 496); the incident rays from A _ after ; reflection take the directions DI Fig. 496 and KH, and their prolonga- tions form a virtual image, a, of the point A, on the secondary axis. Similarly, an image of B is formed at 4; consequently an eye looking MM 2 Fig. 495 532 On Light [540— along the principal axis sees at ad the image of AB. TZhzs image ts virtual, erect, and larger than the object. From what has been stated, it is seen that, according to the distance of the object, concave mirrors produce two kinds of images, or none at all ; a person notices this by placing himself in front of a concave mirror. At a certain distance he sees an image of himself inverted and smaller-—this. is the real image; at a less distance the image becomes confused, and disappears when he is at the focus; still nearer the image appears erect, but larger—it is then a virtual image. 541. Formation of images in convex mirrors.—Let AB (fig. 497) be an object placed in front of a mirror at any given distance. AC and BC are } secondary axes, and it follows, from what has been already stated, that all the rays from A are divergent after reflection, and that their prolongations pass through a point a, which is the. virtual image of the point A. Similarly the rays from B form Fig. 497 a virtual image of it in the point 6. The eye which receives the divergent rays, DE, KH . . - sees in ad animage of AB. Hence, whatever the position of an object in front of a convex mirror, the zmage ts always virtual, erect, and smaller than the object. 542. Formule for spherical mirrors.—The relation between the position of an object and that of its image in spherical mirrors may be expressed by a very simple formula. In the case of concave mirrors, let R be its radius of curvature, # the distance LA of the object L (fig. 498), and #’ the distance 7A of the image from the mirror. In the triangle LM/, the perpendicular MC divides the angle LMZ into two equal parts, and from geometry it follows that the two segments LC, CZ are to each other as the two sides containing the angle ; that is, Clear AM CTEM: therefore C/ x LM =CLx/M. If the arc AM does not exceed 5 or 6 degrees, the lines ML and MZ are. approximately equal to AL and AZ;, that is, to # and f’. Further, C/= CA—A/=R'—97, and also CL=AL—AC=/-R. These values substituted in the preceding equation give ie. (R-p)p=(P-RY2’. From which, transposing and reducing, we have Rp + Rp’ = 299". : : (ft) If the terms of this equation be all divided by f/’R, we suetie a Mog See) — += _ : ‘ ; é (2), i eras which is the usual form of the equation. —543 | Discussion of the Formule for Mirrors eae From the equation (1) we get R = J R? ¢ : : : (3) or, jee on: i = R’ ; : E (4) p which gives the distance of the image from the mirror, in terms of the distance of the object, and of the radius of curvature. 543. Discussion of the formule for mirrors.—We shall now investigate the different values of #’, according to the values of # in the formula (2) or (3). 1. Let the object be placed at an infinite distance on the axis, in which case the incident rays are parallel. Since # is infinite - is zero, and formula (2) at once gives f’= is ; that is, the image is formed in the principal focus, iy = as ought to be the case, for the incident rays are parallel to the axis. u. If the object approaches the mirror, # decreases, and as the denomi- nator of the formula (4) diminishes, the value of Z’ increases ; consequently the image approaches the centre at the same time as the object, but it is always between the principal focus and the centre, for so long as pis > R, we have Soe and < R. ae? i. When the object coincides with the centre, /=R, and, consequently, 2 =k; that is, the image coincides with the object. iv. When the luminous object is between the centre and the principal focus, #< R, and hence from the formula (4), #’>R; that is, the image is formed on the other side of the centre. When the object is in the focus, p= x which gives #’ = a oo; that is, the image is at an infinite distance, for the reflected rays are parallel to the axis. v. Lastly, if the object is between the principal focus and the mirror, we get p< = ; p’ is then negative, because the denominator of the formula (4) 2 is negative. Therefore, the distance /’ of the mirror from the image must be calculated on the axis in a direction opposite to # The image is then virtual, and is on the other side of the mirror. If f’ be negative, the formula (2) becomes 7-7 =F ; in this form it comprehends all cases of virtual images in concave mirrors. In the case of convex mirrors the image is always virtual (538) ; f’ and R are of the same sign, since the image and the centre are on the same side of the mirror, while the object being on the opposite side, # is of the contrary sign ; hence in the formula (2) we get I I 2 pb ra : 5 : ; (5) 534 On Light [543- as the formula for convex mirrors. It may also be found directly by the same geometrical considerations as those which have led to the formula (2) for concave mirrors. The preceding formule are not rigorously true, inasmuch as they depend upon the assumption that the lines LM and /M (fig. 498) are equal to LA and A/: although this is not true, the error diminishes without limit with the angle MCA ; and when this angle does not exceed a few degrees, the error is so small that it may, in practice, be neglected. 544. Calculation of the magnitude of images.—By means of the above formule the magnitude of an image may be calculated when the distance of the object, its magnitude, and the radius of the mirror are given: - For .if -BD be the object (fig. 499), dd its image, and if the distance AK and the radius AC be known, Ao can be calculated Fig. 499 by means of formula (3) of . article 542. Ao known, oC can be calculated. But as the triangles'BCD and dCé are similar, dd: BD! =Co: CK, or if O and I represent respectively the linear dimensions of object and image, = ae a = from formula (1) or (2). Thus, size of the image (linear) _ distance of the image from the centre of curvature size of the object distance of the object from the centre of curvature Or distance of the image from the mirror distance of the object from the mirror {| The brightness of an image formed by a concave mirror is nearly pro- portional to its surface, and to the coefficient of reflection ; and is inversely as the square of the focal distance. 545. Spherical aberration. Caustics.—In the foregoing explanation of the formation of foci and images of spherical mirrors, it has been ob- served that the reflected rays only coincide in a single point when the aper- ture of the mirror does not exceed 8 or Io degrees (537). With a larger aperture the rays reflected near the edges meet the axis nearer the mirror than those that are reflected at a small distance from the centre of the mirror. Hence arises a want of sharpness in these images, which is called spherical aberration by reflection, to distinguish it from the spherical aberration by refraction, which occurs in the case of lenses. Every’ reflected ray cuts the Fig. 500 one next to it (fig. 500), and their points of intersection form in space a curved surface which is called the caustic by reflection. The curve FM represents one of the branches of a section of this surface made by the 547] Parabolic Mirrors 535 plane of the paper. When the light of a candle is reflected from the inside of a tea cup or a glass tumbler, a section of the caustic surface can be seen by partly filling the cup or tumbler with milk. - 546. Applications of mirrors. Heliostat.—The applications of plane mirrors in domestic economy are well known. Mirrors are also frequently used in physical apparatus for sending light in a certain direction. We have already seen an application of this in the heliograph (535). The light of the sun can only be sent in a constant direction by making the mirror movable. It must have a motion which compensates for the continual change in the direction of the sun’s rays produced by the apparent diurnal motion of the sun. This result is obtained by means of a clockwork motion, to which the mirror is fixed, and which causes it to follow the course of the sun. Such an apparatus is called a helzostat. The reflection of light is also used to measure the angles of crystals by means of the instruments known as reflecting gontometers. Concave spherical mirrors are also often used, They are applied for magnifying szrrors, as in the older forms of shaving mirrors. They have been employed for burning mirrors, and are still used in telescopes. They also serve as reflectors, for conveying light to great distances, by placing a luminous object in their principal focus. The search light used by steamers in passing through the Suez Canal by night and by war ships, consists of a powerful electric light placed at the principal focus of a concave spherical reflector. Parabolic reflectors, though theoretically preferable, are not used for this purpose on account of the difficulty of working the parabolic surface. The iniages of objects seen in concave or convex mirrors appear smaller or larger, but otherwise similar geometrically, except in the case where some parts of a body are nearer the mirror than others. The distor- tion of features observed on looking into a spherical garden mirror is more marked the nearer we are to the glass. Objects seen in cylindrical or conical mirrors appear ludicrously distorted. From the laws of reflection the shape of such a distorted figure can be geometrically constructed. In like manner distorted pictures of objects can be constructed which, seen in such mirrors, appear in their normal proportions. They are called axamor- phoses. 547. Parabolic mirrors.—/Para- bolic mirrors are concave mirrors whose surface is generated by the revolution of the arc of a parabola, AM, about its axis AX (fig. 501). It has been already stated that in spherical mirrors the rays parallel to the axis converge only approxi- mately to the principal focus; and reciprocally, when a source of light is placed in the principal focus of these mirrors, the reflected rays are not exactly parallel to the axis. Parabolic mirrors are free from this defect; they are more difficult to construct, but are better for reflectors. It is a property of a parabola Fig. sor 536 On Light [547- that the right line FM, drawn from the focus F to any point M of the curve and the line ML, parallel to the axis AF, make equal angles with the tan- Fig. intersections of reflectors directions at passages. gent TT’ at this point. Hence all rays parallel to the axis after reflection meet in the focus of the mirror F ; and conversely, whena source of light is placed in the focus, the rays incident on the mirror are reflected exactly parallel to the axis. The light thus reflected tends to maintain its intensity even at a great distance, for it has been seen (520) that it is the divergence of the luminous rays which principally weakens the intensity of light. From this property parabolic mirrors are used in carriage lamps, and in the lamps placed in front of and behind railway trains. These re- flectors were formerly used for lighthouses, but have been replaced by lenticular glasses. When two equal parabolic mirrors are cut by a plane perpendicular to the axis passing ape through the focus, and are then united at their as shown in fig. 502, so that their foci coincide, a system is obtained with which a single lamp illuminates in two once. This arrangement is used in lighting staircases and -548] Phenomenon of Refraction $37, Orn rea Reh SINGLE REFRACTION. LENSES 548. Phenomenon of refraction.—Ae/racizon is the deflection or bending which the rays of light experience in passing od/zguely from one medium to another: for instance, from air into water (fig. 504). If the incident ray is perpendicular§ to the surface separating the two media, it .is not bent, but continues its course in a right line (fig. 503). The zncident ray being represented by »O: (fig. 505), the ve- tracted ray is the di- rection OH which light takes in the second medium ; and of the angles SOA and HOB, which these rays form with the normal AB, to the surface which separates the two media, the first is the angle of incidence, and Fig. 503 Fig. £05 Fig. 504 the other the angle of refraction. According as the refracted ray approaches or deviates from the normal, the second medium is said to be more or less refringent or refracting than the first. All the light which falls on the surface of a refracting substance does not completely pass into it ; one part is reflected and scattered (530), while another penetrates into the medium. Mathematical analysis shows that the direction of refraction depends on the relative velocity of light in the two media. On the undulatory theory the more highly refracting medium is that in which the velocity of propaga- tion is less. In uncrystallised media, such as air, liquids, ordinary glass, the luminous ray is singly refracted ; but in certain crystallised bodies, such as Iceland spar, selenite, &c., the incident ray gives rise to two refracted rays. The latter phenomenon is called double refraction, and will be discussed in another part of the book. We shall here deal exclusively with s¢mgle refraction. 549. Laws of single refraction.—When a luminous ray is refracted in passing from one medium into another of a different refractive power, the following laws prevail :— I. Whatever the obliquity of the incident ray, the ratio which the sine of the incident angle bears to the sine of the angle of refraction ts constant for the same two media, and the same coloured light, but varies with different meata. Il. The incident and the refracted rays are in the same plane, which ts perpendicular to the surface separating the two media. These have been known as Descartes’s laws ; they are, however, really due to Willibrod Snell, who discovered them in 1620 ; they are demon- strated by the same apparatus as that S/ used for the laws of reflection (522). ao The plane mirror in the centre of the graduated circle is replaced by a semi- cylindrical glass vessel, filled with water to such a height that its level is exactly the height of the centre (fig. 506). If the mirror, M, be then so inclined that a reflected ray, MO, is directed towards the centre, it is refracted on passing into the water, but it passes out without refraction, because its direction is then at right angles to the curved sides of the vessely3In ‘order to observe “the course of the refracted ray, itis received on a screen, P, which is moved until the image of the aperture in the screen N is formed at its centre. In all positions of the screens N and P, the sines of the angles of incidence and refraction are measured by means of two graduated rules, movable so as to be always horizontal, and hence perpendicular to the diameter AD. On reading off the lengths which are proportional to the sines of the angles MOA and DOP in the scales I and R, the numbers are found to vary with the position of the screens, but their ratio is constant; that is, if the sine of incidence becomes twice or three times as large, the sine of refraction increases in the same ratio, which demonstrates the first law. The second law follows from the arrangement of the apparatus, for the plane of the / Tipit SS a ATTY s cai ny Fig. 506 -551] Effects produced by Refraction 539 graduated limb is perpendicular to the surface of the liquid in the semi- cylindrical vessel. 550. Index of refraction.—The ratio between the sines of the incident and refracted angle is called zadex of refraction, or refractive index of the second medium with respect to the first. Thus if z be the refractive index, and z and rv the angles of incidence and refraction, sin¢=zsinz. The refrac- tive index varies with the media ; for example, from air to water it is 4, and from air to glass it is 3. If the media are considered in an inverse order—that is, if light passes from water to air, or from glass to air—it follows the same course, but ina contrary direction, PO becoming the incident and OM the refracted ray. Consequently the index of refraction is reversed ; from water to air it is then %, and from glass to air 3. 551. Effects produced by refraction.—In consequence of refraction, bodies immersed in a medium more highly refracting than air appear nearer the surface of this medium, but they appear to be more distant if immersed in a less refracting medium. Let L (fig. 507) be an object immersed in a mass of water. In passing thence into air, the rays LA, LB... diverge from the normal to the point of incidence, and take the direction AC, BD... , the prolongations of which in- tersect approximately in the point L’, placed on the perpendicular L’K. Supposing the points A,B... are not far removed from the normal KL, an eye looking vertically downwards and receiving these rays sees the image of Lat L’. Ifthe eye looks obliquely at the object, the image rises to the greater obliquity of the rays LA, LB. ... the higher the object appears. For the same reason a stick placed obliquely in water appears bent, the im- mersed part appearing raised. An experimental illustration of the effect of refraction is the following :— A coin is placed in an empty porcelain basin, and the position of the eye is so adjusted that the coin is just not visible. If now, the position of the eye remaining unaltered, water be poured into the basin, the coin becomes visible. A consideration of fig. 508 will suggest the explanation of this phenomenon. Owing to an effect of refraction, stars are visible to us even when they are below the horizon. For as the layers of the atmo- sphere are denser in proportion as they are nearer the earth, and as the refractive power of a gas increases with its density (562), it follows that on entering the atmosphere the luminous rays become bent, as seen in fig. 505, describing a curve before reaching the Fig. 508 eye, so that we can see the star at S’ along the tangent of this curve instead of at S. In our climate the atmospheric refraction does not raise the stars when on the horizon more than half a degree. The effect of refraction is that objects at a distance appear higher than Fig. 507 540 On Light [551- they are in reality ; our horizon is thereby widened. When individual layers of air refract more strongly than usual, objects may thereby become visible which are usually below the horizon. Thus, from Hastings, the coast of France, which is at a distance of 56 miles, is not unfrequently seen. 552. Total reflection. Critical angle.—When a ray of light passes from one medium into another which is less refracting, as from water into air, it has been seen that the angle of incidence is less than the angle of refraction. Hence, when light is propagated in a mass of water from S to O (fig. 509), there is always a value of the angie of incidence SOB, such that the angle of refraction AOR is a right angle, in which case the refracted ray emerges parallel to the surface of the water. This angle, SOB, 1s called the. watceras angle, since for alla St eater angle, POB, the incident ray cannot emerge, but undergoes an internal reflection, which is called fotal reflection because the incident light is entirely reflected. From the formula sin z= sin y we Fig. 510 see that if 2=90° sin z=1, and if — is the corresponding value of ~ z.e. the p critical angle, sin ”=1. From water to air the critical angie 1S. a0 35 an ne from glass to air, 41° 48’. The occurrence of this internal reflection may be observed by the follow- ing experiment :—An object, A, is placed before a glass vessel filled with water (fig. 510) ; the surface of the liquid is then looked at as shown in the figure, and an image of the object A is seen at a, formed by the rays reflected at mz, in the ordinary manner of a mirror. In total reflection there is no loss of light from absorption or transmission, and accordingly it produces the greatest brilliancy. If an empty test-tube be placed in a slanting position in water, its surface, when looked at from above, shines as brilliantly as pure mercury ; those rays which fall obliquely on the side at an angle greater than the external angle cannot pass into the water, and are, therefore, totally reflected upwards. Ifa little water be passed into the tube, that portion of it loses its lustre. Bubbles, again, in water glisten like pearls, and cracks in transparent bodies like strips of silver, for the oblique rays are totally reflected. The lustre of transparent bodies bounded by plane surfaces, such as the lustre of chandeliers, arises mainly from total reflection. This lustre is the more frequent and the more brilliant the smaller the limiting angle ; the lustre of diamond, therefore, is the most brilliant. 553. Mirage.—The wzzrage is an optical illusion by which inverted images of distant objects are seen asif below the ground orin the atmosphere. This - 553] Mirage 541 phenomenon is of most frequent occurrence in hot climates, and more espe- cially on the sandy plains of Egypt. The ground there has often the aspect of a tranquil lake, on which are reflected trees and the surrounding villages. Monge, who accompanied Napoleon’s expedition to Egypt, was the first to give an explanation of the phenomenon. It is a phenomenon of refraction, which results from the unequal density of the different layers of the air when they are expanded by contact with the heated soil. The least dense layers are then the lowest, and the pencil of light from an elevated object, A (fig. 511), traverses layers which are gradually less refracting ; for, as will be shown presently (562), the refracting power of a gas diminishes with lessened den- sity. The an-. gle of incidence accordingly in- creases from one layer to the other, and ulti- mately reaches the critical an- gle, beyond which internai reflection succeeds to refraction (552). The pencil then rises, as seen in the figure, and undergoes a series of successive refractions, but in the direction contrary to the first, for it now passes through layers which are gradually more refracting. The pencil then reaches the eye with the same direction as if it had proceeded from a point below the ground, and hence it gives an inverted image of the object, just as if it had been reflected at the point O, from the surface of a tranquil lake. The effect of the mirage may be illustrated artificially, though feebly, as Wollaston showed, by looking along the side of a red-hot poker at a word Of? object ter or twelve feet distant. At a distance less Pe than three-eighths . . = oe of an inch from the line of the poker, an inverted image was seen, and within and without that an erect image. A better arrangement than a red-hot poker is a flat sheet-iron box, about 3. feet in length by 5 to 7 inches in height and breadth (fig. 512) ; it is filled with red-hot charcoal and held at a about the level of the eye. Looking over the lid of the box in the direction pm a direct, and in the direction pm’ an inverted image of a distant point, m,is seen. The same phenomenon is observed by looking along the sides. Mariners sometimes see inverted images in the air of ships and distant Fig. 511 542 On Light [553- objects which are still below the horizon ; this is due to the same cause as the mirage, but is in a contrary direction. The lower layers of the air being in contact with the water are cold and dense. The rays of an object, a ship for instance, bent in an upward direction are more and more bent away from the vertical as they are continually passing into gradually less dense layers, and ultimately fall so obliquely on an upper attenuated layer that they are totally reflected downwards, and can thus reach the eye of an observer on the sea or on the shore. Scoresby observed several such cases inthe Polar seas. The twinkling or scintillation of the fixed stars is also to be accounted for by alterations in the direction of their light due to refraction. TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA 554. Media with parallel faces.—Any transparent medium bounded by two parallel plane surfaces is called a A/ate. When light traverses a plate of any substance, the emergent rays are parallel to the incident rays. Let MN (fig. 513) bea glass plate, SA the incident and DB the emergent ray, z and ~ the angles of incidence and of refraction at the entrance of the ray, and, lastly, z’ and 7 the corresponding angles at its emergence. AtA the light undergoes a first refraction, and main? ($49).. At DD ats etractedss sin ¢ ; : sin 2’ second time, and the index is then ~——.. sin 7 But we have seen that the index of re- fraction of glass with respect to air is the reciprocal of the index of air with respect to glass ; hence sin z’_ sin¢ Fig. 513 siny sinz But as the two normals AG and DE are parallel, the angles 7 and 2’ are equal, as being alternate interior angles. As the numerators in the above equation are equal, the denominators must also be equal ; the angles 7’ and z are therefore equal, and hence DB is parallel to SA. 555. Prism.—In optics a frism is any transparent medium comprised between two plane faces inclined to each other. The intersection of these two faces is the edge of the prism, and their inclination is its re- fracting angle. Every section perpendicular to the edge is called a principal section. The prisms used for experiments are Fig. 514 Fig. 515 generally right trian- gular prisms of glass, as shown in fig. 514, and their principal section is a triangle (fig. 515). In this section the point A is called the swmmzt of the —556] Path of Rays in Prism. Angle of Deviation 543 ‘prism, and the right line BC is called the dase: these expressions have reference to the triangle ABC, and not to the prism. 556. Path of rays in prism. Angle of deviation.—When the laws of refraction are known, the path of the rays in a prism is readily determined. Let O be a luminous point (fig. 515) in the same plane as the principal sec- tion ABC of a prism, and let OD be an incident ray. This ray 1s refracted at D, and approaches the normal, because it passes into a more highly refracting medium. At K it experiences a second refraction, but it then deviates from the normal, for it passes into air, which is less refractive than glass. The light is thus refracted twice in the same direction, so that the ray zs deflected towards the base, and consequently the eye which receives the emergent ray KH sees the object O at O’; that is, objects seen through a prism appear deflected towards its summit. The angle OEO’, which the incident and emergent rays form with each other, expresses the deviation of light caused by the prism, and is called ¢he angle of deviation. Besides this, objects seen through a prism appear in all the colours of the rainbow: this phenomenon, known as dsfersion, will be afterwards described (576). The angle of deviation increases with the refractive index of the material of the prism, and also with its refracting angle. It also varies with the angle B ne > s s a ly <7 ay im iss under which the luminous ray enters the prism. The angle of deviation increases up to a certain limit, which is determined by calculation, knowing the angle of incidence of the ray, and the refracting angle of the prism (548). That the angle of deviation increases with the refractive index may be shown by means of the folyfrism. This name is given to a prism formed of several prisms of the same angle connected at their ends (fig. 516). These prisms are made of unequally refracting substances, such as flint glass, rock crystal, or crown glass. If any object—a line, for instance—be looked at 544 On Light [556- through the polyprism, its different parts are seen at unequal heights. The highest portion is that seen through the flint glass, the refractive index of which is greatest ; then the rock crystal ; and so on in the order of the decreasing refractive indices. The prism with variable angle (fig. 517) is used for showing that the angle of deviation increases with the refracting angle of the prism. It con- sists of two parallel brass plates. B and C, fixed on a support. Between these are two glass plates, moving on a hinge with some friction against the plates, so as to close it. When water is poured into the vessel the angle may be varied at will. If a ray of light, S, be allowed to fall upon one of them, by inclining the other more the angle of the prism increases, and the deviation of the ray is seen to increase. 557. Use of right-angled prisms as reflectors.— Prisms whose principal section is an isosceles right-angled triangle afford an important application of total reflection (552). For let ABC (fig. 518) be the principal section of such a prism, O a luminous point, and OH a ray at right angles to the face BC. This ray enters the glass without being re- fracted, and makes with the face AB an angle equal to B—that is, to 45 degrees —and therefore greater than the limiting Hig. angle of glass, which is 41° 48’ (552). The ray OH undergoes, therefore, at H total reflection, which imparts to it a direction HI perpendicular to the second face AC. Thus the hypotenuse surface of this prism produces the effect of the most perfect plane mirror, and an eye placed at I sees O’, the image of the point O. This property of right- angled prisms is frequently used in optical instruments, such as the camera lucida (615) and the prismatic compass (711), instead of metal reflectors, which readily tarnish. They are also largely used in the camera. obscura in changing the direction of images for projection purposes. The newer /gh- house lenses are made up of such prisms. 558. Conditions of emergence in prisms.—In order that any luminous ray refracted at the first face of a prism may emerge from the second, it is necessary that the refractive angle of the prism be less than twice the critical angle of the substance of which the prism is composed. For if LI (fig. 519) be the ray incident on the first face, IE the refracted ray, PI and PE the normals, the ray IE can only emerge from the second face when the incident angle IEP is less than the critical angle (552). But as the incident angle LIN increases, the Fig. 519 angle EIP also increases, while IEP diminishes. Hence, according as the direction of the ray LI tends to become parallel with the face AB, does this ray tend to emerge at the second face. —559] Minimum Deviation 545 Let LI be now parallel to AB, the angle ~ is then equal to the critical angle Z of the prism, because it has its maximum value. Further, the angle EPK, the exterior angle of the triangle IPE, is equal to ~+z’; but the angles EPK and A are equal, because the sides which contain them are at right angles to each other, and therefore A =7+2’; therefore also A=/+7’, for in this case ~=/. Hence, if A=2/ or is >2/, we shall have z’=/ or >J, and therefore the ray would not emerge at the second face, but would be parallel to AC or would undergo internal reflection, and emerge at a third face, BC. This would be much more the case with rays whose incident angle is less than BIN, because we have already seen that z’ would continu- ally increase. Thus in the case in which the refracting angle of a prism is equal to 2/ or is greater, no luminous ray could pass through the faces of the refracting angle. As the critical angle of glass is 41° 48’, and twice this angle is less than 90°, objects cannot be seen through a glass prism whose refracting angle is aright angle. As the critical angle of water is 48° 35’, light could pass through a hollow rectangular prism formed of three glass plates and filled with water. If we suppose A to be greater than / and less than 2/, then of rays inci- dent at I, some within the angle NIB will emerge from AC, others will not emerge, nor will any emerge that are incident within the angle NIA. If we suppose A to have any magnitude less than /, all rays incident at I within the angle NIB will emerge from AC, as also will some of those incident with- in the angle NIA. 559. Minimum deviation. — When a pencil of sunlight passes through an aperture A, in the side of adark cham- ber (fig. 520), the Fig. 520 pencil is projected in a straight line, AC, on a distant screen. But if a ver- tical prism be interposed between the aperture and the screen, the pencil is deviated towards the base of the prism, and the image is projected at D, at some distance from the point C. If the prism be turned so that the incident angle decreases, the disc of light approaches the point C up to a certain position, E, from which it reverts to its original position even when the prism is rotated in the same direction. Hence there is a deviation, EBC, less than any other. It may be proved mathematically that this sz¢n¢mum deviation takes place when the angles of incidence and of emergence are equal. The angle of minimum deviation may be calculated when the incident angle and the refracting angle of the prism are known. For when the deviation is a minimum, then since the angle of emergence 7” is equal to the incident anglez (fig. 519), ~ must equal z’. But it has been shown above (558) that A=7+z’; consequently A=27. ; , ; ; . (1) NN 546 On Light [559- If the minimum angle of deviation LD/ be called d, this angle being ex- terior to the triangle DIE, we readily obtain the equation A=t—r+/7 —-t' = 2-27, whence ad=21—-A : : : (2) which gives the angle d, when z and A are known. From the formule (1) and (2) a third may be obtained, which serves to calculate the index of refraction of a prism when its refracting angle and the minimum of deviation are known. The index of refraction, 7, is the ratio sin Z of the sines of the angles of incidence and refraction ; hence 7 = ——— ; re- sin 7 placing z and 7 from their values in the above equations (1) and (2) we get , (2 + “) sin ( — E ( eae 3) SS BLO sinless 2 560. Measurement of the refractive index of solids.—By means of the preceding formula (3) the refractive index of a solid may be calculated when the angles A and d are known. In order to determine the angle A, the substance is cut in the form of a triangular prism, and the angle measured by means of a goniometer (546). The angle d is measured in the following manner :—A ray, LI, emitted from a distant object (fig. 521), is received on the prism, which is turned in order to obtain the minimum deviation EDL’. By means of a telescope with a graduated circle the angle EDL’ is read off, which the re- fracted ray DE makes with the ray . DL, coming directly from the object ; now this is the angle of minimum deviation, assuming that the object is so distant that the two rays LI and L’D are approximately parallel. These values then only need to be substi- tuted in the equation (3) to give the value of 72. 561. Measurement of the refractive index of liquids.—Biot applied Newton’s method to determining the refractive index of liquids. For this purpose a cylindrical cavity, O, of about 0°75 inch in diameter, is perforated in a glass prism, PQ (fig. 522), from the incident face to the face of emergence. This cavity is closed by two plates of thin glass which are cemented on the sides of this prism. Liquids are introduced through a small stoppered aperture, B. The refracting angle and the minimum deviation of the liquid prism in Fig. 521 —562] Measurement of the Refractive Index of Gases 547 the cavity O having been determined, their values are introduced into the formula (3), which gives the index. 562. Measurement of the refractive index of gases.—A method for this purpose, founded on that of Newton, was devised by Biot and Arago. The apparatus which they used consists of a glass tube (fig. 523), bevelled at its two ends, and closed by glass plates, which are at an angle of 143°. This tube is connected with a bell-jar, H, in which there is a siphon barometer, and with a stopcock by means of which the apparatus can be exhausted, and different gases introduced. When the tube, AB, has been exhausted, a ray of light, SA, is transmitted through it, which is bent away from the normal through an angle ~—z at the first incidence, and towards the normal through an angle z’—7’ at the second. These two deviations being added, the total deviation, d, is y—z+z2’-7’. Inthe case of a minimum deviation, 7=7’ and r=z’, whence G=A— 27, since. 7+7=A (559). The index from vacuum to air, which is evidently SIZ sin Zz has therefore the value sin B si (ee) eee | oft Hence, in order to deduce the refractive index 2 from vacuum into air, which is the absolute index of air, it is merely necessary to know the refracting angle, A, and the angle of minimum deviation, @. To obtain the absolute index of any other gas, we first produce a vacuum, and then introduce the gas; the angles A and d@ having been measured, the above formula gives the index of refraction from the gas to air. Dividing the index of refraction from vacuum to air by the index of refraction from the gas to air, we obtain the index of refraction from vacuum to the gas; that is, its absolute index. It appears probable that certain relations exist between the refractive index, 2, and the density, d, of a body. These relations are of considerable importance in questions of theoretical chemistry regarding the constitution of bodies. They are expressed by the formula R = pa a , which 1s known as the constant of refraction. If this is multiplied by a, the atomic weight, we have the atomic refraction (sar ee: m+2 a SM Lt weight, 7, we have the solecular refraction Pere The following table gives the refractive indices for the three principal Fraunhofer’s lines (586), the red, yellow, and violet ; the last column gives the dispersion (576), or the difference between the extreme red, 7,, and the extreme violet, 7,, rays. Fig. 523 or, if by the molecular NN 2 548 | On Light [562- A | D | H | nr - ne | | | Water . : : t é IEG 20) NOI 331 | 1°344 O01 4 | Alcohol : : : ; Eten BOO da iT 364 hh is3 7s oko) | Crown glass (light) —. SP he: 1757531) Heo Weel a saLLCONY )enet nears ~ 1) OLO TiO12; WTO 3r o7o2I Rock salt. A : : - | 17538 [SAS ee 5OO C031 Flint glass (light). PA eh 6OG2)} 1°000 | TOAO EPO Oasanm ued PrChes vy) : TA 5 I-75 sry Waoo7G | _Calcspar (ordinary) . : Ate tally e) 1659! 17683 7 1 Gorogat & oil), (éxtradrdimary) os aba se 1°483 1°498 | O'015 _ Carbon bisulphide é , Hi eOl 2s yarOsr £5703 \ OOo] | The following are the mean values for a few other substances, and corre- spond nearly to the E line. Ice : ; . ; + Et*3TO Turpentine . : ey 19303 Solution of nitre . 3 Bd Bee ds Rock crystal ; : Ape Vitreous humour of the eye —_—1°339 Benzole ‘ ‘ . nates OO Aqueous _,, Ps in 1355 7, Oil of cassia : : Wr eOes Crystalline lens _,, J 1°384 Diamond . 4 ; Ry ay Ate. Mean refractive indices of gases Vacuum . ‘ : . _1'000000 Carbonic acid ; . 1'000449 Hydrogen . : . 1°000138 Hydrochloric acid . . 4F:000449 Oxygen . : 3 ET OCG27.2 Nitrous oxide . ‘ - 1'000503 Ainge : i 1:900204 Sulphurous acid. . 1°000665 Nitrogen. ; : . 1000300 Ethylene ‘ ; . 1:000678 Ammonia 4 ; . 1°000385 Chlorine . , ; »| ¥1°000772 LENSES, THEIR EFFECTS 563. Different kinds of lenses.—Zezses are transparent media which, from the curvature of their surfaces, have the property of causing the luminous rays which traverse them either to converge or to diverge. According to their curvature they are either stherical, cylindrical, elliptical, or parabolic. Fig. 524 Those used in optics are exclusively spherical. They are commonly made either of crown glass, which is free from lead, or of féz7¢ glass, which con- tains lead, and is more refractive than crown glass. The combination of spherical surfaces, either with each other or with plane surfaces, gives rise to six kinds of lenses, sections of which are repre- —564] Different Kinds of Lenses 549 sented in fig. 524; four are formed by two spherical surfaces and two bya plane and a spherical surface. . M is a double convex, N is a pPlano-convex, O is a converging concavo- convex, P is a double concave, Q is a plano-concave, and R is a atverging concavo-convex. The lenses O and R are also called szenzscus lenses, from | their resemblance to the crescent-shaped moon. : The first three, which are thicker at the centre than at the borders, are’ converging \enses ; the others, which are thinner in the centre, are dverging. In the first group the double convex lens only need be considered, and in the second the double concave, as the properties of each of these lenses apply to all those of the same group. | In lenses whose two surfaces are spherical, the centres for these surfaces are called centres of curvature, and the right line which passes through these two centres is the frimcipal axis. Ina plano-concave or plano-convex lens the principal axis is the perpendicular let fall from the centre of curvature of the spherical face on the plane face. { In order to compare the path of i\ a luminous ray in a lens with that fi in a prism, the same hypothesis is made as for curved mirrors (536) ; that is, the surfaces of these lenses are supposed to be formed of an infinity of small plane surfaces or elements (fig. 525): the zormad at any point is then the perpendicular to the plane of. the corresponding element. It is a geometrical prin- ciple that all the normals to the same spherical surface pass through its centre. On the above hypothesis we can always conceive two plane surfaces at the points of incidence and emergence, which are inclined to each other, and thus produce the effect of a prism. Pursuing this comparison, we may compare the three lenses, M, N, and O, to a succession of prisms having their summits outwards, and the lenses iT | P, Q, and R, to a series having y their summits inwards: from this we see that the first ought to con- Fig. 525 dense the rays, and the latter to disperse them, for we have already seen that when a luminous ray traverses a prism it is deflected towards the base (556). 564. Foci in double convex lenses.—The focus of a lens is the point where the refracted rays, or their prolongations, meet. Double convex lenses have both real and virtual foci, like concave mirrors. 550 On Light [564- Real foci.—We shall first consider the case in which the luminous rays which fall on the lens are parallel to its principal axis, as shown in fig. 526. In this case, any incident ray, LB, in approaching the normal of the point of incidence, B, and in diverging from it at the point of emergence, D, is twice refracted towards the axis, which it cuts at F. As all rays parallel to the axis are refracted in the same manner, it can be shown by calcu- Fig. 526 Jation that they all pass very nearly through the point F, so long as the arc DE does not exceed 10° to 12°. This point is called the principal focus, and the distance FA is the principal focal dts- tance. It is constant in the same lens, but varies with the radii of curvature and the index of refraction. In ordinary lenses, which are of crown glass, and in which the radii of the two surfaces are nearly equal, the principal focus coincides very closely with the centre of curvature. We - shall now consider the\ease. win which the point of light is outside the principal focus, but! sos smear that all inci- dent rays form Fig. 527 a divergent pencil, as shown in fig. 527. The point of light being at L, by comparing the path of a diverging ray, LB, with that of a ray, SB, parallel to the axis, the former is found to make with the normal an angle, LBz, greater than the angle SBz ; consequently, after traversing the lens, the ray cuts the axis at a point, J, which is more dis- tant than the prin- cipal focus, F. As all rays from the point L intersect big. 528 approximately in the same point, /, this latter is the conjugate focus of the point L; this term has the same meaning here as in the case of mirrors, and expresses the relation existing between the two points L and Z, which is of such a nature that, if the luminous point is moved to /, the focus passes to L. —566] Double Concave Lenses Soa According as the point of light comes nearer the lens, the convergence of the emergent rays decreases, and the focus 7 becomes more distant ; when the point L coincides with the principal focus, the emergent rays on the other side are parallel to the axis, and there is no focus, or, what is the same thing, it is infinitely distant. As the refracted rays are parallel in this case, the intensity of light only decreases slowly, and a simple lamp can illuminate great distances. It is merely necessary to place it in the focus of a double convex lens, as shown in fig. 528. Virtual foct.—When a luminous point is placed between the lens and its principal focus, the image or focus of the point is virtual, as shown in fig. 529. In this case the incident rays make with the normal greater angles than those made with the rays FI from the principal focus ; hence, when the former rays emerge, they move farther from the axis than the latter, and form a diverging pencil, HK, GM. These rays cannot pro- duce a real focus, but their prolongations: intersect in some point, 7, on the axis, and this point is the virtual focus of the point L (537). 565. Double concave lenses.—In double concave lenses there are only virtual Fig. 529 foci, whatever the distance of the object. Let SS’ be any pencil of rays parallel to the axis (fig. 530) ; any ray, SI, is refracted at the point of incidence, I, and approaches the normal, CI. At the point of emergence it is also refracted, but diverges from the normal, GC’, so that it is twice refracted in a direction which moves it from the axis, CC’. As the same thing takes place for every other ray, S’KMN, it follows that the rays, after traversing the lens, form a diverging pencil, GHMN. Hence there is no real focus, but the prolongations of these rays cut one another in a point F, which is the principal virtual focus. Hig. 531 In the case in which the rays proceed from a point, L (fig. 531), on the axis, it is found by the same construction that a virtual focus is formed at /, which is between the principal focus and the lens. 566. Experimental determination of the principal focus of lenses.— To determine the principal focus of a convex lens, it may be exposed to the sun’s rays so that they are parallel to its axis. The emergent pencil being received on a ground-glass screen, the point to which the rays converge is readily seen ; it is the principal focus. 552 On Light [566— Or an image of an object is formed on a screen, their respective distances from which are then measured, and from these distances the focus is calculated from the dioptric formula (573). With a double concave lens, the face ad (fig. 532) is covered with an opaque substance, such as lampblack, two small apertures @ and 6 being left in the same prin- cipal section, and at an equal dis- tance from the axis; a pencil of sunlight is then received on the other face, and the screen P, which receives the emergent rays, is Fig. 532 moved nearer to or farther from the lens, until A and B, the spots of light from the small apertures a and 4, are distant from each other by twice ad. The distance DI is then equal to the focal distance FD, because the triangles Fad and FAB are similar. Another method of determining the focus of a concave lens is given in article 572. 567. Optical centre, secondary axis.—In or near every lens there is a point called the optical centre, which is situate on the axis, and which has the property that any luminous ray passing through it experiences no angular deviation ; that is, that the emergent ray is parallel to the incident ray. The existence of this point may be demonstrated in the following manner :— Let two parallel radii of curvature, CA and C’A’ (fig. 533), be drawn to the two surfaces of a double convex lens. Since the two plane elements of the lens at A and A’ are parallel, as being perpendicular to two parallel right lines, it will be granted that the refracted ray AA’ is propagated in a medium with parallel faces. Hence a ray KA, which reaches A at such an inclination Fig. 533 Fig. 534 that after refraction it takes the direction AA’, will emerge parallel to its first direction (554); the point O, at which the right line cuts the axis, is there- fore the optical centre. The position of this point may be determined for the case in which the curvature of the two faces is the same, which is the usual condition, by observing that the triangles COA and C’OA’ are equal, and therefore that OC = OC’, which gives the point O. If the curvatures are unequal, the triangles COA and COA’ are similar, and either CO or C’O may be found, and therefore also the point O. In double concave or concavo-convex lenses the optical centre may be —568] ormation of Images by Double Convex Lenses 553 determined by the same construction. In lenses with a plane face this point is at the intersection of the axis by the curved face. Every right line PP’ (fig. 534), which passes through the optical centre without passing through the centres of curvature, isa secondary axis. From this property of the optical centre, every secondary axis represents a luminous rectilinear ray passing through this point: for, since the thicknesses of the lenses we are dealing with are supposed to be small, it may be assumed that rays passing through the optical centre are in a right line ; that is, that the small deviation may be neglected which rays experience in traversing a medium with parallel faces (fig. 533). So long as the secondary axes only make a small angle with the principal axis, all that has hitherto been said about the principal axis is applicable to them ; that is, that rays emitted from a point P (fig. 534) on the secondary axis PP’ nearly converge to a certain point of the axis P’, and according as the distance from the point P to the lens is greater or less than the principal focal distance, the focus thus formed will be conjugate or virtual. This principle is the basis of what follows as to the formation of images. 568. Formation of images by double convex lenses.—lIn lenses, as well as in mirrors, the image of an object is the collection of the foci of its several points ; hence the images furnished by lenses are real or virtual in the same case as the foci, and their construction resolves itself into determining the position of a series of points, as was the case with mirrors (540). 1. eal tmage.—Let AB (fig. 535) be placed beyond the principal focus. If a secondary axis, Aa, be drawn from the outside point A, any ray AC, from this point, will be twice refracted at C and D, and both times in the same direction, ap- proaching the secondary axis, which it cuts at a. From. what has just been said, the other rays from the point A _ will tense ise eS point a, which is accordingly the conjugate focus of the point A. If the secondary axis be drawn from the point B, it will be seen, in like manner, that the rays from this point intersect in the point 4; and as the points between A and B have their foci between a and 4, a veal but inverted image of AB will be formed at ad. To see this image, it may be received on a white screen, on which it will be depicted, or the eye may be placed in the path of the rays emerging from it. Conversely, if ad were the luminous or illuminated object, its image would be formed at AB. Two consequences important for the theory of optical instruments follow from this :—viz., Ist, zf az object, even a very large one, is ata sufficient distance from a double convex lens, the real and inverted image which is obtained of it is very small—it ts near the prin- cipal focus, but somewhat farther from the lens than this ts ; 2nd, if a very 6 a 554 | On Light [568— small object be placed near the principal focus, but a little in front of tt, the image which ts formed ts at a great aistance—it ts much larger, and that in proportion as the object is near the principal focus. In all cases the object and the image are in the same proportion as their distances from the lens. These two principles are experimentally confirmed by receiving on a screen the image of a lighted candle, placed successively at various distances from a double convex lens. i. Virtual tmage.—There is another case in which the object AB (fig. 536) is placed between the lens and its principal focus. If a secondary axis Oa be drawn from the point A, every ray AC, after having been twice refracted, diverges from this axis on emerging, since the point A is at a less distance than the principal focal distance (564). This ray, continued in an opposite direction, will cut the axis Oa in the point a, which is the virtual focus of the point A. Tracing the secondary axis of the point B, it will be found, in the same manner, that the virtual focus of this point is formed at 3d. There is, therefore, an image of AB at ad. This is a virtual image; tt ts erect, and larger than the object. The magnifying power is greater in proportion as the lens is more convex, and the object nearer the _ principal focus. Weshall presently show how the magni- fying power may be calculated by means of the formule relating to lenses (571). Double convex lenses, used in this manner as magnifying glasses, are called szmple micro- SCOPES. 569. Formation of images in double concave lenses.—Double concave lenses, like convex mirrors, only give virtual images, whatever the distance of the object. Wy UF Let AB (fig. 537) be an object LY st placed in front of sucha lens. If WY =a the secondary axis AO be drawn ae, falta from the point A, all rays, AC, AI, =N from this point are twice refracted --\ in the same direction, diverging XY . from the axis AO; so that the eye, | AY receiving the emergent rays DE and GH, supposes them to proceed from the point where their pro- longations cut the secondary axis AO in the point a. In like manner, drawing a secondary axis from the point B, the rays from this point form a pencil of divergent rays, the direc- tions of which, prolonged, intersect in 4. Hence the eye, looking along the Fig. 536 —570| Spherical Aberration. Caustics 555 principal axis, sees at ad a virtual image of AB, which ts always erect, and smaller than the object. 570. Spherical aberration. Caustics.—In speaking about foci, and about the images formed by different kinds of spherical lenses, it has been hitherto assumed that the rays emitted from a single point intersect also after refraction in a single point. This is virtually the case with a lens whose aperture—that is, the angle obtained by joining the edges to the principal focus—does not exceed 10° or 12°. Where, however, the aperture is larger, the rays which traverse the lens near the edge are refracted toa point F (fig. 538) nearer the lens than the point G, which is the focus of the rays which pass near the axis. The phenomenon thus produced is named spherical aberration by refraction ; it is analogous to the spherical aberration produced by reflection (545). The luminous sur- faces formed by the intersection of the refracted rays are termed caustics by refraction. Spherical aberration is prejudicial to the sharpness and definition of an image. If a ground-glass screen be placed exactly in the focus of a lens, the image of an ob- ject will be sharply defined in’ the centre, but indis- tinct at the edges ; and,’ wzce versa, if the image is sharp at the edges, it will be indistinct in the centre: "This defect is very objection- able, more espe- cially in lenses used Figtese for photography. It is partially obviated by placing in front of the lenses diaphragms provided with a central aperture, called s/ops, which admit the rays passing near the centre, but cut off those which pass near the edges. The image thereby becomes sharper and more distinct, though the illumination is less. If a screen be held between the light and double convex lens which quite covers the lens, but has two concentric series of holes, two images are obtained, and may be received on a sheet of paper. By closing one or the other series of holes by a flat paper ring, it can be easily ascertained which image arises from the central, and which from the marginal rays. When the paper is at a small distance the marginal rays produce the image in a point, and the central ones in a ring; the former are converged to a point, and the latter not. At a somewhat greater distance the marginal rays produce a ring, and the central ones a point. It is thus shown that the focus of the marginal rays is nearer the lens than that of the central rays. Mathematical investigation shows that convex lenses whose radii of curvature stand in the ratio expressed by the formula Y 4-20? +n Yr, 2n+n XN 556 On Light [570— are most free from spherical aberration, and are called lenses of best form: in this formula ~ is the radius of curvature of the face turned to the parallel rays, and 7, that of the other face, while is the refractive index (560). Thus, with a glass whose refractive index is 3. vy,=6r. Spherical aberration is 2. also destroyed by substituting for a lens of short focus two lenses of double focal length, which are placed at a little distance apart. Greater length of focus has the result that for the same diameter the aperture and also the aberration are less; and as it is not necessary to stop a great part of the lens there is a gain in luminosity, which is not purchased by indistinctness of the images, while the combination of the two lenses has the same focus as that of the single lens (572). Lenses which are free from spherical aber- ration are called aplanatic. 571. Formule relating to lenses.— In all thin lenses the relations between, the distances of the image and object, the radii of curvature, and the refrac- tive index may : be expressed by rN N a formula. In ae a | Cp the case of a double convex lens, let P be a luminous point situate on the axis (fig. 539), let PI be anin- eidentiray, Lis its direction within the lens, EP’ the emergent ray, so that P’ is the con- jugate focus of P. Further, let C’Il and CE be the normals to the points of incidence and emergence, and IPA be put equal to a, EP’A’=8, ECA’= IGA=0,'NIB= 7 EC = 7eLk O =7 NH Peers, Because the angle z is the exterior angle of the triangle PIC’, and the angle 7’ the exterior angle of the triangle CEP’, therefore 7=a+6, and vy’ =y+B, whence Fig. 539 Z+7r’'=at+B+y+d. ‘ ; breeds) But at the point I, sin 7=7 sin % and at the point E, sin 7’ =z sin z’ (550), being the refractive index of the lens. Now if the arc AI is only a small number of degrees, these sines may be considered as proportional to the angles z, 7, 2’ and 7’ ; whence, in the above formula, we may replace the sines by their angles, which gives z=mr and r’ = 72’, from which 7+ 7 =a (r+72’). Further, because the two triangles IOE and COC’ have a common equal angle O, therefore 7+2’=y+6, from which 7+”=a (y+6). Introducing this value into the equation (1) we obtain a (y+6)=a+8+y+6, from which (2-1) (y+8)=a+8 (2) Let CA’ be denoted by R, C’A by R’, PA by g, and P’A’ by ’. Then with centre P and radius PA describe the arc Ad, and with centre P’ and radius P’A’ describe the arc A’z. Now when an angle at the centre of a ~572] formule relating to Lenses 554 circle subtends a_certain arc of the circumference, the quotient of the arc divided by the radius measures the angle ; consequently Aa Ad A’ A’/E Al Saray we >a) ai as )Y=-p and 8=—. Therefore by substitution in (2), (#- 1) (ee AT _Ad An Re ae A Now since the thickness of the lens is very small, the angles are also small and Ad, Al, A’E, A’x differ but little from coincident straight lines, and are therefore virtually equal. Hence the above equation becomes (72 —1) (A+y) agthg? : ? : r (3) This is the formula for double convex lenses ; if f be =o —that is, if the incident rays are parallel, we have Neer ~p’ being the principal focal distance. Calling this 4, we get (in Boe te op : : : : (4) from which the value of / is easily deduced. Considered in reference to equation (4), the equation (3) assumes the form Stara (5) eh LEY OW fe which is that in which it is usually employed. When the image is virtual, _ p’ changes its sign, and formula (5) takes the form scat) a | NN einen ae a 6) In double concave lenses #’ and / retain the same sign, but that of p changes ; equation (5) then becomes Toe (7) Lug lalt ele Equation (7) may be obtained by the same reasonings as the other. 572. Combination of lenses.—If parallel rays fall on a convex lens A, which has the focal distance f, and then on a similar lens B with the focal distance 7’, at a distance @ from A, the distance from the lens B at which the image is formed is F, then Stak) i ea Lenk ata If the lenses are close together, so that d@=o0, then 558 | On Light [572- felons? If the lenses have the same curvature, that is f=/, hie ages ; that is to af say, the focal distance of the combination is half that of a single lens. If the second lens is a diverging one of the focal distance /, then T_ 1 _1! . and if the lenses are close together, then See Ein feds f Fiiesaer This formula can be used to determine the focal distance of a concave lens, by combining it with a convex lens of shorter focus, and then deter- mining the focal distance of the combination. 573. Relative magnitudes of image and object. Determination of focus.-—From the similarity of the triangles AOB, aOd (fig. 536), we get for the relative magnitudes of image and object the proportion ioe whence Ree where AB=O is the magnitude of the object, and aé=I that of the image ; while # and 7’ are their respective distances from the lens. Replacing 7’ by its value from the equation 5+ = where the yy image is real, or from the equation ae ve => where it is virtual, we shall obtain the different values of the ratio = for various positions of the object. Le In the first case we have pe ee) Que, Thus if pees <0 Pra i= O Bons In the second case when the image is virtual we shall have ote so that in all cases 1>O. By using the above formula we may easily deduce the focal length of a convex lens where direct sunlight is not available. For if a luminous object be placed on one side of the lens, and a screen on the other side, then by altering the relative positions of the lens and the screen, a position may be found by trial, such that an image of the object is formed on the screen of exactly the same size as the object. Dividing now by 4 the total distance between the object and the screen, we get the focal distance of the lens. Another method is to place on one side of the lens, and a little beyond its principal focus, a brightly illuminated scale, which is best of glass, on which a strong light falls ; on the other side a screen is placed at such a distance as to produce a greatly magnified distinct image of the scale. Then if 7 and L are the lengths of the scale and its image respectively, and d the distance of the screen from the lens, ] a7 sh Heer, ~575] Laryngoscope 559 574. Determination of the refractive index of a liquid.—By measure- ments of focal distance the refractive index of a liquid (561) may be ascertained in cases in which only small quantities of liquid are available. One face of a double convex lens of known focal distance /, and known curvature 7” 1s pressed against a drop of the liquid in question on a plate glass (fig. 540). The liquid forms thereby a plano-concave lens whose radius of curvature 16 7. The focal distance F of the whole system is then determined experimentally; this gives the focal length of the liquid lens f from the formula pees! ae while from the formula z =(#—1) I we get the value of z. r 575. Laryngoscope.—As an application of lenses may be adduced the laryngoscope, which is an instrument invented to facilitate the investigation of the larynx and other cavities of the mouth. It consists of a plano- convex lens L, and a concave reflector M, both fixed to a ring which can be adjusted to any convenient lamp (fig. 541). The flame of a lamp is in the principal focus of the lens, and at the same time is at the centre of curvature of the reflector. Hence the divergent pencil proceeding from the lamp to Cas a the lens is changed after emerging into a parallel pencil. Moreover, the pencil from the lamp, impinging upon the mirror, is reflected to the focus of the lens, and traverses the lens, forming a second parallel pencil which is superposed on the first. This being directed into the mouth of a patient, its condition may be readily observed. 560 On Light [576— CHAP TER ay: DISPERSION AND ACHROMATISM 576. Decomposition of white light. Solar spectrum. Dispersive power.— The phenomenon of refraction is by no means so simple as we have hitherto assumed. When wz¢e light, or that which reaches us from the sun, passes from one medium into another, z¢ zs decomposed tnto several kinds of light, a phenomenon to which the name dzsferston is given. In order to show that white light is decomposed by refraction, a pencil of the sun’s rays SA (fig. 542) is allowed to pass through a small aperture in the window shutter of a dark chamber. This pencil tends to form an oval and colourless image of the sun at K; but if a flint-glass prism arranged hori- zontally be interposed in its path, the beam, on emerging from the prism, becomes refracted to- wards its base, and produces on a distant screen a vertical band rounded at the ends, coloured in all the tints of the rainbow, which is called the Solar spectrum (see Plate: 1,).. elie thig spectrum there is, in reality, an infinity of different tints, which imperceptibly merge into each other, but it is Customary to distinguish seven principal colours. These are vzole¢, indigo, blue, green, yellow, orange, red; they are arranged in this order in the spectrum, the violet being the most refrangible, and the red the least so. They do not all occupy an equal extent in the spectrum, violet having the greatest extent, and orange the least. With transparent prisms of different substances, or with hollow glass prisms filled with various colourless liquids, spectra are obtained formed of the same colours, and in the same order; but when the deviation produced is the same, the length of the spectrum varies with the substance of which the prism is made. The angle of separation of two selected rays (say in the red and the violet) produced by a prism is called the dsferszon, and the ratio of i] LLL Ee Ben SS SSSSSSsSSSSSSSss SSSSSSSSSSSSSSS SESS SSS SSS SST N N ZB Fig. 542 —578] The Colours of the Spectrum 561 this angle to the mean deviation of the two rays is called the dispersive power. This ratio is constant for the same substance so long as the refracting angle of the prism is small. For the deviation of the two rays is proportional to the refracting angle; their difference and their mean vary in the same manner, and therefore the ratio of their difference to their mean is constant. For flint glass this is 0°043 ; for crown glass it is 00246, since the dispersive power of flint is almost double that ‘of crown glass. The spectra which are formed by artificial lights rarely contain all the colours of the solar spectrum ; but their colours are found in the solar spectrum, and in the same order. Their relative intensity is also modified. The shade of colour which predominates in the flame’ predominates also in the spectrum ; yellow, red, and green flames produce spectra in which the dominant tint is yellow, red, or green. 577. Production of a pure solar spectrum.—In the above experiment the spectrum formed is built up of a series of overlapping spectra, and the colours are confused and indistinct. In order to obtain a pure spectrum, the slit, in the shutter of the dark room through which light enters, should be of rect- angular form, from 15 to 25 mm. in height and from 1 to 2 mm. in breadth. The sun’s rays are directed upon the slit by a mirror, or still better by a heliostat (546). An achromatic double convex lens is placed at a distance from the slit of double its own focal length, which should be about a metre, and a screen is placed at the same distance from the lens. An image of the slit of exactly the same size is thus formed on the screen (573). If now there is placed near the lens, between it and the screen, a prism with an angle of about 60°, and with its refracting edge parallel to the slit, a very beautiful, sharp, and pure spectrum is formed on the screen. The prism should be placed so that it produces the minimum deviation. 578. The colours of the spectrum are simple, and unequally refrangible.— If one of the colours of the spectrum be isolated by intercepting the others by means of a screen E, as shown in fig. 543, and if the light thus isolated be allowed to pass througha second prism, B, a refraction will be observed, but the light remains unchanged ; that 1s, the image re- ceived on the screen H is violet if the violet pencil has been allowed to pass, blue if the blue pencil, and so on. Hence the colours of the spectrum are szwzfle ; that is, they cannot be further decomposed by the prism. Moreover, the colours of the spectrum are unequally resrangible ; that is, the glass of the prism possesses a different refractive index for each of the rays of which white light is composed. The elongated shape of the spectrum would be sufficient to prove the unequal refrangibility of the simple colours, for it is clear that the violet, which is most deflected towards the base of the prism, is also most refrangible ; and that red, which is least de- flected, is least refrangible But the unequal refrangibility of simple colours. ORO 562 On Light [578- may be shown by numierous experiments, of which the two following may be adduced :— i. Two narrow strips of coloured paper, red and violet, are fastened close to each other on a sheet of black paper. On looking at them through a prism, they are seen to be unequally displaced, the red band to a less extent than the violet ; hence the red rays are less refrangible than the violet. ii. The same conclusion may be drawn from Newton’s experiment with crossed prisms. On a prism A (fig. 544), in a horizontal position, a pencil of whitelight, S, isreceived, which, if it had_ merely, traversed the | prism nae would form the spectrum vv, on a dis- tant , screen. Buty yadiqeeaet second prism, B, be placed in a vertical Fig. 544 position be- hind the first, in such a manner that the refracted pencil passes through it, the spectrum vu becomes deflected towards the base of the vertical prism ; but, instead of being deflected in a direction parallel to itself, as would be the case if the colours of the spectrum were equally refracted, it is obliquely refracted in the direction 7’v’, proving that from red to violet the colours are more and more refrangible. These different experiments show that the refractive index differs in dif- ferent colours ; even rays which are to perception indistinguishable may dif- fer in refran- gibility. In the red band, for instance, the rays at the extremity of the spec- trum are less refracted than those which are nearer the orange zone. In determining indices of refraction (550), it is usual to take, as the index of any par- ticular substance, the refrangibility of the yellow ray in a prism formed of that substance. 579. Recomposition of white light.—Not merely can white light be resolved into lights of various colours, but by combining the different pencils separated by the prism white light can be reproduced. This may be effected in various ways.. 1 es Wels ~ —=— Seer ee z 4 | AD TAD ELLE LIE LEE UEE LIED OUI TIET IOUT TTI Fig. 545 Fig. 546 —-579] Recomposition of White Light 563 i. If the spectrum produced by one prism is allowed to fall upon a second prism of the same material and the same refracting angle as the first, but inverted, as shown in fig. 546, the latter reunites the different colours of the spectrum, and it is seen that the emer- gent pencil E, which is parallel to the pencil S, is colourless. i. If the spectrum falls upon a double convex lens (fig. 545), a white image of the sun will be formed on a white screen placed in the focus of the lens ; a glass globe filled with water produces the same effect as the Fig. 547 lens. ii. If the spectrum falls upon a concave mirror, a white image is formed on a screen of ground glass placed in its focus (fig. 547). iv. Light may be recomposed by an experiment, which consists in receiving the seven colours of the spectrum on seven small glass mirrors with plane faces ; these mirrors can be so inclined in all positions that thefreflected light may be trans- mitted in any given direction (fig. 548). When the mirrors are suitably ar- ranged, the seven reflected pencils may be caused to fall on the ceiling, so as to form seven distinct images —red, orange, yellow, &c. When the mir- Fieses rors are moved so that the separate images become superposed, a single image is obtained, which is white. v. By means of Newton's disc (fig. 549) it may be shown that the seven colours of the spectrum form white. This is a cardboard disc of about a foot in diameter ; the centre and the edges are covered with black paper, while in the space between there are pasted strips of paper of the colours of the spectrum. They proceed from the centre to the circumference, and their relative dimensions and tints are such as to represent five spectra (fig. 550). When this disc is rapidly rotated, the effect is the same as if the retina received simultaneously the impression of the seven colours. vi. If by a mechanical arrangement a prism, on-which the sun’s light falls, is made to oscillate rapidly, so that the spectrum also oscillates, the middle of the spectrum appears white. These latter phenomena depend on the physiological fact that sensation always lasts a little longer than the impression from which it results (639). 002 6 LL LLL LLL LIL LANDS LLL IS PLETAL ELST TLL ELELLAL TO) 564 | On Light [579- If a new impression is allowed to act, before the sensation arising from the former one has ceased, a sensation is obtained consisting of two impressions. And by choosing the time short enough, three, four, or more impressions may be mixed with each other. With a rapid rotation the disc (fig. 549) Fig. 549 is nearly white. It is not quite so, for the colours cannot be exactly arranged in the same proportions as those in which they exist in the spectrum, and moreover ~zgment colours are not pure (583). ' 580. Newton’s theory of the composition of light.—Newton was the first to decompose white light by the prism, and to recompose it. From the various experiments which we have described, he concluded that white light was not homogeneous, but formed of seven lights unequally refrangible, which he called szmple or primitive lights. Owing to the difference in refrangibility they become separated in traversing the prism. The designation of the various colours of the spectrum is to a very great extent arbitrary ; for, in strict accuracy, the spectrum is made up of an in- finite number of simple colours, which pass into one another by imperceptible gradations of colour and refrangibility. re 581. Colour of bodies.—The natural colour of bodies results from the fact that one portion of the coloured rays contained in white light is absorbed at the surface of the body. If the unabsorbed portion traverses. the body, it is coloured and transparent ; if, on the contrary, it is reflected,. it is coloured and opaque. In both cases the colour results from the constituents which have not been absorbed. Those which reflect or transmit all colours in the proportion in which they exist in the spectrum are white ; those which reflect or transmit none are black. Between these two limits there are infinite tints according to the greater or less extent to —582] Mixed Colours. Complementary Colours 505 which bodies reflect or transmit some colours and absorb others. Thus a body appears yellow because it absorbs all colours with the exception of yellow. In like manner, a solution of ammoniacal copper sulphate absorbs preferably the red and yellow rays, transmits the blue rays almost completely, the green and violet less so; hence the light seen through it is blue. Accordingly bodies have no colour of their own; the colour changes with the nature of the incident light. Thus, if a white body in a dark room is successively illuminated by each of the colours of the spectrum, this has no special colour, but appears red, orange, green, &c., according to the position in which it is placed. If monochromatic light fails upon a body, it appears brighter in the colour of this light if it does not absorb this colour; but black if it does absorb it. Inthe light of a lamp fed by spirit in which some common salt is dissolved, everything white and yellow seems bright, while other colours, such as vermilion, ultramarine, and malachite, are black. This is seen in the case of a stick of red sealing-wax viewed in such a light. In the light of lamps and of candles, which from the want of blue rays appear yellow, yellow and white appear the same, and blue seems like green. In bright twilight or in moonshine the light of coal gas has a reddish tint. 582. Mixed colours. Complementary colours.—By mixed colours we understand the impression of colour which results from the coincident action of two or more colours on the same portion of the retina. This new im- pression is single ; it cannot be resolved into its components; in this respect it differs from a complex sound, in which the ear, by practice, can learn to distinguish the constituents. Mixed colours may be produced by Laméert’s method, which consists in looking in an oblique direction through a vertical glass plate P (fig. 551) ata coloured wafer 4, while, at the same time, a wafer 3 GF of another colour g sends its light by reflection in ees towards the observer’s eye ; if gis placed in a proper position, which is easily found by trial, its image exactly coincides with that of 8. The method of the colour disc (579) affords another means of producing mixed colours. A very convenient way of investigating the phenomena of mixed colours is that of Waxwell’s colour-discs. These consist of discs of cardboard with Wt SS Fig. 552 Fig. 553 Fig. 554 an aperture in the centre, by which they can be fastened on the spindle of the turning-table (fig. 552). Each disc is painted with a separate colour, and, having a radial slit, they may be slid over each other so as to overlap to any desired extent (figs. 553 and 554) ; and thus, when in this way two such 566 On Light [582- discs are rotated, we get the effect due to this mixture of these two colours. It is clear also that the effect of three colours may be investigated in the same way. If, in any of the methods by which the impression of mixed spectral colours is produced, one or more colours are suppressed, the residue corre- sponds to one of the tints of the spectrum ; and the mixture of the colours taken away produces the impression of another spectral colour. Thus, if in fig. 545 the red rays are cut off from the lens L, the light on the focus is no longer white, but greenish blue. In like manner, if the violet, indigo, and blue of the colour disc are suppressed, the rest seems yellow, while the mixture of that which has been taken out isa bluish violet. Hence white can always. be compounded of ¢wo tints ; and two tints which together give white are called complementary colours. Thus of spectral tints vedand greenish yellow are complementary ; so are orange and Prussian blue, yellow and indigo blue, greenish yellow and violet. The method by which Helmholtz investigated the mixture of spectral colours is as follows :—Two very narrow slits, A and B (fig. 555), at right angles to each other, are made in the shutter of a dark room ; at a distance from this is placed a powerfully dispersing prism with its refracting edge Fig. 555 vertical. When the slits are viewed through a telescope, the slit B gives the oblique spectrum LM, while the slit A gives the spectrum ST. These two spectra partially overlap, and when this is the case two homogeneous spectral colours mix. Thus at 1 the red of one spectrum coincides with the green of the other ; at 3, indigo and yellow coincide ; and so forth. When the experiment is made with suitable precautions, the colours ob- tained by mixing the spectral colours will be found in the table on the next page, where the fundamental spectra to be mixed are given in the first horizontal and vertical column, and the resultant colours where these cross. Prismatic spectrum colours may also be investigated by the method of von Bezold, which consists in producing two images of colours by double refraction, and making one cover the other. The mixture of mixed colours gives rise to no new colours. Only the same colours are obtained as a mixture of the primitive spectral colours would yield, except that they are less saturated, as it is called ; that is, more mixed with white. 583. Spectral colours and pigment colours.--A distinction must be made between sfectral colours and pigment colours. Thus a mixture of pigment yellow and pigment blue produces green, and not white, as is the case when the blue and yellow of the spectrum are mixed. The reason of this is that in the mixture of pigments we have a case of subtraction of —584] Flomogeneous Light 567 colours, and not of addition. For the pigment blue in the mixture absorbs almost entirely the yellow and red light ; and the pigment yellow absorbs the blue and violet light, so that only the green remains. In the above series are two spectral colours very remote in the spectrum, which have nearly the same complementary tints ; red, the complementary colour to which is greenish blue ; and violet, whose complementary colour is greenish yellow. Now when two pairs of complementary colours are mixed together they must produce white, just as if only two complementary colours were mixed. But a mixture of greenish blue and of greenish yellow is green. Hence from a mixture of red, green, and violet, white must be formed. This may easily be ascertained to be the case by means of a colour disc on which are these three colours in suitable proportions. Violet Green | Yellow | Red. Red | Purple Rose | Ae Orange Red Yellow | Roe | White vein | Yellow ine Pale blue aoa | Green Blue | Indigo Blue Violet Violet From the above facts it follows that from a mixture of red, green, and violet all possible colours may be constructed, and hence these three spectral colours are called the fumdamental colours. It must be remarked that the tints resulting from the mixture of these three have never the saturation of the individual spectral colours. We have to discriminate three points in regard to colour. In the first place, the ¢z7z, or colour proper, by which we mean that special property which is due to a definite refrangibility of the rays producing it ; secondly, the saturation, which depends on the greater or less admixture of white light with the colours of the spectrum, these being colours which are fully satu- rated ; and thirdly, there is the zz¢emszty, which depends on the amplitude of vibration. 584. Homogeneous light.—The light emitted from luminous bodies is seldom or never quite pure ; on being examined by the prism it will be found to contain more than one colour. In optical researches it is frequently of great importance to procure homogeneous or monochromatic light. Common salt, or, still better, sodium bromide, in the flame of a Bunsen’s lamp gives a yellow of great purity. For red light, ordinary light is transmitted through 568 On Light [584— glass coloured with copper suboxide, which absorbs nearly all the rays excepting the red. A very pure blue is obtained by transmitting ordinary light through a glass trough containing an ammoniacal solution of copper sulphate, and a nearly pure red by transmitting it through a solution of iron sulphocyanide. 585. Properties of the spectrum. —Besides its luminous properties, the spectrum is found to produce calorific and chemical effects. Luminous properties. It appears from the experiments of Fraunhofer and of Herschel that the hight in the yellow part of the spectrum has the greatest intensity, and that in the violet the least. fleating effects. It was long known that the various parts of the spectrum differed in their calorific effects. Leslie found that a thermometer placed in different parts of the spectrum indicated a higher temperature as it moved from violet towards red. Herschel fixed the maximum intensity of the heating effects just outside the red; Berard in the red itself. Seebeck showed that these different results are affected by the nature of the prism used ; with a prism of water the greatest calorific effect is produced in the yellow ; with one of alcohol it is in the orange-yellow ; and with a prism of crown glass it is in the middle of the red. Melloni, by using prisms and lenses of rock salt, and by availing himselt of the extreme delicacy of the thermo-electric apparatus, first made a com- plete investigation of the calorific properties of the thermal spectrum. This result led, as we have seen, to the confirmation and extension of Seebeck’s observations. Chemical properties. In numerous phenomena, light exerts a chemical action. For instance, silver chloride blackens under the influence of light ; transparent phosphorus becomes opaque ; vegetable colouring matters fade ; hydrogen and chlorine gases, when mixed, combine slowly in diffused light, and with explosive violence when exposed to direct sunlight... The chemical action differs in different parts of the spectrum. Scheele found that when silver chloride was placed in the violet, the action was more energetic than in any other part. Wollaston observed that the action extended beyond the violet, and concluded that, besides the visible rays, there are some in- visible and more highly refrangible rays. These are sometimes called the chemical or actinic rays. The most remarkable chemical action which light exerts is inthe growth of plant life. The vast masses of carbon and hydrogen accumulated in the vegetable world. owe their origin to the carbonic acid and aqueous vapour present in the atmosphere. The light which is absorbed by the green parts of plants acts as a reducing agent. The reduction does not extend to the complete isolation of carbon and hydrogen, and the individual stages of the process are unknown to us ; but the general result is, undoubtedly, that under the influence of the sun’s rays the chemical attraction which holds together the carbon and oxygen is overcome ; the carbon, which is set free, assimilates at that moment the elements of water, forming cellulose or woody fibre, while the oxygen returns to the atmosphere in the form of gas. The equivalent of the sunlight which has been absorbed is to be sought in the chemical energy of the separated constituents. When we burn petroleum —586] Dark Lines of the Spectrum 569 or coal, we reproduce, in some sense, the light which the sun has expended in former ages in the production of a primeval vegetable growth. The researches of Bunsen and Roscoe show that whenever chemical action is induced by light, an absorption of light takes place, preferably of the more refrangible parts of the spectrum. Thus, when chlorine and hydrogen unite, under the action of light, to form hydrochloric acid, light is absorbed, and the quantity of chemically active rays consumed is directly proportional to the amount of chemical action. There is a curious difference in the action of the different spectral rays. Moser placed an engraving on an iodised silver plate and exposed it to the light, until an action had commenced, and then placed it under a violet glass in the sunlight. After a few minutes a picture was seen with great distinct- ness, while when placed under a red or yellow glass it required a very long time, and was very indistinct. When, however, the iodised silver plate was first exposed in a camera obscura to blue light for two minutes, and was then brought under a red or yellow glass, an image quickly appeared, but not when placed under a green glass. It appears as if there are vibrations of a certain velocity which could commence an action, and that there are dthers which are devoid of the property of commencing, but can continue and complete an action when once set up. Becquerel, who discovered these properties in luminous rays, called the former exc7ztiéng rays and the latter continuing or phosphorogenic rays. The phosphorogenic rays, for instance, have the property of rendering certain objects self-luminous in the dark after they have been exposed for some time to the hght. 586. Dark lines of the spectrum.—The colours of the solar spectrum are not continuous. For several grades of refrangibility rays are wanting, and, in consequence, throughout the whole extent of the spectrum there are a great number of very narrow dark lines. To observe them, a pencil of solar rays is admitted into a darkened room, through a narrow slit. At a distance of three or four yards we look at this slit through a prism of flint glass, which must be very free from flaws, taking care to hold its edge parallel to the slit. We then observe a great number of very delicate dark lines parallel to the edge of the prism, and at very unequal intervals. The existence of the dark lines was first observed by Wollaston in 1802 ; but Fraunhofer, a celebrated optician of Munich, first studied and gave a detailed description of them. Fraunhofer mapped the lines, and indicated the most marked of them by the letters A, a, B, C, D, E, 4, F, G, H ; they are therefore generally known as Fraunhofer’s lines. The dark line A (see fig. 11 of Plate I.) is at the middle, and B halfway between this and the end of the red portion ; C, at the boundary of the red and orange ; D is in the yellow region ; E, in the green ; F, in the blue ; G, in the indigo ; H, in the violet. There are certain other noticeable dark lines, such as a in the red and @ in the green. In the case of sunlight the positions of the dark lines are fixed and definite ; on this account they are used for obtaining an exact determination of the refractive index of a transparent substance (550) for each colour ; only in this way is it possible accurately to define a colour ; for example, the refractive index of the blue ray is, strictly speaking, that of the dark line F. In the spectra of artificial lights, and of the stars, the relative positions of -the dark lines are changed. In the electric 570 On Light [586— light the dark lines are replaced by brilliant lines. In coloured flames—that is to say, flames in which certain chemical substances undergo evaporation —the dark lines are replaced by very brilliant lines of light, which differ for different substances. _ Lastly, some of the dark lines are constant in position and distinctness, such as Fraunhofer’s lines ; but some of the lines only appear as the sun nears the horizon, and others are strengthened. They are also influenced by the state of the atmosphere. The fixed lines are due to the sun; the variable lines have been proved by Janssen and Secchi to be due to the aqueous vapour in the air, and are called atmospheric or telluric lines. Fraunhofer counted in the spectrum more than 600 dark lines, more or less distinct, distributed irregularly from the extreme red to the extreme violet ray. Brewster counted 2,000. By causing the refracted rays to pass successively through several analysing prisms (588), not merely has the existence of 3,000 dark lines been ascertained, but several which had been supposed to be single have been shown to be compound. Thollon produced a spectrum I5 metres in length in which were 4,000 dark lines. 587. Applications of Fraunhofer’s lines.—Subsequently to Fraunhofer, several physicists studied the dark lines of the spectrum.. In 1822 Sir J. Herschel remarked that by volatilising substances in a flame a very delicate means is afforded of detecting certain ingredients by the bright lines they produce in the spectrum ; and Fox Talbot in 1834 suggested optical analysis as probably the most delicate means of detecting minute portions of a substance. To Kirchhoff and Bunsen, however, is really due the merit of basing a method of analysis on the observation of the lines of the spectrum. They ascertained that the salts of the same metal, when introduced into a flame, always produced lines identical in colour and position, but that lines different in colour, position, or number were produced by different metals ; and finally, that an exceedingly small quantity of a metal suffices to disclose its existence. Hence has arisen a new and powerful method of analysis, known by the name of spectrum analysts. 588. Spectroscope.—The name of spectroscope has been given to the apparatus employed by Kirchhoff and Bunsen for the study of the spectrum. One of the forms of this apparatus is represented in fig.556. It is composed of three telescopes mounted on a common foot, whose axes converge towards a prism, P, of flint glass. The telescope A is the only one which can turn round the prism. It is fixed in any required position by a clamping screw #7. The screw-head 7 is used to focus the eyepiece. The screw-head m serves to change the inclination of the axis. To explain the use of the telescopes B and C we must refer to fig. 557, which shows the passage of the light through the apparatus. The rays. emitted by the flame G fall on the lens a, and are caused to converge to a point 4, which is the principal focus of a second lens c. Consequently the pencil, on leaving the telescope B, is formed of parallel rays (564). This pencil enters the prism P. On leaving the prism the light is decomposed, and in this state falls on the lens x By this lens x a real and reversed image of the spectrum is formed at z. This image is seen by the observer through a magnifying glass, which forms at ss’ a virtual image of the spectrum magni- fied about eight times. ; —588] Spectroscope | 57a The telescope C serves to measure the relative distances of the lines of the spectrum. For this purpose a micrometer is placed at 7, divided Fige 556 into 25 equal parts. A micrometer is formed thus :—A scale of 250 milli- metres is divided with great exactness into 25 equal parts. A photo- Fig. 557 graphic negative on glass of this scale is taken, reduced to 15 millimetres. The negative is taken because then the scale is light on a dark ground. The scale is then placed at m in the principal focus of the lens e ; 572 On Light [588— consequently, when the scale is lighted by the candle F, the rays emitted from it leave the lens ¢ in parallel pencils ; a portion of these, being reflected from a face of the prism, passes through a lens x, and forms a perfectly distinct image of the micrometer at z, thereby furnishing the means of measuring exactly the relative distances of the different spectral lines. The micrometric telescope C (fig. 556) is furnished with several adjusting screws, Zz, 0, ~; of these, z adjusts the focus ; 0 displaces the micrometer in the direction of the spectrum laterally ; vy raises or lowers the micrometer, Fig. 558 which it does by giving different incli- nations to the peestane The opening whereby the light of the flame G enters the telescope B consists of a narrow vertical slit, which can be opened more or less by causing the movable piece a to advance or recede by means of the screw v (fig. 558). When, for purposes of comparison, the spectra of two flames are to be examined simultaneously, a small prism, whose refracting angle is 60°, is placed over the upper part of the slit. Rays from one of the flames, H, fall at right angles on one face of the prism ; they then experience total reflection on a second face, and leave the prism by the third face, and in a direction at right angles to that face. By this means they pass into the telescope in a direction parallel to its axis, without in any degree mixing with the rays which proceed from the second flame, G. Consequently the two pencils of rays traverse the prism P (fig. 557), and form two horizontal spectra, which are viewed simultaneously through the telescope A. In the flames G and H are platinum wires, e, e’. These wires have been dipped beforehand into solutions of the salts of the metals on which experiment is to be made ; and the vaporised metals of these salts give rise to definite lines. Each of the flames G and H is a jet of ordinary gas. The apparatus through which the gas is supplied is known as a Bunsen’s burner. The gas comes through the hollow stem & (fig. 556). At the lower part of this there is a lateral orifice which admits air to support the combustion of the gas. This orifice can be more or less closed by a small diaphragm, which acts as a regulator. If we allow a moderate amount of air to enter, the gas burns with a luminous flame, and the lines are obscured. But if a strong and steady current of air enters, the carbon is rapidly oxidised, the flame loses its brightness, and burns with a pale blue light, but with an intense heat. In this state it no longer yields a spectrum. If, however, a metallic salt is in- troduced either in a solid state or in a state of solution, the spectrum of the metal makes its appearance, and in a fit state for observation. There are three chief types of spectra; the continuous spectra, or those furnished by incandescent solids and liquids (fig. 1, Plate I.) ; the dand or |42ze spectrum, consisting of a number of bright lines, and produced by incandescent gases or vapours ; and adsorption spectra, such as those fur- nished by the sun or fixed stars. For an explanation of these see art. 591 Moy —589] Direct Viston Spectroscope 573 Bodies at a red heat give only a short spectrum, extending at most to the orange; as the temperature gradually rises, yellow, green, blue, and violet successively appear, while the intensity of the lower colours increases. Instead of the prism very pure spectra may also be obtained by means of a grating (661). For more detailed investigations of the spectral lines a ¢vazz of prisms is used. Fig. 559 repre- sents one with nine prisms. The light issuing from’ the collimeter A passes in succession through each of the prisms. As the successive deviations add themselves the dis- persion is very much increased, and } a spectrum of great extent is ob- tained. It is, however, feebly lumi- nous, owing partly to its extension, and partly to the loss of light which is observed through the telescope B, which it undergoes in traversing all these refracting surfaces. In the case of ten prisms the loss of light has been found to amount to ninety-nine per cent. Christie has used with advantage a semt-prism obtained by cutting an isosceles prism by a plane at right angles to the base. These semi- prisms have the advantage that they produce as much dispersion as with several prisms without any appreciable loss in the sharpness of the images ; and without that absorption of light which in the case of a number of prisms is so very considerable. 589. Direct vision spectroscope.—Prisms may be combined so as to get rid of the dispersion without entirely destroying the refraction (596) ; they may, conversely, be combined so that the light is not re- fracted, but is decom- posed and produces a spectrum. | Combina- tions ‘of prisms of this kind are used in what are called direct vision spectroscopes. Fig. 560 repre- sents the section of such an instrument in about 3 the natural size. A system of two flint and three crown-glass prisms is placed in a tube which moves in a second one; at the end of this is an aperture 9, and inside it a slit the width of which can by a special arrangement be regulated by simply turning aring 7 A small achromatic lens is introduced at aa, the focus of which is just outside the slit, so that the rays pass through the train of prisms, and the eye at e sees a virtual image of the slit opened out into a spectrum. Such combinations have the disadvantage of absorbing much light. On passing from one medium into another some light is always lost by Fig. 5590 Fig. 560 574 On Light [589— reflection. This is less the nearer are the refraction indices of the media. Wernicke has constructed a direct vision prism in which the loss of light is greatly reduced. It consists of two prisms of crown glass and glass plates as shown in the figure 561, the hollow space formed is filled with cinnamic ether, which, while it has but a slightly larger refractive index, has three or four times the dispersion of crown glass. . The reversion spectroscope contains two Hie see equal systems of direct vision prisms ar- ranged close to each other, but reversed, so that two spectra are obtained with the colours in opposite order. By suitable micrometric movement of a split lens, the two spectra may be moved apart or nearer each other. Hence it is possible to bring any two identical lines so that they are in the same vertical line. If now the position of these lines in the spectrum is altered, the displacement will take place in the opposite direction in the two spectra, and will therefore be twice as distinct. 590. Experiments with the spectroscope.—The coloured plate at the beginning shows certain spectra observed by means of the spectroscope. No. I represents the continuous spectrum. No. 2 shows the spectrum of sodium. The spectrum contains neither red, orange, green, blue, nor violet. It is marked by a very brilliant yellow ray in exactly the same position as Fraunhofer’s dark line D. Of all metals sodium is that which possesses the greatest spectral sensibility. In fact, it has been ascertained that one two-hundred-millionth of a grain of sodium is enough to cause the appearance of the yellow line. Consequently it is very difficult to avoid the appearance of this line. A very little dust produced in the apartment is enough to produce it—a circumstance which shows how abundantly sodium is distributed. No. 3 is the spectrum of /zthzuwm. It is characterised by a well-marked line in the red called Lia, and by the feebler orange line Lif. Nos. 4 and 5 show the spectra of ces¢um and rubidium, metals discovered by Bunsen and Kirchhoff by means of spectrum analysis. ‘The former is distinguished by two blue lines, Csa and Cs@ ; the latter by two very brilliant dark red lines, Rby and Rbé, and by two less intense violet lines, Rba and Rb8. A third metal, thallium, has been discovered by the same method by Sir W. Crookes in England, and independently by Lamy in France. Thallium is characterised by a single green line. Subsequently to this Richter and Reich discovered in association with zinc a new metal which they call zzd@zum from a couple of characteristic lines which it forms in the indigo ; and recently Boisbaudran has discovered a new metal which he calls gallium associated with zinc in very minute quantities ; and in more recent times germanium, scandium, samarium, and helium have been discovered. The extreme delicacy of the spectrum reactions, and the ease with which they are produced, constitute them a most valuable help in the qualitative analysis of the alkalies and alkaline earths. It is sufficient to place a small portion of the substance under examination on platinum wire as represented ‘in fig. 555, and compare the spectrum thus obtained either directly with that —590] Experiments with the Spectroscope 575 of another substance or with the charts in which the positions of the lines produced by the various metals are laid down. With other metals the production of their spectra is more difficult, especially in the case of some of their compounds. The heat of a Bunsen’s burner is insufficient to vaporise the metals, and a higher tempera- ture must be used. This is obtained by taking electric sparks between wires consisting of the metal whose spectrum is required, and the electric sparks are most conveniently obtained by means of Ruhmkorff’s coil. In order to investigate solutions of salts the apparatus shown in fig. 562 is used. A platinum wire is fixed in the bottom, and over one end a small conical glass tube D is placed ; only so much solution is poured in that by capillary action it just rises to the top of D. Another glass tube fused in a platinum wire is fixed in the cork C, and its free end can be placed at any distance from D. Thus all the metals may be brought within the sphere of spectrum observation. The dispersive power of the apparatus has great influence on the nature of the spectrum; while an apparatus with one prism only gives in a sodium flame the well-known yellow line, an apparatus with more prisms resolves it into two or three lines. It has been observed that the character of the spectrum changes with the temperature ; thus chloride of lithium in the flame of a Bunsen’s burner gives a single intense peach-coloured line; in a hotter flame, as that of hydrogen, it gives an additional orange line; while in the oxyhydrogen jet or the voltaic arc a broad brilliant blue band comes out in addition. The sodium spectrum produced by a Bunsen’s burner consists of a single yellow line; if, by the addition of oxygen, the heat is gradually increased, more bright lines appear; and with the aid of the oxyhydrogen flame the spectrum is continuous. Sometimes also, in addition to the appearance of new lines, an increase in temperature resolves those bands which exist into a number of fine lines, which in some cases are more and in some less refrangible than the bands from which they are formed. It may be supposed that the glowing vapour formed at the low temperature consists of the oxide of some difficultly reducible metal, whereas at the enormously high temperature of the spark these compounds are decomposed, and the true bright lines of the metal are formed. The delicacy of the reaction increases very considerably with the tem- perature. With the exception of the alkalies, it is from 40 to 400 times greater at the temperature of the electric spark than at that of Bunsen’s burner. The spectra of the permanent gases are best obtained by taking the electric spark of a Ruhmkorff’s coil, or Holtz’s machine, through glass tubes of a special construction, consisting of two wide ones connected by a capillary tube (fig. 563), which in the wider parts are provided with electrodes of platinum or aluminium ; they are filled with the gas in question in a state of great attenuation, and are usually known as Ge?ssler’s tubes ; if the spark is passed through hydrogen, the light emitted is bright red, and its spectrum consists of one red, two blue lines, No. 7, the first two of which appear to Fig. 562 576 On Light . [590- coincide with Fraunhofer’s lines C and F, and the third with a line between F and G. No. 6 represents the spectrum of oxygen. No. 8 is the spectrum of nitrogen. The light of this gas in a Geissler’s tube is purple, and the spectrum very complicated. If the electric discharge takes place through a compound gas or vapour, the spectra are those of the elementary constituents of the gas. It seems as if, at very intense temperatures, chemical combination were impossible, and oxygen and hydrogen, chlorine and the metals, could coexist in a separate form, as though mechanically mixed with each other. The nature of the spectra of the elementary gases is very materially in- fluenced by alterations of temperature and pressure. Wiillner made a series of very accurate observations on the gases oxygen, hydrogen, and nitrogen. He not only used gases in closed tubes, which by various electrical means a he raised to different temperatures ; but in one and the same ; series of experiments, in which a small induction coil was used, i he employed pressures varying from 100 millimetres to a frac- | tion of a millimetre ; while in another series, in which a larger lila, @pparatus was used, he extended the pressure to 2,000 milli- metres. At the lowest pressure of less than one millimetre, the spectrum of hydrogen was found to be green, and consisting of six splendid groups of lines, which at a higher pressure than iC 1 millimetre changed to continuous bands ; at 2 to 3 millimetres | the spectrum consisted of the often-mentioned three lines, il which did not disappear under a higher pressure, but gradually became less brilliant as the continuous spectrum increased in extent and lustre. From this point the light, and therefore the spectrum, became feebler. Using the larger apparatus, the band spectrum appeared only under a higher pressure ; at the highest pressure of 2,000 millimetres it gave place to the con- tinuous spectrum, since the bright lines continually extended and ultimately merged into each other. 591. Explanation of the dark lines of the solar spectrum.— It has been already seen that incandescent sodium vapour gives a bright yellow line corresponding to the dark line D of the solar spectrum. Kirchhoff found that, when the brilliant light produced by incandescent lime passes through a flame coloured by sodium in the usual manner, a spectrum is pro- duced in which is a dark line coinciding with the dark line D of the solar spectrum ; what would have been a bright yellow line becomes a dark line when formed on the background of the limelight. By allowing in a similar manner the limelight to traverse vapours of potassium, barium, strontium, &c., the bright lines which they would have formed were found to be converted into dark lines : such spectra are called adsorption spectra. It appears, then, that the vapour of sodium has the power of absorbing rays of the same refrangibility as those which it emits. And the same is true of the vapours of potassium, barium, strontium, &c. This absorptive power is by no means an isolated phenomenon. These substances share it, for ex- ample, with the vapour of nitrous acid, which Brewster found to possess the —— —591] Explanation of Dark Lines of Solar Spectrum 577 following property :—when a tube filled with this vapour is placed in the path of the light either of the sun or of a gas flame, and the light is subsequently decomposed by a prism, a spectrum is produced which is full of dark lines (No. 9, Plate I.) ; and Miller showed that iodine and bromine vapour pro- duced analogous effects. Hence the origin of the above phenomenon is, doubtless, the absorption by the sodium vapour of rays of the same kind—that is, having the same refrangibility—as those which it has itself the power of emitting. Other rays it allows to pass unchanged, but these it either totally or in great part sup- presses. Thus the particular lines in the spectrum to which these rays would converge are illuminated only by the feebly luminous sodium flame, and accordingly appear dark by contrast with the other portions of the spectrum which receive light from the powerful flame behind. By replacing one of the flames G and H (fig. 558) by a pencil of sunlight reflected from a heliostat, Kirchhoff ascertained by direct comparison that the bright lines which characterise iron correspond to dark lines in the solar spectrum. He also found the same to be the case with sodium, magnesium, calcium, nickel, and some other metals. This reversal of the sodium light may be pro- duced even without a prism by an apparatus devised by Bunsen, and shown in fig. 564. It consists of a Woolf’s bottle in which a small quantity of zinc, dilute sulphuric acid, and com- mon salt are placed so that hydrogen is slowly liberated, charged with particles of sodium chloride, or, better, bromide. Through the india- rubber tube L ordinary coal gas is admitted, and issues through the tubes Rand R’. On each of these tubes is a metal burner. The gas burns at the top A with a broad flat flame, C ; the burner B is cylindrical, and over it is placed a conical mantle closed at the top with wire gauze. In this way a small yellow flame is produced. On looking through this against the wide flame, the former appears dark, as if smoky on a light background. The light of the posterior and far brighter flame is absorbed by the front and cooler one, and replaced by light of lesser intensity, which thus appears dark by contrast. From such observations we may draw im- portant conclusions with respect to the consti- , tution of the sun. Since the solar spectrum has . ics u64 dark lines where sodium, iron, &c., give bright ones (No. 11, Plate I.), it is probable that around the solid, or more probably liquid, body of the sun which throws out the light, there exists a vaporous envelope which, like the sodium flame in the experiment described above, absorbs certain rays ; namely, those which the envelope itself emits. Hence pat fs § % 4 g % Ke E % % & & f i * i i % he % % 578 On Light [591- those parts of the spectrum which, but for this absorption, would have been illuminated by these particular rays, appear feebly luminous in com- parison with the other parts, since they are illuminated only by the light emitted by the envelope, and not by the solar nucleus ; and we are at the same time led to conclude that in this vapour there exist the metals sodium, iron, &c. Sir W. Huggins and Miller applied spectrum analysis to the investigation of the heavenly bodies. The spectra of the moon and planets, whose light is reflected from the sun, give the same lines as those of the sun. Uranus proves an exception to this, and is probably still in a self-luminous condition. The spectra of the fixed stars contain, however, dark lines differing from the solar lines, and from one another. Four distinct types of spectra were distinguished by Secchi. The first embraces the white stars, and includes the well-known Sirius anda Lyre. Theirspectra (No. 12, Plate I.) usually contain a number of very fine lines, and always contain four broad dark lines which coincide with the bright lines of hydrogen. Out of 346stars 164 were found to belong to this group. The second group embraces those having spectra intersected by numerous fine lines like those of our sun. About 140 stars, among them Pollux, Capella, @ Aquilz, belong to this group. The third group embraces the red and orange stars, such as a Orionis, 8 Pegasi; the spectra of these (Nos. 13, 14, Plate I.) are divided into eight or ten parallel columnar clusters of dark and bright bands increasing in intensity to the red. Group four is made up of small red stars with spectra constructed of three bright zones increasing in intensity towards the violet. It would thus appear that these fixed stars, while differing from one another in the matter of which they are composed, are constructed on the same general plan as our sun. Huggins has observed a striking difference in the spectra of the nebule ; where they can at all be observed they are found to consist generally of bright lines, like the spectra of the ignited gases, instead of, like the spectra of the sun and stars, consisting of a bright ground intersected by dark lines. It is hence probable that the nebule are masses of glowing gas, and do not consist, like the sun and stars, of a photosphere surrounded by a gaseous atmosphere. We can apply the reasoning of Doppler’s principle (236) to the case of light, and assume provisionally that the motion of light is analogous to that of sound. When a source of light is approaching the earth, the eye receives a greater number of waves in a given time than when there is no relative motion, the waves are shorter ; as it moves away the opposite is the case, the waves are longer. Hence, on the approach of yellow light, for instance, the bright band D will.seem displaced towards the violet end of the spectrum, and as it recedes, towards the red end. This will also be the case with the corresponding dark line, proving that the whole medium is moved at the same time. Accordingly, by observing the displacement of particular lines, conclusions may be drawn as to the relative motions of what are called the fixed stars. Thus, from careful observation of the displacement of the F line in Sirius, Huggins has inferred that it is moving away from the earth with a velocity of 42 miles per second. One of the most interesting triumphs of spectrum analysis has been the discovery of the true nature of the protuberances which appear during a ~592] Uses of the Spectroscope 579 solar eclipse as mountains or cloud-shaped luminous objects varying in size, and surrounding the moon’s disc. During the eclipse of 1868 it had been ascertained by Janssen that pro- tuberances emitted certain bright lines coinciding with those of hydrogen. They have, however, been fully understood only since Sir Norman Lockyer and Janssen have discovered a method of investigating them at any time. The principle of this method is as follows :—When a line of hight admitted through a slitis decomposed by a prism, the length of the spectrum may be increased by passing it through two or more prisms ; as the quantity of light is the same, it is clear that the intensity of the spectrum will be diminished. This is the case with the ordinary sources of light, such as the sun; if the light be homogeneous, it will be merely deviated, and not reduced in intensity, by dispersion. And if the source of light emit light of both kinds, the image of the slit of light of a definite refrangibility, which the mixture may contain, will stand out, by its superior intensity, on the weaker ground of the con- tinuous spectrum. This is the case with the spectrum of the protuberances. Viewed through an ordinary spectroscope, the light they emit is overshadowed by that of the sun ; but by using prisms of great dispersive power the sun’s light becomes weakened, and the spectrum of the protuberances may be observed. Lockyer’s researches leave no doubt that they are ignited masses of gas, principally hydrogen. By altering the position of the slit a series of sections of the prominences is obtained, by collating which the form of the prominence may be inferred. They are thus found to enclose the sun usually to a depth of about 5,000 miles, but sometimes in enormous local accumulations, which reach the height of 70,000 miles. Lockyer has not merely examined these phenomena right on the edge of the sun, but he has been able to observe them on the disc itself. He has shown that some of these protuberances are the results of sudden outbursts or storms, which move with the enormous velocity of 120 miles in a second ; and, by reasoning as above, the direction of this motion has been determined. For a fuller account of this branch of physics, which is incompatible with the limits of this work, the reader is referred to special works. 592. Uses of the spectroscope.—When a liquid placed in a glass tube or in a suitable glass cell is interposed between a source of light and the slit of the spectroscope, the spectrum observed on looking through the telescope will in many cases be found to be traversed by dark bands. No. to, Plate I., represents the appearance of the spectrum when a solution of chlorophy/, the green colouring matter of plants, is thus interposed. In the red, the yellow, and the violet parts, dark bands are formed, and the blue gives way to a reddish shimmer. If, instead of chlorophyll, arterial blood greatly diluted be used, the red of the spectrum appears brighter, but green and violet are nearly extinguished. As these bands thus differ in different liquids as regards position, breadth, and intensity, in many cases they afford the most suitable means of identifying bodies. Sorby and Browning devised a combination of the microscope and spectroscope called the mzcrospectroscope, which renders it possible to examine even very minute traces of substances. This application of the spectroscope has been very useful in investigating substances which have special importance in physiology and pathology ; PP2 580 On Light [592— thus in examining normal and diseased blood, and in ascertaining the rate at which certain substances pass into the various fluids of the system. The characteristic absorption bands which certain liquids, such as wine, beer, &c., present in their normal state, compared with those yielded by adulterated substances, furnish a delicate and certain means of detecting the latter. Thus the adulteration of claret with the juice of elderberries is detected by the appearance of faint bands near line D, which are not seen with pure red wine. The colouring matter of malt and hops is quite distinct from that of many other substances with which it is alleged to be adulterated. An alkaline solution of blood to which ammonium sulphide is added, gives two very powerful absorption bands between D and E, and between Eand0 ; this is the most valuable test for toxicological cases. Blood charged with carbonic oxide is unchanged on the addition of ammonium sulphide, and thus poisoning by carbonic oxide can be detected. So, too, the appear- ance of the characteristic bands of gall in blood, and of albumen in urine, are indications of jaundice and of Bright’s disease respectively. Suppose the slit of the spectroscope be divided into two halves, Ss, and s, (fig. 565), the aperture of each of which can be varied to any measured extent by means of micrometric screws. If then a layer of a substance of known thickness be placed in front of the slit s,, for instance, and the spectrum of a _| particular portion be observed, there will be a i! difference between the luminosities of the two parts of the spectrum ; but by regulating the width of the slit they may be made the same. The lumi- nosities will then be inversely as the width of the slit. Thatis, if the width of each were originally 1, and the uncovered slit had to be narrowed to o°4, the intensity of the light transmitted through the screen would only be o-4 of the incident. Vierordt has based on this a method of quantitative spectrum analysis; thus if the absorption produced by a definite thickness of a solution of known strength be known, the relative concentration of any other solution of the same substance for the same thickness may be determined. 593. Abnormal or anomalous dispersion.—A remarkable exception to the ordinary law of dispersion was discovered by Christiansen, and subsequently confirmed and extended by Soret and Kundt—that the solutions of certain substances, such as indigo and potassium permanganate, give spectra in which the order of the colours is not I [ilfiest «fy dalek ly nach 2 ules ar Wie ae |} the same as in the prismatic Gite FH B C D spectrum. Thus, when a hollow ' glass prism is filled with an TL Poe a ee ee en alcoholic solution of fuchsine, Bam Ci Ds i Ir G H the order of the colours in the Fig. 566 spectrum which it yields is as follows. Violet is /eas¢ refracted, then red, and then yellow, which is vos¢ refracted. If we imagine that the central green of an ordinary spectrum is removed, and then the position of the rest is inverted, we get. an idea of the aunoeual spectrum of fuchsine. This will be seen from fig. 566, in which I represents the position of Fraun- Ie Ty bi | —594] Fluorescence 581 hofer’s lines in the anomalous dispersion of fuchsine, while II represents the position in the normal spectrum. Kundt examined a great number of substances in this direction, mostly the colours derived from aniline, and found that the abnormal dispersion is exhibited by all substances with surface colour. These bodies have the peculiarity that when viewed in diffused light they exhibit a colour complementary to that which they transmit. Thus a thin flake of fuchsine appears green in diffused, but red in transmitted light. Metallic gold appears green in transmitted and reddish yellow by reflected light. The substances in solution are examined by placing them in hollow glass prisms ; if the solutions are weak, the abnormal dispersion of the substance is concealed by that of the solvent, while stronger solutions absorb so much light as to be almost opaque, and prisms of very small refracting angle have to be used. Soret gets rid of this difficulty by immersing the prism contain- ing the solution in glass vessels with parallel sides filled with the solvent. The dispersion due to the solvent is thereby eliminated, and only that of the substance comes into play. Cyanine gives a well-marked abnormal spec- trum, the order of the colours being the following: green, light blue, dark blue, a dark space, red, and traces of orange, the green being the colour which is least refracted. Anomalous dispersion is met with in gases which have marked absorption bands ; thus in iodine for red light 7 = 100205, and for violet = 1°00192. The same explanation cannot be given of this as of the ordinary colour of bodies (581), but the phenomenon must be ascribed to the fact that the bodies in question totally reflect light of certain wave-lengths (651) at almost all incidences, and that these colours are reflected on the surface. Hence it follows that the colour of these bodies in diffused light must be almost com- plementary to the transmitted light—a prevision which experiment confirms. 594. Fluorescence.—Stokes made the remarkable discovery that under certain circumstances the rays of light are capable of undergoing a change of refrangibility. The discovery originated in ey the study of a phenomenon observed by Lb lisp, Brewster, and by Herschel, that some varieties MtEE SE fy of fluorspar, and also the solutions of certain LH IL substances, when looked at by transmitted hght Rts // appear colourless, but when viewed in reflected ALE f light present a bluish appearance. Stokes has found that this property, which he calls fzor- escence from having been observed in fluorspar, is characteristic of a large number of bodies. If by means of a lens of long focus, prefer- ably of quartz, a beam of the sun’s rays is focussed on a solution of quinine sulphate con- tained in a glass trough, a beautiful cerulean blue cone of light (fig. 567) is formed, which is much the brightest on the surface, and the intensity of which rapidly diminishes as it penetrates the liquid. It thus appears that fluorescence is due to an absorption of certain rays ; rays of light which have passed through a sufficient thickness of a fluorescent E = E Ee = FE iz = A= (= = Zz EEE KQKQKKKKUXKcuss Fig. 567 ZZ 582 On Light [594- substance lose thereby the power of exciting fluorescence when they are passed through a second layer of the same substance ; thus a test tube con- taining a fluorescent liquid is brightly luminous when exposed to the sun’s rays, but loses this lustre at once when it 1s dipped in a trough of the same liquid, on the front of which the sun’s rays fall. This also results from a comparison of the absorption spectrum of a fluorescent substance with the appearance presented by this substance when the spectrum falls on it. When the fluorescence begins there also begins the absorption, and to a maximum of absorption corresponds a maximum of fluorescence. The phenomenon is seen when a solution of quinine sulphate, con- tained in a trough with parallel sides, is placed in different positions in the solar spectrum. No change is observed in the less refrangible part of the spectrum, but from about the middle of the lines G and H (coloured Plate) to some distance beyond the extreme range of the violet, rays of a beautiful sky-blue colour are seen to proceed. These invisible ultra-violet rays also become visible when the spectrum is allowed to fall on paper impregnated with a solution of @sculine (a substance extracted from horse-chestnut), an alcoholic solution of stramonium, or a plate of canary glass (which is coloured by means of uranium). If light be allowed to fall on paper impregnated with barium platinomanganide, a beautiful green fluorescence is observed. If a few drops of a strong solution of flworesceine in soda fall into a large beaker of water on the front of which the sun’s rays fall, beautiful fluorescent clouds are first produced, and on shaking the liquid the whole vessel fluoresces with a bright green light. This change arises from a diminution in the refrangibility of those rays outside the violet, which are ordinarily too refrangible to affect the eye. Glass absorbs many of these more refrangible rays, which is not the case nearly to the same extent with quartz. When a prism and trough formed of quartz are used, and the spectrum is received on a sheet of paper on which a wash of solution of quinine sulphate has been made, two juxtaposed spectra can be obtained. That which is on the part coated with quinine sulphate extends beyond the line H to an extent equal to that of the visible spectrum. In the spectrum, thus made visible, dark lines may be seen analogous to those in the ordinary spectrum. The phenomena may be observed without the use of a prism. When an aperture in a dark room is closed by means of a piece of blue glass, and the light is allowed to fall upon a piece of canary glass, it instantly appears self- luminous from the emission of the altered rays. If a test tube is half filled with a solution of quinine sulphate, and on it is poured a freshly pre- pared solution of chlorophyl in ether, the two layers appear colourless and green respectively in transmitted, and sky-blue and blood-red in reflected light. In most cases it 1s the violet and ultra-violet rays which undergo an alteration of refrangibility, but the phenomenon is not confined to them. A decoction of madder in alum gives yellow and violet light from about the line D to beyond the violet ; an alcoholic solution of chlorophyl gives red light from the line B to the limit of the spectrum. In these cases the yellow, the green, and the blue rays experience increase of refrangibility ; the change produces more highly refrangible rays. An exception to this rule —596] Chromatic Aberration 583 is met with in the case of Magdala red. If on a solution of this substance contained in a rectangular glass vessel a solar spectrum is allowed to fall, an orange-yellow fluorescence is found even in the red part of the spectrum. The electric light gives a very remarkable spectrum. With quartz apparatus Sir G. Stokes obtained a spectrum six or eight times as long as the ordinary one. Several flames of no great illuminating power emit very peculiar light. Characters traced on paper with solution of stramonium, which are almost invisible in daylight, appear instantaneously when illu- minated by the flame of burning sulphur or of carbon bisulphide. Robinson found that the light of the aurora is peculiarly rich in rays of high refrangibility. 595. Chromatic aberration.—The various lenses hitherto described (563) possess the inconvenience that, when at a certain distance from the eye, they give images with coloured edges. This defect, which is most observable in condensing lenses, is due to the unequal refrangibility of the simple colours (576), and is called chromatic aberration. For, since a lens may be compared to a series of prisms with infinitely small faces, and united at their bases (563), it not only refracts light, but also decomposes it like a prism. On account of this dispersion, therefore, lenses have really a distinct focus for each colour. In condensing lenses, for example, the red rays, which are the least refrangible, form their focus ata point R on the axis of the lens, (fig. 568) ; while the violet rays, which are most refrangible, coincide in the nearer point V. The foci of the orange, yellow, green, blue, and indigo are be- tween these points. The chro- matic aberration is more per- ceptible in proportion as the Fic. 568 lenses are more convex, and as the point at which the rays are incident is farther from the axis ; for then the deviation, and therefore the dispersion, are increased. If a pencil of rays which has passed through a condensing lens is received on a screen placed at 7 within the focal distance, a bright spot is seen with a red border ; if it is placed at ss, the bright spot has a violet border. The inequality in the refraction of the blue and red rays may be demon- strated by closing’a small aperture, half with red and half with blue glass (fig. 569) ; on each half a black arrow is painted, and a lamp is placed behind it. By means of a lens of 60 cm. focus an image is formed on a screen at a dis- tance of about 2 metres. If the screen is placed so that a sharp image is obtained of the black object on the blue ground, the outlines of the other are confused. To get a sharp image of the arrow on the red ground the screen must be moved farther away. 596. Achromatism.—By combining prisms which have different refracting angles (556), and are formed of substances of 584 On Light [596— unequal dispersive powers (576), white light may be refracted without being dispersed. The same result is obtained by combining lenses of different substances, the curvatures of which are suitably combined. The images of objects viewed through such lenses do not appear coloured, and they are accordingly called achromatic lenses ; achromatism being the term applied to the phenomenon of the refraction of light without decomposition. By observing the phenomenon of the dispersion of colours in prisms of water, of oil of turpentine, and of crown glass, Newton was led to suppose that dispersion was proportional to refraction. He concluded that there could be no refraction without dispersion, and, therefore, that achromatism was impossible. Almost half a century elapsed before this was found to be incorrect. Hall, an English philosopher, in 1733, was the first to construct achromatic lenses, but he did not publish his discovery. It is to Dollond, an optician in London, that we owe the greatest improvement which has been made in optical instruments. He showed in 1757 that by combining two lenses—one a double convex crown glass lens, the other a concavo- convex lens of flint glass (fig. 571)—a lens is obtained which is virtually achromatic. To explain this result, let two prisms, BFC and CDF, be joined and turned in a contrary direction, as shown in fig. 570. Let us suppose in the first case, that both prisms are of the same material, but that the refracting angle of the second, CDF, is less than the refracting angle of the first ; the two prisms will produce the same effect as a single prism, BAF ; that is to say, that white light which traverses it will be not only refracted, but also decomposed. If, on the contrary, the first prism BCF were of crown glass, and the other CFD of flint glass, the dispersion might be destroyed Fig. 570 without destroying the refraction. For, as flint glass is‘more-dispersive than crown, and as the dispersion produced by a prism diminishes with its refracting angle (576), it follows that by suitably lessening the refracting angle of the flint glass prism CFD, as compared with the refracting angle of the crown glass prism BCF, the dispersive power of these prisms may be equalised ; and as, from their position, the dispersion takes place in a contrary direction, it is neutralised ; that is, the emergent rays EO are parallel, and therefore give white light. Nevertheless, the ratio of the angles BCF and CFD, which is suitable for the parallelism of the red rays and violet rays, is not so for the intermediate rays, and, consequently, only two of the rays of the spectrum can be exactly combined, and the achro- j, ==, Matism is not quite perfect. To obtain perfect achromatism, = several prisms would be necessary, of unequally dispersive materials, and with their angles suitably combined. The refraction is not destroyed at the same time as the dis- rig es persion 3 that could only happen if the refracting power of a body varied in the same ratio as its dispersive power, which is not the case. Consequently, the emergent ray EO is not exactly parallel to the incident ray, and there is a refraction without appreciable decomposition. i Mh | \ ul —596] Achromatism 585 Achromatic lenses are made of two lenses of unequally dispersive materials : one, A, of flint glass, is a diverging concavo-convex (fig. 571) ; the other, B, of crown glass, is double convex, and one of its faces may exactly coincide with the concave face of the first. As with prisms, several lenses would be necessary to obtain perfect achromatism ; but for optical instruments two are sufficient, their curvatures being such as to combine not the extreme red and violet, but the blue and orange rays, while at the same time regard is had to the correction for spherical aberration. In Abbé’s afochromatic lenses the crown glass is replaced by fluorspar, and thereby the chromatic as well as the spherical aberration is still further reduced. 586 On Light [597.- CHARTERS V OPTICAL INSTRUMENTS 597. The different kinds of optical instruments.— By the term oftical Zastrument 1s meant any combination of lenses, or of lenses and mirrors. Optical instruments may be divided into three classes, according to the ends they are intended to answer, viz.: 1. Microscopes, which are designed to obtain a magnified image of any object whose real dimensions are too small to admit of its being seen distinctly by the naked eye. 1. Zelescofes, by which very distant objects, whether celestial or terrestrial, may be observed. iu. Jastruments designed to project on a screen a magnified or diminished image of any object which can thereby be either depicted or rendered visible to a crowd of spectators; such as the camera lucida, the camera obscura, photographic apparatus, the magic lantern, the solar microscope, the photo-electric microscope, &c. MICROSCOPES 598. The simple microscope.—The simple microscope, or magnifying glass, is merely a convex lens of short focal length, by means of which we look at objects placed between the lens and its principal focus. Let AB (fig. 572) be the object to be observed, placed between the lens and its principal focus, F. Draw the second- ary axes AO and BO, and also from A and B rays paral- lel to the axis of the lens FO. Now these rays, on pass- ing out of the lens, tend to pass through the second principal focus F’ ; Fig. 572 consequently they are divergent with reference to the secondary axes, and therefore, when produced, will cut those axes in A’ and B’ respectively. These points are the virtual foci of A and B respectively. The lens, therefore, produces at A’B’ an erect and magnified virtual image of the object AB. —599] The Simple Microscope — 587 The position and magnitude of this image depend on the distance of the object from the focus. Thus, if AB is moved to ad, nearer the lens, the secondary axes will contain a greater angle, and the image will be formed at a’b’, and will be much smaller, and nearer the eye. On the other hand, if the object is moved farther from the lens, the angle between the secondary axes is diminished, and their intersection with the prolongation of the re- fracted rays taking place beyond A’B’, the image is formed farther from the lens, and is larger. In a simple microscope both chromatic aberration and spherical aberra- tion increase with the degree of magnification. We have already seen that the former can be corrected by using achromatic lenses (596), and the latter by using stops, which allow the pas- sage of such rays only as are nearly parallel to the axis, the spherical aberration of these rays being nearly inappreciable. Spherical aberration may be still further corrected by using two plano-convex lenses, instead of one very con- vergent lens. When this is done, the plane face of each lens is turned towards the object (fig. 573). Although each lens is less convex than the simple lens which together they replace, yet their joint magnifying power is as great, and with a less amount of sphert- cal aberration, since the first lens diverts towards the axis the rays which fall on the secondlens. This combination of lenses is known as Wollaston’s doublet. There are many forms of the simple microscope. One of the best is that re- presented in fig. 574. On a horizontal support E, which can be raised and lowered by a rack K and pinion D, there is a black eyepiece m, in the centre of which is fitted a small convex lens. Below this is the stage 6, which is fixed, and on : which the object is placed between glass — plates. In orderto illuminate the object powerfully, diffused light is reflected from a concave glass mirror, M, so that the reflected rays fall upon the object. In using this microscope the eye is placed very near the lens, which is lowered or raised until the position is found at which the object appears in its greatest distinctness. 599. Conditions of distinctness of the images.—In order that objects looked at through a microscope should be seen with distinctness, they must have a strong light thrown upon them, but this is by no means enough. It is necessary that the image be formed at a determinate distance from the eye. In fact, there is for each person a distance of most distinct viston—a distance, that is to say, at which an object must be placed from an observer's », “i NE ny Ny le. ait Fig. 573 588 On Light [599- eye in order to be seen with greatest distinctness. This distance is different for different observers, but ordinarily is between 1o and 12 inches. It is, therefore, at this distance from the eye that the image ought to be formed. Moreover, this is why each observer has to focus the instrument ; that is, to adapt the microscope to his own distance of most distinct vision. This is effected by slightly varying the distance from the lens to the object, for we have seen above that a slight displacement of the object causes a great dis- placement of the image. With a common magnifying glass, such as is held in the hand, the adjustment is effected by merely moving it nearer to or farther from the object. In the microscope the adjustment is effected by means of a rack and pinion, which in the case of the instrument shown in fig. 573 moves the eyepiece, but moves the object in the case of the instrument depicted in fig. 574. What has been said about focussing the microscope applies equally to telescopes. In the latter instrument the eye- piece is generally adjusted with respect to the image formed in the focus of the object-glass. In respect of the distinctness of the image the general rules for convex lenses apply. In order to lessen dispersion, lenses have been constructed of diamond, of ruby, and of other precious stones, which for a small amount of dispersion have a great degree of refrangibility. A drop of water or of Canada balsam in a small hole in a thin piece of wood or of metal, acts as a microscope. 600. Apparent magnitude of an object.—The apparent magnitude or apparent diameter of a body is the angle it subtends at the eye of the Fig. 576 observer. Thus, if AB is the object, and O the observer's eye (figs. 575, 576), the apparent magnitude of the object is the angle AOB contained by two visual rays drawn from the centre of the pupil to the extremities of the object. In the case of objects seen through optical instruments, the angles which they subtend are so small that the arcs which measure the angles do not differ sensibly from their tangents. The ratio of two such angles is —-601] Measure of Magnification 589 therefore the same as that of their tangents. Hence we deduce the two following principles :— 1. When the same object ts seen at unequal distances, the apparent diameter varies inversely as the distance from the observer's eye. ll. [2 the case of two objects seen at the same distance, the ratio of the apparent diameters ts the same as that of their absolute magnitudes. These principles may be proved as follows :—i. In fig. 575, let AB be the object in its first position, and ad the same object in its second position. For the sake of distinctness these are represented in such positions that the line OC passes at right angles through their middle points C and c respec- tively. It is, however, sufficient that @ and AB should be the bases of isosceles triangles having a common vertex at O. Now, by what has been said above, AB is virtually an arc of a circle described with centre O and radius OC ; likewise aé is virtually an arc of a circle whose centre is O and radius Oc, Therefore, A Bhi gsm sls ad LOB GO =e TO OCGEOGd Therefore, AOB varies inversely as OC. ii. Let AB and A’B’ be two objects placed at the same perpendicular distance, OC, from the eye, O, of the observer (fig. 576). Then they are virtually arcs of a circle whose centre is O and radius OC. Therefore, AB , AB’ -f OB? = : ape OGemOC =AB:A/B’, a proportion which expresses the second principle. 601. Measure of magnification.—In the simple microscope the measure of the magnification produced is the ratio of the apparent diameter of the image to that of the object, both being at the distance of most distinct vision. The same rule holds good for other microscopes. It is, however, impor- tant to obtain an ex- pression for the mag- nification depending on data that are of easier determination. In fig. 577 let AB Fig, tre be the object, and A’B’ its image formed at the distance of most distinct vision. Let @’d’ be the projection of AB on A’B’. Then, since the eye is very near the glass, the : 1 A’OB’ Vl eie A’B’ magnification equals OP” a ’ A’OB’ and AOB are similar, A’B’: AB=DO:CO. Now DO is the dis- tance of most distinct vision, and CO is very nearly equal to FO, the focal length of the lens. Therefore, the magnification equals the ratio of the But since the triangles 590 On Light [601— distance of most distinct vision to the focal length of the lens. Hence we conclude that the magnification is greater, Ist, as the focal length of the lens is smaller—in other words, as the lens is more convergent ; 2ndly, as the observer’s distance of most distinct vision is greater. A simpler and more general definition of the measure of magnification may be stated thus: Let a be the angular magnitude of the object as seen by the naked eye, 8 the angular magnitude of the image, whether real or virtual, actually present to the eye, then the magnification is 8+a. This rule applies to telescopes. | By changing the lens the magnification may be increased, but only within certain limits if we wish to obtain a distinct image. By means of a simple microscope distinct magnification may be obtained up to 120 diameters. The magnification we have here considered is “ear magnification. Superficial magnification equals the square of the /zzear magnification ; for instance, the former will be 1,600 when the latter is 4o. 602. Principle of the compound microscope.—The compound micro- scope in its simplest form consists of two condensing lenses: one, with a short focus, is called the odject-g/ass, or objective, because it is turned towards the object ; the other is less condensing, and is called the fower, or eyepiece, because it is close to the observer’s eye. Fig. 578 represents the path of the luminous rays and the formation of the image in the simplest form of a compound microscope. An object AB being placed very near the principal focus F of the object-glass M, but a little farther from the glass, a real image, ad, inverted and somewhat magnified, is formed on the other side of the object-glass (568). Now the distance of the two lenses M and N is regulated so that the position of the image aé is between the eyepiece N and its focus F’’.. From this it follows that for the eye at E, looking at the image through the eyepiece, this glass produces the same effect as a simple micro- scope, and in- stead of this image ad, an- other image, 20. Wiga eeSeen. which is virtual, and still more magnified. This second image, Fig. 578 although erect as regards the first, is inverted in reference to the object. It may thus be said that the compound microscope is in effect a simple microscope applied not to the object but to its image already magnified by the first lens. 603. Compound microscope.—The principle of the compound micro- scope has been already (602) explained; the principal accessories to the instrument remain to be described. . Fig. 579 represents a perspective view, and fig. 580 a section, of a com- pound microscope. The body of the microscope consists of a series of brass -603] Compound Mucroscope 591 tubes, DD’, H, and I; in H is fitted the eyepiece O, and in the lower part of DD’, the object-glass 0. The tube I moves with gentle friction in the tube DD’, which in turn can also be moved in a larger tube fixed in the ring E. This latter is fixed to a piece BB’, which, by means of a very fine screw worked by the milled head T, can be moved up and down an inner rod, ¢, not represented in the figure. The whole body of the microscope is raised and lowered with the piece BB’, so that it can be placed near or far from the object to be examined. Moreover, the rod c¢, and all the other pieces of the apparatus, rest on a horizontal axis A, with which they turn under so much friction as to remain fixed in any position in which they may be placed. The object to be observed is placed between two glass plates, V, on a stage, R. This is perforated in the centre, so that light can be reflected upon the object by a concave reflecting glass mirror, M. The mirror is mounted on a jointed support so that it can be placed in any position whatever, so 592 On Light [603— as to reflect to the object either the diffused light of the sky, or that from a candle or lamp. Between the reflector and the stage is a dzaphragm or stop, K, perforated by four holes of different sizes, any one of which can be placed over the perforation in the stage, and thus the light falling on the object may be regulated ; the light can, moreover, be regulated by raising, by a lever z, the diaphragm K, which is movable in a slide. Above the diaphragm is a piece, 7, to which can be attached either a very small stop, so that only very little light can reach the object, or a condensing lens, which illuminates . it strongly, or an oblique prism, represented at X. The rays from the reflector undergo two total reflections in this prism, and emerge by a lenti- cular face that concentrates them on the object, but in an oblique direction, which in some microscopic observations is an advantage. Objects are generally so transparent that they can be lighted from below; but where, owing to their opacity, this is not possible, they are lighted from above by means of a condensing lens mounted on a jointed support, and so placed that they receive the diffused light of the atmosphere. Fig. 580 shows the arrangement of the lenses and the path of the rays in the microscope. At o is the object-glass, consisting of three small con- densing lenses, represented on a larger scale at L, on the right of the figure. The effect of these lenses being added to each other is that they act like a single very powerful condensing lens. The object being placed at z, a very little beyond the principal focus of the system, the emerging rays fall upon a fourth condensing lens, 7, the use of which will be seen presently (605). Having become more convergent, owing to their passage through the lens m, the rays form at @a’a real and magnified image of the object z. This image is between a fifth condensing. lens, O, and the principal focus of this lens. Hence, on looking through this, which acts as a magnifier (568), we see at AA’ a virtual and highly magnified image of aa’, and therefore of the object. The two glasses z and O constitute the eyepiece, in the same manner as the three glasses o constitute the object-glass. The first image, aa’, must be formed not merely between the glass O and its principal focus, but at such a distance from this glass that the second image, AA’, is formed at the observer’s distance of distinct vision. This result is obtained in moving, by the hand, the body DH of the microscope in the larger tube fixed to the ring E, until a tolerably distinct image is obtained ; then turning the milled head T in one direction or the other, the piece BB’, and with it the whole microscope, are moved until the image AA’ attains its greatest distinctness, which is the case when the image aa’ is formed at the distance of distinct vision: a distance which can always be ultimately obtained, for as the object-glass approaches or recedes from the object, the image aa’ recedes from or approaches the eyepiece, and at the same time the image AA’. This operation is called focussing. In the microscope, where the distance from the object-glass to the eyepiece is constant, it is effected by altering their distance from the object. In telescopes, where the objects are inacces- sible, the focussing is effected by varying the distance of the eyepiece and the object-glass. The microscope possesses numerous eyepieces and object-glasses, by means of which a great variety of magnifying power is obtained. A lower —604] Achromatism of the Microscope. Campani’s Eyeptece 593 magnifying power is also obtained by removing one or two of the lenses of the object-glass. The above contains the essential features of the microscope ; it is made in a great variety of forms, which differ mainly in the construction of the stand, the arrangement of the lenses, and in the illumination. For descrip- tions of these the student is referred to special works on the microscope. 604. Achromatism of the microscope. Campani’s eyepiece.—When a ‘compound microscope consists of two single lenses, as in fig. 578, not only is the spherical aberration uncorrected, but also the chromatic aberration, the latter defect causing the images to be surrounded by fringes of the prismatic colours, these fringes being larger as the magnification is greater. With a view to correcting these aberrations the object-glass (see fig. 580) is composed of three achromatic lenses, and the eyepiece of two lenses, z and O; for the first of these, 7, would be enough to produce colour unless the magnifying power were low. The effect of this eyepiece in correcting the colour may be explained as follows :—It will be borne in mind that with respect to red rays the focal length of a lens is greater than the focal length of the same lens with refer- ence to the violet rays. In fact, if in the equation (4) (571) we write R’= oo, we obtain f= Bou mu — 1 which gives the focal length of a plano-convex lens whose refractive index is 2. Now, in flint glass, and for the red ray, 7—1 equals 0°63, and for the violet ray 7—1 equals 0°67. Let aé be the object, O the object-glass, which is corrected for colour. A pencil (fig. 581) of rays falling from @ on O would converge to the focus A without any separation of colours ; but falling on the /feld-glass C, the red Fig. 581 rays would converge to 7, the violet rays to v, and intermediate colours to intermediate points. In like manner the rays from 4, after passing through the field-glass, would converge to 7’, or v’, and intermediate points. So that on the whole there would be formed a succession of coloured images of ad ; viz. a red image at 77’, a violet image at vv’, and between them images ot intermediate colours. Let d be the point of the object which is situated on the axis. The rays from d will converge to R, V, and intermediate points. Now suppose the eye-glass O’ to be placed in such a manner that R is the principal focus of O’ for the red rays, then V will be its principal focus for the violet rays. Consequently, the red rays, after emerging from O, will be parallel to the axis, and so will the violet rays coming from V, and so of any other colour. Accordingly, the colours of @, which are separated by C, are again combined by O’. The same is very nearly true of ~ and v, and of 7’ and v’. Hence a combination of lenses C and O’ corrects the chromatic QQ 594 On Light | [604— aberration that would be produced by the use of a single eye-glass. More- over by drawing the rays towards the axis, it diminishes the spherical aberration, and, as we shall see in the next article, enlarges the field of view. In all eyepieces consisting of two lenses the lens to which the eye is applied is called the eye-dens ; the one towards the object-glass is called the jield-lens. The eyepiece above described was invented by Huyghens, who was not, however, aware of its property of achromatism. He designed it for use with the telescope. It was applied to the microscope by Campani. _ The relation between the focal length of the lenses is as follows: The focal ~ length of the field-glass is three times that of the eye-lens, and the distance between their centres is half the sum of the focal length. It easily follows from this that the image of the point @ would, but for the interposition of the field-lens, be formed at D, which is so situated that CD is three times. DO’; then the mean of the coloured images would be formed midway between C and O’. 605. Field of view.—By the tield of view of an optical instrument are meant all those points which are visible through the eyepiece. The advan- tage obtained by the use of an eyepiece in enlarging the field of view will be: Fig. 582 readily understood by an inspection of the accompanying figure. As before (fig. 582), O is the object-glass, C the field-lens, O’ the eye-lens, and E the eye placed on the axis of the instrument. Let @ be a point of the object ; if we suppose the field-lens removed, the pencil of rays from @ would be brought to a focus at A, and none of them would fall on the eye-lens O’, or pass into the eye E. Consequently, a is beyond the field of view. But. when the field-glass C is interposed, the pencil of rays is brought to a focus. at A’, and emerges from O’ into the eye. Consequently, a is now within the field of view. In this manner the substitution of an eyepiece for a single. eye-lens enlarges the field of view. 606. Magnifying power. Micrometer.—The magnifying power of any optical instrument is the ratio of the magnitude of the image to the mag- nitude of the object. The magnifying power in a compound microscope is the product of the respective magnifying powers of the object-glass and of the eyepiece ; that is, if the first of these magnifies 20 times, and the other: 10, the total magnifying power is 200. The magnifying power depends on the greater or less convexity of the object-glass and of the eyepiece, as well as on the distance between these two glasses, together with the distance of the object from the object-glass. A magnifying power of 1,500 and even upwards has been obtained ; but the image then loses in sharpness what it gains in extent. To obtain precise and well-illuminated images, we must limit the magnifying power to 500 to 600 diameters, which gives a superficial enlargement 250,000 to 360,000 times that of the object. -607] Magnifying Power. . Micrometer 595 The magnifying power is determined experimentally by means of the glass micrometer: this is a small glass plate, on which, by means of a diamond, a series of lines is drawn at a distance from each other of 7 or 45 of a millimetre. The micrometer is placed in front of the object-glass, and then, instead of viewing directly the rays emerging from the eyepiece O, they are received on a piece of glass A (fig. 583), inclined at an angle of 45°, and the eye is placed above so as to see the image of the micrometer lines, which is formed by reflection on a screen E, on which is a scale divided into millimetres. By counting the number of divisions of the scale corresponding to a certain number of lines of the image, the magnifying power may be ~ deduced. Thus, if the image occupies a space of 45 millimetres on the scale and contains 15 lines of the micrometer, the distances between which shall be assumed at ;4, millimetre, the absolute magnitude of the object will be 49, millimetre ; and as the image occupies a space of 45 milli- metres, the magnification will be the quotient of 45 by 743%, or 300. The eye in this experiment ought to be at such a distance from the screen E that the screen is distinctly visible: this distance varies with different observers, but is usually 10 to 12 inches. The magni- fying power of the microscope can also be determined by means of the camera lucida ; it is increased at the expense of brightness, definition, and field. Hence it is usual to have several eyepieces with each microscope so as to obtain greater definition of higher magnification. Nober?’s lines are frequently used as test objects ; these are lines ruled on glass in series ; in the first group the lines are at a distance of z5455 to an inch from the middle of one line to the middle of the next ; in the finest the lines are at a distance of zsp55 Of an inch. Other test objects are the scales of certain butterflies, and various kinds of diatoms. When once the magnifying power is known, the absolute magnitude of objects placed under the microscope is easily deduced. For, as the magni- fying power is the quotient of the size of the image by the size of the object, it follows that the size of the image divided by the magnifying power gives the size of the object : in this manner the diameters of all microscopic objects are determined. Fig. 583 TELESCOPES 607. Astronomical telescope.—The astronomical telescope is used for observing the heavenly bodies : like the microscope, it consists of a con- densing eyepiece and object-glass. The object-glass, M (fig. 584), forms between the eyepiece, N, and its principal focus an inverted image of the heavenly body ; and this eyepiece, which acts as a magnifying glass, then gives a virtual and highly magnified image, a’é’, of the image ad. The astronomical telescope appears, therefore, analogous to the microscope ; but the two instruments differ in this respect, that in the microscope, the object being very near the object-glass, the image is formed much beyond QQ2 596 On Light [607— the principal focus, and is greatly magnified, so that both the object-glass and the eyepiece magnify ; while in the astronomical telescope, the heavenly body being Bat a_ great distance, the incident rays are parallel, and the im- age formed in the principal focus of the Fig. 584 object - glass is much smaller than the object. There is, therefore, no magnification except by the eyepiece, and this ought, therefore, to be of very short focal length. Fig. 585 shows an astronomical telescope mounted on its stand. Above ity; there sashaa. small teiescope which is called the jader. Tele- scopes with a large magnify- ing power are not convenient for finding a star, . asi, they have but a small field of view: the position of the star is, ac- cordingly, _ first sought by the finder, which has a much larger field of view— SS SS that is, takes in maki apo ei a far greater extent ofr athe heavens ; it is then viewed by means of the telescope. The magnification (601) equals ae (fig. 584); that is, it equals tte and therefore is approximately equal to sa F being the focus of the object- OF glass M, and being supposed very nearly to coincide with the focus of the eyepiece N ; it may, therefore, be concluded that the magnifying power is greater in proportion as the object-glass is less convex, and the eyepiece more so. When the telescope is used to make an accurate observation of the stars—for example, the zenith distance, or their passage over the meridian— 608] 7 Terrestrial Telescope 597 a cross wire is added. This consists of two very fine metal wires or spider threads stretched across a circular aperture in a small metal plate ‘fig. 5386). The wires ought to be placed in the position where the inverted image is pro- duced by the object glass, and the point where the wires cross ought to be on the optical axis of the telescope, which thus becomes the “ve of sight or collimation. 608. Terrestrial telescope.—The /errestrial telescope differs from the astronomical telescope in producing images in their right positions. This is effected by means of two condensing glasses, P and Q (fig. 587), placed between the object-glass M and the eyepiece R. The object being sup- posed to be at AB, at a greater distance than can be shown in the drawing, an inverted and saben smaller image is formed at da on the other side of the object-glass. But the second lens, P, is at such a distance that its principal focus coincides with the image ad; from which it follows that the luminous rays which pass through 4, for example, after traversing the lens P,. take a direction parallel to the secondary axis 6O (567... Similarly, the rays passing by a take a direction parallel to the axis @0. After crossing in H, these various rays traverse a third lens Q. The pencil BH converges towards 4’, on a secondary axis O’d’, parallel to its direction ; the pencil A@H converging in the same manner at a’, an erect image of the object AB is pro- duced at a’d’. This image is viewed, as in the astronomical telescope, through a condensing eyepiece R, so placed that it acts as a magnifying glass ; that is, its distance from the image @’0’ is less than the principal focal distance : hence there is formed, at a4”, a virtual image of a/b’, erect and much mag- nified. The lenses P and Q, which only sérve tO! réc- tify the posi- | tion ("of | the image, are fixed ina brass tube, at a con- stant distance, which is equal to the sum of their principal focal distances. The object-glass M moves in a tube, and can be moved to or from the lens P, so that the image aé is always formed in the focus of the lens, whatever be the distance of the object. The distance of the lens R may also be varied so that the image ab” may be formed at the distance of distinct vision. This instrument may also be used as an astronomical telescope by using a different eyepiece : this must have a much greater magnifying power than in the former case. In the terrestrial telescope the magnifying power is the same as in the astronomical telescope, provided always that the correcting glasses, P and Q, have the same convexity. In order to determine directly the magnifying power of a telescope, when this is not great, a divided scale at a distance, or the tiles of a house may be viewed through the telescope with one eye and directly with the other. This with a little practice is not difficult. It is thus observed how many unmagnified divisions correspond to a single magnified one. Thus if two Fig. 587 508 On Light [608- seen through the telescope appear like seven, the magnifying power is 33. Reading ordinary printing from a distance is an excellent means of testing and comparing telescopes. The excellence of a telescope depends also on the sharpness of the images. To test this, various circular and angular figures are painted in black on a white ground, as shown in fig. 588, in about ~ the full size. When these are looked at through the telescope at a distance of 80 or Ioo paces, they should appear sharply defined, perfectly black, without distortion, and without coloured edges. The penetration or penetrating power of a telescope, by which stars are seen which are not visible to the naked eye, depends mainly on the aperture of the object-glass. Even with the strongest magnification the fixed stars appear as luminous points without apparent diameter. 609. Galileo’s telescope.—Galileo’s ‘elescope is the simplest of all tele- scopes, for it consists of only two lenses ; namely, an object-glass, M, and a diverging or double con- cave eyepiece, R (fig. 589), and it gives at once an evect image. Ofpera- glasses are constructed on this principle. Fig; 686 If the object be repre- sented by the right line AB, a real but inverted and smaller image would be formed at da; but in traversing the eyepiece R, the rays emitted from the points A and B are refracted and diverge from the secondary axes 60’ and aO’ which corre- spond to the points 6 and a of the image. Hence, these rays produced backward meet their axes in a’ and 0’; the eye which receives them sees accordingly an erect and magnified image in a’d’, which appears nearer because it is seen under an angle, a’O’0’, greater than the angle, AOB, under which the object is seen. The magnifying power. is equal to the ratio of the angle @’O’d’ to the angle AOB, and is usually from 2 to 4. The distance of the eyepiece R from the image ad is pretty nearly equal to the principal focal distance of this eyepiece ; it follows, therefore, that the difference between the two lenses is the distance between their respective focal distances ; hence Galileo’s telescope is very short and portable. It has the advantage of showing objects in their right position ; and, further, as it has only two lenses, it absorbs very little light : in consequence, how- ever, of the divergence of the emergent rays, it has only a small field of view, and in using it the eye must be placed very near the eyepiece. The eye- piece can be moved to or from the object-glass, so that the image a’0’ is always formed at the distance of distinct vision. The opera-glass is usually double, so as to produce an image in each eye, by which greater brightness is attained. Some attribute the invention of telescopes to Roger Bacon in the thirteenth century ; others to J. B. Porta at the end of the sixteenth ; others, Fig. 588 —611] The Gregorian Telescope 599 again, to a Dutchman, Jacques Metius, who, in 1609, accidentally found that by combining two glasses, one concave and the other convex, distant objects appeared nearer and much larger. Galileo’s was the first telescope directed towards the heavens. By its means Galileo discovered the mountains of the moon, Jupiter’s satellites, and the spots on the sun. 610. Reflecting telescopes.—The telescopes previously described are refracting or dioptric telescopes. It 1s, however, only in recent times that it has been possible to construct achromatic lenses of large size ; before this a concave metallic mirror was used instead of the object-glass. Telescopes of this kind are called reflecting or catoptric telescopes. The principal forms are those devised by Gregory, Newton, Herschel, and Cassegrain. ) 611. The Gregorian telescope.—Fig. 590 isa representation of Gre- gory’s telescope ; it is mounted on a stand, about which it is movable, and can be inclined at any angle. This mode of mounting is optional ; it may be equatorially mounted. Fig. 591 gives a longitudinal section. It consists of a long brass tube closed at one end by a concave metallic mirror, M, which is perforated in the centre by a round aperture through which rays reach the eye. There is a second concave metal mirror, N, near the end of the tube : it is somewhat larger than the central aperture in the large mirror, and its radius of curvature is much smaller than that of the large mirror. The axes of both mirrors coincide with the axis of the tube. As the centre of curva- ture of the large mirror is at O, and its focus at ad, rays such as SA emitted from a heavenly-body are reflected from the mirror M, and form at aé an inverted and very small image of the heavenly body. The distance of the mirrors and their curvatures is so arranged that the position of this image is between the centre, 0, and the focus, /, of the small mirror ; hence the rays, after being reflected a second time from the mirror N, form at a’s’ a magnified and inverted image of ad, and therefore in the true position of the heavenly body.. This image is viewed through an eye- piece, P, which may be either simple or compound, its object being to magnify it again, so that it is seen at a6”. As the objects viewed are not always at the same distance, the focus of the large mirror, and therefore that of the small one, vary in position. And as the distance of distinct vision is not the same with all eyes, the image a’’b” ought to be formed at different distances. The required adjust- ments may be obtained by bringing the small mirror nearer to or farther from the larger one; this is effected by means of a milled head, A (fig. 590), Fig. 590 600 On Light [611— which turns a rod, and this by a screw moves a piece to which the mirror is fixed. 612. The Newtonian telescope.—This instrument does not differ much from that of Gregory ; the large mirror is not perforated, and there is a Fig. 591 small plane mirror inclined at an angle of 45° towards an eyepiece placed in the side of the telescope. The difficulty of constructing metallic mirrors caused telescopes of Gregorian and Newtonian construction to fall into disuse. Of late, how- ever, the process of silvering glass mirrors has been carried to a high state of perfection, and Foucault applied these mirrors to Newtonian telescopes with great success. His first mirror was only four inches in diameter, but he successively constructed mirrors of 8, 12, and 13 inches, and at the time of his death had completed one of 32 inches in diameter. Fig. 593 represents a Newtonian telescope mounted on an equatorial stand, and fig. 592 gives a longitudinal section of it. This section shows how the luminous rays%reflected from the parabolic mirror M meet a small rect- angular prism, 7#z, which replaces the inclined plane mirror used in the old form of Newtonian telescope. After undergoing a total reflection from mz, the rays form at a’d’ a very small image of the heavenly body. This image is viewed through an eyepiece with four lenses placed on the side of the telescope, and magnifying from 50 to 800 times according to the size of the silvered mirror. In reflectors the mirror acts as object-glass, but there is, of course, no chromatic aberration. The spherical aberration is corrected by the form given to the reflector, which is paraboloidal, but slightly modified by trial to suit the eyepiece fitted to the telescope. The mirror when once polished is immersed in a silvering liquid, which consists essentially of ammoniacal solution of silver nitrate, to which some reducing agent is added. When a polished giass surface is immersed in -612] The Newtonian Telescope 601 this solution, silver is deposited on the surface in the form of a brilliant metallic layer, which adheres so firmly that it can be polished with rouge in the usual manner. These new telescopes with glass mirrors have the advantage over the old ones that they give purer images ; they weigh less and are much shorter, their focal distance being only about six times the diameter of the mirror. These details known, the whole apparatus remains to be described. The body of the telescope (fig. 593) consists of an octagonal wooden tube. The end G is open ; the mirror is at the other end. At a certain distance from this i — lla z NO == =r "s : on —= = = end two axles are fixed, which rest on bearings supported by two wooden uprights, A and B. These are themselves fixed to a table, PQ, which turns on a fixed plate, RS, placed exactly parallel to the equator. On the circum- ference of the turning-table there is a brass circle divided into 360 degrees ; and beneath it, but also fixed to the turning-table, there is a circular toothed wheel, in which an endless screw, V, works. By moving this in either direction by means of the handle 7, the table PQ, and with it the telescope, can be turned. A vernier, x, fixed to the plate RS, gives fractions of a degree. On the axis of the motion of the telescope there is a graduated circle, O, which serves to measure the declination of the star—that is, its 602 On Light [612- angular distance from the equator ; while the degrees traced round the table RS serve to measure the right ascension—that is, the angle which the declination circle of the star makes with the declination circle passing through the first point of Aries. In order to fix the telescope in declination, a brass plate, E, 1s fixed to the upright ; it is provided with a clamp, in which the limb O works, and which can be screwed tight by means of a screw with a milled head 7» On the side of the apparatus is the eyepiece 0, which is mounted on a sliding copper plate, on which there is also the small prism #, represented in section in fig. 591. To bring the image to the right place, this plate may be moved by means of a rack and a milled head a. The handle z serves to clamp or unclamp the screw V. The drawing is one taken from a telescope the mirror of which is only 64 inches in diameter, and which gives a magni- fying power of 150 to 200. 613. The Herschelian telescope.—Sir W. Herschel’s telescope, which was for long the most celebrated instrument of modern times, was con- structed on a method differing from those described. The mirror was so in- clined that the image of the star was formed at aé on the side of the telescope near the eyepiece 0; hence it is termed the /ront-view telescope. As the rays in this telescope undergo only a single reflection, the loss of light is less than in either of the preceding cases, and the image is therefore brighter. The magnifying power is the quotient of the principal focal distance of the mirror by the focal distance of the eyepiece. Herschel’s great telescope was constructed in 1789; it was 4o feet in length, the great mirror was 50 inches in diameter. The quantity of light obtained by this instru- ment was so great as to enable its inventor to use magnifying powers far higher than anything which had hitherto been attempted. Herschel’s telescope has been exceeded by one constructed by the late Earl of Rosse. This magnificent instrument has a focal distance of 53 feet, the diameter of the speculum being six feet. It is at present used as a Newtonian telescope, but it can also be arranged as a front-view tele- scope. INSTRUMENTS FOR FORMING PICTURES OF OBJECTS 614. Camera obscura.—The camera obscura (dark chamber) is, as its name implies, a closed space impervious to light. The principle of this apparatus is illustrated by fig. 595. The rays proceeding from an external object AB, and entering by the aperture O on one side, form on the side opposite an image of the object éa in its natural colours, but of reduced dimensions, and in an inverted position. See also art. 516. Porta, a Neapolitan physician, the inventor of this instrument, found that —615] Camera Lucida 603 by fixing a double convex lens in the aperture, and receiving the image on a white screen, it was much brighter and more definite. 615. Camera lucida.—-The camera lucida is a small instrument depend- ing on internal re- flection, and serves for taking an out- line of any object. It was invented by Wollaston in 1804. It consists of a small four - sided glass prism of which fig. 596 gives’ - a section perpendicular to the edges. A is a right angle, and C an angle of 135°; the other angles, B and D, are 673°. The prism rests on a stand, on which it can be raised or lowered, and turned more or less about an axis parallel to the prismatic edges. When the face AB is turned towards the object, the rays from the object fall nearly perpen- dicular on this face, pass into the prism without any appreciable refrac- tion, and are totally refracted from BC ; for as the line ad is perpendicular to BC, and zL to AB, the angle avL will equal the angle B ; that is, it will contain 673°, and this being greater than the critical angle of glass (552), the ray Lz will undergo total reflection. The rays are again totally reflected from o, and emerge near the summit, D, in a direction almost perpendicular to the face DA, so that the eye which receives the rays sees at L’ an image of the object L. Ifthe outlines of the image are traced with a pencil, a very correct design is obtained ; but unfortunately there is a great difficulty in seeing both the image and the point of the pencil, for the rays from the object give an image which is far- ther from the eye than the pencil. This is ‘corrected by placing between the eye and prism a lens, I, which gives to the rays from the pencil and those from the object the same divergence. In this case, however, it is necessary to place the eye very near the edge of the prism, so that the aperture of the pupil is divided into two parts, one of which sees the image and the other the pencil. Amici’s camera lucida, represented in fig. 597, is preferable to that of Wollaston, inasmuch as it allows the eye to change its position to a con- siderable extent without ceasing to see the image and the pencil at the same time. It consists of a rectangular glass prism ABC, having one of the faces enclosing the right angle turned towards the object to be depicted, while the other is perpendicular to an inclined plate of glass, mw. The rays Fig. 595 Fig. 596 Fig. 597 604 On Light [615~ LI, proceeding from the object, and entering the prism, are totally reflected from its base at D, and emerge in the direction KH. They are then partially reflected from the glass plate #2 at H, and form an image of the object L, which is seen by the eye in the direction OL’. The eye at the same time sees through the glass the point of the pencil applied to the paper, and thus the outline of the picture may be traced with great exactness. 616. Magic lantern.—This is an apparatus by which a magnified image of small objects may be projected on a white screen inadark room. A typical form is the sczopticon, fig..598) The box Cj the side of which is shown removed, 1s. constructed of sheet iron; é is the flame of a lamp V, with two long flat wicks, fed by petroleum py from the reservoir B. i at The box is airtight, | | ga. and the chimney F producing a_ good draught, the air is. compelled to pass through the wicks, by which smoke and smell are avoided, and a flame of high illuminating power is produced. The ends of the box are closed by glass platesz7 andz. G isa hinged door, and on its inside is a concave mirror ; 0 and 9, are two plano-convex lenses ; # a spring clamp, in which is. placed the transparent picture. The sliding piece supports the lens tube, in which are two achromatic lenses a and 0, the fine adjustment of which is effected by the screw S. The rays from the flame e, reinforced by the reflection from G, falling upon the: lenses 0, 0,, are made parallel, or, at all events, very slightly divergent ; these lenses are accordingly called the con- densing lenses. Passing through the object which is depicted on the slide placed in #, they are concentrated to an image which is received on a screen. The image is inverted, and hence, if objects are to be seen in their erect position, they must be drawn inverted. But ordinary drawings are easily adjusted by fixing an equilateral rectangular prism, P (fig. 599), in front of the lens tube, so that the hypotenuse surface is horizontal. The parallel rays falling on the prism are inverted in consequence of refraction at the sides and total reflection from the hypotenuse surface, so that an upright position is obtained instead of a reverse one. The dotted lines. abcde and fehik give the path of two rays. —617] Solar Microscope 605 The apparatus can be used for projecting on a screen not only horizontal images, such as those of magnetic curves, but also simple physical experiments, such as the expansion of a liquid in a thermometer, the divergence of the gold leaves of an electroscope, and so forth. Dissolving views are obtained by arranging two magic lanterns, A and B, whichare quite alike, with different pictures, in such a manner that both pictures are produced on exactly the same part E of a screen F G (fig. 600). The object-glasses of both lanterns can be closed by toothed plates (fig. 601), so that when one, A, passes slowly in front of the object-glass e, a second one, B, exposes the other at the same time, the motion being effected by the rack and pinion motion M. In this way one picture is gradually seen to change into the other. In the better forms the two lanterns are arranged vertically. Ih — ‘j 7 Fig. 600 Fig. 601 The magnifying power of the magic lantern is obtained by dividing the distance of the lens from the image by its distance from the object. If the image is 100 or 1,000 times farther from the lens than the object, the image will be 100 or 1,000 times as large. Hence a lens with a very short focus can produce a very large image, provided the screen is sufficiently large. 617. Solar microscope.—The solar microscope is a magic lantern illumi- nated by the sun’s rays which serves to produce highly magnified images of very small objects. It is worked in a dark room : fig. 602 represents it fitted in the shutter of a room, and fig. 603 gives the internal details. The sun’s rays fall on a plane mirror, M, placed outside the room, and are reflected towards a condensing lens, 7, and thence to a second lens, 0 (fig. 603), by which they are concentrated at its focus. The object to be magnified is at this point ; itis placed between two glass plates, which, by means of a spring, 7, are kept in a firm position between two metal plates, m. The object thus strongly illuminated is very near the focus of a system of three condensing lenses, x, which forms upona screen ata suitable distance an inverted and greatly magnified image, ad. The distance of the lenses o and x from the object is regulated by means of screws, C and D. 606 On Light [617- As the direction of the sun’s light is continually varying, the position of the mirror outside the shutter must also be changed, so that the reflection is always in the direction of the AXxiIShMAOLAwtie microscope. The most exact apparatus for this purpose is 4m the heliostat Ee WAN (546); but as li? this instrument is very expen- sive, the object is usually at- tained by _ in- clining the mirror 1).. a greater or less extent by means of an endless screw B, and at the same time turning the mirror io round the lens 7 by a knob A, which moves in a fixed ste The solar microscope labours under the objection of concentrating great heat on the object, which soon alters it. This is partially obviated by inter- posing a layer of a saturated solution of alum, which, being a powerfully athermanous substance (442), cuts off a considerable portion of the heat. Fig. 602 Fig. 603 The magnifying power of the solar microscope may be deduced experi- mentally by substituting for the object a glass plate marked with lines at a distance of 745 or z$,5 of a millimetre. Knowing the distance of these lines on the image, the magnifying power may be calculated. The same method is used with the electric light. According to the magnifying power which it is desired to, obtain, the objective x is formed of one, two, or three lenses, which arerall achromatic. 618. Photo-electric microscope.—This is in effect a solar microscope which is illuminated by the electric light instead of by the sun’s rays. The —618] Photo-electric Microscope 607 electric light, by its intensity, its steadiness, and the readiness with which it can be produced at any time of the day, has in practice replaced the use of sunlight. The microscope alone will be described here: the production of the electric light will be considered under the head of Galvanism. Fig. 604 represents the arrangement devised by Duboscq. A solar microscope, ABD, identical with that already described, is fixed on the outside ef a brass box. In the interior are two charcoal points which do || Th dl oe fy ee ei : = ie Mi ‘i KG ce Fig. 604 not quite touch, the space between them being exactly on the axis of the lenses. The electricity of one pole of a powerful battery reaches the charcoal a by means of a copper wire K ; while the electricity from the opposite pole of the battery reaches ¢ by a second copper wire H. During the passage of the electricity a luminous arc is formed between the two ends of the carbons, which gives a most brilliant light, and power- fully illuminates the microscope. This is effected by placing at D in the inside of the tube a condensing lens, whose principal focus corresponds to the space between the two charcoals. In this manner the luminous rays which enter the tubes D and B are parallel to their axis, and the same effects are produced as with the ordinary solar microscope ; a magnified image. of the object placed between two plates of glass is produced on the screen. 608 On Light [618- In continuing the experiment the two carbons become consumed, and to an unequal extent, a more quickly than ¢c. Hence, their distance increasing, the light becomes weaker, and is ultimately extinguished. In speaking afterwards of the electric light, the working of the apparatus P, which keeps these charcoals at a constant distance, and thus ensures a constant light, will be explained. The part of the apparatus MN may:be considered as a universal phofo- genic apparatus. The microscope can be replaced by the headpieces of the phantasmagoria, the polyorama, the megascope, by polarising apparatus, &c., and in this manner is admirably adapted for exhibiting optical phenomena to a large auditory. Instead of the electric light, we may use with this apparatus the oxyhydrogen or Drummond's light, which is obtained by heat- ing a cylinder of lime in the flame produced by the combustion of hydrogen or of coal gas in oxygen gas. 619. Lighthouse lenses.—Lenses of large dimensions are very difficult of construction ; they further produce a considerable spherical aberration, and their thickness causes the loss of much -. light. =In order to avoid these incon- veniences, echelon lenses have been constructed. They consist of a plano- convex alens,4.-C (figs. 605 and 606), surrounded by a # series of annular and concentric segments;, A, B, each of which has a plane face on the same side as the plane face of the central lens, while the face on the other side has such a _ curvature that the foci of the different segments coincide in the same point. These rings form, to- gether with the central lens, a single lens, a sec- ‘tion of which is represented in fig. 606. The drawing was made from a lens of about 2 feet in diameter, the segments of which are formed of a single —620] Photography 609 piece of glass ; but, with larger lenses, each segment is likewise formed of several pieces. Behind the lens there is a support fixed by three rods, on which a body can be placed and submitted to the sun’s rays. As the centre of the support coincides with the focus of the lens, the substances placed there are melted and volatilised by the high temperature produced. Gold, platinum, and quartz are melted. The experiment proves that heat is refracted in the same way as light ; for the position of the focus for heat rays is identical with that of the focus for the rays of light. Formerly, parabolic mirrors were used in sending the light of ne and lighthouses to great distances, but they have been supplanted by the use of lenses of the above construction. In most cases oil is used in a lamp of special construction. The light is placed in the principal focus of the lens, so that the emergent rays form a parallel beam (fig. 528), which loses in- tensity only by absorption in the atmosphere, and can be seen at a distance of about 40 miles. In order that all points of the horizon may be succes- sively illuminated, the lens is continually moved round the lamp by a clock- work motion, the rate of which varies with different lighthouses. Hence, in different parts the light alternately appears and disappears after equal intervals of time. These alternations serve to distinguish lighthouses from an accidental fire or a star. By means, too, of the number of times the light disappears in a given time, and by the colour of the light, sailors are enabled to distinguish the lighthouses from one another, and hence to know their position. Of late years the use of the electric light has to a large extent been sub- stituted for that of oil lamps. A description of the apparatus will be given in a subsequent chapter. PHOTOGRAPHY 620. Photography is the art of producing permanent images of objects by utilising the changes which certain substances undergo in the presence of light. Although the darkening effect of light on silver chloride was known to the alchemists of the sixteenth century, no real advance can be said to have been made until nearly a century later, when Scheele, the Swedish chemist, inves- tigated the effect of sunlight on silver chloride (1770). Thirty-two years later Thomas Wedgewood and Humphry Davy read a paper before the Royal Institution, entitled ‘A Method of copying Paintings on Glass, and of making Profiles by the agency of Light upon Nitrate of Silver.’ In 1810 Dr. Seebeck observed, when projecting the solar spectrum on to paper moistened with a solution of silver chloride, that the silver was not merely blackened, but an approximation to the natural colours was pro- duced in their relative position in the spectrum. In 1814 Niepce patented a process of ‘héliographie’ by coating a metal plate with a solution of bitumen dissolved in oil of lavender, and exposing in thecamera. After an exposure of several hours, the plate was developed by a mixture of oil of lavender in white petroleum, which dissolved the unaffected parts of the film away. This was the first process by which photographic RR 610 On Light [620- images could be preserved. This process was tedious and inefficient, and quite useless for portraying living objects, and it was not until 1839 that a really practical method was discovered. In that year, Daguerre in Paris and Fox Talbot in England published their respective processes, and laid the foundation of modern photography. In Daguerre’s process, the Daguerreotyfe, the picture is produced on a piece of highly burnished electro-plated copper. This is rendered sensitive - by exposing it to the action of iodine vapour, which forms a thin layer of silver iodide on the surface, and further sensitised by treatment with bromine and calcium hydrate, by which a silver bromiodide is formed. The plate is then exposed in a camera, such as is depicted in figs. 607 and 608. The brass tube A contains an achromatic condensing lens, which can be moved by means of a rackwork motion, by the milled head D. At the opposite end of the box is a ground plate, E, which slides in a groove, B, in which the case containing the plate also fits. The camera being placed | in position before the object, the sliding part of the box is adjusted until the image is produced on the glass with the utmost sharp- ness ; this is the case when the glass slide is exactl in focus. The final adjustment is made by means of the milled head D. The glass slide is then replaced by the case containing the sensitive plate : the slide which protects it is raised, and the plate exposed for a given time, which varies with the amount and nature of light reflected from the object, the size of the aperture of the lens, and other conditions. The plate is now Fig. 607 B | c SISSY ZI < N f iu is ls Le & =! Vp ht We Z LU i ADB tt LEZ SLY 7t§ ; t= SS e namie ES il iLL WT 2 < Wii Wi TY TULIUADELUNLy See ants! \ | = [———e 7 ae Fei SA ee SR / 2 Bill “ iI eee Zo Nay aul il y . fj lis - ace @ 1) la ee ‘ 7 i fo ee ii ies ee /*9| LINES OF EQUAL MAGNETIC VARIATION, 1882. tl i mince i | HAA 7 bi til requ el | al ins ze Ue ERE {| iy Ue ey | Nef ieee hh) —709] Declination Compass 691 as the reflection of a ray of light (534) and very sensitive instruments (716). In this country the north pole moves every day from east to west from sun- rise until one or two o’clock ; it then tends towards the east, and at about ten o’clock regains its original position. During the night the needle is almost stationary. Thus the westerly declination is greatest during the warmest part of the day. At Paris the mean amplitude of the diurnal variation from April to September is from 13’ to 25’, and for the other months from 8’ to 10’. On some days it amounts to 25’, and on others does not exceed 5’. The greatest variation is not always at the same time. The amplitude of the daily varia- tions decreases from the poles towards the equator, where it is very slight. ‘Thus in the island of Rewak it never exceeds 3’ to 4’. 708. Accidental variations and perturbations.—The declination is accidentally disturbed in its daily variations by many causes, such as earth- quakes, the awrora borealis, and volcanic eruptions. The effect of the aurora is felt at great distances. Auroras, which are only visible in the most northerly parts of Europe, act on the needle even in these latitudes, where accidental variations of 1° or 2° have been observed. In _ polar regions the needle frequently oscillates several degrees ; its irregularity on the day before the aurora borealis is a presage of the occurrence of this phenomenon. Another remarkable phe- nomenon is the simultaneous occurrence of magnetic per- turbations in very distant countries. Thus Sabine men- tioneda magnetic disturbance which was felt simultaneously at Toronto, the Cape, Prague, » and Van Diemen’s Land. x - Such simultaneous perturba- 2 ae tions have received the name = of magnetic storms (716). 709. Declination com- pass.—The declination com- ass isan instrument by which the magnetic declination of : : : any place may be determined SS ee = when its astronomical me- Fig. 673 ridian is known. The form represented in fig. 673 consists of a brass box, AB, in the bottom of which is a graduated circle, M. In the centre is a pivot on which oscillates a very light lozenge-shaped magnetic needle, a4. To the box are attached two uprights supporting a horizontal axis, X, on which is fixed an astronomical telescope, L, movable in a vertical plane. The box rests on a foot, P, about v2 \LLe 692 On Magnetism [709- which it can turn in a horizontal plane, taking with it the telescope. A fixed circle, QR, which is called the azzmuth circle, measures the number of degrees through which the telescope has been turned, by means of a vernier, V, fixed to the box. The inclination of the telescope, in reference to the horizon, may be measured by another vernier, K, which moves with the axis of the telescope, and is read off on a fixed graduated arc, +. The first thing in determining the declination is to adjust the compass horizontally by means of the screws SS, and the level 7. The astronomical meridian is then found, either by an observation of the sun at noon exactly, or by any of the ready methods known to astronomers. The box AB is then turned until the telescope is in the plane of the astronomical meridian. The angle made by the magnetic needle with the diameter N, which corre- sponds with the zero of the scale, and is exactly in the plane of the telescope, is then read off on the graduated limb, and this is east or west, according as the pole a of the needle stops at the east or west of the diameter N. 710. Correction of errors.—These indications of the compass are only correct when the magnetic axis of the needle—that is, the right line passing through the two poles—coincides with its axis of figure, or the line connect- ing itstwoends. This is not usually the case, and a correction must therefore be made; which is done by the method of reversion. For this purpose the needle is not fixed in the cap, but merely rests on it, so that it can be removed and its position reversed ;. thus what was before the lower is now the upper face. The mean between the observations made in the two cases. gives the true declination. For, let NS be the astronomical meridian, ad the axis of figure of the needle, and sm its magnetic axis (fig 674). ‘The true declination is not the arc Na, bat the arc Nw, which is greater. If now the needle be turned, the line #z2 makes the same angle with the meridian NS ; but the north end of the needle, which was on the right of 77, is now on the left (fig. 675), so that the declination, which was previously too small by a certain amount, is now too large by the same amount. Hence the true declination is given by the mean of these two observations. _ 711. Mariner’s compass.—The magnetic action of the earth has received its most important application in the szariner’s compass. This is a declina- tion compass used in guiding the course of a ship. Fig. 676 represents a view of the whole, and fig. 677 a vertical section. It consists of a cylindrical case, BB’, which iS supported on gzmibals so as to keep the compass in a horizontal position in spite of the rolling of the vessel. These are two concentric rings one of which attached to the case itself, moves about the axis xd which. Fig. 674 Fig, 675 —711] Mariner's Compass. Prismatic Compass 693 plays in the outer ring’AB, and this moves in the supports PQ, about the axis #77, at right angles to the first. In the bottom of the box is a pivot, on which is placed, by means of an agate cap, a magnetic bar, ad, which is the needle of the compass. On this is fixed a disc of mica, a little larger than the length of the needle, on which is traced a star or vose, with thirty-two branches, making the eight points or ae 676 rhumbs of the wind, the demi-rhumbs, and the quarters. The branch ending in a small star, and called N, corresponds to the bar ad, which is underneath the disc. The compass is placed near the stern of the vessel in the dzznacle. Knowing the direction of the compass in which the ship is to be steered, the pilot has the rudder turned till the direction coincides with the sight-vane passing through a line d marked on the inside of the box, and parallel with the keel of the vessel. The prismatic compass is greatly used for surveying, more especially for military purposes ; it differs from the mariner’s compass mainly in its dimensions, and in the way in which obser- vations are made. It consists of a shallow metal box about 2} inches in diameter (fig. 678); the needle, which is fixed below the compass card, plays on a pivot much as in Fig. 677 fig. 677. Ais a metal frame across which is stretched a horsehair, forming a sight-vane. Exactly opposite this is a right-angled prism P enclosed in a 694 On Magnetism [711-— metal case, with an eyehole and a slit as represented at the side of the figure (fig. 678). When an observation is to be made, the compass is held horizontally, and so that the slit in the prism, the hair of the sight-vane, and the distant object are seen to be in the same line; the observer, looking through the eyehole, notes the angle which the needle makes ; a similar observation is made with another object, and thus the angle between them, or their dearzng, is given. The sight-vane is connected with a lever, and can be turned down, when it presses the magnet on the pivot, thus keeping it rigid, so that the compass can be transported 1 in any position. As the image is seen through the convex face of the prism it 1s magnified, and as it is seen by reflection it is reversed, so that in order to read the figures correctly they must be reversed on the card ; the reflection being total there is little loss of light. 712. Inclination. Magnetic equator.—It might be supposed from the northerly direction which the magnet needle takes, that the force acting upon it is situated in a point of the horizon. This is not the case, for if the needle be so arranged that it can move freely in a vertical plane about a hori- zontal axis, it will be seen that, although the centre of gravity of the needle coincides with the centre of suspension, the north pole in our hemisphere dips downwards. In the other hemisphere the south pole is inclined downwards. The angle which the magnetic needle makes with the horizon, when the vertical plane, in which it moves, coincides with the magnetic meridian, is called the zzclination or dip of the needle. In any other plane than the magnetic meridian the inclination zzcreases, and is 90° in a plane at right angles to the magnetic meridian. For the magnetic inclination represents. the direction of the total magnetic force, and may be resolved into two forces, one acting in a horizontal and the other in a vertical plane. When the needle is moved so that it is at right angles to the magnetic meridian, the horizontal component can only act in the direction of the axis of suspen- sion, and therefore cannot affect the needle, which is then solely influenced by the vertical component, and stands vertically. The following considera- tions will make this clearer :— . Let NS (fig. 679) represent a magnetic needle capable of moving in a vertical plane. Let NT represent, in direction and intensity, the entire force of the earth’s magnetism acting on the pole N. Then NT can be re- solved into the forces N% and NV ; TNA~ being the angle of inclination or dip. NT is termed the otal force M ; and its components are N/, or the horizontal force H,and NV, orthe vertical force Z. Now it is clear that the greater the se of dip, TN4, the less becomes.* Nf, or the horizontal force, and the greater NV, or he vertical force. Hence, in high latitudes, the directive force of a compass, which depends on the foetal force, 1S (ese than in low latitudes. At the magnetic poles the horizontal force al be zzZ, and the vertical force a maximum ; here, there- fore, the needle will be vertical. At the magnetic equator the reverse is the Fig. 679 oo a UTS TET ers "EQ8I “did OLLANOVW ‘IVNOA AO SANTI —712] Inclination. Magnetic Equator 695 case, and the needle will be horizontal. Hence the oscillations of a compass needle, by which, as will presently be explained, the strength of the earth’s magnetism is measured, become fewer and fewer in a given time as the magnetic poles are approached, although there is really an increase in the total force of the earth. Again, the reason why a dip needle stands vertical when placed E. and W. is clearly that in those positions the horizontal force now acting at right angles to the plane of motion of the needle is ineffectual to move it, and therefore merely produces a pressure on the pivot which supports the needle. But the vertical component of the total force remains unaffected by the new position of the needle. Acting, therefore, entirely alone when the dip needle is exactly E. and W., this vertical component drags the needle into a line with itself ; that is, g0° from the horizontal plane. The value of the dip, like that of the declination, differs in different localities. It is greatest in the polar regions, and decreases with the latitude to the equator, where it is approximately zero. In London at the present time (1897) the dip-is 67° 13’... In the southern hemisphere the inclination 1s again seen, but in a contrary direction ; that is, the south pole of a needle dips below the horizontal line. The magnetic poles of the earth are those places in which the dipping- needle stands vertical ; that is, where the inclination is go°. In 1831 the first of these, the terrestrial north pole, was found by Sir James Ross in 96° 43’ west longitude and 70° north latitude. The same observer found in the South Sea, in 76° south latitude and 168° east longitude, that the inclin- ation was 88° 37’. From this and other observations, it has been calculated that the position of the magnetic south pole was at that time in about 154° east longitude and 753° south latitude. The line of no declination passes through these poles, and the lines of equal declination converge towards them. The magnetic equator, or actinic line, is the line which joins all those places on the earth where there is no dip: that is, all those in which the dipping-needle is quite horizontal. It is a somewhat sinuous line, not differ- ing much from a great circle inclined to the equator at an angle of 12°, and cutting it on two points almost exactly opposite each other—one in the Atlantic and one in the Pacific. These points appear to be gradually moving their position, and travelling from east to west. Lines connecting places in which the dipping-needle makes equal angles are called zsoclinic lines. They have a certain analogy and parallelism with the parallels of latitude, and the term magnetzc latitude is sometimes used to denote positions on the earth with reference to the magnetic dip. Plate IV. is an inclination map for the year 1882, the construction of which is quite analogous to that of the map of declination. The inclination is subject to secular variations, like the declination, as is readily seen from a comparison of maps of inclination for different epochs. At Paris, in 1671, the inclination was 75° ; since then it has been continually decreasing : in 1835 it was 67° 24’; in 1849, 67°; in 1859, 66° 16’; in 1869, Cpeaacin 1570.06 (32 : in 1603.05 a7 Gain 1og1, G5) BF s7itt TS693..65° 6" '; in 1895, 65°°5’; in 1896, 65°2, and in 1897, 65°'1’. The following table gives the alterations in the inclination at London, 696 On Magnetism [712- from which it will be seen that since 1723, in which it was at its maximum, it has continually diminished by an average of something more than three minutes in each year :— Year | Inclination | Year | Inclination | ‘T3570 | jd lee. 1828 69° 47’ 1600 "4 TO | 1838 OOe Fy” 1676 | 73. 26)! ARE Sie Air) 68° 31’ L723 Gl VATASE | 1859 683 2x7 ie, AZT 2° 19° 1874 07d 34 1780s DEE St 1876 eye sy 5700 44 yal geey | 1878 67. 3 1800 70. 85° 1880 C7 ea) iozt ee Phere Rt 1881 Gi ss) 713. Inclination compass.—An z7clination compass, or dip circle, is an instrument for measuring the magnetic inclination or dip. One form, repre- sented in fig. 680, though not best adapted for the most accurate measure- ments, is well suited for illustrating the principle. It consists of a graduated iy horizontal brass circle m, sup- (20; Pe ported on three legs, provided TK with levelling screws. Above iP oe this circle there is a plate A, movable about a vertical axis, yu [J dl a_@ gy ah and supporting, by means of two aa | CTT We iii in, — aa columns, a second graduated ies IT ee circle M, which measures the He, L7 i j . : | é | inclination. The needle rests | j ‘i on a frame 7, and the diameter i | | passing through the two zeros i | of the circle N can be ascer- ss = S tained to be perfectly horizontal — 1 by means of the spirit-level 1. Sal, Li a Ww; To observe the inclination, Sz nt AS ‘ the magnetic meridian must first be determined, which is effected by turning the plate A —— | = on the circle wz, until the needle z 5 ae Te = is vertical, which is the case aU : when it is in a plane at right = angles to the magnetic meri- Fig. 680 dian (712). The plate Ais then turned go° on the circle mm, by which the vertical circle M is brought into the magnetic meridian. The angle dca, which the magnetic needle makes with the horizontal diameter, is the angle of inclination. There are here several sources of error, which must be allowed for. The most important are these :—i. The magnetic axis of the needle may not his —715] Astatic Needle and Astatic System 697 coincide with its axis of figure; hence an error which is corrected by a method of reversion analogous to that already described (710). ii. The centre of gravity of the needle may not coincide with the axis of suspension, and then the angle dca is too great or too small, according as the centre of gravity is below or above the centre of suspension ; for in the first case the action of gravity is in the same direction as that of magnetism, and in the second it is in the opposite direction. To correct this error, the poles of the needle must be reversed by remagnetising it in such a way that what was a north 1s now made a south pole. The inclination is now re-determined, and the mean taken of the results obtained in the two groups of opera- tions. iil. The plane of the ring may not coincide with the true magnetic meridian. It should be in that plane when the needle has its minimum deviation ; an observation of this kind should therefore be taken along with that previously described, by which the needle is moved 90° from its maxi- mum deviation. The dip circle may be used to determine the inclination in another way. It is first allowed to oscillate in the magnetic meridian, and then in a plane at right angles to it. If the number of oscillations in a given time in the first position be z, and in the second position z,, then in the first position the whole force of the earth’s magnetism E acts, and in the second posi- tion only the vertical component, which is E sin x, x being the angle of dip. Now, since the forces acting on the needle are, from the laws of the pendulum (55), as the squares of the number of oscillations in a given time, we have a = Za from which sin += ae Basin 247,” sine 714. Astatic needle and astatic system.—An astatic needle is one which is uninfluenced by the earth’s magnetism. A needle movable about an axis in the plane of the magnetic meridian and parallel to the inclination would be one of this kind; for the terrestrial magnetic couple, acting then in the direction of the axis, cannot impart to the needle any determinate direction. An astatic system is a combination of two needles of the same moment joined parallel to each other with the poles in contrary directions, as shown in fig. 681. If the two needles have exactly the same magnetic moment, the opposite actions of the earth’s magnetism on the poles a and 6 and on the poles a and J& counter- balance each other ; the system is then completely astatic. A single magnetic needle may also be rendered astatic by placing a large magnet near-it. By repeated trials a certain position and distance can be found at which the action of the magnet on the needle just neutralises that of the earth’s mag- netism, and the needle is free to obey any third force ; in other words, the field (721) due to the magnet just neutralises the earth’s field. 715. Force of the earth’s magnetism.—If a magnetic needle be moved from its position of equilibrium, it will revert to it after a series of oscilla- U Fig. 681 698 . On Magnetism [715- tions, which follow laws analogous to those of the pendulum (81). If the magnet be removed to another place, and caused to oscillate during the same length of time as the first, a different number of oscillations will be observed. And the earth’s magnetic force in the two places willbe respect- ively proportional to the squares of the number of oscillations. If at M the number of oscillations in a minute had been 25 =~, and at another place M’, 24 =2’, we should have— Force of the earth’s magnetism at M__ 7” _ 625 Force of the earth’s magnetism at M’ 27? 576 = 1'085. That is, if the force of the magnetism at the second place is taken as unity, that of the first is 17085. If the magnetic condition of the needle had not changed in the interval between the two observations, this method would give the relation of the forces at the two places. In these determinations of the force, it would be necessary to have the oscillations of the dip-needle, which are produced by the total force of the earth’s magnetism. These, however, are difficult to obtain with accuracy, and therefore those of the declination needle are usually taken. The force which makes the declination needle oscillate is only a portion of the total magnetic force, and is smaller in proportion as the inclination is greater. If a line ac=M (fig. 682) represent the total force, the angle z the inclination, then the horizontal component a= H is M cosz. Hence, to express the total force in the two places by the oscillations of the declina- tion needle, we must substitute the values M cos z and M’ cos z’ for M and M’ in the preceding equation, and we have— Vi) COs Cae. Weazie GOS 2 M’cosz” 7’ M’ 2x” cosz That is to say, having observed in two different places the number of oscillations, 2 and 7’, that the same needle makes. in the same time, the ratio of the magnetic forces in the two places will be found by multiplying the ratio of the square of the number of oscillations by the inverse ratio of the cosines of the angle of dip. Plate V. is a chart representing the horizontal component of the earth’s force. Knowing the angle of dip z, the total force M, or the vertical force Z, in any place, may be obtained from the values in the chart by the formula M =H secz; and Z=H tanz. The total force is least near the magnetic equator, and, increasing with the latitude, is greatest near, but not quite at, the magnetic poles ; the places of maximum intensity are conveniently named the magnetic foct. The chart shows that the horizontal force diminishes as we go towards the poles: this is not inconsistent with the above statement if we take the dip into account (712). The lines connecting places of equal force are called zsodynamic lines. They are not parallel to the magnetic equator, but seem to have about the same direction as the isothermal lines. According to Kuppfer, the force appears to diminish as the height of the place is greater ;'a needle which made one oscillation in 24’ vibrated more slowly by o'o1” at a height of | pee ea ZQOl ¢ MOUVOA IVINOZIMOH TVNOF JO SUNIT —716] Magnetic Observatories 699 1,000 feet ; but, according to Forbes, the force is only z7455 less at a height of 3,000 feet. There is, however, some doubt as to the accuracy of these observations, owing to uncertainty as to the correction for temperature. The intensity varies in the same place with the time of day: it attains its maximum between 4 and 5 in the afternoon, and is at its minimum between 10 and 11 in the morning. It is probable, though it has not yet been ascertained with certainty, that the force undergoes secular variations. From measurements made at Kew it appears that on the whole the total force experiences a very slight annual increase (706). 716. Magnetic observatories.—During the last few years great attention has been devoted to the observation of the magnetic elements, and observa- tories for this purpose have been fitted up in different parts of the globe. These observations have led to the discovery that the magnetism of the earth is in a state of constant fluctuation, like the waves of the sea or the pressure of the atmosphere. In studying the variations of the declination, &c., the mean of a great number of observations must be taken, so as to eliminate irregular disturbances and bring out the general laws. The principle on which magnetic observations are automatically recorded is as follows :—Suppose that in a dark room a bar magnet is suspended horizontally, and at its centre is a small mirror ; suppose further that a lamp sends a ray of light to this mirror, the inclination of which is such that the ray is reflected, and is received on a horizontal drum placed underneath the lamp. The axis of the drum is at right angles to the axis of the magnet ; it is covered with sensitive photographic paper, and is rotated uniformly by clockwork. If now the magnet is quite stationary, as the drum rotates, the reflected spot of light will trace a straight line on the paper with which the revolving drum is covered. But if, as is always the case, the position of the magnet varies during the twenty-four hours, the effect will be to trace a sinuous line on the paper. These lines can afterwards be fixed by ordinary photographic methods. If we know the distance of the mirror from the drum, and the length of the paper band which comes under the influence of the spot of light in a given time—twenty-four hours, for instance—the angular deflection at any given moment may be deduced by a simple calculation (534). The observations made in the English magnetic observatories were reduced by Sabine, and revealed some curious facts in reference to mag- netic storms (708). He found that there is a certain periodicity in their, appearance, and that they attain their greatest frequency about every ten years. Independently of this, Schwabe, who for many years studied the sub- ject, found that the spots on the sun, seen on looking at it through a coloured glass, vary in their number, size, and frequency, but attain their maximum about every ten or eleven years. Now Sabine established the interesting fact that the period of their greatest frequency coincides with the period of greatest magnetic disturbance. Other remarkable connections between the sun and terrestrial magnetism have been observed; one, especially, of recent occurrence has attracted considerable attention. It was the flight of a large luminous mass across a vast sun-spot, while a simul- taneous perturbation of the magnetic needle was observed in the observatory at Kew ; subsequent examination of magnetic observations in various parts 700 On Magnetism [716- of the world showed that within a few hours one of the most violent magnetic storms ever known had prevailed. It seems, however, that these accidental variations in the declination can- not be due to changes in any a@vect action of a possible magnetic condition of either the sun or the moon. For it can be shown that if the magnet- isation of the latter were as powerful as that of the earth, the deflection which it could produce would not amount to the 34th of a second, a quantity which cannot be measured. In order to produce a variation of 10’, such as is frequently met with, the magnetisation of the sun or of the moon must be 12,000 times that of the earth ; in other words, a more powerful de- gree of magnetisation than that of powerfully magnetised steel bars. Magnetic storms are nearly always accompanied by the exhibition of the aurora borealis in high latitudes ; that this is not universal may be due to the fact that many auroras escape notice. The converse of this is true, that no great display of the aurora takes place without a violent magnetic storm. The centre or focus towards which the rays of the aurora converge lies approximately in the prolongation of the direction of the dipping-needle ; and it may be mentioned in this connection that the appearances of the aurora borealis have the same periods as the sun spots. —718] The Torston Balance FO! CHARTER ed bi LAWS OF MAGNETIC ATTRACTION AND REPULSION 717. Law of decrease with distance.—Coulomb discovered the remark- able law in reference to magnetism, ¢hat magnetic attractions and repulstons are inversely as the squares of the distances of the acting poles. He proved this by means of two methods :—(i.) that of the torsion balance, and} (ii.) that of oscillations. 718. 1. The torsion balance.—This apparatus depends on the principle that, when a wire is twisted through a certain angle, the angle of torsion is proportional to the force of torsion (90). It consists (fig. 683) of a glass case closed by a glass top, with an aperture 7z near the edge, to allow the introduction of a mag- net, A. In another aperture in the centre of the top a glass tube fits, provided at its upper extremity with a micrometer. This consists of two circular pieces : @, which is fixed, is divided on the edge into _ 360°, while on one e, which is mov- able, there is a mark, c, to indicate its rotation. D and E represent the two pieces of the micrometer on a larger scale. On E there are two uprights connected by a horizontal axis, on which is a very fine silver wire supporting a mag- netic needle, ad. On the side of the case there is a graduated scale, which indicates the angle of the needle ab, and hence the torsion of the wire. When the mark c of the disc E is at zero of the scale D, the case is so arranged that the wire supporting the needle and the zero of the scale in the case are in the magnetic meridian. The needle is then removed from its stirrup, and replaced by an exactly similar one of copper, or any unmagnetic substance ; the tube, and with it the pieces D and E, are then turned so that the needle stops at zero of the graduation. The magnetic needle aé, being now replaced, is exactly in the magnetic meridian, and the wire is without torsion. Before introducing the magnet A, it is necessary to investigate the action 702 On Magnetism - 4718- of the earth’s magnetism on the needle ad, when the latter is removed out of the magnetic meridian. This will vary with the moment of the needle, with the dimensions and nature of the particular wire used for suspension, and with the intensity of the earth’s magnetism in the place of observation. Ac- cordingly the piece E is turned until ad makes a certain angle with the mag- netic meridian. Coulomb found in one of his experiments that E had to be turned 36° in order to move the needle through 1°; that is, the earth’s magnetism was equal to a torsion of the wire corresponding to 35°. Asthe force of torsion is proportional to the angle of torsion when the needle is deflected from the meridian by 2, 3 . . . degrees, the directive action of the earth’s magnetism is equal to 2,3... times 35°. The action of the earth’s magnetism having been determined, the magnet A is placed in the case so that similar poles are opposite each other. In one experiment Coulomb found that the pole a was repelled through 24°. Now the force which tended to bring the needle into the magnetic meridian was represented by 24° + 24 x 35 = 864, of which the part 24° was due to the torsion of the wire, and 24 x 35° was the equivalent in torsion of the directive force of the earth’s magnetism. As the needle was in equilibrium, it is clear that the repulsive force which counterbalances these forces must be equal to 864°. The disc was then turned until a6 madean angle of 12°. To effect this, eight complete turns of the disc were necessary. The total force which now tended to bring the needle into the magnetic meridian was com- posed of :—1st, the 12° of torsion by which the needle was distant from its starting point ; 2nd, of 8 x 360° = 2880, the torsion of the wire ; and 3rd, the force of the earth’s magnetism, represented by a torsion of 12 x 35°. Hence the forces of torsion which balance the repulsive forces exerted at a distance of 24° and of 12° are— 24° : 864 iy 3312 Now, 3312 is very nearly four times 864 ; hence for half the distance the repulsive force is four times as great. 719. il. Method of oscillations.—A magnetic needle oscillating under the influence of the earth’s magnetism may be considered as a pendulum, and the laws of pendulum motion apply to it (55). The method of oscilla- tions consists in causing a magnetic needle to ay oscillate first under the influence of the earth’s magnetism alone, and then successively under the combined influence of the earth’s magnetism and of a magnet placed at unequal distances, The following determination by Coulomb will illustrate the use of the method. A magnetic needle was used which made 15 oscillations in a minute pe ee I under the influence of the earth’s magnetism alone. Nike hey Sayan R being the radius. If there is a sphere, or uniform spheroidal shell of matter, which acts on an external point, according to the inverse square of the distance, the total action of this sphere is the same as if the whole matter were concentrated at the centre. This was first proved by Newton in the case of gravitation ; but it also applies to electricity, and hence, in calculating the potential at any point outside a sphere possessing a uniform charge, we need only consider its distance from the centre, and for such a case we may write the value of the potential V = 2 a If a charge of electricity, Q, is imparted to two insulated conducting spheres whose radii are respectively 7 and 7’, and which are connected by a long fine wire, the capacity of which may be neglected, the electricity will distribute itself over the two spheres, which will possess the charges g and g’; that is, g+g’=Q (1). The whole system will be at the same / potential V, such that V= Yn ao (2). Combining these two equations and ipa reducing, we get for the quantities g and g’ on each sphere g= cla and r+r ge te ie Now, since the diameter of any sphere with which we can ex- +r periment is infinitely small compared with that of the earth, it follows that when a sphere is connected with the earth by a fine wire the quantity of electricity which it retains is infinitely small, The densities on the two spheres are d=—%_ and d= 2—, from which Anr? 4n7r by equation (2) it 1s readily, deduced@thated :.@°=7" : 7-;, that is,. the. elec- tric densities on two spheres in distant connection are inversely as_ the radii. If, for instance, a fine wire is connected with a charged insulated sphere, the distant ‘pointed end of the wire may be regarded as a sphere 740 Frictional Electricity [764— with an infinitely small radius, and thus the density upon it would be in- finitely great. 765. Action of points.—We have just seen that the density on a point in connection with a conductor charged with electricity may be considered to be infinitely great, but the greater the density the greater will be the tendency of electricity to overcome the resistance of the air, and escape, for the electro- static pressure is proportional to the square of the density (759). If the hand is brought neara point on a conductor connected with an electrical machine in action, a slight wind is felt ; and if the disengagement of electricity takes place in the dark a luminous brush is seen. . If an electrified conductor is to retain its electricity, all sharp points and edges must be avoided ; on the other hand, to facilitate the outflow of electricity in apparatus and experiments (787), frequent use is made of this action of points. A flame acts like a very fine point in diffusing electricity. 766. Loss of electricity.—Experience shows that electrified bodies gradually lose their electricity, even when placed on insulating supports. This loss is mainly due to the insulating supports. The charge is gradually dissipated in consequence of the electricity either 2 passing through the supports or creeping over the eI surface. t All substances conduct electricity in some degree ; those which are termed insulators are simply very bad conductors. An electrified con- ductor resting on supports must therefore lose a certain quantity of electricity, either by penetra- tion into its mass or along the surface. This loss of electricity is a main cause of difficulty in ex- periments on the quantitative laws of electricity ; it 3 varies with the electric density, and increases with YYW: the hygrometric state of the air, though it does not seem that the loss from this cause is due toa direct conductivity by moist air. Lord Kelvin ascribes the greater part of the loss to the conducting layer of moisture which covers the supports; and he finds that, in comparison with this, the direct loss by even moist air is inconsiderable. Hence it is necessary in electric experiments to rub the supports with warm cloths, and to surround electrified bodies by glass vessels containing substances which absorb moisture, such as calcium chloride, or pumice soaked with sulphuric acid. Brown shellac and ebonite are the best insulators ; glass is a hygroscopic substance, and must be dried with great care. It is best covered with a thin layer of shellac varnish, as has already been stated. Mascart’s insulator is admirably adapted for supporting bodies charged with electricity. It consists of ‘a glass vessel of special shape (fig. 714),. to the glass vase of which is fused the stem. This passes through the neck and supports the plate, P ; the neck is enclosed by an ebonite stopper, and inside the vessel is sulphuric acid, so that the stem A is always dry. {HWY Fig. 714 —767] Electrical Influence or Induction TAT CHAPTER: Hi ACTION OF ELECTRIFIED BODIES-ON BODIES IN THE NATURAL STATE. INDUCED ELECTRICITY. ELECTRIC MACHINES 767. Electric influence or induction.—An insulated conductor, charged with either kind of electricity, acts on bodies in a neutral state placed near it in a manner analogous to that of the action of a magnet on soft iron; that is, attracts the opposite and repels the like kind of electricity. The action thus exerted is said to take place by zzflwence or induction. The phenomena of induction may be demonstrated by means of a brass cylinder placed on an insulating support, and with two small electric pendulums at the ends, consisting of pith balls suspended by linen threads (fig. 715). If this apparatus is placed near an insulated conductor m i i ii ii i TTT TTT MTT AIIWE Wap eaE TAUNTS = ME RSET HATRORTE TOE GRAL 0 i 4 HTM GREGG i NAA BS ie eel ES POS inn HTN ACMI ATTEN charged with either kind of electricity—for instance, the conductor of an electric machine, which is charged with positive electricity—free electricity will be developed at each end, and both pendulums will diverge. If, while they still diverge, a stick of sealing-wax, excited by friction with flannel, is | approached to that end of the cylinder nearest the conductor, the ccrre- sponding pith ball will be repelled, indicating that it is charged with the same kind of electricity as the sealing-wax—that is, with negative electricity ; while if the excited sealing-wax is brought near the other ball it will be attracted, showing that it is charged with positive electricity. If, further, a glass rod 748 Frictional Electricity [767- excited by friction with silk, and therefore charged with positive electricity, is approached to the end nearest the conductor, the pendulum will be at- tracted; while if it is brought near the other end, the corresponding pendulum will be repelled. If the influence of the charged conductor is suppressed, either by removing it or placing it in communication with the ground, the opposite electricities will recombine, and the pendulums exhibit no divergence. The cause of this phenomenon is obviously a decomposition of the neutral electricity of the cylinder by the free positive electricity of the conductor ; the opposite or negative electricity being attracted to that end of the cylinder nearest the conductor, while the similar electricity is repelled to the other end. Between these two extremities there is a space destitute of free electricity. This is seen by arranging on the cylinders a series of pairs of pith balls suspended by threads. The divergence is greatest at each extremity, and there is a line at which there is no divergence at all, which is called the zeutral line. The two electricities, although equal in quantity, are not distributed over the cylinder in a symmetrical manner ; the attraction which accumulates the negative electricity at one end is, in consequence of the greater nearness, greater than the repulsion which drives the positive electricity to the other end, and hence the neutral line is nearer one end than the other. Nor is the electricity induced at the two ends of the cylinder under the same conditions. That which is repelled to the distant extremity is free to escape if a communication be made with the ground ; whilst, on the other hand, the unlike electricity which is attracted is held bound or captive by the inducing action of the electrified body. Even if contact be made with the ground on the face of the cylinder adjacent to the inducing body, the electricity induced on that face will not escape. The repelled electricity, however, on the distant surface is not thus bound; it is free to escape by any conducting channel, and hence will immediately disappear wherever contact be made between the ground and the cylinder. Both the pith balls will collapse, and all signs of electricity on the cylinder depart, with the escape of the repelled or free electricity. But now, if communication with the ground be broken, and the inducing body be discharged or removed toa considerable distance, the attracted or bound electricity is itself set free, and diffusing over the whole cylinder causes the pith balls again to diverge, but now with the opposite electricity to that of the original inducing body. The reason for the escape of the repelled electricity is as follows :—If the cylinder be placed in connection with the ground, by metallic contact with the posterior extremity, and the charged conductor be still placed near the anterior extremity, the conductor will exert its inductive action as before. But it is now no longer the cylinder alone which is influenced. It isa conductor consisting of the cylinder itself, the wire, and the whole earth. The neutral line will recede indefinitely, and, since the conductor has ' become infinite, the quantity of neutral fluid decomposed will be increased. Hence, when the posterior extremity is placed in contact with the ground, the pendulum at the anterior extremity diverges more widely. If the con- necting-rod be now removed, neither the quantity nor the distribution will be altered ; and if the conductor be removed or be discharged, a charge of negative electricity will be left on the cylinder. It will, in fact, remain —768] Faraday s Ice-Pail Experiments 7AO charged with electricity, the opposite of that of the charged conductor. Even if, instead of connecting the posterior extremity of the cylinder with the ground, any other part had been so connected, the general result would be the same. All the parts of the cylinder would be charged with negative electricity, and, on breaking the connection with the earth, would remain so charged. Thus a body can be charged with electricity by induction as well as by conduction. But, in the latter case, the charging body loses part of its electricity, which remains unchanged in the former case. The electricity imparted by conduction is of the same kind as that of the electrified body, while that excited by induction is of the opposite kind. To impart electricity by conduction, the body must be quite insulated ; while in the case of induction it must be in con- nection with the earth—at all events momentarily. A body electrified by induction acts in turn on bodies placed near it, separating the two electricities in a manner shown by the signs on the sphere. What has here been said has reference to the inductive action exerted on good conductors. Bad conductors are not so easily acted upon by induction, owing to the great resistance they present to the circu- lation of electricity ; but, when once charged, their electric state is more permanent. This is analogous to what is met with in magnetism; a magnet in- stantaneously magnetises a piece of soft iron, but this is only temporary, and depends on the continuance of the action of the magnet ; a magnet magnetises steel with far greater difficulty, but this magnetisation is permanent. The fundamental phenomena of induction may also be conveniently in- vestigated and demonstrated by means of the apparatus represented in fig. 716, which consists of a narrow cylindrical brass tube BA, supported by an insulating glass handle, and held over the excited cake of an electrophorus (775). 1 768. Faraday’s experiments.—The following experiments of Faraday, which are often known as ‘the ice-pail.experiments,’ from the vessels with which they were originally made, are excellent illustrations of the operation of induction, and are of great theoretical importance :— A carefully insulated metal cylinder, A, fig. 717, is connected by a wire with an electroscope E, at some distance. When an insulated brass ball C, charged with positive electricity, which is small in comparison with the size of the cylinder, is lowered into the cylinder, the leaves of the electro- 750 Frictional Electricity [768- scope diverge, and, as can be shown, with positive electricity, and the divergence increases until a certain depth is attained, when there is no further increase. The divergence now remains constant, whatever be the position of the ball, and when the inside and outside are tested with the proof plane they are found to be charged with negative and positive respec- tively. Ifthe ball is withdrawn the leaves of the electroscope’ collapse, and there is no electrification on the cylinder; the quantities of negative and positive electricity developed on the two surfaces are accordingly equal to each other. If now the ball, while still charged with positive electricity, be brought as before into the cylinder, and be allowed to touch the inside, there is no altera- tion, not even a momentary one, at the moment of contact, in the divergence of the leaves of the electroscope; but if the ball be withdrawn it will now be found to be neutral, as is also the inside of the cylinder, while the outside is charged with positive electricity. When the ball touches the interior, the system forms only a single conductor, and al! the elec- Fig. 717 tricity passes to the outside; but since the charge as indicated by the electro- scope does not alter, it follows that the positive of the ball and the negative of the inside of the cylinder are equal to each other. If, while the ball charged with positive electricity is inside the cylinder, the latter is momentarily put to earth, the gold leaves collapse, and the proof plane, if applied to the outside, removes no trace of electricity ; the cylinder ‘behaves towards all external bodies as if it were neutral. The internal surface is, however, covered with a layer of negative electricity, and this is equivalent to the positive charge of the ball, for all trace of electricity dis- appears if the ball is made to touch the side. If the ball, after the cylinder has been momentarily connected to earth, be removed without having touched the sides, the negative passes to the outside and forms there a layer which is distributed as was the layer of positive electricity before the cylinder was connected with the ground. The cylinder is thus finally charged with a quantity of electricity equal and of opposite sign to that of the inducing body. Four such cylinders (fig. 718) are placed concentrically within each other, _and are insulated from each other by discs of shellac, and the outer one is -connected with the electroscope. On introducing the charged ball into the central cavity the leaves diverge just as if the intermediate ones did not exist. Each of these is charged with equal quantities of opposite electricities, -all equal in value to that of the sphere. The internal charge of the cylinder is the same as if all the intermediate cylinders were suppressed, and the charge does not vary even when the intermediate ones are connected with .each other or are touched by the electrified ball C. -769] Specific Inductive Capacity 751 If, while C is in its original condition, the internal cylinder, 4, is con- nected with the ground, the leaves collapse, and the other cylinders are in the neutral state ; the two layers which remain, positive on C, and negative on the adjacent cylinder, are without action on an external point. If any other cylinder be thus treated, the external ones are reduced to the neutral state. With the aid of :the cylinder (fig. 717) it is easy to demonstrate that by friction both electricities are produced at the same time, and in equal quan- tities. For if the flannel and sealing-wax in fig. 702 after being 479 rubbed are placed simultaneously in the cylinder no divergence is produced, while if each is intro- duced separately, they produce equal divergence but of opposite sign. = _ Whenever a charge of elec- = ~ tricity exists there is somewhere an equivalent and corresponding charge of electricity of the opposite kind. This may seem inconsistent with the fact that an insulated sphere may have a charge of one kind of electricity. But it is to be remembered that this is in effect the case of a Leyden jar (792) in which the dielectric is the layer of air between the sphere and the sides of the room which form the outer coating. 769. Specific inductive capacity.—Hitherto any possible influence of the medium which separates the electrified from the unelectrified body in the case of induction has been disregarded. It has been tacitly assumed that electric actions are exerted at a distance, and the medium has been looked upon as an inert mass through which the forces can act, but which itself is destitute of any active properties. The researches of Faraday, however, prove that this is not the case ; that the medium is of fundamental import- ance, and that it is in it and not in the conductors that the electrification must be sought. If the medium does play the essential part in the phe- nomena of induction, it is not likely that all insulating bodies possess it in the same degree. This seems to have been known to Cavendish. To determine this point Faraday used the apparatus represented in fig. 710, of which fig. 720 represents a vertical section. It consists of a brass sphere made up of two halves, P and Q, which fit accurately into each other, like the Magdeburg hemispheres. In the interior of this spherical envelope there is a smaller brass sphere C, connected with a metal rod, terminating ina ball B. The rod is insulated from the envelope PQ bya thick layer of shellac A. The space ez receives the substance whose inductive power is to be determined. The foot of the apparatus is provided with a screw and stopcock, so that it can be screwed on the air-pump, and the air in #7 either rarefied or exhausted. ° Two such apparatus perfectly identical are used, and at first they only contain air. The envelopes PQ are connected with the ground, and the knob B of one of them receives a charge of electricity. The sphere C thus becomes charged like the inner coating of a Leyden jar (792). The layer Fig. 718 752 Frictional Electricity [769— mm represents the insulator which separates the two coatings. By touching B with the proof plane, which is then applied to the torsion balance, the quantity of free electricity is measured. In one experiment Faraday observed a torsion of 250°, which represented the free electricity on B, and was proportional to its total charge. The knob B was then placed in metallic connection with the knob B’ of the other apparatus, and the torsion was now found to be 125°, showing that the electricity had become equally distributed on the two spheres, as might have been anticipated, since the pieces of apparatus were quite equal, and each contained air in the space mz. MMe... Fig.720 This experiment having been made, the space wz in the second appa- ratus was filled with the substance whose inductive power was to be deter- mined: for example, shellac. The other apparatus, in which ez is filled with air, having been charged and connected with the torsion balance, the deflection C was measured. Let it be taken as 290°, the number observed by Faraday in a special case. When the knob B of the first apparatus was connected with the knob B’ of the second, the deflection was not found to be 145°, as would be expected. The apparatus containing air produced an angle of 114°, and that with shellac of 113°. Hence the former had lost 176° and had retained 114°, while the latter ought to have shown 176° instead of 113°. The second apparatus had taken more than half the charge, and hence a larger quantity of electricity had been condensed by the shellac. Of the total quantity of electricity, the shellac had taken 176° and the air 114°; hence the inductive power of air is to that of shellac.as 114: 1763; or ~769] Specific Inductive Capacity AGS as 1:1°55:; that is, the inductive power of shellac is more than half as great again as that of air. By the following simple experiment the influence of the medium may be shown :—At a fixed distance above a gold-leaf electroscope let an elec- trified sphere be placed, by which a certain divergence of the leaves is produced. If now, the charge remaining the same, a disc of sulphur or of shellac is interposed, the divergence increases, showing that inductive action takes place through the sulphur to a greater extent than through a layer of air of the same thickness. These experiments show, therefore, that insulators differ in the facility with which they allow inductive actions to take place through them. To express this properly, Faraday ascribed to them a varying sfecijfic inductive capacity, and he spoke of them as dze/ectrics, as it is through them that the electric forces are transmitted. The following are the mean values which have been obtained by various improved methods for the specific inductive capacities of dielectrics, or what are called the delectric constants or dielectric coefficients. Their exact deter- mination presents considerable difficulty :— Air. ; 1°00 Snellacu : : ae gan! Paraffine 2°02 Ebonite . : : Se eile India-rubber 222 Sulphur : SIT Gutta-percha . 4°2 Glass. : : By Seto: 0 Alcohol 25 Water” = : : ce A condenser with a glass plate would thus have five or six times the capacity of an air condenser of the same dimensions, or the same capacity as an air condenser of the same surface, but five or six times as thin. A very interesting relation exists between the dielectric constant. 4, and the refractive index, 7, of certain substances. Thus the following numbers have been found :— R VR nt Sulphur . : : god 1°96 2°04 Resin ; : : Hey: 1°59 1°54 Paraffine . 2°32 1°52 1°53 Oil of turpentine 2°23 1°49 1°47 where 7 is the refractive index (562), and ./£ the square root of the di- electric constant. To this, which is of great theoretical importance, we shall afterwards recur. In crystallised bodies the dielectric constant varies with the direction of the axes. Thus with a crystal of native sulphur Boltzmann found the values 4°77, 3°97, and 3°81 for the direction of the longest, mean, and shortest axes respectively. Hopkinson found the following numbers for the dielectric constants of certain liquids: petroleum 2:10, oil of turpentine 2°23, olive oil 3°16, and castor oil 4°78. Faraday was not able to detect any difference in the dielectric constants -of various gases. Boltzmann has shown, however, that there are differences ‘among them, and that there is a very close agreement between the square Ze 754 Frictional Electricity [769— root of their dielectric constants and their refractive indices, as is seen from the following table :— R SAR n Vacuum. : . _T'00000 I‘00000 10000 Atco tine : ; . 1°00059 T°000295 1000294 Carbonic acid. . 100095 1°00047 3 1000449 Hydrogen . : . 100026 10001 32 1000128 Ethylene . ; {, TGO0OT3I 1000656 1'000678 770. Faraday’s theory of induction.—The experiments of Faraday on the: part which the medium plays in inductive actions, with their subsequent mathematical expression, and development by Maxwell, have led to a profound alteration in the mode of interpreting electrical phenomena. Faraday regarded conductors as in a certain sense qualitatively different from non-conductors ; these he called azelectrics, to express that they allow electrical forces to be transmitted through them ; electric forces cannot pene- trate into the interior of conductors, but are absorbed on the surface just as. light is absorbed by an opaque body. - Faraday assumed that insulators or non-conductors consisted of a number of molecules, possibly spherical in shape, which are perfect conductors and are disseminated in, and separated from each other by, a non-conducting medium. When placed in an electric field, the inductive action may be taken: to be that electrification is produced in the conducting molecules, positive on one face and negative on the opposite one, the molecules being thus arranged in polar chains ; those faces of the molecules which are turned towards the inducing body having electricity of the opposite kind to that of the latter, while those which are turned away from it have electricity of the like kind. In the interior of the medium where successively the positive face of one mole- cule is presented to the negative of the next, the two electricities neutralise each other throughout, but when the non-conductor is bounded by conductors, and the boundaries ofan electrical field are always conductors, the free electri- fication is no longer neutralised, but constitutes the charge of electricity which is perceived. This is analogous to the action of a magnet on iron filings, where: they acquire a polar arrangement along the direction of the lines of force ; the polar chains in electrification representing the lines of electrical force. This action Faraday called delectric polarisation. \We may add that the lines of electrical force tend to con- tract in the direction of their length, and they repel each other at right angles thereto. The following experiment was devised by Faraday to illus- trate the folarisation of the Fig. 721 medium, as: he called it.” He placed small filaments of silk in a vessel of turpentine (fig. 721), and, having placed two conductors in the liquid on opposite sides, he charged one by connecting it with an electrical machine at work, and placed the other in connection with the ground. The particles of silk immediately arranged themselves end to end, and adhered -771] Faradays Theory of Induction 755 closely together, forming a continuous chain between the two sides. If the chain is broken it again forms, while when the electrical action ceases the particles disperse. An experiment by Matteucci also supports Faraday’s theory. He placed several thin plates of mica closely together, and provided the outside ones with metallic coatings, like a fulminating pane (791). Having electrified the system, the coatings were removed by insulating handles, and on examining the plates of mica successively, each was found charged with positive electricity on one side and negative electricity on the other. Kleiner extended this experiment by charging a condenser the insulator of which was mica, and determining the quantity of electricity by measuring the discharge. He then recharged the condenser to the same extent, split off films successively and discharged them by the same plates, and found thus, that allowing for unavoidable losses of insulation, the charge on each film was the same. 771. Conducting sphere in a uniform field.—In the case of a conducting sphere placed in.a uniform electric field, it is easy to trace out the degree of electrification at any point. If we think of each smallest part as possessing in the neutral state equal charges of positive and negative electricity, it is evident that, in an electric field, these charges being acted on by equal opposite forces must undergo displacements in opposite directions, and that there will thus be a resultant positive charge on one side of the sphere and a negative charge on the other. From the uniformity of the field and the geometrical symmetry of the sphere, we may infer that the electrifica- tion will be symmetrical with respect to the diameter of the sphere parallel to the force of the field and to the plane through the centre perpendicular to this diameter. Further, since the sphere is a conductor, the condition of equilibrium will be that in which the resultant electric force at any point in or on the sphere is zero ; that is to say, it will be such that the force due to the electrification of the sphere itself is, everywhere within the sphere, equal and opposite to that of the field, and at the outside, such thatwhen compounded with the force of the field the resultant is perpendicular to the surface. In the figure let G be ‘the centre of the sphere, and let the: force of the field act from left to mght parallel to the diameter MN. When the sphere is unelectrified, we may think of it as having equal quantities of positive and negative electricity uniformly distri- buted through it; that is, we may suppose two uniform spheres of positive and negative electricity respectively to be superposed, each having the same radius and the same centre C as the given conducting sphere. Then the effect of the field may be described as consisting in the displacement of the negative sphere through the very small dis- tance CA towards the left, and the displacement of the positive sphere through an equal distance CB towards the right. These displacements will result in the production of a layer of free negative electricity over the surface of the left- hand hemisphere and of free positive electricity over that of the right-hand sale 756 Frictional Electricity [771- hemisphere, but there will be no free electricity elsewhere, since the two spheres of opposite electricity overlap and neutralise each other. It is easily shown that this electrification satisfies the conditions pointed out above. It is evidently symmetrical relatively both to the diameter MN and to the equatorial plane perpendicular to this diameter. To determine the direction and intensity of the force inside the sphere resulting from this electrification, consider a point P distant AP from the centre of the negative sphere and BP from that of the positive sphere. Instead of estimating the force at this point due to the free surface-charges, we will do what is evidently the same thing, that is, calculate the resultant effect at P of the uniform spherical negative Phares with centre A and the similar positive charge with centre B. In each case the force due to electricity situated farther from the centre than the point P will vanish, so that the problem is reduced to finding the resultant force at P due to a negative sphere with centre A and radius AP, together with a positive sphere with centre B and radius BP. Each of these spheres acts as though the whole quantity of electricity contained in it were concentrated at the centre. If we put p for the common density of the two spheres of electricity, we have, for the quantity of negative electricity which acts as though it were concentrated at A, the expression 4 7 AP® p, or Qy say. The force due to this at the point P is Q,/AP*=¢# mp AP, and it acts in the direction PA. Similarly, the quantity of positive electricity that we have to regard as concentrated at B is Q,=4a BP® p, and the force due to it is Q:/BP?=# wp BP acting in the direction BP. Consequently the sides BP and PA Re the triangle BPA are respectively proportional to the forces which act along them, and therefore the third side BA is proportional to the resul- tant force at P and parallel to it. If we put / for this resultant, we have the following proportion : whence J = §mpBA. It is to be observed that this result does not depend on the position of the point P ; it would therefore be the same whatever point of the conducting sphere were taken for discussion. This is the same thing as saying that the internal force due to the free surface-electrification is everywhere the same ; further, it acts everywhere in the direction BA, that is, parallel to but opposite to the force of the undisturbed external field. Let F stand for the force of the field, then, anywhere inside the sphere, the total force is F—f; but, as was pointed out above, since the sphere is a conductor and in electric equilibrium, this must vanish, whence we get nah ilatt pBA= rein The distance BA between the centres of the imaginary spheres of posi- tive and negative electricity is evidently the same as the thickness, measured parallel to the field, or in the figure parallel to the diameter MN, of the supposed surface layers of free electricity. The radial thickness at any point, —771] Conducting Sphere tn a Untform field VAY: say L, such that the radius drawn to it makes an angle a with MN, is BA cos a, which gives the thickness =o for points in the great circle perpen- dicular to MN (a=90°), and gives negative values for points still farther from N, as it should do. As the quantity BA does not depend on the particular sphere considered, it may be better to represent it by a more general symbol, say 6. The pro- duct po may receive a more satisfactory physical interpretation as follows. Suppose S to be the measure of a very small area about the point N, then Spé will denote the quantity of electricity on this area, and we may give any values we please to the separate factors p and 6 without altering this quan- tity so long as the product pd remains constant. Let this constant product be denoted by ¢,: we may then suppose 6 to diminish without limit, p increasing at the same time, so that we always have and the charge on the area S may be written So, and may be thought of as a mere surface-layer without finite thickness. Dividing this charge by the area over which it is distributed, we must interpret the quotient o, as the surface-density of the charge at N. Similarly the surface-density at any other point is given by the formula go =p0d COS a=a, Cosa if we assign the proper value to a. For instance, for the point M (a= 180°) we get o=——07, It remains to 5 SEN that the electric force at the surface of the sphere has no component along the surface, in other words, that it acts along the radius. Taking any point L on the Sree we will consider separately the components due to the electrification of the sphere and to the field respec- tively, which act at right angles to the radius at this point, and shall be able to prove that they are equal and opposite to each other. Seeing that the angle ALB is very small, it is bisected (very nearly) by the radius CL. We will put 6 for this angle, 7 for the radius, and a for the angle LCN. The force at L due to the sphere of positive electricity is : . . . mp j acting along BL ao 6), and its component perpendicular to the radius is b 4 1 §= 46 sin a 41) = sind 6= eras 4 sin a, since, as can be easily seen, sin $ d= p Be b without appreciable error. Similarly, the force due to the sphere of negative 3 . . electricity is 4 mp BY acting along LA (=a), and its component at right angles a~ to LC is 4 mp Bs sin + 6, which may be written, without sensible error, a 3 . . 4 ape ie 1 sina. Hence the total force perpendicular to the radius due to i the electrification of the sphere is 3 Vas 3 "+ =4 ao peer 2) 4 1 gj a $ mp0. 3 sin a 3 * a ot ante 758 Frictional Electricity [771- But, since a and /are very nearly equal and ~ is intermediate, 7*(a* + d°)/a°d° = 2, consequently the component force in question becomes 2 Oh deel 4 no, sina=F sina, and acts along the surface in the direction from N towards M.: The component at right angles to the radius due to the force of the field is at once seen to be F sin a acting in the direction from M towards N. These two components accordingly neutralise each other, or the final resul- tant acts along the radius. 772. Communication of electricity at a distance.—In the experiment represented in fig. 715 the opposite electricities of the conductor and the cylinder tend to unite, but are prevented by the resistance of the air. If the electric density is increased, or if the distance of the bodies is diminished, the opposed electricities at length overcome this obstacle ; they rush together and combine, producing a spark, accompanied by a sharp sound. The negative electricity separated on the cylinder being thus neutralised by the positive electricity of the charged body, a charge of positive electricity remains on the cylinder. The same phenomenon is observed when a finger is presented to a strongly electrified conductor. The latter decomposes by induction the neutral electricity of the body, the opposite electricities com- bine with the production of a spark, while the electricity of the same kind as that of the electrified conductor, which is left on the body, passes off into the ground. The striking distance varies with the density, the shape of the bodies, their conducting power, and with the resistance and pressure of the inter- posed medium. 773. Motion of electrified bodies.—The various phenomena of attrac- tion and repulsion, which are among the most frequent manifestations of electrical action, may all be explained by reference to the laws of induction. If M (fig. 723) is a fixed insulated conductor charged with positive electricity, and N is a movable insulated body—for instance, an electrical pendulum—there are three cases to be considered :-— If the pendulum is suspended by an insulating thread, such as dry silk, M, acting inductively on N, attracts the negative and repels the positive electricity, so that the maxima of density are respectively at the points @ and 6. Nowa is nearer c than 6 is ; and, since attractions and repulsions are inversely as the square of the distance, the attraction between a and c is greater than the repulsion be- tween 6 and c; and, therefore, N will be attracted to M bya force equal to the excess of the attractive over the repulsive force. If the thread is not an insulation, then the electricity of the same kind as the inducing body passes to earth through the thread and the supports, and the attraction is stronger than in the previous case. The uninsulated pendulum is more sensitive than the insulated one, and should always be used when we wish to ascertain whether a body is electri- fied or not ; but the insulated one must be used if we desire to ascertain the kind of electricity with which a body is charged. For this purpose electri- = —~774] Gold-leaf Electroscope 759 ‘city of known kind is imparted to the ball, and then attraction or repulsion is observed when the charged body is approached according as its electricity is of the opposite or the like kind to that of the body under investigation. 774. Gold-leaf electroscope.—The name e/ectroscope is given to instru- ments for detecting the presence and determining the kind of electricity in any body. The original pith-ball pendulum is an electroscope ; but, though sometimes convenient, it is not sufficientiy delicate. The gola-leaf electroscope consists of a glass cylinder B (fig. 724), stand- ing on a metal base, which thus communicates with the ground. A metal rod terminating at its upper extremity in a knob C, and holding at its lower end two narrow strips of gold-leaf, 7 7, fits in the neck of the cylinder, which is coated with an insulating varnish. The air in the interior is dried by quicklime, or by calcium chloride, and on the insides of the glass there are two strips of gold-leaf, a, communicating with the ground. These, being charged by induction with the opposite electricity to that of the gold leaves, increase the divergence, and therefore the delicacy of the apparatus. They also prevent the leaves when diverging too suddenly from adhering to the sides. When the knob is touched with a body charged with either kind of electricity, the leaves diverge ; usually, however, the apparatus is charged by induction thus :— If an electrified body—a stick of rubbed sealing-wax, for example—is brought near the knob, it will separate the two electricities, attracting unlike electricity to the knob, and retaining it there and repelling electricity of the same kind to the gold leaves, which consequently diverge. In this way the presence of an electrical charge is ascertained, but not its quality. To ascertain the £z7d of electricity the following method is pursued :—It the knob is touched by the finger while the instrument is under the influence of the body A, which we will suppose has a negative charge, the negative electricity produced by induction passes off into the ground, and the previously divergent leaves will col- lapse; there only remains positive electricity retained in the knob by in- duction from A. If now first the finger is removed, and then the electrified body, the positive electricity previously retained by A will spread over the sys- tem, and cause the leaves to diverge. If now, -while the system is charged with positive electricity, a positively electrified body—as, for example, an excited glass rod—is approached, the leaves will diverge more widely ; for the electricity of the same kind will be repelled to the ends. If, on the contrary, an excited shellac rod is presented, the leaves will tend to collapse, the electricity with which they are charged being attracted by the opposite electricity. Hence we may 760 Frictional Electricity [774— ascertain the kind of electricity either by imparting to the electroscope electricity from the body under examination, and then bringing near it a rod charged with positive or negative electricity ; or by charging the electroscope with a known kind of electricity, and bringing the electrified body in question near the electroscope. The gold-leaf electroscope 1s sometimes used as an electrometer, or measurer of electricity, the angle of divergence of the leaves being measured ; this is done by placing behind them a graduated scale ; for small angles the quantity of electricity is nearly proportional to the sine of half the angle of divergence. An electroscope in which, as in this case, the whole electrical force depends on the electrification of the body to be investigated is called an zatostatic one ; those in which an independent field is maintained, as is that of Bohnenberger (839) or of Thomson (802), are called heterostatic. ELECTRICAL MACHINES 775. Electrophorus.—It will now be convenient to describe the various electrical machines, or apparatus for generating and collecting large quantities of statical electricity. One of the most simple and inexpensive of these is the electrophorus, which was invented by Volta. It consists of a cake of resin, B (fig. 726), say about 12 inches in diameter, and an inch thick, which is placed on a metal surface, or frequently fits into a wooden mould lined with tinfoil, which is called the form. Besides this there is a metal disc of a diameter somewhat less than that of the cake, and provided with an in- sulating glass handle ; this is the cover. The mode of working isas follows : All the parts of the apparatus having been well dried, the cake, which is placed in the form, or rests on a metal surface, is briskly flapped with silk, —776] Electrophorus 761 or, better, with catskin, by which it becomes charged with negative electri- city. The cover is then placed on the cake. Owing, however, to the minute rugosities of the surface of the resin, the cover comes in contact with only a few points, and, from the non-conductivity of the resin, the negative electricity of the cake does not pass off to the cover. It acts by induction on the cover, attracting the positive electricity to the under surface, and repelling the negative electricity to the upper. If the upper surface be now touched with the finger, the negative electricity passes off, and the cover remains charged with positive electricity, held, however, by the negative electricity of the cake ; the two electricities do not unite, in consequence of the non-conductivity of the cake (fig. 725). If now the cover be raised by its insulating handle, the charge diffuses itself over the surface ; and if a conductor be brought near it (fig. 726), a smart spark passes. The metal form on which the cake rests plays an important part in the action of the electrophorus, as it increases the quantity of electricity, and makes it more permanent. For the negative electricity of the upper surface of the resin, acting inductively on the neutral electricity of the lower, decom- poses it, retaining on the under surface the positive electricity, while the negative electricity passes off into the ground. The positive electricity thus developed on the under surface reacts on the negative electricity of the upper surface, binding it, and causing it to penetrate into the badly conducting mass, on the surface of which fresh quantities of electricity can be excited far beyond the limits possible without the action of the form. For this reason the electrophorus, once charged, retains its state for a considerable time, and sparks can be taken even after a long interval. If the form be insulated, the charge obtained from it is far less than if it is on a conducting support. For, the negative electricity developed by induction on the lower surface being now unable to escape, the condensing action referred to cannot take place, and only a feeble charge can be given to the resin. The retention of electricity is greatly promoted by keeping the cake on the form, and placing the cover upon it, by which the access of air is hindered. Instead of a cake of resin, a disc of gutta-percha, or vulcanised cloth, or vulcanite, may be substituted; and, of course, if glass, or any material which is positively electrified by friction, be used, the cover acquires a negative charge. The electrophorus is a good instance of the conversion of work into electropotential energy (65). When the cover is lifted from the excited cake work must be expended in order to overcome the attraction of the electricity in the cake for the opposite electricity developed by induction on the cover ; and the equivalent of this work appears in the form of the electricity thus detached. Accordingly, when a Leyden jar (792) is charged either by the machine or by the electrophorus, the energy of the charge is a transformation of the work of the operator. 776. Plate electrical machine.—The first electrical machine was invented by Otto von Guericke, the inventor also of the air-pump. It consisted of a sphere of sulphur, which was turned on an axis by means of the hand, while the other hand, pressing against.it, served as a rubber. Resin was after- wards substituted for the sulphur, which, in turn, Hawksbee replaced by a glass cylinder. In ali these cases the hand served as rubber ; and Winckler, 7062 Frictional Electricity [776- in 1740, first introduced cushions of horsehair, covered with silk, as rubbers. At the same time Bose collected electricity, disengaged by friction, on an insulated cylinder of tin plate. Lastly, Ramsden, in 1760, replaced the glass cylinder by a circular glass plate, which was rubbed by cushions. The form which the machine has now is but a modification of Ramsden’s original machine. Between two wooden supports (fig. 727) a circular glass plate P is sus- pended by an axis passing through the centre, turned by means of a handle M. The plate revolves between two sets of cushions or rubbers, F, of leather or of silk, one set above the axis and one below, which, by means of screws, can be pressed as tightly against the glass as may be desired. The plate also passes between two brass rods, shaped like a horseshoe, and provided with a series of points on the sides towards the glass ; these rods are fixed to larger metallic cylinders C C, which are together called the prime con- ductor. The latter are insulated by being supported on glass feet, and are connected with each other by a smaller rod ~ The action of the machine is thus explained. By friction with the rubbers the glass becomes positively and the rubbers negatively electrified. If now the rubbers were insulated, they would receive a certain charge of negative electricity which it would be impossible to exceed, for the tendency of the opposed electricities to reunite would be equal to the power of the friction to decompose the neutral state. But the rubbers communicate with the ground by means of a chain; and, consequently, as fast as the negative electricity is generated, it is continually reduced to zero by contact with the ground. The positive electricity of the glass acts then by induction on the conductor, attracting the negative electricity. This negative electricity collects on the points opposite to the glass. Here its tendency to discharge becomes so high that it passes across the intervening space of air, and neutralises the positive electricity on the glass. The prime conductor thus loses its negative electricity and remains charged with positive electricity. The plate accordingly gives up nothing directly to the prime conductors ; but its own positive charge is partly neutralised by the negative drawn from the points. If the hand be brought near the conductor when charged, a spark follows, which is renewed as the machine is turned. In this case the posi- tive electricity decomposes the neutral electricity of the body, attracting its negative electricity, and combining with it when the two have a sufficient tension. Thus, with each spark, the conductor reverts to the neutral state, but becomes again electrified as the plate is turned. 777. Precautions in reference to the machine.—The glass, of which the plate is made, must be as little hygroscopic as possible. Of late ebonite has been frequently substituted for glass; it has the advantage of being neither hygroscopic nor fragile, and of readily becoming electrified by friction. It cannot, however, be relied on, as its surface in time undergoes a change, especially if exposed to the light, whereby it becomes a conductor. The plate is usually from 54, to 4 of an inch in thickness, and from 20 to 30 inches in diameter, though these dimensions are not unfrequently exceeded. The rubbers require great care, both in their construction and their pre- servation. They are commonly made of leather, stuffed with horsehair. —777] Plate Electrical Machine 763 Before use they are coated with powdered aurum musivum (tin sulphide), or graphite, or amalgam. The action of these substances is not very clearly understood. Some consider that it merely consists in promoting friction. Others, again, believe that a chemical action is produced, and assign in support of this view the peculiar smell noticed near the rubbers when the machine is worked. Amalgams, perhaps, promote most power- fully the disengagement of electricity. Avzenmayer’s amalgam is the best of them. It is prepared as follows: One part of zinc and one part of tin are melted together and removed from the fire, and two parts of mercury Binminy. FF _ ®>*” FI = =_22qmmn I UTERAC TUTORS WA (NNN oe LOTTE a es _ MN _ eee mn il SS Fig. 727 stirred in. ‘The mass is transferred to a wooden box containing some chalk, and then well shaken. The amalgam, before it is cold, is powdered in an iron mortar, and preserved in a stoppered glass vessel. For usea little cacao butter or lard is spread over the cushion, some of the powdered amalgam sprinkled over it, and the surface smoothed by a ball of flattened leather. In order to avoid a loss of electricity, two quadrant-shaped pieces of oiled silk are fixed to the rubbers, so as to cover the plate on both sides: one at the upper part from a to F, and the other in the corresponding part of the lower rubbers. ‘These flaps are not represented in the figure. Yellow oiled 764 Frictional Electricety [777— silk is the best, and there must be perfect contact between the plate and the cloth. Ramsden’s machine, as represented in fig. 727, gives only positive elec- tricity. But it may be arranged so as to give negative electricity by placing it on a table with insulating supports. The conductor is connected with the ground by a chain, and the machine worked as before. The positive electricity passes off by the chain into the ground, while the negative elec- tricity remains on the supports and on the insulated table. On bringing the finger near the uprights, a sharper spark than the ordinary one is obtained. Winter compared the working of an electrical machine directly with the indications of an hygrometer, and found that the length of the spark obtain- able is inversely as the hygrometric state. 778. Maximum of charge.—It is impossible to exceed a certain limit of electrical charge with the machine, whatever precautions are taken, or however rapidly the plate is turned. This limit is attained when the loss of electricity equals its production. The loss depends on three causes : i. The loss by the atmosphere, and the moisture it contains. 11. The loss by the sup- ports. i. The recombination of the electricities of the rubbers and the glass. The first two causes have been already mentioned. With reference to the last, it must be noticed that the electrical charge increases with the rapidity of the rotation, until it reaches a point at which it overcomes the resistance presented by the non-conductivity of the glass. At this point, a portion of the two electricities separated on the rubbers and on the glass recombines, and the charge remains constant. It is, therefore, ultimately independent of the rapidity of rotation. 779. Quadrant electrometer.—The electrical charge is roughly measured by the guadrani or Henley’s electrometer, which is attached to the conductor. This is a small electric pendulum, consisting of a wooden rod d, to which is attached an ivory or cardboard scale (fig. 728). In the centre of this isa small index of straw, movable on an axis, and termi- nating in a pith ball. Being attached to the con- ductor, the index diverges as the machine is charged, ceasing to rise when the limit is attained. When the rotation is discontinued the index falls rapidly if the airis moist ; but in dry air it falls but slowly, showing, therefore, that the loss of electricity in the latter case is less than in the former. 780. Armstrong’s hydro-electric machine.—In this machine electricity is produced by the disengagement of aqueous vapour through narrow orifices. The dis- covery of the machine was occasioned by an accident. A workman having accidentally held one hand ina jet of steam, which was issuing from an orifice in a steam boiler at high pressure, while his other hand grasped the safety-valve, was astonished at experiencing a smart shock. Lord Armstrong (then Mr. Armstrong, of Newcastle), whose attention was drawn to this phenomenon, ascertained that the steam was charged with positive electricity, and, by repeating the experiment with an insulated locomotive, he found that the boiler was negatively charged. Armstrong —780] Armstrong's Hydro-electric Machine 765 believed that the electricity was due to a sudden expansion of the steam ; Faraday, who afterwards examined the question, ascertained its true cause, which will be best understood after describing a machine which Armstrong devised for reproducing the phenomenon. It consists of an insulated wrought-iron boiler (fig. 729), with a central fire, about 5 feet long by 2 feet in diameter, and provided at the side with a gauges. OQ.) 0 Cais pers the stopcock, and Ti Mf above this is the i box B, in which areduatherns atubes through which the steam is disen- gaged. On these are fitted jets of a pil peculiar construc- WA tion, shown in the Se section of one of fe A i them, M, _ repre- (\ nt sented on a larger ae W777 scale. They are | lined with hard wood in a manner represented by the diagram. The box B contains. cold water. Thus the steam, before es- caping, undergoes partial condensa- tion, and becomes charged with ve- sicles of water—a necessary condi- tion, for Faraday found that no electricity is produced when the steam is perfectly dry. The development of electricity in the machine was at first attributed to the condensation of the steam, but Faraday found that it is solely due to the friction of the globules of water against the jet. For if the little cylinders which line the jets are changed, the kind of electricity is changed ; and if ivory is substituted, little or no electricity is produced. The same effect is produced if any fatty matter is introduced into the boiler. In this case the linings are of no use. Electricity is disengaged in case the water is pure, and the addition of acid or saline solutions, even in minute quantity, prevents any disengagement of electricity. If turpentine is added to the boiler the effect is reversed—the steam becomes negatively, and the boiler positively, electrified. With a current of moist air Faraday obtained effects similar to those of this apparatus, but with dry air no effect is produced. 7606 Frictional Electricity [780— _ When liquefied carbonic acid issues from the metal cylinder in which it is stored (385), the cylinder is found to be strongly positive, the electrification being due to the friction of particles of solidified carbonic acid against the sides of the jet. 781. Holtz’s electrical machine.—Before the end of last century elec- trical machines were known in this country in which the electricity was not developed by friction, but by the continuous inductive action of a body already electrified, as the electrophorus ; within the last few years such machines have been re-invented and come into use. The form represented in fig. 730 was invented by Holtz, of Berlin. = —— SO ENA Fig. 730 It consists of two c.rcular plates of thin glass at a distance of 3 mm. from each other ; the larger one, AA, which is 2 feet in diameter, is fixed by means of 4 wooden rollers a, resting on glass axes and glass feet. The diameter of the second plate, BB, is 2 inches less ; it turns on a horizontal glass axis, which passes through a hole in the centre of the large fixed plate without touching it. In the plate A, on the same diameter, are two large apertures or windows, FF’. Along the lower edge of the window F, on the posterior face of the plate,a band of paper, #, is glued, to which is connected a tongue of thin cardboard, 7, joined to ~ by a thin strip of paper, and pro- jecting into the window. At the upper edge of the window, F’, there are corresponding parts, f’and 7’. The papers f and #’ constitute the armatures. —781] Floltz’'s Electric Machine 707 The two plates, the armatures, and their tongues are covered with shellac varnish, but more especially the edges of the tongues. In front of the plate B, at the height of the armatures, are two brass combs, OO’, supported by two conductors of the same metal, CC’. In the front end of these conductors are two moderately large brass knobs, through which pass two brass rods terminated by smaller knobs, 77’, and provided with ebonite handles, KK’. These rods, besides moving with gentle friction in the knobs, can also be turned so as to be more or less near and inclined towards each other. The plate BB is turned by means of a winch M, anda series of pulleys which transmit its motion to the axis; the velocity which it thus receives is I2 to I5 turns in a second, and the rotation should take place in the direction indicated by the arrows—that is, towards the points of the cardboard tongues 77’. To work the machine, the armatures #/’ must be first Avi#zed—that is,. one of the armatures is positively and the other negatively electrified. This is effected by means of a plate of ebonite, which is excited by striking it with catskin ; the two knobs 77’ having been connected so that the two conductors C, C’ form only one, as seen in fig. 731, which shows by a hori- zontal section, through the axis of rotation, the relative arrangement of the plates and of the conductors. The electrified ebonite is then brought near one of them—4, for instance—and the plate B is turned. The ebonite is charged with negative electricity, and this withdraws the positive electricity of the armature and charges it negatively. This latter acting by induction through the plate BB, as it turns on the conductors OCC’O’ (fig. 731), attracts through the comb O the positive electricity which collects on the front face of the movable plate ; while at the same time negative electricity, repelled on the comb O’, collects, like the former, on the front face of the plate B. Hence, the two electricities béing carried along by the rotation, at the end of half a turn all the lower half of the plate B, from Z# to F’ (fig. 732), is posi- tively electrified, and its upper surface from f’ to F negatively. But the two opposite electricities above and below the window F’ concur in decomposing the electricity of the armature f’m’ ; the part J’ 1s positively electrified, while negative electricity is liberated by the tongue 7’, and is deposited on the inner face of the plate B B, which from its thinness almost completely neutralises the positive electricity on the anterior face. The two armatures are then primed, and the same effect as at F’ is produced at F on the armature # z—that is, that the opposite electricities. above and below ~ 2 decomposing a new quantity of neutral electricity, the negative charge of the part / increases, while the positive electricity which 768 Frictional Electricity [781— is liberated by the tongue z neutralises the negative electricity which comes from F’ towards F; and so forth, until, the machine having attained its maximum charge, there is equili- brium in all its parts. From that point it only keeps itself up, and in perfectly dry air it may work for a long time without its being neces- sary to employ the ebonite plate. Ifthis is removed, and the: knobs + and 7’ are moved apart (fig. 732) to a distance de- pendent on the power of the machine, [while the rotation is continued, a torrent of sparks strikes across from one knob to the other. With plates of equal dimensions Holtz’s machine is far more powerful than the ordinary electrical machine (776). The power is still further increased by suspending to the conductors C C’ two condensers (788), or small Leyden jars, H H’ which consist of two glass tubes coated with tinfoil, inside and out, to a fifth of their height. Each of them is closed by a cork through which passes a rod, communicating at one end with the inner coating, and suspended to one of the conductors by a crook at the other end. The two external coatings are connected by a conductor, G. They are, in fact, only two small Leyden jars (792), one of them, H, becoming charged with positive electricity on the inside and negative on the outside; the other, H’, with negative electricity on the inside and positive on the outside. Becoming charged by the play of the machine, and being discharged at the same rate by the knobs 77’, they strengthen the spark, which may attain a length of 6 or 7 inches. The current of the machine is utilised by placing in front of the frame two brass uprights, Q Q’, with binding screws in which are copper wires ; then, by means of the handles K K’, the rods which support the knobs 77 are in- clined, so that they are in contact with the uprights. The current being then directed by the wires, a battery of six jars can be charged in a few minutes, water can be decomposed, a galvanometer deflected, and Geissler’s ‘tubes illuminated. Kohlrausch found that a Holtz machine with a plate 16 inches in dia- meter, and making 5 turns in three seconds, produced a constant current capable of decomposing water at the rate of 3} millionths of a milligramme ina second. This is equal to the effect produced by a single Grove’s cell in a circuit of 45,000 ohms resistance. Rossetti, who made a series of measurements with a Holtz machine, found that the strength of the current is nearly proportional to the velocity Fig. 732 —782] Wimshurst’s Machine 769 of the rotation ; it increases a little more rapidly than the rotation. The ratio of the velocity of rotation to the strength of the current is greater when the hygrometric state increases. The current produced by a Holtz machine is comparable with that of a voltaic couple. Its electromotive force and resistance are constant, provided the velocity of rotation and the hygrometric State are constant. The electromotive force is independent of the velocity of rotation, but diminishes as the moisture increases ; it is nearly 52,000 times as great as that of Daniell’s cell. The internal resistance is independent of the moisture, but diminishes rapidly with increased velocity of rotation. Thus with a velocity of 120turns in a minute itis represented by 2,810 million ohms (1000), and with a velocity of 450 turns it is 646 million ohms. Holtz’s machine is very much affected by the moisture of the air ; but Ruhmkorff found that by spreading on the table a few drops of petroleum, the vapours which condense on the machine protect it against the moisture of the atmosphere. Holtz’s machine affords a means of making a curious experiment on reversibility. \f the two combs of a machine in the ordinary state are con- nected with the poles of a second similar one, which is then set in action, the combs of the first become luminous, and the plate begins to rotate, but in the opposite direction to its ordinary course ; the electricity thus transmits the motion of the second machine to the first ; the one expends what the other produces. It may also be observed that the two machines are con- nected by opposite poles, and the system constitutes a circuit which is tra- versed in a definite direction by a continuous electrical current. A very simple and efficient machine of this kind is made by Voss of Berlin. One with a plate of 10 inches diameter produces a spark of 4 to 5 inches. 782. Wimshurst’s machine.—This is the simplest and most efficient of all induction machines. It consists (fig. 730) of two circular glass discs mounted on a fixed horizontal spindle in such a way as to be rotated in opposite directions at a distance of not more than a quarter of an inch apart. Both discs are well varnished, and attached to the outer surface of each are narrow radia sections of tinfoil arranged at equal angular distances apart. Attached to the fixed spindle on which the discs rotate is a bent conduct- ing rod, at the ends of which are two fine wire brushes ; twice during each revolution two diametrically opposite conductors are put in connection with each other by means of this conductor, as they just graze the tips of the brushes. At the back is a similar one at right angles to that in front, and there is a position of maximum efficiency, which is when they make an angle of 45° with the fixed collectors. There are two forks provided with combs directed towards each other, and towards the two discs which rotate between them; they are supported horizontally on Leyden jars, to which are also attached the terminal electrodes or dischargers, the distance apart of which can be varied by turning the Leyden jar from which they rise. . The machine is self-exciting, and requires neither friction, nor the spark from any outside exciter, to start it. It is one of the most remark- 3.) 770 Frictional Electrecety [782- able features of this machine, that under ordinary conditions it attains its full power after the second or third turn. The initial charge is probably obtained from the electricity of the air, or from the frictional resistance ' against it. With a machine having plates 17 inches in diameter, a powerful spark discharge passes between the two electrodes when they are 4 to 5 inches apart, in regular succession, at the rate of 2 or 3 for every turn of the handle. A machine with 12 plates, 30 inches in diameter, when driven at a speed of 200 turns per minute, produces sparks between the terminals of 13} inches in length ; and when the terminals are closed by a wire of 3,000 ohms wl] SE iy | resistance (1000) a current of two-thirds of a millimpere is produced. With these machines the increase of electricity has been found proportional to the speed of rotation up to 5,000 turns in a minute. It is not easy to give a satisfactory account of the theory of the machine. Mr. Wimshurst considers that its remarkable efficiency may be partly due to the duplex action of the apparatus, both plates being active and con- tributing electricity to the collecting combs, the sector-shaped plates of tin- foil acting as z#zductors when in their position of lowest efficiency as carriers, and as carriers when in the positions at which their inductive effect is at a minimum, and vice versd ; and as it follows from the construction of the instrument that the inductors of the one disc are at a position of highest —784] Work required for the Production of Electricity 771 efficiency when those of the other are at their lowest, and vzce versd, and as this applies with equal force to the sectors when considered as carriers, it also follows that the charging of the electrodes, and therefore the discharge between them, is by mutual compensation maintained constant. 783. Work required for the production of electricity.—In all electrical machines electricity is only produced by the expenditure of a definite amount of energy, as will at once be seen by a perusal of the preceding descriptions. The action of those machines, however, which work continuously is some- what complex. Not only is electricity produced, but heat also ; and it has been hitherto impossible to estimate separately the work required for the heat from that required for the electricity. This is easily done in theory, but not in practice: it would be, for instance, difficult to determine the tem- perature of the cushion, or of the plate of a Ramsden machine. By means of a Lane electrometer (799) it was found that, taking as unit the quantity of electricity produced by one turn of a Ramsden machine with a plate 39 inches in diameter, that produced by a Holtz machine with a plate of 21 inches was 0°86; but as for the same work the former made I | and the latter Io turns in a second, it follows that the quantities produced were as 1:8°6. Comparing the quantities per unit of surface, the yield of the Holtz machine is more than 12 times that of the Ramsden. In lifting the plate off a charged electrophorus a certain expenditure of energy is needed, though it be too slight to be directly estimated (775). With a Holtz machine it may be readily shown by experiment that there is a definite expenditure of energy in working it. If such a machine be turned without having been charged, the work required is only that necessary to overcome the passive resistances due to friction. If, however, a charged ebonite plate is approached to one of the sectors, as soon as the peculiar sound indicates that the machine is at work, it will be observed that there must be a distinct increase in the mechanical effort necessary to work the machine. The work required to charge an unelectrified conductor to a given poten- tial may be deduced from the following considerations :—To impart to a body which is at potential V a quantity of electricity Q would require an amount of work represented by QV (762). But if the body be unelectrified it is at the outset at zero potential; and we may conceive the electricity imparted to it in a series of 2 very small charges of g each, such that azg=Q; and as the potential rises proportionally to the number of charges, it may be assumed that the work done is equal to that required to charge the body to an average potential of $V ; hence the work in question W =4QV. From the relation between the quantity of heat produced by the current of a Holtz machine working under definite conditions, and the amount of -work expended in producing the rotation of the plate, Rossetti made a ‘determination of the mechanical equivalent of heat, which gave the number 1,397, agreeing therefore very well with the numbers obtained by other methods (509). 784. Thomson’s water-dropping collector.—This may be given as an illustration of an arrangement by which a known charge may be almost indefinitely multiplied, Se 772 Frictional Electricity [784— A and B, fig. 731, are insulated metal cylinders called the zaductors, and are in metallic connection with two cylinders a and 4, also insulated, called the: receivers, each having a funnel the nozzle ot which isin the centre of the cylinder. Water from the pipe e falls in drops through the metal taps ¢ and d, the nozzles of which are: in the centre of the cylinders A and B. Take first the case of the cylinder A, and suppose it to possess a small negative charge at the outset, the drops as they fall will be charged negatively by induction, the corresponding positive going to earth, through e. Falling on the funnel of the receiver 4 they impart to it the whole of their charge, and the water as it issues will be neutral. But the negative charge of B is shared with 4, which is thus negatively electrified,. and the drops which fall through it are positively electrified and give up their posi- tive charge to a, which strengthens the positive of A. By this means even with a very slight original charge they will strengthen each other, until even sparks. Fig. 734 pass. It is not even necessary to give a charge at the outset ; the ordinary electricity i, “ 5) Ee, 3 of the atmosphere is sufficient. The energy in this apparatus is derived from that of the falling body, and would be exactly equivalent to it if there were no loss, and if the drops. reached the.funnel without any velocity. EXPERIMENTS WITH THE ELECTRICAL MACHINE 785. Electrical spark.—One of the most curious phenomena observed with the electrical machine is the spark drawn from the conductor when a finger is. presented to it. The positive electricity of the conductor, acting inductively on the neutral electricity of the body, decomposes it, repelling the positive and attracting the negative. When the attraction of the opposite electricities. is sufficiently great to overcome the resistance of the air, they recombine with a smart crack and a spark. The noise of the crack is due to the con- densation of the air suddenly heated and expanded by the passage of electricity and reaching the ear as sound waves. The spark is instantaneous, and is accompanied by a sharp prickly sensa-. tion, more especially with a powerful machine. Its shape varies. When it strikes at a short distance it is rectilinear, as seen in fig. 735. Beyond two: or three inches in length the spark becomes irregular, and has the form of a sinuous curve with branches (fig. 736). If the discharge is very powerful, the spark takes a zigzag shape (fig. 737). These latter two appearances are: seen in the discharge of lightning. —786] Electrical Chimes Yi A spark may be taken from the human body by aid of the zzszzlating stool, which is simply a low stool with stout glass legs. The person standing on this stool touches the prime conductor, and, as the human body is a con- ductor, the electricity is distributed over its surface as over an ordinary insulated metallic conductor. The hair diverges in consequence of repulsion, ae a peculiar sensation 1s felt on the face, and if another person, standing on the ground, presents his hand to any part of the body, a smart crack with a pricking sensation is produced. A person standing on an insulated stool may be negatively electrified by being struck with a catskin. If the person holding the catskin stands on an insulated stool, the striker becomes positively and the person struck negatively electrified. 786. Electrical chimes.—The electrical chimes is a piece of apparatus consisting of three bells suspended to a horizontal metal rod (fig. 738). Two of them, A and B, are in metallic connection with the conductor ; the middle bell hangs by a silk thread, and is thus insulated from the conductor, but is connected with the ground by means of a chain. Between the bells are small copper balls suspended by silk threads. When the machine is worked, the bells A and B, being positively electrified, attract the copper balls, and after contact repel them. Being now positively electrified, they are in turn attracted by the middle bell, C, which is charged with negative electricity by induction from A and B. After contact they are again repelled, an this process is repeated as long as the machine is in action. Fig. 739 represents an apparatus originally devised by Volta for the purpose of illustrating what he supposed to be the motion of hail between 774 Frictional Electricity ['786— two clouds oppositely electrified. It consists of a tubulated glass shade, with a metal base, on which are some pith balls. The tubulure has a metal cap, through which passes a brass rod, provided with a metal disc or sphere at the lower end, and at the upper with a ring, which touches the prime conductor. When the machine is worked, the sphere becoming positively electrified en attracts the light pith balls, which are then immediately repelled, and, having | lost their charge of positive electricity, 4 are again attracted, again repelled, and so on, as long as the machine continues to:-be worked. An amusing modification of this experiment is frequently made by placing between the two plates small pith figures, somewhat loaded at the base. When the machine is worked, the figures execute a regular dance. Fig. 738 Fig. 740 787. Electric whirl or vane.—The electric whzv/ or vane consists of 5 or 6 wires, terminating in points, all bent in the same direction, and fixed in a central cap, which rotates on a pivot (fig. 740). When the appa- ratus is placed on the conductor, and the machine worked, the whirl begins to revolve in a direction opposite that of the points. This motion is not analogous to that of the hydraulic tourniquet (151).. It is not caused by a flow of material fluid, but is owing to a repulsion between the electricity of the points and that which they impart to the adjacent air by conduction. The electricity, being accumulated on the points in a high state of density, passes into the air, and, imparting thus a charge of electricity, repels this electricity, while it is itself repelled. That this is the case is evident from the fact that » on approaching the hand to the whirl while in motion, a slight draught is ~787] Electrical Whirl or Vane 775 felt, due to the movement of the electrified air, while in vacuo the apparatus does not act at all. This draught or wind is known as the electrical aura. If the experiment is made in water, the fly remains stationary, for water is a good conductor ; but in olive oil, which is a bad conductor, the whirl rotates. When the electricity thus escapes by a point, the electrified air is repelled so strongly as not only to be perceptible to the hand, but also to engender a current strong enough to blow out a candle. Fig. 741 shows this experi- Fig. 741 Fig. 742 ment. The same effect is produced by placing a taper on the conductor and bringing near it a pointed wire held in the hand (fig. 742). The current arises in this case from the flow of air electrified with the contrary electricity which escapes by the point under the influence of the machine. The loss of electricity in this way by contact with easily moving bodies is analogous to the transmission of heat by convection. The electrical orrery and the electrical inclined plane are analogous in their action to these pieces of apparatus. The velocity of the electrical aura has been determined by placing a wire gauze connected with earth at a fixed distance from the point, and an anemometer at varying distances behind the gauze. The velocity of the wind was found to diminish with the distance, but not in direct proportion ; at a distance of 22 inches it was 54 feet per second, while at 60 inches its velocity was 2 feet per second. The production of the electrical aura is accompanied by luminous phenomena which can be seen in the dark. If positive electricity escapes from the point, a violet aigrette is formed ; while when the electricity is negative a small brilliant star forms on the point. It is pretty certain that in these experiments it is not the air itself, but the particles in it, whether of dust or of moisture, which become electrified. This may be illustrated by the following simple experiment. A glass globe is filled with dense smoke of turpentine or of sal-ammoniac (fig. 743), and the bared end of a guttapercha-covered wire is held in it while the other end is connected with an electrical machine. On giving the machine two or three turns the smoke is rapidly deposited, and the inside becomes quite clear. Here the smoke consists of solid particles, which become 776 frictional Electricity [787- polarised by induction and attract each other like the particles of silk in fig. 721. They thereby become agglomerated, and are deposited on the sides where they are retained if the sides are coated with glycerine. Nahrwold proves that if air is freed from dust by filtration, it takes little if any charge from an electrified point. Fig. 743 This phenomenon is employed industrially in the deposition of finely suspended powders, as in lead works. Two conductors provided with points are connected respectively with a positive and negative source of electricity : the powder electrified by the one point is repelled and is precipitated on the other. —788} Condensers or Accumulators O97 CHAPTER iw CONDENSATION OR ACCUMULATION OF ELECTRICITY 788. Condensers or accumulators.—There are apparatus for condensing or accumulating a large quantity of electricity on a comparatively small surface. The phenomena may be conveniently illustrated by means of Epenus’s condenser, fig. 744, which consists of two circular brass plates A and B, mounted on glass legs and provided with pith ball pendulums. Be- tween these is a support C for a glass plate or other solid insulator, and all these can be moved along a support and fixed in any position. a Bi 2 \ If the insulated metal plate B is connected with the prime conductor of an electrical machine which we will suppose gives when worked a small but constant supply of electricity, it will acquire the potential of the machine. If now, breaking connection with the machine, the second plate A is brought near the first, the divergence of the pith ball on B is less, showing that the potential has fallen. If the plate A is moved away, the divergence rises to the original amount, indicating that it has acquired the original potential. Now the charge’ E of any conductor equals N and since, apart from 778 Frictional Electricity ['788— losses by leakage, the quantity of electricity on the plate B is not altered in this series of operations, while the potential is lowered, it follows necessarily that the capacity of the plate B must have been altered by the presence of the second one ; so that E= C’V”: On now connecting the plate B with the prime conductor, while A is near it the machine must be worked some time before the divergence of the pith balls indicates that the plate has again acquired the potential of the machine. il rT | Fig. 745 At this point equilibrium is established, and a limit to the charge is attained which cannot be exceeded, for the potential of B cannot rise above that ot the machine. The effects described are more marked if the plate A is put to earth, and if the two are in contact with a solid dielectric such as glass or ebonite. It follows from this series of experiments that the presence of the second plate has enabled the first one to take a greater charge of electricity than when it is alone. This property is what is called the condensation or accumu- /ation of electricity, and any arrangement in which one conductor is placed in connection with a source of electricity separated by an insulator from a second conductor, in conducting communication with the earth, is called a condenser, the former plate being the collecting, and the other the condensing plate. For the calculation of the charge which a condenser can acquire we refer to art. 806. 789. Slow discharge and instantaneous discharge.—While the plates A and B are in contact with the glass (fig. 721), and the connections inter- rupted, the condenser may be discharged either by a slow or by an instan- taneous discharge. To do this slowly, the plate B is touched with the finger and a spark passes. If A be now touched, a spark passes, and so on by continuing to touch alternately the two plates. The discharge only takes place slowly ; in very dry air it may require several hours. An instantaneous discharge may be effected by means of the d¢scharging rod (fig. 746). This consists of two bent brass rods, terminating in knobs —790} Limit of the Charge of Condensers 779) and joined by a hinge. When provided with glass handles, as in fig. 746, it forms a glass discharging rod. In using this apparatus one of the knobs is pressed against one plate of the condenser, and the other knob. brought near the other. At a certain distance the opposite electricities unite and a spark strikes from the plate to the knob. When the condenser is discharged by the chs. charger no sensation is experienced, even though the latter be held in the hand; of the two conductors the electricity chooses the better, and hence the discharge is effected through the metal, and not through the body. But if, while one hand is in contact with one plate, the other touches the second, the discharge takes place through the breast and arms, and a considerable shock is felt; and the larger the surface of the condenser, and the greater the electric density, the more violent is the shock. 790. Limit of the charge of condensers.—The quantity of electricity which can be accumulated on each plate is, c@/er7s partbus, proportional to the potential of the electricity on the conductor, and to the surface of the plates ; it decreases as the insulating plate is thicker, and it differs with the specific inductive capacity (769) of the substance. There is, however, a limit in the case of each condenser beyond which it cannot be charged. The effect of dielectric polarisation (770) is to put the medium into a state of strain from which it is always trying to release itself, and which is the equivalent of the work done in charging a condenser. This is, indeed, the seat of the electrical energy. It is as if two surfaces were pulled together by elastic threads which repelled each other laterally. When the strain exceeds a certain limit, a discharge takes place through the mass of the dielectric, generally accompanied by light and sound, and with a temporary or perma- nent rupture of the dielectric according as it is fluid or solid. This is what occurs when a substance—glass, for instance—is exposed to a continually increasing weight ; a point is ultimately reached at which the glass gives way, and the weight at that point is a measure of the resistance to fracture of the glass. In like manner, the point at which the electrical discharge takes place is a measure of the electrical strength of the dielectric. This electrical strength is greater in glass than in air, and in dense than in rarefied air. Thus to produce a spark of o°5 cm. in air at the pressures 20, 180, and 685 mm. respectively, the potentials required were 3°23, 12°2, and a6. We may, following Maxwell, further illustrate this point by the twisting of a wire : a wire in which a small mechanical force produces a permanent twist corresponds to the case of the conduction of electricity in a good conductor ; one which having been twisted, reverts to its former shape when the twisting couple is removed, is completely elastic, and corresponds to a perfect insulator with respect to the charge employed. If no permanent twist can be given to the wire by a force which does not break it, the wire is brittle. A dielectric such as air, which does not transmit electricity except by disruptive discharge, may be said 0 be electrically brittle. Fig. 746 780 Frictional Electricety [791- 791. Fulminating pane. Franklin’s plate.—This is a simple form of the condenser, and consists of a glass plate fixed ina wooden frame (fig. 747) ; on each side of the glass, pieces of tinfoil are fastened opposite each other, leaving a space free between the edge and the frame. It is well to cover this part of the glass with an insulating ‘layer of shellac’ varnish. One of the sheets of tinfoil is connected with the ring on the frame by a strip ot tinfoil, so that it can be connected with the ground = by means of a chain. To charge the pane the insulated side is connected with the machine. As the other side communicates with the ground, the two coatings play exactly the part of the condenser. On both plates there are accumulated large quantities of contrary electricities. The pane may be discharged by touching one knob of the discharger against the lower surface, while the other is brought near the upper coating. A spark ensues, due to the recombination of the two electricities ; but the operator experiences no sensation, for the discharge takes place through the wire. But if the connection between the two coatings be made by touching them with the hands, a violent shock is felt in the hands and breast, for the combination then takes place through the body. 792. Leyden jar.—The Leyden jar, so named from the town of Leyden, where it was invented, is essentially a modified condenser, or fulminating pane rolled up. Fig. 748 represents a Leyden jar of the usual French shape in the process of being charged. It consists of a glass jar of any conve- nient size, the interior of which is either coated with tinfoil or filled with thin leaves of copper, or with gold-leaf. Up to a Fig. 748% certain distance from the neck the outside is coated with tinfoil. The neck is provided with a cork, through which passes a brass rod, which terminates at one end in a knob, and communicates with Fig. 747 —792] Leyden Jar ite the metal in the interior. The metallic coatings are called respectively the inner and outer coatings or armatures. Like any other condenser, the jar is charged by connecting one of the coatings with the ground, and the other with the source of electricity. When it is held in the hand by the outer coating, and the knob presented to the positive conductor of the machine, positive electricity is accumulated on the inner and negative electricity on the outer coating. The reverse is the case if the jar is held by the knob, and the outer coating presented to the machine. The positive charge acting inductively across the dielectric glass decomposes the electricity of the outer coating, attracting the negative and repelling the positive, which escapes by the hand to the ground. Thus it will be seen that the action of the jar is the same as that of the condenser, and all that has been said of this applies to the jar, substituting the two coatings for the two plates A and B of fig. 742. Like any other condenser, the Leyden jar may be discharged either slowly or instantaneously. For the latter purpose it is held in the hand by the outside coating (fig. 749), and the two coatings are then connected by means of the simple discharger. Care must be taken to touch /frs¢ the external coating with the discharger, otherwise a smart shock will be felt. To discharge it slowly the jar is placed on an insulated plate, and first the inner and then the outer coating touched, either with the hand or with a metallic conductor. A slight spark is seen at each discharge. ree in ion Ua << HH = = Fig. 749 Fig. 750 Fig. 750 represents a very pretty experiment for illustrating the slow discharge. ‘The rod terminates ina small bell, @, and the outside coating is connected with an upright metal support, on which is a similar bell, e. Between the two bells a light brass ball is suspended by a silk thread. The jar is then charged in the usual manner and placed on the support m. The internal coating contains a quantity of free electricity ; the pendulum is. attracted and immediately repelled, striking against the second bell, to which it imparts its free electricity. Being now neutralised, it is again 782 Frictional Electricity {792- attracted by the first bell, and so on for some time, especially if the air be ‘dry, and the jar somewhat large. This is sometimes spoken of as the cov- vective discharge, since the electricity is carried by moving ponderable bodies. 793. Leyden jars with movable coatings.—This apparatus (fig. 751) is used to demonstrate that in the Leyden jar the opposite electricities are not accumulated on the coatings merely, but are stored up in a state of strain into which the glass is put, and this state of strain is the mechanical equiva- lent of the work done in charging the jar. It consists of a slightly conical glass vessel, B, with movable coatings of zinc or tin, Cand D. ‘These ‘separate pieces placed one in the other, as shown in figure A, form a complete Leyden jar. After the jar is charged, it is placed on an insu- Fig. 751 lating cake ; the inner coating is first removed by the hand, or better bya glass rod, and then the glass vessel. The coatings are found to contain little or no electricity, and if they are placed on the table they are restored to the neutral state. Nevertheless, when the jar is put together again, as represented in the figure at A, a shock may be taken from it almost as strong as if the coatings had not been removed. It is therefore concluded that the coatings principally play the part of conductors, distributing the electricity over the surface of the glass, which thus becomes polarised, and retains this state even when placed on the table, owing to its imperfect conductivity. The experiment may be conveniently made without any special form of apparatus by forming a Leyden jar, of which the inside and outside coatings are of mercury, charging it ; then, having mixed the two coatings, the apparatus is put together again, upon which a discharge may be once more taken. 794. Lichtenberg’s figures.—This experiment well illustrates the oppo- site electrical conditions of the two coatings of a Leyden jar. Holding a jar charged with positive electricity by the hand, a series of lines are drawn with the knob on a cake of resin or vulcanite ; then having placed the jar on an insulator, it is held by the knob, and another series traced by means of the outer coating. If now a mixture of red-lead and flour of sulphur be projected on the cake, the sulphur will attach itself to the positive lines, and the red lead to the negative lines ; the reason being that in mixing the powders the sulphur has become negatively electrified, and the red lead -795] Residual Charge 753 positively. The sulphur will arrange itself in tufts with numerous diverging branches, while the red lead will take the form of small circular spots, in- dicating a difference in the two electricities on the surface of the resin (809). These figures form, in short, a very sensitive electroscope for investigating the distribution of electricity on an insulating surface (754). Fig. 752 represents the ap- pearance of a plate of resin, which has been touched by the knob of a Leyden jar charged with positive electri- city, and has then been dusted with lycopodium powder. 795. Residual charge.—Noi only do the eléctricities adhere to the two surfaces of the in- sulating medium which sepa- rates them, but they penetrate to a certain extent into the interior, as is shown by the following experi- ment :—A condenser is formed of a plate of shellac and movable metal plates. It is then charged, retained in that state for some time, and after- wards completely discharged. On removing the metal coatings and ex- amining both surfaces of the insulator, they show no signs of electricity. After some time, however, each face exhibits the presence of some electricity of the same kind as that of the plate with which it was in contact while the apparatus was charged. This is explained, by some, as a kind of electrical absorption. A phenomenon frequently observed in Leyden jars is of the same nature. When a jar has been completely discharged by bringing the inner and outer coatings in metallic contact, and is then allowed to stand a short time, it exhibits a second charge, which is called the electric restdue. ‘The jar may be again discharged, and a second residue will be ieft, feebler than the first, and so on, for three or four times. Indeed, with a delicate electroscope a long succession of such residues may be demonstrated. The residue is greater the longer the jar has remained charged. The magnitude of the residue further depends on the amount of the charge, and also on the degree in which the metal plates are in contact with the insulator. It varies with the nature of the substance, but there is no residue with either liquids or gases. Faraday found that with paraffine the residue was greatest, then with shellac, while with glass and sulphur it was least of all. Kohlrausch has found that the residue is nearly proportional to the thickness of the insulator. If successive small charges, alternately positive and nega- tive, be imparted to the jar, it is found that the residual charges come out in the reverse order to that in which the original charges go in. This residue is not to be confounded with that observed when a Leyden jar is discharged at the greatest striking distance (810). Fig. 752 784 Frictional Electricity ['795- According to Riess about 44 of the quantity of electricity in a condenser is discharged when the coatings are brought within striking distance d, by means of metal conductors. If the coatings are now brought to a distance 7s @, a second discharge takes place by which +4 of the electricity remaining is got rid of, and so on always in the same ratio until the effects are imper- ceptible. Maxwell proved that a dielectric composed of strata of different insulators may exhibit the phenomena of the residual charge, even though none of the substances composing it exhibit it when alone. A series of superimposed liquid insulators with definite boundaries shows a residual charge ; this is not the case if they are well mixed by shaking. From what has been said as to the state of mechanical strain in which the dielectric of a condenser is thrown when charged with electticity (793), it is not difficult to account for the phenomenon of the residual charge. An elastic body, such as a steel plate, which has been twisted or bent, reverts to its original state when the force which brought about the deformation ceases to act, but not at once quite completely. A certain length of time is required for this alteration to take place, but the change is promoted by any gentle mechanical action, such as tapping, which gives the molecules a certain freedom of motion. Dr. Hopkinson made an experiment with a Leyden jar which is quite ana- logous to this. A glass vessel (fig. 754) contains sul- phuric acid, and init is placed a thinner one, about half fall of the same liquid. Platinum wires dip in the two liquids, one of which is in connection with the prime conductor of an electrical machine, while the other is connected with the earth. The arrangement forms, in short, a con- denser, the coatings of which are sulphuric acid. When, after being thus charged, the jar is discharged, a residual discharge may be taken after some time by again connecting the wires ; if, however, the inner jar be gently tapped with a piece of wood, the residue makes its appearance much more rapidly. The same observer draws a parallel between the phenomena of the residual charge and those of residual magnetism (736). 796. Electric batteries. —The charge which a Leyden jar can take depends on the extent of the coated surface, and for small thicknesses is inversely proportional to the thickness of the insulator. Hence, the larger and thinner the jar the more powerful the charge. But very large jars are expensive, and liable to break; and when too thin, the accumulated electricities discharge themselves through the glass, especially if it is not quite homogeneous. Leyden jars have usually from 4 to 3 square feet of coated surface. For more powerful charges electric batteries are used. An electric battery consists of a series of Leyden jars, whose internal and external coatings are respectively connected with each other (fig. 754). They are usually placed in a wooden box lined on the bottom with tinfoil, which is connected with two metal handles in the sides of the box. The inner coatings are connected with each other by metal rods, and the battery is charged by connecting them with the prime conductor, while the outer ~799] Charging by Cascade 785 coatings are connected with the ground by means of a chain fixed to the handles. A quadrant electrometer (fig. 728) indicates the charge of the bat- tery. Although a large quantity of electricity 1s accu- mulated in the ap- paratus, the diver- gence is not great, — for itis simply due | ' bc com to the free electri- me off) 8 t é city (onsithe (inner a! coating. Thelarger and more numerous they are, the longer is the time required to charge the bat- tery, but the- ef- fects are so much the more powerful (806). To discharge a battery, the coatings are connected by means of the discharging rod, the outside coating being touched first. Care is required, for with large batteries serious and even fatal accidents may occur. 797. The universal discharger.—This is an almost indispensable appa- ratus in experiments with the electric battery. On a wooden stand (fig. 755) are two glass legs, each provided with universal joints, in which movable brass rods are fitted. Between these legs is a small ivory table, on which is placed the object under experiment. The two metal knobs being directed towards the objects, one of them is connected with the outer coating of the battery, and the moment communication is made between the outer and the inner coating by means of the glass discharging rod, a violent shock passes through the object on the table. 798. Charging by cascade.—A series of Leyden jars are placed each separately on insulating supports. The knob of the first is in connection with the prime conductor of the machine, and its outer coating joined to the knob of the second, the outer coating of the second to the knob of the third, and so on, the outer coating of the last communicating with the ground. The inner coating of the first receives a charge of positive electricity from the machine, and the corresponding positive electricity set free by induction on its outer coating, instead of passing to the ground, gives a positive charge to the inner coating of the second, which, acting in like manner, develops .a charge in the third jar, and so on to the last, where the positive electricity developed by induction on the outer coating passes to the ground. The jars may be discharged either singly by connecting the inner and outer coatings of each jar, or simultaneously by connecting the inner coating of the first with the outer of the last. In this way the quantity of electricity necessary to charge one Jar is available for charging a series of jars. 799. Measurement of the charge of a battery. Lane’s electrometer.— 3E | “ ‘i a q Fig. 754 786 Frictional Electricity [799- When the outer and inner coatings of a charged Leyden jar are gradually brought nearer each other, at a certain distance a spontaneous discharge Opes ensues. The dis- tance is called the striking or spark- ing atstance. For the same charge it is inversely pro- portional to the pressure of the air (790), and, with the same jar, but different charges, Ay iM TS —— _ SSS aaa directly propor- tional to the elec- tric density of that point of the inner coating at which the discharge takes place. As the density of any point of the inner coating, other Fig. 755 is proportional to the quantity of electricity in a jar. things remaining the same, is pro- portional to the entire charge, the striking distance The measurement of the charge of a battery, however, by means of the striking distance, can only take place when the charge disappears. By means of Lane’s electrometer, which depends on an application of this principle, the charge of a jar or battery may be measured. This appa- ratus, ¢ (fig. 756), consists of an ordinary Leyden jar, near which there is a Toe UL Tt NM at aD SR ua Fig. 756 vertical metallic support. At = the upper end is a brass rod, " with a knob at one end, which can be placed in metallic con- nection with the outside of the jar : the rod being movable, the knob can be kept at a measured distance from the knob of the inner coating. Fig. 756 repre- sents the operation of measuring the charge of a jar by means of this apparatus. The jar 4, whose charge is to be measured, is placed on an insulated stool with its outer coating in metallic connection with the inner coating of Lane’s jar ¢, —801] Volta’s Condensing Electroscope 787 the outer coating of which is put to earth ; @ is the conductor of the machine. When the machine is worked, positive electricity passes into the jar 0 ; a proportionate quantity of positive electricity is repelled from its outer coating and forms a charge on the inner coating of the electrometer. When this has reached a certain limit, it discharges itself between the two knobs, and as often as such a discharge takes place, the same quantity of positive electricity will have passed from the machine into the battery ; hence its charge is proportional to the number of discharges of the electrometer. 800. Harris’s unit jar—Harris’s unit jar (fig. 757) is an application of the same principle, and is often convenient for measuring quantities of electricity. It consists of a small Leyden phial, 4 inches in length and # inch in diameter, coated to about an inch from the end, so as to expose about 6 inches of coated surface. It is fixed horizontally on a long insulator, and the charging rod connected at P with the conductor of the machine, while the outer coating is connected with the jar or battery by the rod ¢ /. When the charge of electricity in the interior has reached a certain potential depending on the distance of the two balls m and a, a discharge ensues, and marks a certain quantity of electricity received as a charge by the battery, in terms of the charge of the small jar. 801. Volta’s condensing electroscope.—The condensing electroscope invented by Volta is a modification of the ordinary gold-leaf electroscope (774). The rod to which the gold-leaves are affixed terminates in a disc instead of in a knob, and there is another disc of the same size provided with an insulating glass handle. The discs are covered with a layer of insulating shellac varnish (fig. 758). To render very small quantities of electricity perceptible by this apparatus, one of the plates, which thus becomes the collecting plate, is touched with the body under examination. The other plate, the condensing plate, is con- nected with the earth by touching it with the finger. The electricity of the body, being diffused over the collecting plate, acts inductively through the varnish on the other plate, attracting the opposite electricity, but repelling that of like kind. The two electricities thus become accumulated on the two plates just as in a condenser, but there is no divergence of the leaves, for the opposite electricities counteract each other. The finger is now removed, and then the source of electricity, and still there is no diver- gence ; but if the upper plate is raised ‘fig. 759) the neutralisation ceases, and the electricity being free to move diffuses itself over the rod and the leaves, which then diverge widely. The delicacy of this electroscope is in- creased by adapting to the foot of the apparatus two metal rods, terminating in knobs ; for these knobs, being excited by induction from the gold-leaves, react upon them. A still further degree of delicacy is attained if the rods are replaced by two Bohnenberger’s dry piles (839), one of which presents its positive and the other its negative pole. Instead of two gold-leaves there our 2 ste I= Fig. 757 788 Frictional Electricety [801 - is only one; the least trace of electricity causes it to oscillate either to one side or to the other, and at the same time shows the kind of electricity. The condensing electroscope is useful in cases where a large quantity of electricity is available, but at a potential too low to be capable of affecting the ordinary electroscope. Its capacity is made large by the use of the two condensing plates, and thus it receives a relatively large charge when brought into contact with the source. This larger charge must, when connection with the source is broken and the upper plate is removed, raise the potential of the electroscope in proportion to its fall in capacity, since Q = VC (762) and Q is constant. The potential may be thus sufficiently raised to cause a divergence of the gold-leaves. 802. Quadrant electrometer.—Lord Kelvin devised a very sensitive form of electrometer by which accurate measurements of potential may be made. One form of thisinstrument represented in fig. 760 consists of two pairs of quadrants, AA’ BB’, of thin sheet metal, which together form a flat cylindrical box, cut into four equal sectors by two diametral sections at right angles to each other. Each of these quadrants is suspended to the top of the case by a glass stem, and the alternate pairs are con- nected with each other by wires. Each of the pairs is also connected with an insulated binding screw, so that connection can be made with bodies on the outside. In the middle of the quadrant is hung, by a bifilar suspension, what is cailed the zeed/e, which is essentially two quadrants of thin sheet aluminium —803] Quadrant Electrometer 789 (fig. 761) ; for the sake of lightness, parts are cut out as shown by the dotted lines in the figure. If now all the quadrants are in the same electrical condition, the adjust- ment is made so that the two fibres of the suspension are in the same plane which is symmetrical with refer- ence to the space between the quadrants. If now the two pairs of quadrants are at different po- tentials, as when, for instance, they are connected with the two poles of a voltaic cell by means of the binding screws, and if the needle is charged to a given potential, which is usually positive and much higher than that of either pair of quad- rants, one end of the needle will be repelled by the pair of quadrants which are electrified like itself, and will be attracted by the other pair. Fig. 760 Fig. 761 It will thus be subject to the action of a couple tending to set it obliquely to the slit. In order to render the slightest motion of the needle visible, a small silver concave mirror with a radius of about a metre is fixed above it. The light of a petroleum lamp, not represented in the figure, strikes against this, and is reflected as a spot on a horizontal scale. Any deflection of the needle, either on one side or the other, is indicated by the motion of the spot of light on the scale (534). In order to keep the potential of the needle as constant as possible, it is connected with the inner surface of a Leyden jar, sometimes tormed by a glass vessel forming part of the outer case of the electrometer. In the more com- plete forms of instrument there is a small electrical machine (called the veplenisher) whereby the potential of the jar and needle can be brought to any required value, and also a subsidiary electrometer (the gage) which shows when the right value is attained. 803. Thomson’s absolute electrometer.—Another class of electrometers, also invented by Lord Kelvin, give a direct measure of electrical constants 790 Frictional Electricety [803- in absolute measure. Fig. 762 represents a modified form of the electro- meter for class experiments. Two plane metal discs A and B, about 1o cm. in diameter, are kept at a distance from each other, which is small in proportion to their diameters, but which can be very accurately measured. Out of the centre of the upper one is cut a disc ¢; this is suspended by insulating threads from one end of the arm a é of a balance, at the other end of which is a counterpoise, or a scalepan 7. At the end of the arm is a fork, across which is stretched a fine wire ; when the disc is exactly in the plane of the circular band or ring which surrounds it, and which is called the guard ring, this fine wire is. exactly across the interval between two marks in the upright, and its posi- tion can be accurately determined by means of the lens C. The disc and the guard ring are kept at a constant potential, being connected by a wire with a constant source of electri- city, while the other can be kept at any potential or put to earth. Suppose now that the whole system is at the same potential, and that the disc is exactly balanced so as to be in the plane of the guard ring. If now A is electrified to a given potential, while the plate B is connected with the earth, then the body charged with electricity of higher potential—that is, the disc—will be urged towards the body of lower potential, the fixed plate ; and in order to retain it exactly in the plane of the guard ring the force applied at the other end of the lever must be increased. This may be done by altering the distance of the counterpoise, or by adding weights to a scalepan, and the additional weight thus applied is a measure of the attractive force. This may be proved as follows. Let A’OA (fig. 7622) be a plane con- ducting surface of unlimited extent electrified to surface density o, and let P be a point in the neighbour- hood. The charge on a small area a,at A, is ao, and the force which this exerts on a unit charge at P is A’ One: A ao|AP?in the direction AP. Simi- Fig. 7624 larly the force at P due to an equal area at A’, situated symmetrically with respect to P, is ac/A’P*? along A’P. Resolving these two forces into components normal to the surface and parallel thereto, it is easy to see that the latter components are equal and opposite and so cancel each other ; consequently, the effective component of the force at P, due to each small Fig. 762 —803] Thomson's Absolute Electrometer 791 part of the surface, is the component parallel to OP. For the small area at A, this component is ig LOM Weare HA =i £OSTA ION AP? AP Ap? But @ OP/AP, or a cos APO, is the projection of the area a on a sphere through A with centre P, and this projected area divided by the square of the radius AP is the measure of the solid angle which the area a subtends at P. If we put » for this solid angle we have, for the normal component, oy OE eter Ap2 AP Now the resultant force at P due to the whole charged surface may be regarded as the sum of the normal (or effective) forces due to all the small parts of which the surface may be considered as made up ; it may therefore be written (@,+@,+@,+ ....)7=20.0;3 that is to say, the resultant force is obtained by multiplying the total solid angle which the surface subtends at P by the surface-density of the charge. For a surface extending in all directions to a distance which is great in com- parison with OP, the total solid angle is the same as that which a hemisphere subtends at its centre, or 27; hence we get the result that the intensity of the force which any plane surface, uniformly electrified to density o, exerts at a point, whose shortest distance from the surface is small in comparison with its distance from any part of the boundary, is 270, or the force which acts upon a charge Q in the neighbourhood of the surface is 2noQ, and is a repulsion if « and Q are of the same sign and an attraction if they are of opposite signs. In the present case, o being the surface-density of the plate A and disc ¢, the charge of the latter is So, if S is the area of the disc. Again the lower, earth-connected plate, B, becomes electrified to density —a, and consequently the disc is attracted towards the plate B with a force = 2707S. This force can be measured in dynes as explained above (p. 790), and from the result we have to deduce the difference of potentials between the two discs A and B. Calling the potential of the former V, that of the latter V’, and d@ the distance between the plates, we may write, V-We=/fd if f stands for the force which would be exerted upon a unit of positive electricity anywhere between the plates. In words, this equation is a state- ment that the difference of potentials is equal to the work that must be done against electric force to carry a unit of positive electricity from plate B to plate A 760). The force / is made up of a repulsion 270 due to the plate A, and an attraction 270 due to the plate B, or, altogether, f= 470. Conse- quently . Vie aro: 792 Frictional Electricity [803— but, as has been already proved, 2707S =F, oro = , ane 27 Hence V-VWetgnd JE = a, /BmE. 275 5 If the disc ¢ is circular and its radius is a, we have S=7a’, and the difference of potentials is given by the very simple formula ViW= 2, /8r. It is also clear that the experiment may be modified by making F constant and the distance variable. By means of micrometric arrangements the distance of the plates may be varied and measured with very great accuracy. This principle is applied in a portable form of this electrometer. 804. Potential and capacity of a condenser.— These may be most con- veniently investigated by considering the case of a spherical jar. Let us suppose A (fig. 763) to represent an isolated metal sphere of radius R, and let us consider it placed in conducting communication with a source of, say, positive electricity, which is supposed to be at a constant potential V. Then its potential V is zs its charge g= VR, and the ratio of charge to po- tential, or the capacity of the sphere, is R. Suppose now this sphere to be surrounded by a concentric conducting shell or envelope B, which is in connection with the earth, then from the in- ductive action set up, there will now be two electrical layers—one the sphere A, and the other on the inner surface of the sphere B. These will have no action on any external point, which is | only possible provided the charges are equal and contrary. If+Q is the charge on the inner, then — Q is that on the outer sphere (768). ' The sphere A, being still connected with the source, has still the potential V, but its present charge Q. is greater than the charge g which produced the same potential when it was isolated. In the present case, the potential is V= _ i where the first term Fig. 763 on the right is the potential at the centre due to the charge Q of the sphere A taken by itself, and the second term is the potential at the centre due to the charge — Q of the surrounding shell. The charge Q is consequently = V ie R’—-R F 2 . = te es , if we write Z for R’—R the thick- ness of the air-space between the two spherical surfaces. If we multiply numerator and denominator of this expression by 4m, the , ~ ie = 7 when S=47RR’ 7 7 and the capacity is now expression for the capacity takes the form C= —805] Effects of the Electric Discharge 793 is the geometric mean of the areas of the two charged concentric surfaces. If the radii are nearly equal, that is ¢ small, this mean area is nearly enough equal to the area of either sphere. If instead of air there be a solid or liquid dielectric, whose specific induc- tive capacity is x, the formula becomes Q= NEE If the dielectric be partly air and partly some other material, such as glass, then if the thick- ee DOE oy are expression @ is sometimes i ( Mal x) K written Z’, and represents the thickness of the layer of air equivalent to it in specific inductive capacity. It is also called the reduced thickness. Thus, suppose a sphere of radius R=1Io cm., and this is surrounded by an earth-connected metal shell of radius R’ = 10°2 cm., then the thickness of the dielectric (assumed to be air) is 0°2, and the oe: of this condenser is 510 or 51 times as great as that of the ene sphere R. The ratio of the capacities in the two cases is called the condensing force of the given condenser. The formula obtained above for the capacity of a spherical condenser ness of this latter is 6, Q= with spheres of nearly equal radius, namely, ae applies very nearly indeed vis to any condenser formed, like a Leyden jar, of a thin uniform layer ofa di- electric between two parallel conducting surfaces. If R’ is so great that the value of R in the denominator may be disre- garded, we get C=R, which is the expression for the capacity of an isolated sphere (762) ; such a sphere may indeed be regarded as a condenser, in which the layer of air, between it and the sides of the room, represents the dielectric. When z identical Leyden jars are joined in surface, we have a condenser whose capacity is equal to the -fold capacity of a single jar. If these jars are joined in cascade, the capacity of the system is that of a single jar, the dielectric of which is 7 times as thick. THE ELECTRIC DISCHARGE 805. Effects of the electric discharge.—The recombination of the two electricities which constitutes the electrical discharge may be either con- tinuous or sudden: conéimuous, or of the nature of a current, as when the two conductors of a Holtz’s machine are joined by a chain or a wire ; and sudden or disruptive, as when the opposite electricities accumulate on the surface of two adjacent conductors, till their mutual attraction is strong enough to overcome the intervening resistances, whatever they may be. But the difference between a sudden and a continuous discharge is one of degree, and not of kind, for there is no such thing as an absolute non-conductor, and the very best conductors, the metals, offer an appreciable resistance to the passage of electricity. Still the difference at the two extremes of the scale is sufficiently great to give rise to a wide range of phenomena. Riess showed that the discharge of a battery does not consist in a 794. Frictional Electricity [805- simple union of the positive with the negative electricity, but that it consists of a series of successive partial discharges. The direction of the discharge depends mainly on the length and nature of the circuit. Feddersen examined the discharge of a Leyden jar by the arrangement represented in fig. 764, in which the spark of the Leyden jar passes between Fig. 764 the knobs a and 4. On the axis xx, which by means of clockwork is rotated at a known and uniform rate, are two long focus concave mirrors, d and c ; to the axis is also attached a brass strip, the ends of which, / and g, just touch the bare ends of the insulated wires at the moment the spark passes between a@ and 6; at this instant the spark is in the same vertical plane as the principal axis of the mirror. The image of the spark is reflected on the ground glass plate %. Observed in this manner the spark is seen as a narrow band of light, the length of which varied with the duration of the discharge. The duration was found to increase with the striking distance, and with the number of jars. When the resistance through which the circuit took place was small, it was found that the discharge was an oscillatory one, consisting of a series of separate discharges in alternating directions ; the image was traversed by a number of dark lines. With a greater resistance the discharge was a single continuous one, and its image was that of a continuous band of light. With very great resistance the discharge was an zzfermittent one, and consisted of sparks following each other at irregular intervals. These oscillatory discharges may be illustrated by means of a simple hydrostatical experiment. Suppose that in the U-tube (fig. 765) is a valve, S, by which the two tubes are separated, and that water is poured in one so that it is at the height +L above the level OO, and in the other in the corresponding distance —L’ below the level. When the valve is suddenly opened, the water passes through, and only comes to rest in the position OO after several oscillations about this level. Sup- pose the valve to be suddenly closed during the oscillation, it may easily happen that the water is higher in that limb in which it was previously lower. This would represent the case observed by Oettingen with the electrical residues, who found them to be sometimes negative and sometimes positive. -806] Work done by the Discharge of a Leyden Jar 795 Again, if the valve is only slightly opened so that great resistance is offered, the water slowly sinks to its level, the discharge is continuous, and there are no oscillations ; this corresponds to the case in which the elec- trical resistance is very great. We may further compare the dielectric in a state of strain, like the glass of a charged Leyden jar, to a steel band, clamped at one end; if the free end is pulled aside, the plate is in a state of strain, and when this strain is removed the plate comes to rest after making a series of oscillations. To prevent these oscillations the plate must be exposed to a great resistance, by being placed, for instance, in a viscous liquid; in like manner, as we have seen, by offering a great resistance to the electrical discharge, it becomes continuous. The rate at which a vibrating steel plate or a stretched string comes to rest will depend on its mass and on its inertia. In like manner the period of oscillation of an electrical discharge depends on a certain coefficient of self-induction (932), which represents the electro-magnetic inertia of the medium about the circuit. The oscillatory nature of the discharge has been confirmed by the observa- tions of Paalzow on the luminous phenomena seen in highly rarefied gases when it takes place in them, as well as by the manner in which a magnet affects the phenomena. It is also proved by the simultaneous transport of matter between two different electrodes (808). Von Helmholtz had already inferred the necessity of such an oscillating motion from the laws of the con- servation of energy, and Lord Kelvin and Kirchhoff deduced the conditions under which it occurs. 806. Work done by the discharge of a Leyden jar.—The work required 2 2 to charge a Leyden jar is We" Cee a => a V’ ; that is, is pro- portional to the surface and to the square of the potential, and is inversely as the reduced thickness of the insulator. From the principle of the con- servation of energy, this stored-up energy reappears when the jar is dis- charged. It shows itself partly in the form of a spark, partly in the heating effect of the whole system of conductors through which the discharge takes place. When the armatures are connected by a thick short wire, the spark is strong and the heating effect small; if, on the contrary, the jar is dis- charged through a long fine wire, this becomes more heated, but the spark is weaker. If a series of identical jars are each separately charged from the same source, they will each acquire the same potential, which will not be altered if all the jars are connected by their inner and outer coatings respectively. The total charge will be the same as if the battery had been charged directly from the source, and its energy will be W=43Vzg =4VQ ; that is, the energy of a battery of 7 equal jars is the same as that of a single jar of the same thickness but of z times the surface. Let us consider two similar Leyden jars having respectively the capaci- ties c and c’; let one of them be charged to potential V, and let the other remain uncharged. Suppose now that the inner and outer coatings of the jars are respectively connected with each other. Then the energy of the Ci? charged jar alone is W=4-—< , and when it is connected with the other, @ 796 ) Frictional Electricity [806— the original charge will spread itself over the two, so that the energy of the 2 charge in the two jars is W’= mes Hence W : W’=c+c’:c; and there- fore, since c+c’ is always greater than c, there must be a loss of energy. In point of fact, when a charged jar is connected with an uncharged one, a spark passes, the connecting wire is heated, which together are the equivalent of this loss of energy. It follows, further, that when two jars at different potentials are united there is always a loss of energy. If a series of # similar jars are joined in surface, and a given charge of electricity is imparted to them, the energy is inversely as the number of jars; but, when charged from a source of constant potential, the energy is proportional to the number of jars. If, however, the jars are arranged in cascade, then for a given charge the energy is z times that of a single jar, while for a given potential it is 7 times smaller. It is sometimes con- venient to arrange the jars in a combination of the two systems. 807. Physiological effects.—The shock from the electrical machine has been already noticed (792). The shock taken from a charged Leyden jar by grasping the outer coating with one hand and touching the inner with the other is much more violent, and has a peculiar character. With a small jar the shock is felt in the elbow ; with a jar of about a quart capacity it is felt across the chest, and with jars of still larger dimensions in the stomach. A shock may be given to a large number of persons simultaneously by means of the Leyden jar. For this purpose they must form a chain by join- ing hands. If, then, the first touches the outside coating of a charged jar, while the last at the same time touches the knob, all receive a simultaneous shock, the intensity of which depends on the charge, and on the number of persons receiving it. Those in the centre of the chain are found to receive a less violent shock than those near the extremities. With large Leyder jars and batteries the shock is sometimes very dan- gerous. Priestley killed rats with batteries of 7 square feet coated surface, and cats with a battery of about 4} square yards coating. Experience shows that the physiological effect varies with the electrical energy ; thus a discharge from an ordinary electrical machine which gives a spark of nearly a foot may be taken without danger, while one of a few millimetres from a battery of large capacity could not be borne. The duration of the discharge has also an influence ; a battery which gives a violent shock when discharged in ordinary conditions, gives but a feeble one when discharged through a moist string, which only delays the rapidity of the discharge. 808. Luminous effects. —The recombination of two electricities of high potential (76c) is always accompanied bya disengagement of light, as is seen when sparks are taken from a machine, or when a Leyden jar is discharged. The better the conductors on which the electricities are accumulated, the more brilliant is the spark ; its colour varies not only with the nature of the bodies, but also with the nature of the surrounding medium and with the pressure. The spark between two charcoal points is yellow, between two balls of silvered copper it is green, between knobs of wood or ivory it is crimson. In air at the ordinary pressure the electric spark is white -809] Spark and Brush Discharge TOF and brilliant; in rarefied air it is reddish; and in vacuo it is violet. In oxygen, as in air, the spark is white; it is reddish in hydrogen, and green in the vapour of mercury ; in carbonic acid it is also green, while in nitrogen it is blue or purple, and accompanied by a peculiar sound. In general, the higher the potential the greater is the lustre of the spark. When these sparks are examined by the spectroscope (588) they show the lines characteristic of the metals between which the spark passes, and also of the gas in which it takes place. If the knobs are of different metals the lines of both are seen. Part of the energy is accordingly consumed in detaching and volatilising the metal particles on the two electrodes ; when a powerful discharge takes place between a knob of gold and one of silver, some of the latter metal is found on the gold knob, while some gold also is: found on the silver knob. This is a direct proof that the discharge is an oscillatory one (805). 809. Spark and brush discharge.—The shapes which luminous electric phenomena assume may be classed under two heads—the sfarf and the brush. The brush forms when the electricity leaves the conductor in a continuous flow; the spark, when the discharge is discontinuous. The formation of one or the other depends on the nature of the conductor and of the conductors in its vicinity ; and small alterations in the position of the surrounding conductors transform the one into the other. The spark which at short distances appears straight, at longer distances. has a zigzag shape with diverging branches. Its length depends on the density at the part of the conductor from which it is taken ; and to obtain the longest sparks the electricity must be of as high a density as possible, but not so high as to discharge spontaneously. With long sparks the luminosity is different in different parts of the spark. The brush derives its name from’ the radiating divergent arrange- ment of the light, and presents the appearance of a luminous cone, whose apex touches the conductor. Its size and colour differ with the nature and form of the conductor ; it is accompanied by a peculiar hissing noise, very different from the sharp crack of the spark. Its luminosity is far less than that of the spark ; for while the latter can easily be seen by daylight, the former is only visible in a darkened room. The brush discharge may be obtained by placing on the conductor a wire filed round at the end, or, with a powerful machine, by placing a small bullet on the conductor. The brush from a negative conductor is less than from a positive conductor ; the cause of this difference has not been satisfactorily made out, but it may originate in the fact, which Faraday has observed, that negative electricity discharges into the air at a somewhat lower density than positive electricity ; so that a negatively charged knob sooner attains that density at which spontaneous discharge takes place, than does a positively charged one, and therefore discharges the electricity at smaller intervals and in less quantities. When electricity, in virtue of its high density and consequently high electrostatic pressure, issues from a conductor, no other conductor being near, the discharge takes place without noise, and at the places at which it appears there is a pale blue luminosity called the electrical glow, or on points a star-like centre of light. It is seen in the dark by placing a point on the conductor of the machine. It may be regarded as a very short brush. 798 Frictional Electricity [810— 810. Striking distance.—Sir W. Harris by means of his unit jar, and Riess by independent researches, found that for small distances the striking distance is directly proportional to the quantity of electricity, and in- versely proportional to the coated surface ; in other words, it is pro- portional to the po- tential.” For thise/ex- periments Riess used the spark micrometer, which consists of two _metal knobs, Aand B (fig. 9766). prowaded with binding screws, aand 6, and on insu- lating supports, the distance of which from each other could be varied by a micrometric screw. The striking distance varies slightly with the shape of the electrodes ; thus for the same distance the difference of potential required is slightly greater for two spheres than for two plates. The high temperature and short duration of the spark produces a sudden expansion of the air through which it passes, and a compression of the surrounding air. Hence a wave of compression starts from the path of the spark which produces the sound. For greater distances the difference of potential increases less rapidly than the distance, and the greater the distance the less is the rate of increase ; this is seen from the following tables: In the experiments the discharging knots were 2°2 cm. in diameter. Distance | Volts | Distance | Volts cm. cm. orl | 5,490 5°0 | 94,800 O'5 | 26,7 30 70 | 107,700 me | 48,600 ifexe) 119,100 2°0 | 64,800 | 12°0 | 124,200 3°0 76,800 | 15°0 | 127,800 The striking distance in air is virtually the same for the spark proper as for the brush. The influence of pressure on the electric discharge may be studied by means of the electric egg. This consists of an ellipsoidal glass vessel (fig. 767) with metal caps at each end. The lower cap is provided with a stop- cock, so that it can be screwed into an air-pump, and also into a heavy metallic foot. The upper metal rod moves up and down ina leather stuffing- box; the lower one is fixed to the cap. A vacuum having been made, the stopcock is turned, and the vessel screwed into its foot ; the upper part is then connected with a powerful electrical machine, and the lower -812] Fleating Effects 799 one with the ground. On working the machine, the globe becomes filled with a feeble violet light continuous from one end to the other, and resulting from the recomposition of the positive electricity of the upper cap with the negative of the lower. If the FF air is gradually allowed to enter by opening the stop- | cock, the light now appears white and brilliant, and is : only seen as an ordinary intermittent spark. If by means of such an apparatus the pressure of the air is gradually increased, the striking distance is diminished, and with a pressure of 50 atmospheres the discharge of even a powerful machine is stopped. Some beautiful effects of the electric discharge are obtained by means of Geissler’s tubes (590), which will be noticed under Dynamical Electricity. 811. Luminous tube and square.—The /umiznous tube (fig. 768) is a glass tube about a yard long, round which are arranged in a spiral form a series of lozenge-shaped pieces of tinfoil, between which are very short intervals. There is a brass cap with hooks at each end, in which the spiral terminates. If one end be presented to a machine in action, while the other is held in the hand, sparks appear simultane- ously at each interval, and produce a brilliant lumi- nous appearance, especially in the dark. The luminous pane is constructed on the same principle, and consists of a square of ordinary glass, on which is fastened a narrow Strip of tinfoil folded parallel to itself for a great number of times. Spaces are cut out of this strip so as to represent any figure, a portico for example. The pane being fixed between two insulating supports, the upper extremity of the strip is connected with the electrical machine, and the Fig. 768 lower part with the ground. When the machine is in operation, a spark appears at each interval, and reproduces in luminous flashes the object repre- sented on the glass. 812. Heating effects.—Besides being luminous, the electric spark is a source of great heat. When it passes through inflammable liquids, as ether or alcohol, it inflames them. An arrangement for effecting this is repre- sented in fig. 769. It is a small glass cup through the bottom of which passes a metal rod, terminating in a knob and fixed to a metal foot. A £00 Frictional Electricity [812— quantity of liquid sufficient to cover the knob is placed in the vessel. The outer coating of the jar having been connected with the foot by means of a chain, the spark which passes when the two knobs are brought near each other inflames the liquid. With ether the experiment succeeds very well, but alcohol requires to be first warmed. Coal gas may also be ignited by means of the electric spark. A person standing on an insulated stool places one hand on the conductor of amachine which is then worked, while he presents ibis: the other to the jet of gas issuing from S25 = =a a metallic burner. The spark which — — 5 passes ignites the gas. When a battery AADIGAESESCOTASENATIOETGSAUNASAUANTSTONN PETE SOUOTSOTONUUNUAGTOET COUT UTA TNTOSOUT TPP TTTE TUTTE is discharged through an iron or steel Fig. 769 wire, the latter becomes heated, and is even made incandescent or melted if the discharge is very powerful. If a jar is discharged, and the discharge does no other work, then the whole of the energy of the charge (804) appears in the form of heat ; and if the expression for the energy of a condenser $ = (806) be divided by Joule’s equivalent (509), we have H =3 ey as the expression for the total heatin 5 ’ 2 jc p § due to any charge. The laws of this heating effect were investigated independently by Harris and by Riess by means of the e/ec- tric thermometer. In its later forms as modified by Riess, this consists of a glass bulb (fig. 770), closed by a stopper, ¢c, and at- tached toacapillary tube which is bent =. twice, and termi- = nates in an enlarge- ment ; this contains coloured liquid, The whole appa- ratus is fixed on a hinged support, A, which works on the base B, so that it can be inclined and fixed at any given angle. The diameter of the tube being very small compared with that of the enlargement, a considerable displacement of the liquid may take place along the scale without any material alteration in pressure. Before making the experiment the stopper c is opened so as to equalise the pressure. Be- ~813] Magnetic Effects Sol tween the binding screws a and @a fine platinum wire is stretched. When a Leyden jar is discharged through the wire it becomes heated, expands the air in the bulb, and the expansion is indicated by the motion of the liquid along the graduated stem of the thermometer. In this way it was found that the heat in the wire is proportional to the square of the quantity of electricity divided by the surface—a result which follows from the formula already g riven (806). Riess also found that wzth the same charge, but with wires of different dimensions, the rise of temperature ts inversely as the fourth power of the diameter. Thus, compared with a given wire as unity, the 7zse oy temperature in a wire of double or treble the diameter would be 4; or 4, as small; but as the masses of these wires are four and nine times as Lee the PER produced would be respectively } and 4 as a as in a wire of unit thickness. If a jar charged to a given potential is discharged through the evel thermometer, the discharge will take place at a certain smalgnte distance, and a certain Gepression will be produced which is a measure of the heating effect int he thermometer. If now a card is interposed in the path of the discharge, a certain proportion of its energy will be expended in the mechanical perforation of the card, and the proportion in the thermometer will beless. Thus Riess found that that charge which, when passed through air, produced a depression of 15°9, when passed in addition through one card, two cards, and a plate of mica, produced depressions of 11°7, 80, and 6°8 respectively ; showing that the heating effect was less according as more of the energy of the discharge was used for other purposes. When an electric discharge is sent through gunpowder placed on the table of a Henley’s discharger, it is not ignited, but is projected in all directions. But if a wet string is interposed in the circuit, a spark passes which ignites the powder. This arises from the retardation which electricity experiences in traversing a semi-conductor, such as a wet string ; for the heating effect is proportional to the duration of the discharge. When a charge is passed through sugar, heavy spar, fluor-spar, and other substances, they afterwards become phosphorescent in the dark. Eggs, fruit, &c., may be made luminous in the dark in this way. When a battery is discharged through a gold leaf pressed between two glass plates or between two silk ribbons, the gold is volatilised in a violet powder which is finely divided gold. In this way what are called electric portraits are obtained. Siemens showed that when a jar is charged and discharged several times in succession the glass becomes heated. Hence during the discharge there must be movements of the molecules of the glass, as Faraday sup- posed (770) ; we have here, probably, something analogous to the heating produced in iron when it is rapidly magnetised and demagnetised. 813. Magnetic effects.—By the discharge of a large Leyden jar or battery, a steel wire may be magnetised if it is laid at right angles to a con- ducting wire through which the discharge is effected, either in contact with the wire or at some distance. And even a steel rod or needle may be magnetised by placing it inside a spiral of insulated copper wire, A (fig. 771), and passing one or more discharges through it. The polarity depends on the direction in which the electricity enters the coil and the way in which the 3F 802 Frictional Electricity [813- wire is coiled, Thus if the jar is charged in the inside with positive elec- tricity, and the direction in which the wire is coiled is that in which the hands of a watch move, that end at which the positive electricity enters will be a south pole. It is, however, frequently observed that the magnetism is abnormal, and that for the same charge of the jar the north pole is first at one end and then at the other. This is to be re- ferred to the oscillatory character of the dis- charge (805), the position of the poles corre- sponding to that of the last oscillation ; uniform results are obtained when a wet string is in- Fig. 771 cluded in the circuit. To effect a deflection of the magnetic needle by the electric current pro- duced by frictional electricity is more difficult. It may be accomplished by'making use of a galvanometer consisting of 400 or 500 turns of fine silk- covered wire, which is further insulated by being coated with shellac varnish and by separating the layers by means of oiled silk. When the prime con- ductor of a machine in action is connected with one end of the galvanometer wire, and the other with the ground, a deflection of the needle is produced. 814. Mechanical ef- fects.—The mechanical ef- fects are the violent lacera- tions, fractures, and sudden expansions which ensue when a powerful discharge is passed through a badly conducting substance. Glass is perforated, wood and stones are fractured, and gases and liquids are Pn ii oT TTT = violently disturbed. The Ah =I / = mechanical effects of the UTATT ANT : ITU TA UMMA electric spark may be de- Fig. 772 monstrated by a variety of experiments. Fig. 772 represents an arrangement for perforating a piece of glass or card. It consists of two glass columns, with a horizontal cross-piece, in which is a pointed conductor, B. The piece of glass, A, where the point touches it, is surrounded by shellac or oil, to prevent dispersion of electricity over the surface ; it is placed on an insulating glass support, in which is placed a second conductor, terminating also in a point, which is connected with the outside of the battery, while the knob of the inner coating is brought near the knob of B. When the discharge passes between the two conductors the glass is perforated. The experiment succeeds with a single jar only —814] Mechanical Effects 803 when the glass is very thin ; otherwise a battery must be used. To perforate a glass plate 1°5 cm. thick, a striking distance of 16 cm. is required. When the discharge takes place through a piece of cardboard between two points exactly opposite each other, the line of perforation is quite straight ; but if not exactly opposite, a slight hole is seen near the negative point. This phenomenon, which is known as Lullin’s experiment, is probably connected with the fact that negative electricity discharges into air more readily than positive (809) ; in other words, that positive electricity must be raised to a higher potential in order to discharge, which is held to favour the view that there is a specific difference between the two kinds of electricity. The perturbation and sudden expansion which the discharge produces may be illustrated by means of what is known as K7zunersley’s thermometer. This consists of two glass tubes (fig. 773), which fit into metallic caps and communicate with each other. At the top of the large tube is a rod termi- nating in a knob, and moving in a stuffing-box, and at the bottom there is a similar rod with a knob. The apparatus contains water up to the level of the lower knob. When the electric discharge passes between the two knobs, the water is driven out of the larger tube and rises to a slight extent in the small one. The level is immediately re-established, and therefore the phenomenon cannot be due to a rise of temperature. If the upper knob inside a Kinnersley’s thermometer be replaced by a point, and the outside knob is connected with the prime conductor of a machine at work, the electricity discharges itself in the form of a brush, and a permanent displacement of the liquid in the stem shows that this is due to the heating effect of the brush discharge. For the production of mechani- cal effects the universal discharger (fide 773 mise OF great’ service. A piece of wood, for instance, placed on the table between the two con- ‘ductors, is split when the discharge passes. When the discharge is passed through a thin wire this is kinked and bent, and the effects are the more marked as the discharges are stronger and more frequent. At the same time, with certain metals, a fine dust is given off due to a purely mechanical action. A Leyden jar when charged undergoes a true expansion which isnot that due to heat. Electrical polarisation produces characteristic deformations which are known as electrostriction. This was most completely investigated by Quincke, one of whose experiments*is represented in fig. 774. It consists of a glass ZF 2 804 frictional Electricity [814— bulb A about 2 inches in diameter at the end of a narrow capillary tube K, on an enlargement in which a platinum wire, B, is fused. The bulb and a portion of the stem con- tains a conducting liquid, such as water or sulphuric acid, and it is placed in a vessel of ice-cold water, K, which can be connected with the earth by a conduct- ing wire, G. If now this condenser is charged by con- necting the wire B with an electrical machine, while: G is in connection with the earth, there is a distinct depression of the liquid in the tube. When the jar is discharged the liquid resumes its original level. Hence this cannot have been due to heat, apart from the fact that the temperature was kept constant ; nor is it due to a contraction of the thickness of the glass.. The same results are obtained if the outer coating is. insulated by resting it on shellac, T, which in turn is insulated by resting ona slab of india-rubber, the inner coating being put to earth. Similar effects are observed with solid condensers of other materials, and also with liquids. 815. Chemical effects.—When two gases which act on each other are mixed in the proportions in which they combine, a single spark is often: sufficient to determine their combination ; but when either of them is in great excess, a succession of sparks is necessary. Priestley found that when a series of electric sparks was passed through moist air, its volume diminished, and blue litmus introduced into the vessel was reddened. This, Cavendish discovered, was due to the formation of nitric acid. Several compound gases are decomposed by the continued action of the electric spark. With ethylene,, sulphuretted hy- drogen, and ammonia, the decomposition is: complete; while carbonic acid is partially decom- posed into oxy- gen and car- bonic oxide. The electric discharge also by suitable means can feebly decompose water, oxides, and salts; but, though the same in kind, the chemical effects of statical electricity are by no means so powerful and varied as those of dynamical electricity. The chemical action of the spark is easily demon- strated by means of a solution of potassium iodide. A small lozenge- shaped piece of filtering paper, impregnated with this solution, is placed on a glass plate, and one corner connected with the ground. When a few sparks from a conductor charged with positive electricity are taken at the other corner, brown spots are produced, due to the separation of iodine. The electric pistol is a small apparatus which serves to demonstrate the chemical effects of the spark. It consists of a brass vessel (fig. 775), in -816] Chemical Effects 805 which is introduced a detonating mixture of two volumes of hydrogen and one of oxygen, and which is then closed with a cork. In a tubulure in the side there is a glass tube, in which fits a metal rod, terminated by the knobs Aand B_ The vessel is held as represented in fig. 776, and brought near the machine. The knob A becomes negatively, and B positively, electrified by induction from the machine, and a spark passes between the conductor and A. Another spark passes at the same time between the knob B and the side ; this determines the combination of the gases, which is accompanied by a great disengagement of heat, and the vapour of water formed acquires such an expansive force that the cork is projected with a report like that of a pistol. Among the chemical effects must be enumerated the formation of ozone, which is recognised by its peculiar odour, and by certain chemical properties. The odour is perceived when electricity issues from a conductor into the air .~~-——7 a through a series of points. It has been established that ozone is an allotropic modification of oxygen. With these effects may be associated Z a certain class of phenomena observed ~ lat when gases are made to act as the dielec- ai(]| } tric in a charged Leyden jar. An appa- ratus by which this is effected is repre- , sented in fig. 777; it is a modification of one invented by Siemens. It consists of a glass cylinder, E, containing dilute sulphuric acid ; ais a glass tube closed a1) at the bottom, and also containing sul- phuric acid, in an enlargement of which at the top the inner tube ec fits. Thereis a tube, 7, by which gas enters, and one, a’, by which it emerges. When the acids in E and é are respectively connected with the two combs of a Holtz machine, or with the two terminals of a Ruhmkorff’s coil, a certain condition or strain (770) is produced in the dielectric, which is known ie as the szlent discharge or the electric Sein efiuvium. What that condition is cannot be definitely stated ; but it gives rise to powerful and characteristic chemical actions, often differing from those produced by the spark. By this apparatus large quantities of ozone may be produced. | 816. Duration of the electric spark.—Wheatstone measured the duration of the electric spark by means of the rotating mirror which he invented for this purpose. At some distance from this instrument, which can be made to rotate with a measured velocity, a Leyden jar is so arranged that the spark of its discharge is reflected from the mirror. Now, from the laws of reflec- tion (534) the image of the luminous point describes an arc of double the number of degrees which the mirror describes, in the time in which the mirror passes from the position in which the image is visible to that in which it ceases to be so. If the duration of the image were absolutely instanta- ACOA TOT RAT ae CA 806 Frictional Electricity {816— neous, the arc would be reduced to a mere point. Knowing the number of turns which the mirror makes in a second, and measuring, by means of a divided circle, the number of degrees occupied by the image, the duration of the spark would be determined. In one experiment Wheatstone found that this arc was 24°. Now, in the time in which the mirror traverses 360° the image traverses 720°; but in the experiment the mirror made 800 turns in a second, and therefore the image traversed 576,000° in this time ; and as the arc was 24°, the image must have lasted the time expressed by 572455, or satéu5 Of a second. Thus the discharge is not instantaneous, but has a certain duration, which, however, is excessively short. To determine the duration of the electric spark, Lucas and Cazin used a method by which it may be measured in millionths of asecond. The method is an application of the vernier (10). A disc of mica 15 centimetres in dia- meter is blackened on one face, and at the edge are traced 180 equal divi- sions in very fine transparent lines. The disc is mounted on a horizontal axis, and by means of a gas engine it may be made to turn with a velocity of 00 to 300 turns ina second. A second disc of silvered glass of the same radius is mounted on the same axis as the other and very close to it ; at its upper edge six equidistant transparent lines are traced, forming a vernier with the lines on the mica. For this, the distance between two consecutive lines on the two discs is such that five divisions of the mica disc D C corre- spond to six divisions of the glass disc MoD : AB, as seen in fig. 778. Thus the vernier \ ; gives the sixths of a division of the mica ‘ \ \ | p disc (10). In the apparatus the lines AB pine Auk a are not above the lines CD, but are at the Fig. 778 same distance from the axis, so that the latter coincide successively with the former. The mica disc is contained in a brass box, D (fig. 779), on the hinder face of which is fixed the vernier. In the front face isa glass window, O, through which the coincidence of the two sets of lines can be observed by means of a magnifying lens, L. The source of electricity is a battery of 2 to 8 jars, each having a coated surface of 1,243 square centimetres, and charged continuously by a Holtz machine. The spark strikes between two metal balls aand 4, 11 millimetres in diameter. Their distance can be varied, and at the same time measured, by means of a micrometric screw, 7 The two opposite electricities arrive by wires 7 and 7, and the sparks strike at the principal focus of a condensing lens placed in the collimator C, so that the rays which fall on the vernier are parallel. The motion is transmitted to the toothed wheels and to the mica disc by means of an endless band, which can be placed on any one of three pulleys. P, so that the velocity may be varied. At the end of the axis of the pulleys is a bent wire which moves a counter, V, that marks on three dials the number of turns of the disc. These details being premised, suppose the velocity of the disc is 400 turns in a second. In each second 4oo x 180, or 72,000 lines pass before the observer’s eye in each second ; hence an interval of 73455 of a second elapses. between two consecutive lines. But as the spark is seen only when one of the lines of the disc coincides with one of the six lines of the ver- —816] Duration of the Electric Spark 807 nier, and as this gives sixths of a division of the movable disc, when the latter has turned through a sixth of a division, a second coincidence is produced ; so that the interval between two successive coincidences is I 72000 x 6 That being the case, let the duration of a spark be something between 23 and 46 ten-millionths of a second ; if it strikes exactly at the moment of a coincidence, it will last until the next coincidence ; and owing to the per- sistence of impressions on the retina (639) the observer will see two luminous = 0'0000023 of a second. lines. But if the spark strikes between two coincidences and has ceased when the third is produced, only one brilliant line is seen. Thus, if with the above velocity sometimes 1 and sometimes 2 bright lines are seen, the dura- tion of the spark is comprised between 23 and 46 ten-millionths of a second. By experiments of this kind, with a striking distance of 5 millimetres between the balls a and 4, and varying the number of the jars, Lucas and Cazin obtained the following results :— Duration in millionths Number of jars of a second Ls é ; : ; : Pats 4 ; ; : ; AT 6 45 8 47 808 Frictional Electricity [816— It will thus be seen that the duration of the spark increases with the number of jars. It also increases with the striking distance ; but it is inde- pendent of the diameter of the balls between which ang the spark strikes. The spark of electrical machines a \ has so short a duration that it could not be measured with the chronoscope. 817. Velocity of electricity.—To determine the . velocity of electricity, Wheatstone constructed an ami apparatus the principle of which will be understood from fig. 780. Six insulated metal knobs were ar- ranged in a horizontal line on a piece of wood called — tl p- a spark board; of these the knob I was connected with the outer, while 6 could be connected with the inner coating of a charged Leyden jar; the knob 1 was the tenth of an inch distant from the knob 2 ; while between 2 and 3a quarter of a mile of insulated wire was interposed ; 3 was likewise a tenth of an inch from 4, and there was a quarter of a mile of wire between 4 and 5 ; lastly, 5 was a tenth of an inch from 6, from whicha wire led directly to the inner coating of the Leyden jar. Hence, when the jar was discharged by connecting the wire from 6 with the inner coating of the jar, sparks would pass between 1 and 2, between 3 and 4, and between 5 and 6. Thus the discharge, supposing it to proceed from the inner coating, has to pass in its course through a quarter of a mile of wire between the first and second spark, and through the same distance between the second and third. The spark board was arranged at a distance of 10 feet from the rotating mirror, and at the same height, both being horizontal; and the observer looked down on the mirror. Thus the sparks were visible when the mirror made an angle of 45° with the horizon. Now, if the mirror were at rest, or had only a small velocity, the images of the three spots would be seen as three dots :, but when the mirror had a certain velocity these dots appeared as lines, which were longer as the rotation was more rapid. The greatest length observed was 24°, which, with 00 revolutions in a second, can be shown to correspond to a duration of 57353 of a second. Witha sow rotation the lines present the appearance ; they are quite parallel, and the ends in the same line. But with greater velocity, and when the rotation took place from left to right, they presented the appearance , and when it turned from right to left the appearance , because the image of the centre spark was formed after the lateral ones. Wheatstone found that this displacement amounted to half a degree before or behind Be others ; accordingly this arc corre- sponds to a duration of about the ;;23555 of a second ; the space traversed in this time being a quarter of a mile, gives for the velocity of electricity in the wire used 288,000 miles ina fecoati which is greater than that of light. For Atmospheric Electricity reference must be made to the chapter on Meteorology. ee 780 —818] Galvani’s Experiment and T. heory 809 BOOK xX DYNAMICAL ELECTRICITY CHAPTER «I VOLTAIC PILE. ITS MODIFICATIONS 818. Galvani’s experiment and theory.—The fundamental experiment which led to the discovery of dynamical electricity is due to Galvani, Pro- fessor of Anatomy in Bologna. Occupied by investigations on the in- fluence of electricity on the nervous excitability of animals, and especially of the frog, he ob- served that when the lumbar nerves of a dead frog were connected with the crural muscles by a metallic circuit, the latter became briskly contracted. To repeat this celebrated experi- ment, the legs of a recently killed frog are prepared, and the lumbar nerves on each side of the vertebral column are exposed in the form of white threads. A metal conductor, com- Fig. 781 posed of zinc and copper, is then taken (fig. 781), and one end introduced between the nerves and the vertebral column, while the other touches one of the muscles of the thighs or legs ; at each contact a:smart contraction of the muscles ensues. Galvani had some time before observed that the electricity of machines produced in dead frogs analogous contractions, and he attributed the pheno- mena first described to an electricity inherent in the animal. He assumed 7, oe y Z iwMYG $l Z Zip MT ¢ SELL LALLA 810 Dynamical Electricity [818— that this electricity, which he called wztal fluid, passed from the nerves to the muscles by the metallic arc, and was thus the cause of contraction. This theory met with great support, especially among physiologists, but it was not without opponents. The most considerable of these was Alexander Volta, Professor of Physics in Pavia. 819. Volta’s fundamental experiment.—Galvani’s attention had been exclusively devoted to the nerves and muscles of the frog; Volta’s was directed upon the connecting metal. Resting on the observation, which Galvani had also made, that the contraction is more energetic when the con- necting arc is composed of two metals than when there is only one, Volta attributed to the metals the active part in the phenomenon of contraction. He assumed that the disengagement of electricity was due to their contact, and that the animal parts officiated only as conductors, and at the same time as a very sensitive electroscope. By means of the condensing electroscope, which he had then recently invented, Volta devised several modes of showing the disengagement of electricity on the contact of metals, of which the following is the easiest to perform :— The moistened finger being placed on the upper plate of a condensing electroscope (fig. 758), the lower plate is touched with a plate of copper, ¢, soldered to a plate of zinc, z, which is held in the other hand. On breaking the connection and lifting the upper plate (fig. 759), the gold leaves diverge, and, as may be proved, with negative electricity. Hence, when soldered together, the copper is charged with negative electricity, and the zinc with positive electricity. The electricity could not be due either to friction or pressure ; for if the condensing plate, which is of copper, is touched with the zinc plate z, the copper plate to which it is soldered being held in the hand, no trace of electricity.is observed. A memorable controversy arose between Galvani and Volta. The latter was led to give greater extension to his contact theory, and propounded the principle that when ¢wo heterogeneous substances are placed in contact, one of them always assumes the positive and the other the negative electrical condition. In this form Volta’s theory obtained the assent of the principal philosophers of his time. Galvani, however, made a number of highly interesting experiments with animal tissues. In some of these he obtained indications of contraction, even though the substances in contact were quite homogeneous. $20. Disengagement of electricity in chemical actions.—The contact theory which Volta had propounded, and by which he explained the action of the pile, soon encountered objectors. Fabroni,a countryman of Volta, having observed that, in the pile, the discs of zinc became oxidised in contact with the acidulated water, thought that this oxidation was the principal cause of the disengagement of electricity. In England Wollaston soon advanced the same opinion, and Davy supported it by many ingenious experiments. It is true that in the fundamental experiment of the contact theory (819) Volta obtained signs of electricity. But De la Rive showed that if the zinc is held in a wooden clamp, all signs of electricity disappear, and that the same is the case if the zinc is placed.in gases, such as hydrogen or nitrogen, which exert upon it no chemical action. De la Rive accordingly concluded -820] Desengagement of Electrictty in Chemtcal Actions 811 that in Volta’s original experiment the disengagement of electricity is due to the chemical actions which result from the perspiration and from the oxygen of the atmosphere. The development of electricity in chemical actions may be demonstrated in the following manner by means of the condensing electroscope (801) :—A disc of moistened paper is placed on the upper plate of the condenser, and on this a zinc capsule, in which some very dilute sulphuric acid is poured. A platinum wire, communicating with the ground, but insulated from the sides of the vessel, is immersed in the liquid, and at the same time the lower plate of the condenser is also connected with the ground by touching it with the moistened finger. On breaking contact and removing the upper plate, the gold leaves are found to be positively electrified, proving that the upper plate has received a charge of negative electricity. By a number of analogous experiments it may be shown that various. chemical actions are accompanied by a disturbance of the electrical equili- brium ; though of all chemical actions those between metals and liquids are: the most productive of electricity. All the various resultant effects are in accordance with the general rule, that when a liquid acts chemically on a metal the liquid assumes the positive, and the metal the negative, condition. In the above experiment the sulphuric acid, by its action on zinc, becomes positively electrified, and its electricity passes off through the platinum wire into the ground, while the negative electricity excited on the zinc acts on the condenser just as an excited rod of sealing-wax would do. In many cases the electrical indications accompanying chemical actions. are but feeble, and require the use of a very delicate electroscope to render them apparent. Thus, one of the most energetic chemical actions, that of sulphuric acid upon zinc, gives no more free electricity than water alone does. with zinc. Opinion—which, in this country at least, had, mainly by the influence of Faraday’s experiments, tended in favour of the purely chemical origin of the electricity produced in voltaic action—-has of late inclined more and more towards the contact theory. The following experiments, due to Lord Kelvin, afford perhaps the most conclusive arguments hitherto adduced in favour of the latter view :— A very light metal bar is suspended by fine wire, so as to be movable about an axis perpendicular to the plane of a disc made up of two half discs, one of zinc, Z, and the other of copper, C (fig. 782). The light bar is counterpoised so as to be exactly over one half of the line of separa- tion of the two discs. When the discs are placed in contact and the bar is charged posi- tively by being connected with a Leyden jar, the barmoves from the zinc towards the copper ; if the jar, and therefore the bar, is charged negatively, its motion is in the opposite direction. The same results are ob- tained when the discs are connected by a wire, thus showing that the contact of the two metals causes fhem to assume different electrical conditions, the zinc taking the positive, and the copper the negative, electricity. When, however, the two halves, instead of being in metallic contact, are , Fig. 782 S12 Dynamical Electricity [820- connected by a drop of water, no change is produced in the position of the bar by altering its electrification, provided it hangs quite symmetrically rela- tively to the two halvesof the ring. This result shows that, under the circum- stances mentioned, no difference is produced in the electrical condition of the two metals. Hence the conclusion has been drawn by Lord Kelvin and others, that the movement of electricity in the galvanic circuit is entirely due to the electrical difference produced at the surfaces of contact of the dis- similar metals. These results have been confirmed by some very careful experiments by Professor Clifton. There are, however, other facts which are not easily harmonised with this view ; and indeed the last-mentioned experiment can hardly be regarded as proving that in a// cases two different metals, connected by an electrolytic liquid (864), assume the same electrical condition. It may, however, be regarded as possible, or even probable, that the contact between the metals and the liquids of a cell contributes, at least in some cases, to the production of the current. A most complete discussion of the question as to the seat of electromotive forces in the voltaic cell is published in a series of papers by Prof. Lodge in the nineteenth volume of the ‘ Philosophical Magazine.’ 821. Current electricity.—When a plate of zinc and a plate of copper are partially immersed in dilute sulphuric acid, no electrical or chemical change is apparent beyond perhaps a slight disengagement of hydrogen from the surface of the zinc plate. If now the plates are placed in direct contact, or, more conveniently, are connected by a metal wire, the chemical action sets in, a large quantity of hydrogen is disengaged ; but this hydrogen is no longer dis- engaged at the surface of the zinc, but at the surface of the copper plate. Here then we have to deal with something more than mere chemical action, for chemical action would be unable to explain either the increase in the quantity of hydrogen disengaged when the metals touch, or the fact that this hydrogen is now given off at the surface of the copper plate. At the same time, if the wire is examined it will be found to possess many remarkable thermal, magnetic, and other properties which will be afterwards described. In order tounderstand what here takes place, let us suppose that we have two insulated metal spheres, and that one is charged with positive and the other with negative electricity, and that they are momentarily connected by means of a wire. Electricity will pass from a place of higher to a place of lo wer potential—that is, from the positive along the wire to the negative— and the potentials become equal. This is, indeed, nothing more than an electrical discharge taking place through the wire ; and during the infinitely short time in which this is accomplished, it can be shown that the wire exhibits certain heating and magnetising effects, of which the increase of temperature is perhaps the easiest to observe. If now we can imagine some agency by which the different electrical conditions of the two spheres are renewed as fast as they are discharged, which is what very nearly takes —822] Voltatc Couple. Electromotive Series 813 place when the two spheres are respectively connected with the two con- ductors K and K’ of a Holtz machine (figs. 730, 731), this equalisation of potentials, thus taking place, is virtually continuous, and the phenomena above mentioned are also continuous. Now this is what takes place when the two metals are in contact in a. liquid which acts upon them unequally. This is independent of hypothesis as to the cause of the phenomena—whether the electrical difference is pro- duced only at the moment of contact of the metals, or whether it is due to the chemical action, or tendency to chemical action, between the metal and the liquid. The rapidly succeeding series of equalisations of potential, which takes place in the wire, being continuous, so long as the chemical action continues, is what is ordinarily spoken of as the electrical current. If we represent by +¢ the potential of the copper plate, and by —e the potential of the zinc, then the electrical difference—that is, the difference of potentials—is +e—(-e)=2e. And this is general ; the essential point of any such combination as the above is, that it maintains, or tends to maintain, a difference of potentials, which difference is constant. If, for instance, the zinc plate be connected with the earth which is at zero potential, its potential also becomes zero ; and since the electrical difference remains constant, we have for the potential of the copper plate +2e. Similarly, if the copper be connected with the earth, the potential of the zinc plate is negative and is -- 2e. The conditions under which a current of electricity is formed in the above experiment may be further illustrated by reference to the conditions which determine the flow of water between two reservoirs containing water at dif- ferent levels. If they are connected by a pipe, water will flow from the one at a higher level to the one at a lower level until the water in the two. is at the same level, when of course the flow ceases. If we imagine the lower reservoir so large that any water added to it would not affect its level— if it were the sea, for example—that would represent zero level, and if the: higher reservoir could be kept at a constant level there would be a constant flow in the pipe. We must be careful not to dwell too much on this analogy. It is not to: be supposed that in speaking of current of electricity we mean to assert that anything actually flows—that there is any actual transfer of matter. We say ‘electricity flows’ or ‘acurrent is produced,’ in much the same sense as that in which we say ‘sound or light travels.’ 822. Voltaic couple. Electromotive series.—The arrangement just described, consisting of two metals in metallic contact, and a conducting liquid in which they are placed, constitutes a szwple voltaic element, or couple, or cell. So long as the metals are not in contact, the couple is said to be: open, and when connected it is closed. According to the chemical view, to which we shall for the present pro- visionally adhere, it is not necessary for the production of a current that one of the metals be unaffected by the liquid, but merely that the chemical action upon the one be greater than upon the other. For then we may assume that the current produced would be due to the difference between the differ- ences of potential which each of the metals separately produces by its con-. tact with the liquid. _ If the differences of potentials were absolutely equal— a condition, however impossible of realisation with two distinct metals—we: S14 | Dynamical Electricety [822~- must assume that when the metals are joined no current would be produced. The metal which is most attacked is called the foszt7ve or generating plate, cand that which is least attacked the zegat¢zve or collecting plate. The posi- tive metal determines the direction of the current, which proceeds zz the liquid from the positive to the negative plate, and owt of the liquid through the connecting wire from the negative to the positive plate. In speaking of the advection of the current the direction of the positive electricity is always understood. In the fundamental experiment, not only the connecting wire, but also the liquid and the plates, are traversed by the electrical current—are the scene -of electrical actions. The mere immersion of two different metals in a liquid is not alone suffi- cient to produce a continuous current ; there must be chemical action. When a platinum anda gold plate are connected with a delicate galvanometer, and immersed in pure nitric acid, no current is produced ; but on adding a drop of hydrochloric acid a strong current is excited, which proceeds in the liquid from the gold to the platinum, because the gold is attacked by the nitro- hydrochloric acid, while the platinum is less so, if at all. As a voltaic current is produced whenever two metals are placed in metallic contact in a liquid which acts more powerfully upon one than upon the other, there is a great choice in the mode of producing such currents. In reference to their electrical deportment, the metals have been arranged in what is called an electromotive series, in which the most electroposttive are at one end, and the most electronegative at the other. Hence when any two of these are placed in contact in dilute acid, the current in the connecting wire proceeds from the one lower in the list to the one higher. The principal metals range themselves as follows :— {?- 210 5. Iron Io. Silver 2. Cadmium 6. Nickel 11. Gold aan 7. Bismuth 12. Platinum 4. Lead 8. Antimony 13. Graphite 9g. Copper It will be seen that the electrical deportment of any metal depends on the metal with which it is associated. Iron, for example, in dilute sulphuric acid is electronegative towards zinc, but is electropositive towards copper ; copper in turn is electronegative towards iron and zinc, but is electropositive towards silver, platinum, or graphite. 823. Electromotive force.—The force in virtue of which continuous electrical effects are produced throughout a circuit consisting of two metals in metallic contact in a liquid which acts unequally upon them, is usually called the electromotive force. The electromotive force of a cell (written shortly E.M.F.) is equal to the difference of potentials of the terminals of the cell, when these terminals are not connected so that no current is flow- ing. The E.M.F. of the cell is the same whether a current is flowing or not, depending only on the metals and liquid used, but the difference of potential of the terminals falls as soon as a current is allowed to flow, to a greater extent as the current is stronger. The electromotive force of a cell is greater in proportion to the distance of the two metals from each other in the series. That is to say, it is greater the greater the difference between —823] Electromotive Force 815 the chemical action upon the two metalsimmersed. Thus the electromotive force between zinc and platinum is greater than that between zinc and iron, or between zinc and copper. The law established by experiment is, that ¢ie electromotive force between any two metals ts equal to the sum of the electro- motive forces between all the intervening metals. Thus the electromotive force of a cell having zinc and platinum for its plates, is equal to the sum of the electromotive forces of cells having zinc and iron, iron and copper, and copper and platinum. ; The electromotive force of acellisinfluenced by the condition of the metal for given metals ; rolled zinc, for instance, is negative towards cast zinc. It also depends on the degree of concentration of the liquid; in dilute nitric acid zinc is positive towards tin, and mercury positive towards lead ; while in con- centrated nitric acid the reverse is the case, mercury and zinc being respec- tively electronegative towards lead and tin. The nature of the liquid also influences the direction of the current. If two plates, one of copper and one of iron, are immersed in dilute sulphuric acid, a current is set up proceeding through the liquid from the iron to the copper ; but if the plates, after being washed, are placed in solution of potassium sulphide, a current is produced in the opposite direction—the copper is now the positive metal. Other examples may be drawn from the following table, which shows the electric deportment of the principal metals with three different liquids. It is arranged like the preceding one : each metal being electropositive towards any one lower in the list, and electro- negative towards any one higher. Caustic potass Hydrochloric acid ee Zinc Zing Zinc Tin Cadmium Copper Cadmium Tin Cadmium Antimony Lead Tin Lead Iron Silver Bismuth Copper Antimony Iron Bismuth Lead Copper Nickel Bismuth Nickel Silver Nickel Silver Antimony Iron A voltaic current may also be produced by means of two liquids and one metal. This may be shown by the following al experiment :—In a beaker containing strong nitric acid is placed a small porous pot (fig. 784), con- taining strong solution of caustic potass. If now two platinum wires connected with the two ends of a galvanometer (842) are immersed respectively in the alkali and in the acid, a voltaic current is produced, proceeding in the wire from the nitric acid to the potass, which thus correspond re- spectively to the negative and positive plates in ordinary couples. A metal which is acted upon by a liquid can be protected from solution by placing in contact with it a more electropositive metal, and thus forming 816 Dynamical Electricity [823- a simple voltaic circuit. This principle is the basis of Davy’s proposal to. protect the copper sheathings of ships, which are rapidly acted upon by sea- water. If zinc or iron is connected with the copper, the metal so used is dis- solved and the copper protected. Davy found that a piece of.zinc the size of a nail was sufficient to protect a surface of forty or fifty square inches ; unfortunately the proposal has not been of practical value, for the copper must be attacked to a certain extent to prevent the adherence of marine plants and shellfish. 824. Poles and electrodes.—If the wire oapeeee the two terminal plates of a voltaic couple is cut, it is clear, from what has been said about the nin and direction of the current, that positive electricity will tend to accumulate at the end of the wire attached to the copper or negative plate, and negative electricity on the wire attached to the zinc or positive plate. These terminals have been called the oles of the battery. For experimental purposes, more especially in the decomposition of salts, plates of platinum are attached to the ends of the wires. Instead of the term? poles, the word electrodes (7Aextpov, and 6d0s, a way) is frequently used ; for these are the ways through which the respective electricities emerge. It isimportant not to confound the positive A/aze with the positive fole or electrode. The positive pole is that connected with the negative plate, while the negative pole is connected with the unm 4m | em! positive plate. i), ssa | 825. Voltaic pile. Voltaic battery.—When a acne series of voltaic cells is arranged so that the on wi zinc of one cell is connected with the copper TTT Mu of another, the zinc of this with the copper of another, and so on, the arrangement is called a vol- taic battery ; and by its means the effects produced by a single cell are capable of being very greatly —— Za __ increased. Hl nn il The earliest of these arrangements was devised by —————_—— Volta himself. It consists (fig. 785) of a series of discs piled one over the other in the following order :—At the bottom, on a frame of wood, is a disc of copper, then a disc of cloth moistened by acidulated water or by brine, then a disc of zinc ; on this a disc of copper, and another disc of moistened cloth, to which again follow as many sets of copper-cloth-zinc, always in the same order, as may be convenient, the highest disc being of zinc. The discs are kept in a vertical position by glass rods. It will be readily seen that we have here a series of simple voltaic couples, the moisture in the cloth acting as the liquid in the cases already mentioned, and that the terminal zinc is the negative and the terminal copper the positive pole. From the mode of its arrangement, and from its, discoverer, the apparatus is known as the voltaic pile, a term applied to all apparatus of this kind for accumulating the effects of dynamical electricity. ig Ma —826] Wollaston’s Battery 817 The distribution of electricity in the pile varies according as it is in con- nection with the earth by one of its extremities, or as it is insulated by being placed on a non-conducting cake of resin or glass. In the former case, the end in contact with the ground is neutral, and the rest of the apparatus contains only one kind of electricity ; this is negative if the copper disc, and positive if the zinc disc, is in contact with the ground. In an insulated pile the electricity is not uniformly distributed. By means of a proof plane and electroscope it may be demonstrated that the middle part is in a neutral state, and that one half is charged with positive and the other with negative electricity, the potential increasing from the middle to the ends. The half terminated by a zinc disc is charged with nega- tive electricity, and that by a copper with positive electricity. The pile is thus similar to a charged Leyden jar; with this difference, however, that when the jar has been discharged by connecting its two coatings, the elec- trical effects cease ; while in the case of the pile, the cause which originally brought about the distribution of electricity restores this state of charge after the discharge ; and the continuous’ succession of charges and dis- charges forms the current. The effects of the pile will be discussed in other places. 826. Wollaston’s battery.—The original form of the voltaic pile has a great many inconveniences, and possesses now only an historical interest. It has received a great many improvements, the principal object of which has been to facilitate manipulation, and to produce greater electromotive force. One of the earliest of these modifications was the crown of cups, or couronne des tasses, invented by Volta himself. An improved form of this is known as Wollaston’s battery (fig. 786) ; itZis arranged so that when the current is not wanted the action of the battery can be stopped. eile: 818 Dynamical Electricity [826- The plates Z are of thick rolled zinc, and usually about eight inches in length by six in breadth. The copper plates, C, are of thin sheet, and bent so as to surround the zincs without touching them, contact being prevented by small pieces of cork. To each copper plate a narrow strip of copper, a, is soldered, which is bent twice at right angles and is soldered to the next zinc plate ; and the first zinc, Z, is surrounded by the first copper C ; these two constitute a couple, and each couple is immersed in a glass vessel, con- taining acidulated water. The copper, C, is soldered to the second zinc by the strip 0, and this zinc is in turn surrounded by a second copper, and so on. 3 Fig. 786 represents a pile of sixteen couples united in two parallel series of eight each. All these couples are fixed to across frame of wood, by which they can be raised or lowered at pleasure. When the battery is not wanted, the couples are lifted out of the Jiquid. The water in these vessels is usually acidulated with 4 sulphuric and 4 nitric acid. 827. Enfeeblement of the current in batteries. Secondary currents. The various batteries already described—Volta’s, Wollaston’s, and Hare’s, which consist essentially of two metals and one liquid—labour under the objection that the currents produced rapidly diminish in'strength. This is due principally to three causes : the first is the decrease in the chemical action owing to the neutralisation of the sulphuric acid by its com- bination with the zinc. This is a necessary action, for upon it depends the current ; it therefore occurs in all batteries, and is without remedy except by replacement of acid and zinc. The second is due to what is called Jocal action ; that is, the production of small closed circuits in the active metal, owing to the impurities it contains. These local currents rapidly wear away the active plate, without contributing anything to the continuance of the general current. They are remedied by amalgamating the zinc with mercury, by which chemical action is prevented until the circuit is closed, as will be more fully explained (837). The third arises from the production of an inverse electromotive force, which acting against the electromotive force of the battery or cell tends to destroy it totally or partially. Inthe fundamental experiment (fig. 783), when the circuit is closed, zinc sulphate is formed, which dissolves in the liquid, and at the same time a layer of hydrogen gas is gradually formed on the surface of the copper plate. This diminishes the activity of the combination in more than one way. In the first place, it interferes with the contact between the metal and the liquid ; in the second place, in proportion as the copper becomes coated with hydrogen, we have virtually a plate of hydrogen instead of a plate of copper opposed to the zinc, and in addition, the hydrogen, by reacting on the zinc sulphate, which accumulates in the liquid, gradually causes a deposition of zinc on the sur- face of the copper ; hence, instead of having two different metals unequally attacked, the two metals become gradually less different, and, consequently, the total effect becomes weaker and weaker. The folarisation of the plate (as this phenomenon is termed) may be destroyed by breaking the circuit and exposing the copper plate to the air; the deposited hydrogen is thus more or less completely got rid of, and on again closing the circuit the current has nearly its original strength. The same result is obtained when the current of another —829] Daniell’s Battery . 819 battery is transmitted through the battery in a direction opposite to that of the first. When platinum electrodes are used to decompose water, a similar pheno- menon is produced, called polarisation of the electrodes, which may be illus- trated by an arrangement represented in fig. 787, in which B is a constant cell, V a voltameter (868), G a galvano- meter (842), and H a mercury cup. The wire L being disconnected from H, a current is produced in the volta- meter, the direction of which is from ° 5 ony P to P’; if nowthe wire F be detached —.) from sd, thd: be connected there. (lw with, a current is produced through Pll the galvanometer, the direction of B which is from P’ to P; that is, the opposite of that which the cell had produced in the voltameter. Becquerel and Faraday have shown that this polarisation of the metals results from the deposits caused by the passage of the current, and an important application of this phenomenon will be found described farther on (872), Fig. 787 CONSTANT CURRENTS 828. Constant currents.—With few exceptions, batteries composed of elements with a single liquid have almost gone out of use, in consequence of the rapid enfeeblement of the current due to polarisation. They have been replaced by batteries with two liquids, which are called constant batteries, because their action continues without material alteration for a considerable period of time. The essential point to be at- tended to in securing a constant current is to prevent the polarisation of the inactive metal ; in other words, to hinder any permanent depo- sition of hydrogen on its surface. This is effected by placing the inactive metal in a liquid upon which the deposited hydrogen can act chemically. 829. Daniell’s battery.—This was the first form of the constant battery, and was_ in- vented by Daniell in the year 1836. As re- gards the constancy of its action, it is perhaps still the best of all constant batteries. Fig. 788 represents a single element. A glass or porce- lain vessel, V, contains a saturated solution of copper sulphate, in which is immersed a copper perforated cylinder, G, open at both ends. At the upper part of this cylinder there is an annular shelf, G, perforated and below the level of the solution ; this is intended to support crystals of copper sulphate to replace that decom- posed as the electrical action proceeds. Inside the cylinder is athin porous 2 en. 820 Dynamical Electricity ) [829- vessel, P, of unglazed earthenware, which contains dilute sulphuric acid, and in itis placed the cylinder of amalgamated zinc, Z. Two thin strips of copper p and 2, fixed by binding screws to the copper and to the zinc, serve for connecting the elements in series. When the circuit of a Daniell’s element is closed, the hydrogen resulting from the action of the dilute acid on the zinc, ates of being liberated on the surface of the copper plate, meets with tive copper sulphate, and reduces it with the formation of sulphuric acid and metallic copper, which is deposited on the surface of the copper plate. In this way copper sulphate in solution is taken up ; and if it were all consumed, hydrogen would be deposited on the copper, and the current would lose its constancy. This loss is prevented by the crystals of copper sulphate which keep the solution saturated. The sulphuric acid produced by the decomposition of the sulphate permeates the porous cylinder, and tends to replace the acid used by its action on the zinc ; and as the quantity of sulphuric acid formed in the solution of copper sulphate is regular, and proportional to the acid used in dissolving the zinc, the action of this acid on the zinc is regular also, and thus a constant current is maintained. In order to join together several of these elements to form a battery, the zinc of one 1s counestc# by a copper wire or strip with the copper of the next, and so on from one element to another, as shown in fig. 792, for another kind of battery. Fig. 789 represents one form of a standard Daniell. The = vessel A contains dilute sul- j ANT phuric acid of specific gravity LL mer } Ge HM | I'075, and in it is a plate, Z, of S |__| S S|. — amalgamatedzinc. A, contains saturated solution of copper sul- phate, and in it is a plate of = copper, K. The syphon tube, = : === C C,, which connects the two SSS SSS Ss vessels, is closed at both ends Fig. 789 by bladder, and is filled with dilute sulphuric acid. The current produced bya Daniell’s cell is constant for some hours ; its action is stronger when it is placed in hot water. Its electromotive force is about 1°08 volt. Taking the cost of the materials consumed in working a Daniell’s cell, but allowing for the copper deposited, and assuming that 70 per cent. of the electrical energy is obtained in mechanical work, it appears that the expense per horse power per hour is at least two shillings and sixpence. 830. Grove’s battery.—In this battery the copper sulphate solution is replaced by nitric acid, and the copper by platinum, by which greater electro- motive force is obtained. Fig. 790 represents one of the forms of a couple of this battery. It consists of a flat rectangular glass or porcelain vessel, partially filled with dilute sulphuric acid (1:8); of a zinc plate bent into a U shape, a flat porous pot contains strong nitric acid and a thin platinum foil -831] Bunsen’s Battery 821 which can be connected with the zinc of the next cell by a suitable binding screw. In this battery the hydrogen, which would be disengaged on the platinum, meeting the nitric acid, decomposes it, forming hyponitrous acid, which dissolves, or is disengaged as nitrous fumes. Grove’s battery is the most convenient, and one of the most powerful of the two fluid batteries. It is, however, expensive, owing to the high price of platinum ; besides which the platinum is hable, after some time, to become brittle and break very easily. But as the platinum is not con- sumed, it retains most of its value, and when the plates which have been used in a battery are heated to redness they regain their elasti- city. 831. Bunsen’s battery. — Aumsen’s, also known as the gzzc carbon battery, was invented in 1843 ; it is in effect a Grove’s battery, where the plate of platinum is replaced by a cylinder of carbon. This is made either of the graphi- Fig. 790 toidal carbon deposited in gas retorts, or by calcining in an iron mould an intimate mixture of coke and bituminous coal, finely powdered and strongly compressed. Both those modifications of carbon are good conductors. Each element consists of the following parts: 1, a vessel, F (fig. 791), either of stoneware or of glass, containing dilute sulphuric acid ; 2, a hollow cylinder, Z, of amalgamated zinc ; 3, a porous vessel, V, in which ts ordinary nitric acid ; 4, a rod of carbon, C, pre- Fig. 791 pared in the above manner. In the vessel F the zincis first placed, and init the carbon C in the porous vessel V as seen in P. To the carbon is fixed a binding screw, 7, to which a copper wire is attached, forming the positive pole. The zinc is provided with a similar binding screw, 7, and wire, which is thus a negative pole. A single cell of the ordinary dimensions, 20 cm. in height and 9 cm. in 822 Dynamical Electricity [831— diameter, has a resistance of about 0°14 ohm, and taking its E.M.F. at 1°82 (835), gives a current of 12 to 13 amperes when on short circuit, that is when it is closed without measurable external resistance. When the cells are arranged to form a battery (fig. 792) each carbon is. connected to the zinc of the following cell by means of the clamps wm, and a strip of copper, ¢, represented in the top of the figure. The copper is pressed at one end between the carbon and the clamp, and at the other it is soldered to the clamp , which is fitted on the zinc of the following cell, and so forth. The Senay of the first carbon and that of the last zinc are alone provided with binding screws, to which are attached the wires. —\ me IW Fig. 792 The chemical action of Bunsen’s battery is the same as that of Grove’s. Being as powerful as and less costly than Grove’s, it is very generally used on the Continent ; but though its first cost is less, it is more expensive to work, and is not so convenient to manipulate. Callan’s battery is a modified form of Grove’s. Instead of zinc and plati- num, zinc and platinised lead are used ; and instead of nitric acid Callan used a mixture of sulphuric acid, nitric acid, and saturated solution of nitre. The battery is said to be equal in its action to Grove’s, and is much cheaper. Callan also constructed a battery in which zinc in dilute sulphuric acid forms the positive plate, and cast iron in strong nitric acid the negative. Under these circumstances the iron becomes passive ; it is strongly elec- tro-negative, and does not dissolve. If, however, the nitric acid becomes: too weak, the iron dissolves with disengagement of nitrous fumes. After being in use some time, all the batteries in which the polarisation is prevented by nitric acid disengage nitrous fumes in large quantities, and this is a serious objection to their use, especially in closed rooms. To prevent this, nitric acid is frequently replaced by chromic acid, or by a mixture of 4 parts potassium bichromate, 4 parts sulphuric acid, and 18 water. The liberated hydrogen reduces the chromic acid to the state of chromic oxide, which combines with the sulphuric acid forming chromous ~833] Recent Batteries 823 sulphate. With the same view, sesquichloride of iron is sometimes substi- tuted for nitric acid ; it becomes reduced to protochloride. But the action of the elements thus modified is considerably less than when nitric acid is used, owing to the greater resistance. 832. Smee’s battery.—In this battery the polarisation of. the negative plate is prevented by mechanical means. Each cell consists of a sheet of platinum placed between two vertical plates of zinc, but as there is only a single liquid, dilute sulphuric acid, the elements have much the form of those in Wollaston’s battery. The adherence of hydrogen to the negative plate is prevented by covering the platinum with a deposit of finely divided platinum. In this manner the surface is roughened, and the disengagement of hydrogen facilitates toa remarkable extent, and consequently the resistance of a couple diminishes. For platinum, silver covered with a deposit of finely divided platinum is frequently substituted, as being cheaper. 833. Recent batteries.—The mercury sulphate battery (fig. 793), de- vised by Marié Davy, is essentially a zinc-carbon element, but of smaller dimensions than those elements usually are. In the outer vessel, V, ordi- nary water or brine is placed, and in the porous vessel mercury sulphate. This salt is agitated with about three times its volume of water, in which it is difficultly soluble, and the liquid poured off fromthe pasty mass. The carbon being placed in the porous vessel, the spaces are filled with the residue, and then the decanted liquid poured into it. Chemical action takes place when the cell is closed. The zinc decom- poses the water, liberating hydrogen, which, traversing the porous vessel, | LLL =a || LEZLLLL, ZZ reduces the mercury sulphate, forming metallic mercury, which collects at the bottom of the vessel, while the sulphuric acid formed at the same time traverses the diaphragm to act on the zinc, and thus increases the action. The mercury which is deposited may be used to prepare a quantity of sulphate equal to that which has been consumed. A small quantity of the solution of mercury sulphate may also pass through the diaphragm ; but this is rather advantageous, as its effect is to amalgamate the zinc. The electromotive force of this element is about a quarter greater than that of Daniell’s element, but it has greater resistance ; it is rapidly exhausted 824 Dynamical Electricity [833— when continuously worked, though it appears well suited for discontinuous work, as with the telegraph, and with alarums. Gravity batteries.—The use of porous vessels is open to many objections, more especially in the case of Daniell’s battery, in which they gradually become encrusted with copper, and so destroyed. A kind of battery has been devised in which the porous vessel is entirely dispensed with, and the separation of the liquids is effected by the difference of density. Such batteries are called gravity batteries. Fig. 794 represents a form devised by Callaud. V isa glass or earthenware vessel at the bottom of which is a copper plate soldered to a wire insulated by gutta-percha. On the plate is a layer of crystals of copper sulphate, C ; the whole is filled with water, and the zinc cylinder, Z, is immersed in it. he lower part of the liquid becomes saturated with copper sulphate ; the action of the battery is that of a Daniell, and the zinc sulphate, which gradually forms, floats on the solution of copper sulphate owing to its lower density. This battery is easily manipulated, and when not agitated works constantly for some time, provided care be taken to replace the water lost by evaporation ; the consumption of copper sulphate is economical. Metdinger’s element, which is much used in Germany for telegraph purposes, is essentially a gravity battery of special construction, with zinc in solution of magnesium sulphate, and copper in solution of copper sulphate. Minotto’s battery.—This may be described as a Daniell’s element, in which the porous vessel is replaced by a layer of sawdust or of sand. At the bottom of an earthenware vessel (fig. 795) is placed a layer of coarsely powdered copper sulphate a, and on this a copper plate provided with an insulated copper wire z. On this there is a layer of sand or of sawdust dc, and then the whole is filled with water, in which rests a zinc cylinder Z, or the earthenware vessel may be nearly filled with moistened sawdust, and a zinc slab placed on the top. The action is just that of a Daniell; the sawdust prevents the mixture of the liquids, but it also offers great resist- ance, which increases with its thickness. From its simplicity and economy, and the facility with which it is constructed, the pale merits increased attention. De la Rue and Miiller’s element consists of a glass tube about 6 inches long by 0°75 inch in diameter, closed by a vulcanised india-rubber stopper through which passes a zinc rod 0°18 inch in diameter and 5 inches -long. A flattened silver wire also passes through the stopper to the bottom of the tube, in which is placed about half an ounce of silver chloride, the greater part of the cell being filled with solution of sal-ammoniac. The hydrogen evolved at the negative plate reduces the chloride to metallic silver, which is thereby recovered. Since there is only one liquid, and the solid electro- lyte is not acted upon when the circuit is open, the element is easily worked and requires little attention. It is very compact, 1,000 elements occupying a space of less than a cubic yard ; De la Rueand Miiller have used as many as 14,400 such cells in investigations on the'stratification of the electric light. A battery of 8,040 of these cells gave a spark 4 of an inch in length in air under the ordinary atmospheric pressure ; while under a pressure of a quarter of an atmosphere the striking distance was 14 inch (810). The electromotive force of a silver chloride cell is 1°03 volt, and that of -833] Recent Batteries 825 one made with silver bromide is 07908; hence a series of three of the silver chloride cells with one of bromide gives an average electromotive force of I volt (835). Latimer Clark’s element is much used as a standard of electromotive force. One form of it, represented in fig. 796, consists of two verti- cal glass branches, with platinum wires sealed in the closed ends, and joining in a neck in which is a ground glass stopper with a thermo- meter. In one of these branches is mercury forming the negative plate, and in the other an amalgam of zinc and mercury forming the positive plate. On the mercury is placed a paste formed by triturating together mercurous sul- phate with mercury and zinc sulphate, and on both the amalgam and the paste is a layer of crystals of zinc sulphate, the vessel being filled with saturated solution of zinc sulphate. This cell is not at all adapted for anything of the nature of continuous work, but it furnishes a standard of E.M.F. which when the cell is con- structed with the proper precautions can always be reproduced and always reliedon. Its E.M.F. is 1°435 [1 —0°0078 (¢—15)] volts, where ¢ is the temperature Centigrade. A convenient form of element for many purposes is the fotasstum bichromate, or, as it is frequently termed, the dzchromate element (fig. 797). It consists of a zinc plate, Z, attached to a brass rod, which slides up and down in a brass tube in an ebonite or porcelain cover, so that it can be wholly or partially immersed in the liquid. This is necessary, since the zinc is attacked by the exciting liquid when the cell is not closed. Two graphite plates, C C, are similarly fitted in the cover, and by means of strips of brass the carbon and the zinc plates are respectively in connection with the binding screws, which thus form the poles. The exciting liquid is a mixture of I part of potassium bichromate, 2 of sulphuric acid, and Io of water. Instead of potassium bichromate, chromic acid, which is now prepared industrially at a cheap rate, is often used. The electromotive force is about 2 volts ; when the element is closed by a wire of small resistance its E.M.F. increases slightly at first, then remains constant for some time, after which it rapidly sinks to half its original amount. In MViaudet’s element a zinc cylinder dips in a solution of common salt and surrounds a porous cell, in which is a carbon plate surrounded by pieces of carbon and filled with chloride of lime, which does not act on the zinc even when the circuit is closed. The electromotive force is 1°7 volt. Fig. 796 ’ 826 Dynamical Electricity [833— The element of Lalande and Chaperon consists of zinc in a 30 per cent. solution of caustic potass and copper in contact with copper oxide which acts as depolariser. The E.M.F. is 0°85 volt, and there is no action unless the circuit is closed. To prevent the absorption of carbonic acid by the potass, the solution is covered with paraffine oil. 834. Leclanché’s element.—This consists (fig. 798) of a rod of carbon, C, placed in a porous pot, which is then very tightly packed with a mixture of pyrolusite (manganese peroxide) and gas graphite, M, covered over with a layer of pitch. To the top of the carbon is firmly attached a mass of lead, L, to which is affixed a binding screw. The positive plate is a rod of zinc, Z, in which is fixed a copper wire. The exciting liquid consists of a strong solution of sal-ammoniac, contained in a glass vessel, G, which is not more than one-third full. The E.M.F. of the element is 1°4 volt, or about one-third greater than that of a Daniell’s element ; its internal resistance varies of course with the size, from 4 to 8 ohms. The battery is not adapted for continuous work as in heavy telegraphic circuits, or in electro-plating, since it soon becomes polarised ; it has, however, the valuable property of quickly regaining its original strength when left at rest, and is extremely well adapted for * discontinuous work, such as that of elec- trical bells. A modification of this element by von Beetz for therapeutic purposes consists of a test tube in the bottom of which is fused a platinum wire; this is then covered to one-third the height with a layer of a mixture of bruised gas cokeand pyrolusite. In other respects the element is con- structed like that of De la Rue and Muller. A rod of carbon 42 x 12x 35, inches should have a maximum resistance of 1 ohm; but good plates made from the carbon of gas retorts do not average more than o'5, and in some cases o'I ohm. If the resistance equals an ohm, the con- ducting power of carbon is about 0°003 that of mercury. A drawback to the use of carbon is that, from its porosity, the exciting liquid rises, and forms local currents at the junction with the binding screw, which injure or destroy contact. This may be remedied to a very great extent by soaking the plates before use in hot melted paraffine, which penetrates into the pores, expelling the air. On cooling, it solidifies and prevents the capillary action mentioned+¢above. By carefully scraping the paraffine from the outside, a surface is exposed which is as good a conductor as if the pores were filled with air. Measurements have shown that the resistance of a plate thus prepared is not altered. In a recent modification of this cell the porous cell is dispensed with, Oe 9 2 Fig. 798 —836] Electromotive Force of Different Elements 827 and the carbon plate C placed between two similar flat prisms, made by compressing a mixture of 55 parts of graphite, 4o parts of pyrolusite, and 5 parts of shellac in steel moulds at a temperature of 100° under a pressure of 300 atmospheres. The resistance of this form of element is from o-g to 1°8 ohm. 835. Electromotive force of different elements.--The following numbers represent the electromotive force in volts of some of.the elements most fre- quently used. Volts Daniell’s element . . set up with water . ‘ 1°08 % . : . pure zinc and pure water, afin aie copper and pure ateniesie solution of copper sulphate , el tO Peclanchecs ; . zinc in saturated solution BE am- monium chloride . ; : 4S IvGlarics. 4... , ? Z : ‘ 5 : RE Bunsen’s * carbon in nitric acid ; : Rey: “s € carbon in chromic acid . : be 2°02 Grove’s ¥ platinum in nitric acid. ; el OG The cell of greatest electromotive force as yet observed was examined by Beetz, and consists of potassium amalgam in caustic potash, combined with pyrolusite in a solution of potassium permanganate. Its E.M.F. is three times as great as that of a Daniell’s element. The standard of electromotive force on the C. G. S. system is the Volz. This is equal to 100,co0,0co or 10° absolute electromagnetic units (999). The vo/¢ is rather less than the electromotive force of a Daniell’s cell, the mean value of which may be taken at 1°08 volt. The unit of current, which is called an ampere, is the current due to an electromotive force of one volt working through a resistance of one ohm. The coulombé is the practical unit of electrical quantity ; it is that quantity of electricity which passes in a second through the section of a conductor traversed by a current of an ampere. 836. Comparison of the voltaic battery with a frictional electrical machine.—Except in the case of batteries consisting of a very large number of couples, the difference of potentials between the terminals is far weaker than in frictional electrical machines, and is insufficient to give any visible spark. With Dela Rue and Miller’s great battery the striking distance between two terminals was found to increase with the potential, but for high potentials rather more rapidly than in direct ratio. Thus while the striking distance was o’oI2 in., with the potential due to 1,200 of their cells, it was 0'049 in. with 4,800 cells, and 0°133 in. with 11,000 cells. In the case of a small battery or of a single cell, very delicate tests are required to detect any signs of free electrification. But by means of a con- densing electroscope, and by careful insulation, it can be shown that one pole possesses a positive and the othera negative charge. Inthe experiment for proving this one ef the plates of the electroscope is connected with one pole, and the other with the other pole or with the ground. The electroscope 828 Dynamical Electricity [836— thus becomes charged, and on breaking the connection and raising the plate electroscopic indications are observed (801). On the other hand, the strength of current which a voltaic element can produce in a good conductor is far greater than that which can be pro- duced by a machine. Faraday immersed two wires—one of zinc, and the other of platinum, each ;4, of an inch in diameter—in acidulated water for ;3, of a second. The effect thus produced on a magnetic needle in this short time was greater than’ that produced by 23 turns of the large electrical machine of the Royal Institution. Nystrom ascertained by quantitative nieasurements that the potential of the charge of the cover of an ordinary electrophorus is not less than 50,000 times as great as the potential of a Meidinger’s cell (833) ; that is, that not less than 50,000 of those elements would be required to produce the same potential as the electrophorus. In practice, a far greater number would be needed, owing to the difficulty of getting good insulation. 837. Amalgamated zinc. Local currents.—Perfectly pure distilled zinc is not attacked by dilute sulphuric acid, but becomes so when immersed in that liquid in contact with a plate of copper or of platinum. Ordinary commercial zinc, on the contrary, 1s rapidly dissolved by dilute acid. This is due to what is called /ocal action (827), arising from impurities which are always present in commercial zinc. To understand this effect, con- sider two portions a and @ of a plate of zinc placed in dilute acid (fig. 799), @ representing pure zinc, while 4 is supposed to represent such an impurity as a particle of lead or iron. Here are all the conditions for the production of an electrical cur- rent, two different metals in metallic connection, and in contact with a liquid, which acts upon them unequally ; the effect is that a current is produced from a to 4 through the liquid, and the zinc is eaten away. All ordinary zinc contains metallic impurities, such as lead and iron, which realise the above conditions, forming innu- merable local electrical currents, which rapidly wear away the active plate without contributing anything to the general current. Zinc, when amalgamated, acquires the properties of perfectly pure zinc, and is unaltered by dilute acid, so long as it is not in contact with a copper or some other metal plate immersed in the same liquid. To amalgamate a zinc plate, first immerse the plate in dilute sulphuric or hydrochloric acid so as to obtain a clean surface, and then place a drop of mercury on the plate and spread it over with a brush. The amalgamation takes place immediately, and the plate has the brilliant aspect of mercury. Zinc and other metals are readily amalgamated by dipping them in an amalgam of one part sodium and 200 parts of mercury. Zinc may also be amalga- mated in the mass by melting it in a closed vessel with 4 per cent. of mercury, and running it into moulds. The amalgamation of the zinc removes from its surface all the impurities, especially the iron. The mercury effects a solution of pure zinc, which covers the surface of the plate as with a liquid layer. The process was first applied to electrical batteries by Kemp. Amalgamated zinc is not attacked so long —839] Bohnenberger’s Electroscope 829 as the circuit is not closed—that is, when there is no current ; when closed the current is more regular, and at the same time stronger, for the same quantity of metal dissolved. 838. Dry piles—In dry piles the liquid is replaced by a solid hygro- metric substance, such as paper. They are of various kinds ; in Zambonvs, which is most extensively used, the materials are tin or silver and man- ganese peroxide. To construct one of these piles a piece of paper silvered or tinned on one side is taken ; the other side of the paper is coated with finely powdered manganese peroxide by slightly moistening it, and rubbing the powder on with a cork. Having placed together seven or eight of these sheets, they are cut by means of a punch into discs an inch in diameter. These discs are then arranged in the same order, so that the tin or silver of each disc is in contact with the manganese of the next. Having piled up 1,200 or 1,800 couples, they are placed in a glass tube, provided with a brass cap at each end. Ineach cap there isa rod and knob, by which the leaves can be pressed together, so as to produce better contact. The knob in contact with the manganese corresponds to the positive pole, while that at the other end, which is in contact with the silver or tin, is the negative pole. Dry piles are remarkable for the duration of their action, which may last for several years. Their action depends greatly on the temperature and on the hygrometric state of the air. It is stronger in summer than in winter, and the action of a strong heat revives it when it appears extinct. A Zambonr’s pile of 2,000 couples gives neither shock nor spark, but can be used to charge a Leyden jar and other condensers. What are known as @ry bat/eries are often convenient, especially for trans- port. The positive and negative plates are imbedded in some porous material such as sawdust, cocoanut fibre, gypsum, infusorial earth, or the like, which has been soaked or boiled with a suitable liquid. They are covered with a layer of pitch in which is an aperture for the disengagement of gas. They are best suited for discontinuous work. 839. Bohnenberger’s electroscope.— Bohnenberger constructed a dry- pile electroscope of great delicacy. It is a condensing electroscope (fig. 758), from the rod of which is suspended a single gold leaf. This is at an equal distance from the opposite poles of two dry pi'es placed vertically, inside the bell jar, on the plate of the apparatus. When the gold leaf has any free electricity it is attracted by one of the poles and repelled by the other, and its electricity is obviously contrary to that of the pole towards which it moves. 830 Dynamical Electricity [840- CHARTER): DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS 840. Detection and measurement of voltaic currents.—The remark- able phenomena of the voltaic battery may be classed under the heads phy- siological, chemical, mechanical, and physical effects ; and these latter may be again subdivided into the thermal, luminous, and magnetic effect. For ascertaining the existence and measuring the strength of voltaic currents, the magnetic effects are more suitable than any of the others, and, accord- ingly, the fundamental magnetic phenomena will be described here, and the description of the rest postponed to a special chapter on Electro- magnetism. 841. Oersted’s experiment.—Oersted published in 1838 a discovery which connected magnetism and electricity in a most intimate manner, and became, in the hands of Ampere and of Faraday, the source of a new branch of physics. The fact discovered by Oersted is the directive action which a fixed current exerts at a distance on a magnetic needle. To make this experiment a copper wire is suspended horizontally in the direction of the magnetic meridian over a movable magnetic needle, as repre- sented in fig. 800. So long as the wire is not traversed by a current, the needle remains parallel to it ; but as soon as the ends of the wire are respectively connected with the poles of a battery or of a single cell, the needle is de- flected, and tends to take a position which ts the more nearly at right angles to the magnetic meridian as the current 7s Stronger. In reference to the direction in which the poles are deflected, there are several cases which may, however, be referred to a single principle. Remembering our assumption as to the direction of the current in the connecting wire (824), the preceding experi- ment presents the following four cases :— i. If the current passes above the needle, and goes from south to north, the north pole of the magnet is deflected towards the west ; this arrangement is represented in the above figure. i. If the current passes below the needle, also from south to north, the north pole is deflected towards the east. —842] Galvanometer or Multiplier 831 11. When the current passes above the needle, but from north to south, the north pole is deflected towards the east. iv. Lastly, the deflection is towards the west when the current goes from north to south below the needle. Ampére has given the following memoria technica by which all the various directions of the needle under the influence of a current may be remembered, If we imagine an observer placed in the connecting wire in such a manner that the current entering by his feet issues by his head, and that his face is always turned towards the needle, we shall see that in the above four posi- tions the north pole is always deflected towards the left of the observer. By thus personifying the current, the different cases may be comprised in this general principle : /z the directive action of currents on magnets, the north pole ts always deflected towards the left of the current. 842. Galvanometer or multiplier.—The name galvanometer, or some- times multiplier or rheometer, is given to a very delicate apparatus by which the existence, direction, and intensity of currents may be determined, It was invented by Schweigger a short time after Oersted’s discovery. 2 In order to understand its principle, let us suppose a magnetic needle suspended by a filament of silk (fig. 801), and surrounded in the plane of the magnetic meridian by a copper wire, #vofg, forming a complete circuit round the needle in the direction of its length. When this wire is traversed by a current, it follows, from what has been said in the previous paragraph, that in every part of the circuit an observer lying in the wire in the direction of the arrows, and looking at the needle ad, would have his left always turned towards the same point of the horizon, and consequently, that the action of the current in every part would tend to turn the north pole in the same direction ; that is to say, that the actions of the four branches of the circuit concur to give the north pole the same direction. By coiling the copper wire in the direction of the needle, as represented in the figure, the action of the current has been multiplied. If, instead of a single one, there are several circuits, provided they are insulated, the action becomes still more multiplied, and the deflection of the needle increases. Nevertheless, the action of the current cannot be multiplied indefinitely by increasing the number of windings, for, as we shall presently see, the strength of a current diminishes as the length of the circuit is increased. As the directive action of the earth continually tends to keep the needle 832 Dynamical Electricity [842- in the magnetic meridian, while the action of the current tends to turn it at right angles to the meridian, the effect of the current is increased by the use of an astatic system of two needles (714), as shown in fig. 802. The action of the needle is then very feeble, since it depends on the difference of their moments, and this difference may be made as small as we please. The action of the current on the two needles becomes increased. In fact, the action of the circuit, from the direction of the current indicated by the arrows, tends to deflect the north pole of the lower needle towards the west. The upper needle, a’b’, is subjected to the action of two contrary currents, 770 and gf, but as the first is nearer, its action preponderates. Now this current, passing below the needle, evidently tends to turn the pole a’ towards the east, and, consequently, the pole J’ towards the west ; that is to say, in the same direction as the pole a of the other needle. From these principles it will be easy to understand the action of the multiplier. The apparatus represented in fig. 803 consists of a thick copper . plate, D, resting on levelling screws ; on this is a rotating plate, P, of the same metal, to which is fixed a copper frame, the breadth of which is almost equal to the length of the needles. On this is coiled a great number of turns of wire covered with silk. The two ends terminate in binding screws, z and o. Above the frame is a gradu- ated circle, C, with a central slit parallel to the direction in which the wire is coiled. The zero corresponds to the position of this slit, and the graduations extend on each side of this zero up to go°. By means of a very fine filament of silk, an astatic system is suspended ; it con- sists of two needles ad and a’b’, one above the scale, and the other within the cir- cuit itself. These needlés, which are joined together by copper wire, like those in fig. 681 and fig. 802, and cannot move separately, must not have exactly the same magnetic moment ; for if they are exactly equal, every current, strong or weak, would always put them at right angles to the coil. When an experiment is to be made with this instrument, the diameter, to which corresponds the zero of the graduation, is brought into the magnetic Sa = Ge = \. ; SULT Tn EET TTP bt lat ff i AY \ eC! | —S=- ME | “ See cm rer. —843] Dead-beat Galvanometer — 833 meridian by turning the plate P until the end of the needle a4 corresponds to zero. The instrument is fixed in this position by means of the screw clamp T. The length and diameter of the wire vary with the purpose for which the galvanometer is intended. For one which is to be used in observing the currents due to chemical actions, a wire about } millimetre in diameter, and making about 800 turns, is well adapted. Those for thermo-electric currents, where the E.M.F. is low, require a thicker and shorter wire ; for example, thirty turns of a wire 3 millimetre in diameter. For very delicate experi- ments, as in physiological investigations, galvanometers with as many as 30,000 turns have been used. By means of a delicate galvanometer consisting of 2,000 or 3,000 turns of fine wire, the coils of which are carefully insulated by means of silk and shellac, currents, such as those due to the electrical machine (813), may be shown. One end of the galvanometer is connected with the prime con- ductor, or one electrode (fig. 730) and the other with the ground or with the other electrode, and when the machine is worked the needle is deflected, affording thus an illustration of ‘the identity of statical with dynamical electricity. The deflection of the needle increases with the strength of the current ; the relation between the two is, however, so complex, for the type of galvanometer described above, that it cannot well be deduced from theoretical considerations, but requires to be determined experimentally for each instrument. And in the majority of cases the instrument is used as a galvanoscope—that is, to ascertain the presence and direction of currents —rather than as a galvanometer in the strict sense; that is, as a measure of their intensity.. The term ga/vanometer is, however, commonly used. In the aferential galvanometer the frame is provided with two coils of wire of the same kind and dimensions, carefully insulated from each other, and pro- vided with suitable binding screws, so that separate currents can be passed through each of them. If the currents are of the same strength but in different directions, no deflection is produced ; where the needle is deflected one of the currents differs from the other. Hence the apparatus is used to ascertain a difference in strength of two currents, and to this it owes its name. | 843. Dead-beat galvanometer.—When a current is passed through a galvanometer, the needle does not usually at once attain its final position of equilibrium, but oscillates about this position, which in observations causes much loss of time. If such a needle is surrounded by a mass of a good conductor such as copper, currents are induced in the mass which, as will afterwards be explained (926), impede, or damp, the motion of the magnetic needle and tend to bring it to rest. Such an arrangement is called a damper, and in practice is frequently used ; the copper frame on which the wires of the galvanometer are coiled, and the wires themselves, act in this way. The natural logarithm of the ratio of the amplitudes of two successive oscillations of the needle is called the Jogarithmic decrement. The logarithmic decrement A is proportional to the product of the damping power ¢ and the time of a single oscillation ¢; that is, \=e¢, By diminish- ing the directive powerof the earth on the magnet by making it astatic, the 3H 834 Dynamical Electricity [843—- logarithmic decrement becomes infinite, and the needle attains its position of equilibrium without oscillations. Galvanometers in which the needle acquires at once this final deflection are known as aperiodic, or dead-beat galvanometers. To this class belong that of Deprez and D’Arsonval represented in fig. 804, which is a development of Lord Kelvin’s syphon recorder (913). Between the branches of a strong horseshoe magnet is a light iron cylinder, which is supported independently and becomes magnetised by induction. Between this and the magnet is a light rectangular wire coil, supported by wires conveying the current which are in connection with binding screws. When the current passes, the coilis deflected at right angles to the field, and equilibrium is established when the electro-magnetic action is equalled by the torsion of the wire. The motion of the coil can be read off by a spot of light reflected from a mirror (844) attached to it, and _ for small angles the current is proportional tothe tangent of the angle of deflection (845). In- duction currents due to the motion of the coil in the field are produced, and as this is very powerful, the galvanometer is virtually dead-beat when closed by a small resistance. When a current of very small duration is passed through a galvanometer, a momentary de- flection or swung or throw of the needle will be produced. It can be shown that the product of a —— = ; SS ——— — constant into the sine of half ‘gl oP ah ee WL the angle of the first swing is Fig. 804 then a measure of the strength of. the... current, +.so ; that jem momentary currents of different strengths are passed through one and the same galvanometer, they will be measured by the sines of the corresponding angles of deflection, or by the angles themselves where these are small. The condition is that the duration of the current must be small in comparison with the time of oscillation of the needle of the galvanometer. This is known as the ballistic method (82) of measuring currents, and the galvano- meters adapted for the purpose are known as éadlistic galvanometers. 844. Thomson’s marine galvanometer.—During the laying of submarine cables the want was felt of a galvanometer which should be sufficiently sensitive to test insulation, and at the same time be unaffected by the pitch- ing and rolling of the ship. To supply this want, Lord Kelvin invented his marine galvanometer. B (fig. 805) represents a coil of many thousand turns ' of very fine copper wire, carefully insulated throughout, terminating in the binding screws, EE. In the centre of this coil is a slide, which carries the magnet, the arrangement of which is represented on a larger scale in D. —844] Thomson's Marine Galvanometer 835 The magnet itself is made of a piece of fine watch-spring about a centimetre in length, and does not weigh more than a grain ; it is attached to a small and very slightly concave mirror of very thin silvered glass. A single fibre of silk is stretched across the slide, and the mirror and magnet are attached to it in such a manner that the fibre passes exactly through the centre of gravity in every position. As the mirror and magnet weigh only a few grains, they retain their position relatively to the instrument, however the ship may pitch and roll. The slide fits ina groove in the coil, and the whole is enclosed within a wrought-iron case with an aperture in front and a wrought-iron lid on the top. The effect of this is to act as a magnetic screen and thereby counteract the influence of terrestrial magnetism when the ship changes its course. Underneath the coil is a large bent steel magnet N, which compensates the earth’s directive action upon the magnet D (714); and in the side of the case, and on a level with D, a pair of magnets, C, are placed with opposite rr | h LTT yeti) my) poles together. Bya screw, suitably adjusted, the poles of the magnets may be brought together ; in which case they quite neutralise each other, and thus exert no action on the suspended magnet, or they may be slid apart from each other in such a manner that the action of either pole on D prepon- derates to any desired extent. This small magnet is thus capable of very delicate adjustment. The large magnet, N, and the pair of magnets, C, are analogous to the coarse and fine adjustment of a microscope. At a distance of about a metre, there is a scale with the zero in the centre and the graduation extending on each side. Underneath this zero point is a narrow slit, through which passes the light of a paraffine lamp, and which, traversing the window, is reflected from the bent mirror against the graduated scale. By means of the adjusting magnets the image of the slit is made to fall on the centre of the graduation. This being the case, if any arrangement for producing a current, however weak, be connected with the terminal, the spot of light is deflected either to ZH2 836 Dynamical Electricity [844~ one side or the other, according to the direction of the current ; the stronger the current the greater the deflection of the spot ; and if the current remains of constant strength for any length of time, the spot is stationary in a cor- responding position, and without appreciable error the strength of the current may be taken to be represented by the number of divisions read off. In the later and more improved form of this instrument a current of the one thousand-millionth of an ampere will produce a deflection of one division of the scale. The movement, on a screen, of a spot of light reflected from a body, is the most delicate and convenient means of observing motions which of them- selves are too small for direct measurement or observation. Hence this principle is frequently applied in experimental investigations and in lecture illustrations (534). It is used in observing the motion of oscillating bodies, in measuring the variations of magnetism, in determining the expansion of solids, &c. 845. Tangent compass, or tangent galvanometer.—When a magnetic needle is suspended in the centre of a voltaic circuit in the plane of the magnetic meridian, it can be proved that the strength of a current is directly proportional to the tangent of the angle of deflection, provided the needle is sufficiently small compared with the diameter of the circuit. An instrument based on this principle is called the fangent galvanometer or fangent compass. It consists of a copper ring, 12 inches in diameter (fig. 806) and about an inch in breadth, mounted vertically on a stand; the lower half of the ring is generally fitted in a semicircular frame of wood to keep it steady. In the centre of the ring is suspended a delicate magnetic needle, whose length must not exceed -/; or 34, of the diameter of the circle. Underneath the —_ @ needle there is a graduated circle. Fane =m The ends of the ring are prolonged in copper wires, fitted with mercury cups, ad, by which the ring can be connected with a battery orelement. The ring is placed in the plane of the magnetic meridian, and the deflection of the needle is directly read off on the circle, and its tangent obtained from a table of tangents. For the more accurate measurement of the deflection a light index is sometimes placed at right angles to the needle. On account of its small resistance, the tangent galvanometer is well adapted for measuring currents of low potential, in which a considerable quantity of electricity is set in motion—that is, for measuring strong currents. To prove that the strengths of currents are proportional to the tangents Fig. 806 —845] Tangent Compass, or Tangent Galvanometer 837 of the corresponding angles of deflection, let NS (fig. 807) represent the ring of the galvanometer and ws the needle, and let @ be the angle of deflection produced when a current C is passed. Two forces now act upon each pole of the needle—the force of the earth’s magnetism, which we will denote by H, which tends to place the needle in the magnetic meridian, and the force due to the strength of the current C, which strives to place it at right angles to the magnetic meridian. Let the magnitudes of these forces be represented by the corresponding lines az and 67. Resolving these forces parallel and perpendicular to the needle, we have mg and #f as the components acting in opposite directions on the needle; and since the needle is at rest these forces must be equal. The components parallel to the needle are without effect. The angle zag is equal to the angle ¢, and therefore 7g=an sin $ ; and in like manner the angle 47f is equal to @ and zf=6z cos ¢ ; and therefore : sin since 2f=ng, 61 cos @=an sin q, or b4=an she pager p; but 4” Is cos proportional to the current = KC, where K is a constant and az =H, there- fore KC =H tan ¢. If any other current is passed through the galvanometer, we shall have similarly C’=H tan ¢’; and since the earth’s magnetism does not appre- ciably alter in one and the same place, C: C’=tan ¢: tan ¢’. In this reasoning it has been assumed that the action of the current on the needle is the same whatever be the angle by which the needle is deflected. This only holds when the dimensions of the needle are small compared with the diameter of the ring : it should not be more than 4 or #4 the diameter, so that the field in which it moves is sensibly constant. This is especially the case with the reflecting galvano- meter, in which the current strength may without ap- preciable error be considered proportional to the number of divisions read off by the telescope. Wiedemann’s tangent galvanometer consists of a short thick copper tube, in which is suspended, instead of a needle, a thin piece of soft iron, silvered on one side so as to act as a mirror, the position of which can be observed by a telescope and scale (534). On each side of the copper tube, and sliding in grooves, are coils of wire which can be pushed over the tube. By this lateral arrange- ier fa? ment of the current in reference to the magnetic needle, the error of the tangent galvanometer is diminished ; for when the needle is deflected, though one end moves away from the current, the other approaches it. In the tangent galvanometer of Helmholtz and of Gaugain the wires are coiled on the surface of a cone the angle of which is 120°, and the point on which the needle works is placed in the position of the corresponding apex of the cone: the law of the tangent holds then even with longer needles, and especially if the wire is divided between two such cones, placed on opposite sides of the needle. . If the ring of the tangent galvanometer is so constructed that it can turn about its horizontal diameter, which is in the magnetic meridian, the 838 Dynamical Electricity [845— action of the current on the needle is inversely proportional to the cosine of the angle 6, through which the ring is turned. Hence by increasing 6 we may make the action of any current on the needle as small as we please, and thus very powerful currents may be measured by this instrument. 846. Sine galvanometer.—This is another form of galvanometer for measuring powerful currents. Round the circular frame M (fig. 809}, several turns of stout insulated copper wire are coiled, which terminate on the binding screws at E. Ona table in the centre of the ring there is a magnetic needle, #z ; a second light needle, 7, of glass or aluminium, fixed to the first, serves as pointer along the graduated circle N. Two copper wires, a, 6, from the source of electricity to be measured, are connected with E. The circles M and N are supported on a foot O, which can move about a vertical axis passing through the centre of a fixed horizontal ercle ik The circle M being then placed in the magnetic meridian, and therefore in the same plane as the needle, the current is allowed to pass. The needle being deflected, the circuit M is turned until it coincides with the vertical plane passing through the magnetic needle 7. The directive action of the current is now exerted perpendicularly to the direction of the magnetic needle, and it may be shown that the strength of the current is propor- tional to the sine of the angle through which the galvanometer has been turned: this angle is measured on the circle H by means of a vernier on the piece C. The latter, fixed to the foot O, turns it by means of a knob A. This angle being known, and hence its sine, the strength of the current may be thus de- ———— ————_ pn UNIT vii ee Pe till al Ui} Fig. 80% Fig. 809 duced : let 772’ be the direction of the magnetic meridiarf, C the strength of the current, and H the directive action of the earth. If the direction and intensity of this latter force are represented by a@&, it may be replaced 847] Ohn’s Law 839 by two components, af and ac (fig. 808). Now, as the first has no directive action on the needle, the component ac must alone counterpoise the force due to the current C; call this force 2C where & is a constant. Then &kC=ac. But in the triangle ack, ac=ak cos cak, from which ac=H sin d, for the angle caz is the complement of the angle d, and aé is equal to H ; hence, lastly, #C =H sin d, which was to be proved. In like manner for any other current C’, which produces a deflection a’, we shall have £C’=H sin @., whence (> C=sined ssid . 847. Ohm’s law.—For a knowledge of the conditions which regulate the action of the voltaic current, science is indebted to the late G. S. Ohm. His results were at first deduced from theoretical considerations ; but by his own researches as well as by those of Fechner, Pouillet, Daniell, De la Rive, Wheatstone, and others, they received the fullest confirmation, and their great theoretical and practical importance has been fully established. 1. The force or cause by which electricity is set in motion in the voltaic circuit is called the electromotive force. The quantity of electricity which in any unit of time flows through a section of the circuit is called the zzfenszty, or, perhaps better, che strength of the current. Ohm found that this strength is the same in all parts of one and the same circuit, however heterogeneous they were; one and the same magnetic needle is deflected to the same extent over whatever part of the circuit it is suspended; and the same voltameter, wherever interposed in the circuit, indicates the same disengage- ment of gas ; he also found that the strength is proportional to the electro- motive force. It has further been found that when the current from the same element is passed respectively through a short and through a long wire of the same material, its action on the magnetic needle is less in the latter case than in the former. Ohm accordingly supposed that in the latter case there was a greater veststance to the passage of the current than in the former; and he proved that ‘for a constant electromotive force ¢he strength of the current ts inversely proportional to the resistance, On these principles Ohm founded the celebrated law which bears his name, that ¢he strength of the current ts equal to the electromotive force divided by the reststance. This is expressed by the simple formula guides R where C is the strength of the current, E the electromotive force of the cell or battery, and R the resistance of the circuit. i. As applied to a portion of the circuit Ohm’s law may be stated thus : let y be the resistance of a conductor forming part of a closed circuit, through which a current C flows, and let e be the difference of potential between the ends of 7, the C= .. iii. The resistance of a conductorjdepends on three elements : its comdzc- tivity, which is a constant special property, determined for each conductor ; its sectzon ; and its /emgth. ‘The resistance is obviously inversely proportional to the conductivity ; that.1s, the less the conducting power, the greater the 840 Dynamical Electricety [847— resistance. It has been proved that ¢he reststance ts inversely as the section and directly as the length of a conductor. If then x is the conductivity, the section, and A the length of a conductor, we have Ree K@ iv. Ina circuit containing a voltaic battery composed of different elements, the strength of the current is equal to the sum of the electromotive forces of all the elements divided by the sum of the resistances. - Usually, however, a battery is composed of elements of the same kind, each having the same electromotive force and the same resistance. In any simple circuit there are essentially two resistances to be con- sidered : 1. That offered by the liquid conductor between the two plates, which is called the zz¢ernal resistance ; and 2. That offered by the interpolar conductor which connects the two plates outside the liquid ; this conductor may either consist wholly of metal, or be partly of metal and partly of liquids to be decomposed ; it is the external resistance. Calling the former R and the latter 7, Ohm’s formula becomes E eheyy 6 v. If any number, 7, of similar elements are joined together, there is m times the electromotive force, but at the same time z times the internal resistance, and the formula becomes - ee : C=2R+r7 interpolar, 7, is very small—which is the case, for instance, when it is a short, thick copper wire—it may be neglected in comparison with the internal resistance, and then we have If the resistance in the ae: Cs22a mR R’ that is, a battery consisting of several elements produces in this case no greater effect than a single element. vi. If, however, the external resistance is very great, as when the current has to work a long telegraphic circuit, advantage is gained by using a large number of elements, for then we have the formula if is very great as compared with zR, so that the latter may be neglected, the expression becomes that is, the strength, within certain limits, is pr portional to the number of elements. In the case of a thermo-electric pile (972), which consists of very short metallic conductors, the internal resistance R is so small that it may be -847] Ohm's Law 841 neglected, and the strength is inversely as the length of the connecting wire. vil. If the plates of an element be made zz times as large, there is no increase in the electromotive force, for this depends solely on the nature of the metals and of the liquid (822); but the resistance is 7 times as small, for the section is 7 times as large: the expression becomes then Py 8 772i8 R R+wmr Wmr7r Hence, an increase in the size of the plate—or, what is the same thing, a decrease in the internal resistance—does not increase the strength to an indefinite extent ; for ultimately the resistance of the element R vanishes in comparison with the resistance 7, and the strength continually approximates to the value C = E r vill. Ohm’s law enables us to arrange a battery so as to obtain the greatest effect in any given case. For instance, with a battery of six elements there are the following four ways of arranging them :—1. In a single series (fig. 810), in which the zinc Z of one element 1s united with the copper C of the 842 Dynamical Flectrecity [847- second, the zinc of this with the copper of the third,and so on. 2. Arranged in a system of three double elements, each element being formed by joining two of the former (fig. 811). 3. In a system of two elements, each of which consists of three of the original elements joined, so as to form one of triple the surface (fig. 812). Lastly, of one large element, all the zincs and all the coppers being joined, so as to form a pair of six times the surface (fig. 813). With a series of twelve elements there may be six different combinations, and so on for a larger number. Now let us suppose that in the particular case of a paneer of six elements the internal resistance R of each element is 3, and the external resistance y=12. Then in the first case where there are six elements arranged in series we have the value | CE SE eee ee a 6R+r 6x3+12 30 If they were united so as to form three elements, each of double the surface as in the second case (fig. 811), the electromotive force would then be three times the electromotive force in each element : there would also bea resistance R in each element, but this would be only half as great, for the area of the plate is now double ; hence the strength in this case would be ; 2k; 2b. 6E CORR Gian ea aPiae coe Te f (2) I a+r EE agree 2) accordingly this change would lessen the strength. If, with the same elements, the resistance in the connecting wire were only ~= 2, we should have the values in the two cases respectively— The result in the latter case is, therefore, more favourable. If the re- sistance ~ were 9, the strength would be the same in both cases. Hence, then, by altering the size of the plates or ‘their arrangement, favourable or unfavourable results are obtained according to the relation between R and 7 848. Arrangement of multiple battery for maximum current.—-It can be shown that z7 amy given combination the maximum effect ts obtained when the total resistance of the battery ts egual to the external resistance. For let N be the total number of cells available for a given combination, and let 2 be the number of cells arranged fandem, or in series—that is, when the zinc of one is connected with the copper of the next, and so on; then there will be N elements arranged abreast or in parallel. If e be the elec- nt - 848] Arrangement of Multiple Battery 843 tromotive force and ~ the resistance of one cell, while 7 is the external resistance, then the strength of the current will be Came ne etere, ur nr Ah EL CO MRIS a N N Ne nN oe 45 {ir : ME EeTA Ass f ur Therefore C is a maximum when N He iS. a@ minimum, » Sut — x u Ip y un ri . , MANY oi ia mr = is a constant, therefore the sum —_ +“ is a minimum when “ = f . N N 2 N n 9 , ads : : that is, when N =/, or when the total internal resistance is equal to the external resistance. > For if « and ~~ are any two quantities whose product is A’, then 25 _ A? 2474+ A?-2Ar+2Ar_(x-A) Cae eer ive See als ao Na eee oe ac 8 This is greater than 2A unless x—A =o, in which case it is equal to 2A, and is a minimum. In that case x=A, and therefore It follows thus from the above formula that the best effect is obtained N/ “it If in a given case we have 8 elements, each offering a resistance 15 and an interpolar with the resistance 4o, we get z=4°6. But this is an impossible arrangement, for it is not a whole number, and the nearest whole number must be taken. This is 4; and it will be found, on making a calculation analogous to that above, that when the battery is arranged so as to form 4 elements, each of double surface, the greatest current is obtained. when 2= The formula for the strength of current from several elements, C eae may also be applied to the currents produced by a magneto-electrical machine (940). In that case z stands for the number of coils which in a given. time cut the lines of force of a magnetic field. The principle that the best effect is obtained when the total internal is equal to the total external resistance, holds also for the currents produced by these machines. ~ 844 Dynamical Electricity [849- CHAP TreRe ii) EFFECTS OF THE CURRENT 849. Physiological actions.—Under this name are included the effects produced by a battery current on living organisms or tissues. When the electrodes of a battery of many cells are held in the two hands a violent shock is felt, especially if the hands are moistened with acidulated water, which increases the conductivity. The violence of the shock increases with the number of elements used, and with a large number—as 200 Bunsen’s cells—is even dangerous. The power of contracting upon the application of a voltaic current seems to be a very general property of fvotopflasm—the physical basis of both animal and vegetable life ; if, for example, a current of moderate strength is passed through such a simple form of protoplasm as an amceba, it imme- diately withdraws its processes, ceases its changes of form, and contracts into a rounded ball—soon, however, resuming its activity upon the cessation of the current. Essentially similar effects of the current have been observed in the protoplasm of young vegetable cells. If a frog’s fresh muscle (which will retain its vitality for a considerable time after removal from the body of the animal) is introduced into a galvanic circuit, no apparent effect will be observed during the steady passage of the current, but every opening or closure of the circuit will cause a muscular contraction, as will also any sudden and considerable alteration in the strength of the current. By very rapidly interrupting the current, the muscle can be thrown into a state of uninterrupted contraction, or physiolo- gical ¢e¢anis, each new contraction occurring before the previous one has passed off. Other things being equal, the amount of shortening exhibited by the muscles increases, up to a certain limit, with the intensity of the current. These phenomena entirely disappear with the life of the muscle ; hence the experiments are somewhat more difficult with warm-blooded animals, the vitality of whose muscles, after exposure or removal from the body, is maintained with more difficulty ; but the results of careful experi- ment are exactly the same here as in the case of the frog. The influence of an electric current upon living nerves is very remark- able ; as a general rule, it may be stated that its effect is to throw the nerve into a state of activity, whatever its special function may be: thus, if the nerve be one going to a muscle, the latter will be caused to contract ; if it be one of common sensation, pain will be produced ; if one of special sense, the sensation of a flash of light, or of a taste, &c., will be produced, accord- ing to the nerve irritated. These effects do not manifest themselves during the even passage of the current, but only when the circuit is either opened or —850] Electrotonus 845 closed, or both. Of course the continuity of the nerve with the organ where its activity manifests itself must be maintained intact. The changes set up by the current in the different nerve-trunks are probably similar, the various sensations, &c., produced depending on the different terminal organs with which the nerves are connected. Professor Burdon Sanderson has ascertained that the movement which causes the Dionea muscipula (Venus’s fly-trap), one of those which are called carnivorous plants, to close its hairy leaves and thereby entrap in- sects which alight upon it, is accompanied by an electrical current in a manner analogous to that manifested in muscular contraction. The manner in which the irritation is caused seems immaterial. 850. Electrotonus.—In a living nerve, as will be stated more fully in Chapter X., certain parts of the surface are electropositive to certain other parts, so that if a pair of electrodes connected with a galvanometer be applied to these two points, a current will be indicated ; if now another part of the nerve be interposed in a galvanic circuit, it will be found that, if this extra- neous current be passing in the same direction as the proper nerve-current, the latter is increased, and vice versé ; and this although it has previously been demonstrated experimentally that none of the battery current escapes down the nerve, so as to exert any influence of its own on the galvanometer. This alteration of its natural electromotive condition, produced through the whole of a nerve by the passage of a constant current through part of it, is known as the e/lectrotonic state ; it is most intense near the extraneous, or, as it is called, the exczting current. It continues as long as the latter is pass- ing, and is attended with important changes in the erczfadbz/zty of the nerve, or, in other words, the readiness with which the nerve is thrown into a state of functional activity by any stimulus applied to it. Pfluger, who has inves- tigated these changes, has named the part of the nerve through which the exciting current is passing the zw¢rapolar region ; the condition of the nerve close to the positive pole is called amelectrotonus ; that near the negative pole, kathelectrotonus. The excitability of the nerve is diminished in the anelectrotonic region, so that with a motor nerve, for example, a stronger stimulus than before would need to be applied at this part in order to obtain a muscular contraction ; in the kathelectrotonic region, on the contrary, the excitability of the nerve is heightened. Moreover, with an exciting current of moderate strength, the power of the nerve to conduct a stimulus is lowered in the anelectrotonic region, and increased in the kathelectrotonic ; with strong currents it is said to be diminished in both. These facts have to be taken into account in the scientific application of galvanism to medical purposes. If, for instance, it is wished to diminish the excitability of the sensory nerves of any part of the body, the current should be passed in such a direction as to throw the nerves of that part into a state of an electrotonus —and similarly in other cases. If a powerful electric current be passed through the body of a recently killed animal, violent movements are produced, as the muscles ordinarily retain their vitality for a considerable time after general systematic death : by this means, also, life has been re-established in animals which were appa- rently dead—a properly applied current stimulating the respiratory muscles to contract. * 846 Dynamical Electricity [851- 851. Heating effects.—When a voltaic current is passed through a metal wire the same effects are produced as by the discharge of an electric battery (812) ; the wire becomes heated, and even incandescent if it is very short and thin. With a powerful battery all metals are melted, even iridium and platinum, the least fusible of metals. Carbon is the only element which has not hitherto been fused by it. Despretz, however, with a battery composed of 600 Bunsen’s elements joined in six series (831), raised rods of very pure carbon to such a temperature that they were softened and could be welded together, yielding an incipient fusion. A battery of 30 to 40 Bunsen’s elements is sufficient to melt and volatilise fine wires of lead, tin, zinc, copper, gold, silver, iron, and even platinum, with differently coloured sparks, Iron and platinum burn with a brilliant white light ; lead with a purple light ; the hght of tin and of gold is bluish-white ; the hght of zinc is a mixture of white and gold ; finally, copper and silver give a green light. The thermal t effects of the voltaic current aréwi usediwnfar firing mines for ~ military — pur- poses and _ for blasting opera- tions. The fol- lowing arrange- ment (fig. 814) serves to illus- trate the prin- ciple :—Two moderately stout copper wires, 20’, insulated by being covered with gutta-percha, are deprived of this coating at the ends, which are then passed through and through the box in the manner represented in the figure. The distance between them is 2 of an inch, and a very fine platinum wire is soldered across. The object of arranging the wires in this manner is that they shall not be in contact, and that the strain which they exert may be spent on the box, and not on the platinum wire joining them, which, being extremely thin, would be broken by even a very slight pull. The box is then filled with fine grained powder, and the lid tied down. The wires of the fuse are then carefully joined to the long con- ducting wires which lead to the battery: these should be of copper, and as thick as is convenient, so as to offer very little resistance. The fuse is then introduced into the charge to be fired: if it is for a submarine explosion, the powder is contained in a canister, the neck of which, after the introduction of the fuse, is carefully fastened by means of cement: When contact is made with the battery, the current traversing the platinum wire renders it incandescent, which fires the fuse ; and thus the ignition is communicated to the charge in which it is placed. Fig. 814 -852] Laws of Heating Effects. Galvanothermometer. 847 When any circuit is closed, a definite amount of heat, H, is produced throughout the entire circuit ; and the amount of heat, 2, produced in any particular part of the circuit bears to the total heat, H, the same ratio which the resistance, ~ of this part bears to R, that of the entire circuit. That is h:H=r:R. Hence, in firing mines, the wire to be heated should be of as small section and of as small conductivity as practicable. These conditions are well satisfied by platinum, which has over iron the advantage of being less brittle and of not being lable to rust. Platinum too has a low specific heat, and is thus raised to a higher temperature, by the same amount of heat, than a wire of greater specific heat. On the other hand, the con- ducting wires or /eads should present as small a resistance as possible, a condition satisfied by a stout copper wire; and again, as the heating effect of any circuit is proportional to the square of the electromotive force, and inversely as the resistance, a battery with a high electromotive force and small resistance, such as Grove’s or Bunsen’s, should be selected. Another application of the heating effect is to what are called safety catches or automatic cut-outs. These are lengths of lead wire or strips interposed in the circuit of the powerful currents used for electrical lighting and the like. Their dimensions are calculated so that when the current attains a certain strength, the heat generated is sufficient to melt them and thus break the continuity of the circuit. As this can be arranged with great accuracy, it is possible so to regulate the circuit that it shall not exceed a certain limit. By means of a heated platinum wire, parts of the body may be safely cauterised which could not be got at by a red-hot iron; the removal of tumours and the like may be effected by drawing a loop of cold platinum wire round their base, making the wire hot by a current, and gradually pulling its ends together. It has been observed that when the temperature of the wire is about 600° C., the combustion of the tissues 1s so complete that there is no haemorrhage ; while at 1,500° the action of the wire is like that of a sharp knife. For other purposes of this galvanic cautertsation, platinum wire coiled -in grooves cut in a porcelain rod is used. 852. Laws of heating effects. Galvano- thermometer.—Although the thermal effects are most obvious in the case of thin wires, they are by no means limited to them. The laws of the heating effect were investigated by Lenz, by means of an apparatus called the Galvanothermometer (fig. 815). A wide- mouthed stoppered bottle was fixed upside down, with its stopper, 4, in a wooden box ; 7 y N “ the stopper was perforated so as to give pas- 7 ddd si Y sage to two thick platinum wires, connected 2 'Yff jj at one end with binding screws, ss, while their {/ VM free ends were provided with platinum cones by which the wires under investigation could be readily affixed ; the vessel contained alcohol, the temperature of which was indicated by a thermometer fitted in a cork inserted in a hole made in 8.48 Dynamical Electricity [852— the bottom of the vessel. The current is passed through the platinum wires, and its strength measured by means of a tangent compass inter- posed in the circuit. By observing the increase of temperature in the thermometer in a given time, and knowing the weight of the alcohol, the mass of the wire, the specific heat, and the calorimetric values (462) of the vessel, and of the thermometer, compared with alcohol, the heating effect which is produced by the current in a given time can be calculated. By apparatus of this kind the truth of the following law may be esta- blished. The heat disengaged in a given time, ¢, ts directly proportional to the square of the strength of the current, and to the resistance. This is known as /ow/e’s daw, and is expressed in the formula JH = 2 C7RL= Bed =EC/, where J is the mechanical equivalent of heat. If we divide the values E,C, Rexpressed in ergs, by the mechanical equivalent of a water-gramme degree, that is, by 4°16 10’, we get the value H in water-cramme degrees. In the above formula the symbols H, C, R, E refer to the whole circuit. If H denote the heat developed in a wire of resistance 7, in a time # due to the passage of a current C, the potential difference at the ends of ~ 29 e° being 2, the corresponding formule are JH =C?77— Cez—_7 je If the current passes through a chain of alternate links of platinum and silver wire of equal sizes, the platinum becomes more heated than the silver from its greater resistance ; and with a suitable current the platinum may become incandescent while the silver remains dark. This experiment was devised by Children. If a long thin platinum wire is raised to dull redness by passing a voltaic current through it, and if part of it is cooled down by being dipped in hot water, the resistance of the cooled part is diminished, the strength of the current increases, and the rest of the wire becomes brighter than before. If, on the contrary, a part of the feebly incandescent wire is heated by a spirit-lamp, the resistance of the heated part increases ; the effect is the same as that of introducing additional resistance, the strength of the current diminishes, and the wire ceases to be incandescent in the non- heated part. Radiation and convection of heat lower the temperature to which a wire is raised by the passage of a given current through it. A round wire is more heated by the same current than the same wire which has been beaten out flat: for the latter with the same section offers a greater surface to the cooling medium than the other. For the same reason, when a wire is stretched in a glass tube on which two brass caps are fitted air-tight, and the wire is raised to dull incandescence by the passage of a current, the incan- descence is more vivid when the air has been pumped out of the tube, because it now simply loses heat by radiation, and not by communication to the surrecunding medium. Similarly, a current which will melt a wire in air will raise it only to dull redness in ether, and in oil or in water will not heat it to redness at all, for the liquids conduct heat awav more readily than air does. -854] Relation of Heating Effect to Work of a Battery 849 From the above laws it follows that the heating effect is the same in a wire whatever be its length, provided the current is constant ; but it must be remem- bered that by increasing the length of the wire we increase the resistance, and consequently, to maintain the current constant, we must apply a larger E.M.F. ; further, in a long wire there is a greater surface, and hence more heat is lost by radiation and by conduction. It must be added that Joule’s law only holds provided the current does no external work, such as inductive actions on adjacent conductors, or mag- nets—that, in short, the thermal is the only action of the current. 853. Graphical representation of the heating effects in a circuit. The law representing the production of heat in a circuit in the unit of time is very well seen by the following geometrical construction, due to Professor Foster. The heat H produced in a circuit in the unit of tinie is proportional to the square of the strength of the current C, and to the resistance R (851), 2 thatiseri aC Riesput since.© == (847), we have H = a Draw a straight line DAB (fig. 816), and from any point A init drawa line AC, at right angles to DAB, and of a length proportional to the electro- motive force of $e) ice.) shay. off a length AB proportional to the resistance n of the circuit. Join CB, and at GAdraw a; line at right angles to +BG band, let Le) : RB D be the point % sie B where this line ng cuts the line DAB. Then the length AD is proportional to the eat produced in the whole circuit in unittime. For the triangles ADC and ACB are similar, anditherefore"AD:AC = AC:AB; that is, AD ee that is) HAE The above construction holds good if R and E, instead of being the resistance of the whole circuit and the E.M.F. of the battery, are respectively the resistance of any part of the circuit and the potential difference at the ends of this part. 854. Relation of heating effect to work of a battery.—In every closed circuit chemical action is continuously going on ; in ordinary cir- cuits, the most common action is the solution of zinc in sulphuric acid, which may be regarded as an oxidation of the zinc to form zinc oxide, and a combination of this zinc oxide with sulphuric acid to form water and zinc sulphate. It is a true combustion of zinc, and this combustion serves to maintain all the actions which the circuit can produce, just as all the work which a steam-engine can effect has its origin in the combustion of fuel (493). : By independent experiments it has been found that, when a given weight a1 850 Dynamical Electricity [854— of zinc is dissolved in sulphuric acid, a certain definite measurable guantity of heat is produced, which, as in all cases of chemical action, is the same, whatever be the rapidity with which this solution is effected. If this solution takes place while the zinc is associated with another metal so as to form a voltaic couple, the rapidity of the solution will be altered and the whole cir- cuit will become heated—the liquid, the plates, the containing vessel as well as the connecting wire. But although the distribution of the heat is thus altered, its quantity is not. If the values of all the several heating effects in the various parts of the circuit be determined, it will still be found that however the resistance of the connecting wire be varied, the sum of these values is exactly equivalent to the heat produced by the solution of a certain weight of zinc. If the couple is made to do external mechanical work, the case is dif- ferent. Joule made the following remarkable experiment :—A small zinc and copper couple was arranged in a calorimeter, and the amount of heat determined while the couple was closed for a certain length of time by a short thick wire. The couple still contained in the calorimeter was next connected with a minute electromagnetic engine (920), by which a weight was raised, It was then found that the heat produced in the calorimeter in a given time—while, therefore, a certain amount of zinc was dissolved—was less while the couple was doing work than when it was not; and the amount of this diminution was the exact thermal equivalent of the work performed in raising the weight (509). That the whole of the chemical work and disengagement of heat in the circuit of an ordinary cell has its origin in the solution of zinc in acid is confirmed by the following experiment, due to Favre :— ' In the muffle of his calorimeter (473), five small-zinc platinum elements were introduced ; the other muffle contained a voltameter. Now when the element was closed until one equivalent of zinc was dissolved in the whole of the cells, 4 of an equivalent of water should be decomposed in the voltameter (868), which was found to be the case. In one case the current of the battery was closed without inserting the voltameter, and the heat disengaged during the solution of one equivalent of zinc was found to be 18,796 thermal units ; when, however, the voltameter was introduced, the quantity disengaged was only 11,769 thermal units. Now the difference, 7,027, is represented by the chemical work of decomposing 4 of an equivalent of water : this agrees 34,462 5 very well with the number, 6,892 = , which represents the heat disen- gaged during the formation of 4 of an equivalent of water. However complicated may be the chemical processes involved in a voltaic combination, the total heat produced in it is the sum of the quantities of heat which are produced and absorbed in these various chemical processes. We may illustrate this important principle by reference to the element of De la Rue and Miller (833), the chemical actions in which are perhaps the simplest of all constant elements. The normal action is that, when the element is closed, zinc decomposes ammonium chloride with the formation of zinc chloride, while the liberated ammonium unites with the chlorine of the silver chloride, re-forming ammonium chloride and depositing silver. The heat of decomposition and of re-formation of the ammonium chloride —855] Luminous Effects 851 compensate one another, and the net result is the formation of zinc chloride, and the decomposition of silver chloride. Now the heat produced in the formation of a molecule of zinc chloride (ZnCl,) is 112,840 gramme units, and that of the equivalent silver chloride (2Ag Cl) is 58,760. The difference is 54,080, which is less than 58,360, the heat required to decompose a mole- cule of water. Hence it is that one such element will not effect a continuous decomposition of water, but at least two are required for the purpose. In like manner the heat available by the substitution of zinc for copper in one Daniell’s cell is represented by 47,300, and accordingly at least two of these elements are also required. In some cases, however, the current of a single cell does produce a feeble but continuous decomposition of water. This arises from the fact that the water of the voltameter contains air in solution, and the hydrogen as it is liberated unites with the dissolved oxygen. This process is known as electrolytic convection. This principle is, however, not of universal validity. Fora great number of cells the electrical energy is less than corresponds to the thermal tonation, and part of their energy is transformed into heat ; while for a small number the electrical energy is greater ; such cells when closed absorb heat from the surrounding medium. 855. Luminous effects.—Luminous effects are obtained when the battery is sufficiently powerful, by bringing the two electrodes very nearly in contact ; a succession of bright sparks springs sometimes across the interval, which follow each other with , such rapidity as to produce i continuous light. Although ian ni the quantity of electricity f put in motion by the voltaic current iS very +f | great, the distance across which the spark passes is very small. Jacobi found that with a battery of 12 Grove’s elements the elec- trodes could be approached within o70013 mm. before the spark passed. When one terminal of a battery of a few elements is connected’ with a file, and an iron wire connected with the other is moved | over the file, a stream of brilliant luminous sparks is obtained, which obviously arises from a combustion. The most beautiful effect of the electric light is obtained when two pencils of charcoal are connected with the terminals of the battery in the manner represented in fig. 817. The charcoal 6 is fixed, while the charcoal @ can zi 2 852 Dynamical Electricety | [855- be raised and lowered by means of a rack and pinion motion, ¢. The two charcoals being placed in contact, the current passes, and their ends soon become incandescent. If they are then removed to a distance of about the tenth of an inch, according to the strength of the current, a luminous arc extends between the two points, which has an exceedingly brilliant lustre, and is called the voltaic arc. The length of this arc varies with the strength of the current. In air it may exceed 2 inches, with a battery of 600 elements, arranged in six series of 100 each, provided the positive pole is uppermost, as represented in the figure ; if it is undermost, the arc is about one-third shorter. In a partial vacuum the distance of the charcoals may be greater than in air ; in fact, as the electricity meets with no resistance, it springs between the two charcoals, even before they are in contact. The voltaic arc can also be produced in liquids, but it 1s then much shorter, and its brilliancy is greatly diminished. The voltaic arc has the property that it is attracted when a magnet is pre- sented to it—a case of the action of magnets on currents (889). The voltaic arc may be considered as formed of a very rapid succession of bright sparks. Its colour and shape depend on the nature of the conduc- tors between which it is formed, and it is probably due to the incandescent particles of the conductor, which are volatilised and transported in the direc- tion of the current; that is, from the positive to the negative pole. The more easily the electrodes are disintegrated by the current, the greater is the distance at which the electrodes can be placed. Charcoal, which is a very friable substance, is one of the bodies which give the largest luminous Ar: Davy first made the experiment of the electric light in 1801, by means of a battery of 3,000 plates, each four inches square. He used charcoal points made of light wood charcoal which had been heated to redness, and im- mersed in a mercury bath ; the mercury penetrating into the pores of the charcoal increased its ponductiany When any substance was introduced into the voltaic arc produced by this battery, it became incandescent ; pla- tinum melted like wax in the flame of a candle ; sapphire, magnesia, lime, and most refractory substances were fused. Fragments of diamond, of charcoal, and of graphite rapidly disappeared without undergoing any previous fusion. As charcoal rapidly burns in air, it was necessary to operate in vacuo, and hence the experiment was for a long time made by fitting the two points in an electric egg, like that represented in fig. 767. At present the electrodes are made of gas graphite, a modification of charcoal deposited in gas retorts ; this is hard and compact, and only burns slowly in air ; hence it is unneces- sary to operate in vacuo. When the experiment is made in vacuo, there is no combustion, but the charcoal wears away at the positive pole, while it is somewhat increased on the negative pole, indicating that there is a transport of solid matter from the positive to the negative pole. It appears from the researches of Edlund that the disintegration of the electrodes which takes place when the voltaic arc is formed gives rise to a counter-electromotive force which is analogous to the polarisation which takes place in the decomposition of water (863), and the existence of which —857] Regulator of the Electric Light 853 can be demonstrated by similar experiments. The magnitude of this force varies with the nature of the electrodes ; it is greatest with carbon, amount- ing to 35 volts ; with iron it is 25 ; copper, 24; zinc, 19; and cadmium 10 volts. The resistance of the arc itself, due to the medium, increases like other resistances with the distance of the terminals; it diminishes as the strength of the current increases, for then the temperature increases. With carbon electrodes, it was found to amount to 1°3 ohm for each mm. of distance. This counter-electromotive force explains how it is that a continuous arc can only be obtained by the application of considerable electromotive force. 856. Foucault’s experiment.—This consists in projecting on a screen the image of the charcoal points produced in the camera obscura at the moment at which the electric light is formed (fig. 818). By means of this i nt irk ( ul It : Fig. 818 experiment, which is made by the photo-electric microscope already de- scribed (fig. 604), the two charcoals can be readily distinguished, and the positive charcoal is seen to become somewhat hollow and diminished, whiie the other increases. The globules represented on the two charcoals arise from the fusion of a small quantity of silica contained in the charcoal. When the current begins te pass, the negative charcoal first becomes luminous, but the light of the positive charcoal is the brightest ; as it also wears away about twice as rapidly as the negative electrode, it ought to be rather the larger. 857. Regulator of the electric light.—When the electric light is to be used for illumination, it must be as continuous as other modes of lighting. For this purpose, not only must the current be constant, but the distance of the charcoals must not alter, which necessitates the use of some arrange- ment for automatically bringing them nearer together in proportion as they 854 Dynamical Electricity [857— wear away. One of the best modes of effecting this is by an apparatus in- vented by Duboscq. In this regulator the two charcoals are movable, but with unequal veloci- ties, which are virtually proportional to their waste. The motion is trans- mitted by a drum placed on the axis xy (fig. 819). This turns, in the direc- tion of the arrows, two wheels, aand 4, the diameters of hich AYE "AS "ites and which respectively trans- mit their motion to two rackworks, CGC and ti.) @ lowers the positive charcoal, ~p, by means of a rod sliding in the tube H, while the other C’ raises the negative charcoal, 2, half as rapidly. By means of the milled head y the drum can be wound up, and at the same time the positive charcoal moved by the hand; the milled head 2 moves the negative charcoal also by the hand, and independently of the first. For this pur- pose the axis, xy, consists of two parts pressing against each other with some force, so that, while the milled head x is held between the fingers, the other, y, may be moved, and by holding the latter we may move the former. But the friction is sufficient when the drum works to move the two wheels a and 4 and the two rackworks. The two charcoals being placed in contact, the cur- rent of a powerful battery of 40 to 50 elements reaches the apparatus by means of the wires E and E’. The current rising in H descends by the positive charcoal, then by the negative charcoal, and reaches the apparatus, but without passing into the rackwork C, or into the part on the right of the plate N ; these pieces being insulated by ivory discs placed at their lower part. Thecurrent ultimately reaches the bobbin B, which forms the foot of the regulator, and passes into the wire E’. Inside the bobbin is a bar of soft iron, which is magnetised as long as the current passes in the bobbin, and demagnetised when it does not pass, and this temporary magnet is —858] Browning's Regulator 855 the regulator. It acts attractively on an armature of soft iron, A, open in the centre so as to allow the rackwork C’ to pass, and fixed at the end of a lever, which works on two points, 77, and transmits a slight oscillation to a rod, ad, which, by means of a catch, z, seizes the wheel z,as is seen ona larger scale in fig. 820. By an endless screw, and a series of toothed wheels, the stop is transmitted to the drum, and the rackwork being fixed, the same is the case with the carbons. This is what takes place so long as the ‘magnetisation in the bobbin is strong enough to keep down the armature A; but in proportion as the carbons wear away, the current becomes feebler, though the voltaic arc continues, so that ultimately the attraction of the magnet no longer counterbalances a spring 7, which continually tends to raise the armature. It then ascends, the piece @d disengages the stop 2, the drum works, and the carbons come nearer; they do not, however, touch, because the strength of the current gains the upper hand, the armature A is attracted, and the carbons remain fixed. As their distance only varies within very narrow limits, a regular and continuous light is obtained with this apparatus until the carbons are quite used. By means of a regulator, Duboscq illuminates the photogenic apparatus represented in fig. 604, by which all optical experiments may be performed for which sunlight was formerly essential. 858. Browning’s regulator. —A much simpler apparatus, represented in fig. 821, has been devised by Brown- ing, which is less costly than the other lamps, and also requires a smaller number of elements to work it. The current enters the lamp by a wire at- tached to a binding screw on the base of the instrument, passing up the pillar by the small electro-magnet to the centre pillar along the top of the hori- zontal bar, down the left-hand bar through the two carbons, and away by a wire attached to a binding screw on the left hand. A tube holding the upper carbon slides freely up and down a tube at the end of the cross-piece, and would by its own weight rest on the lower carbon, but the electro-mag- net is provided with a keeper, to which is attached a rest that encircles the carbon tube and grasps it. When the = electro-magnet works and attracts the SSS keeper, the rest tightens, and thereby i . prevents the descent of the carbon. When the keeper is not attracted the rest loosens, and the carbon-holder descends. When the two carbons are in contact, and the battery circuit is com- pleted, the current traverses both carbons and no light is produced.: But if Fig. 821 856 Dynamical Electricity [858- the upper carbon is raised ever so little, a brilliant light is emitted. When the lamp is thus once set to work, the rod attached to the upper carbon may be let go, and the magnet will afterwards keep the lamp at work For when some of the carbon is consumed, and the interval between the two 1s increased, the current is enfeebled and the magnet loses some of its power, the keeper loosens its hold on the carbon, which descends by its own weight As the carbons approach, the current strength increases ; the magnet again draws on the keeper, and the keeper again checks the descent of the carbon, and so forth. Thus the points are retained at the right distances apart, and the light is continuous and brilliant. Stohrer has devised a regulator for the electrical light which is very simple in principle, and which also only requires a few elements. Its essen- tial features are represented in fig. 822, in which @ is a cylinder containing vaseline and surrounded by the wire of the circuit f In this is a hollow cylindrical floater a, nearly as wide as the vessel ; at its top is a copper tube ¢, in which the carbon point @ can be fixed. A stout copper wire fixed to the bottom of the float dips in an iron tube filled with mercury, with which is connected one pole of the battery ; the other pole is connected with the carbon a’, which is supported in a suitable manner. The size of the float is such that it moves slowly upwards, so that the carbon d presses with but very slight force against @. The pressure can be regulated by small weights on the collar ¢c. An insulated wire forming part of the cir- cuit is coiled in a spiral & round the cylinder, and aids the regulation. 859. Properties and intensity of the electric light.—The electric light has similar chemical properties to sunlight; it effects the combination of chlorine and hydrogen, acts chemi- cally on silver chloride, and can be applied in photography. Passed through a prism, the electric light, like that of the sun, is decomposed and gives a spectrum. Wollaston, and more especially Fraunhofer, found that the spectrum of the electric light differs from that of other lights, and of sunlight, by the presence of several very bright lines, as has been already stated (586). Wheatstone was the first to observe that, with electrodes of different metals, the spectrum and the lines are modified. Masson, who experimented upon the light of the electric machine, that of the voltaic arc, and that of Ruhmkorff’s coil, found the same colours in the electric spectrum as in the solar spectrum, but traversed by very brilliant luminous bands of the same shades as that of the colour in which they occur. The number and position of these bands do not depend on the intensity of the light, but, as we have seen (855), upon the substances between which the voltaic arc is formed. With carbon the lines are remarkable for their number and brilliancy ; with zinc the spectrum is characterised by a very marked apple-green tint ; silver produces a very intense green; with lead a violet tint predominates, and so on with other metals. Bunsen, in experimenting with 48 couples, and removing the charcoals to -860] Electric Lighting 857 a distance of a quarter of an inch, found that the intensity of the electric light is equal to that of 572 candles. Fizeau and Foucault compared the chemical effects of the sun and the electric lights by investigating their action on iodised silver plates. Re- presenting the intensity of the sun’s light at midday at 1,000, these physicists found that the light from a battery of 46 Bunsen’s elements was 235, while that from one of 80 elements was only 238. It follows that the intensity does not increase to any material extent with the number of the couples ; but ex- periment shows that it increases considerably with their surface. For with a battery of 46 elements, each consisting of three elements, with their zinc and copper respectively united so as to form one element of triple surface (847), the intensity was 385, the battery working for an hour ; that is to say, more than a third of the intensity of the solar light. Too great precautions cannot be taken against the effects of the electric light when they attain a certain intensity. The light of 109 couples may produce very painful affections of the eyes. With 600, a single moment’s exposure to the light is sufficient to produce very violent headaches and pains in the eye, and the whole frame is affected as by a powerful sunstroke. 860. Electric lighting.—Great progress has been made in the applica- tion of the electric light to purposes of ordinary illumination. This progress has been mainly due to the improvements which have been made in the means of generating elec- tricity, for which some form of mag- neto- or dynamo- electrical machine (934, 939), driven by steam or water power or by gas engines (486), is used. So long as the electricity from the voltaic battery was alone avail- able for the pro- duction of the elec- tric light, no great extension was pos- sible, for the cost and inconvenience a were far too great at pa .to permit it to be | B _ ia used for anything = ~eee' more than lecture Seca purposes and oc- casional scenic il- lumination. Very considerablé improvements have also been made in the lamps Fig. 824 858 Dynamical Electricity [860- which are ordinarily divided into avc lamps, in which the hght is produced between carbon points automatically kept at a constant distance by the action of the current itself, and zzcandescent lamps, in which the light is produced by the incandescence of a thin continuous solid conductor. To this may be added the electrical candles, of which the best known is the Jablochkofgf candle. It consists (fig. 823) of two rods of gas carbon, a and 6, from 2 to 4 mm. in diameter, separated by a layer of kaolin or Chinese clay about 2 mm. thick, fixed respectively in the supports, to which the positive and negative electrodes A B are respectively attached. The rods are insulated from each other by the whole being bound by some insulating material. The current is started by a small piece of carbon, 2, placed across the top. As the arc passes, the kaolin melts away, and the arrangement may therefore fitly be called a candle. The positive electrode wears away twice as fast as the negative, which would soon destroy the arc, but by using alternating currents the unequal waste of the carbons is pre- vented. Fig. 818, which represents one of the forms of an arc lamp, may be taken as an example of the manner in which the regulation of the arc is effected. Reynier s electric lamp, fig. 824, consists of a rectangular copper rod, B, moving in a copper tube A, guided by four pulleys, 7, of which only two are shown ; to B is fixed a cross-piece holding a thin carbon pencil, a, the lower part of which passes through a silver guide, and its end presses, but not quite over the centre, against a carbon disc, #z, which moves about a hori- zontal axis. The piece supporting this is insulated from A, but is connected with the negative pole by a wire, 4. The positive current, entering by A, passes by C to a small block of carbon, 0, which presses against the pencil. Thus the current passes through only a very small portion of this pencil, and it is this small portion which becomes incandescent and forms the are. The rod, as it burns away and sinks by its own weight, rotates the disc 7 slowly, and prevents its being irregularly worn away. When either of the carbon electrodes which produce the electric light is increased in size, its increase of temperature is lessened, while that of the other is greater. When the negative electrode is large the light of the positive electrode is very bright. This is seen in Werdermann’s electric lamp, which consists essentially of a carbon disc about 2 inches in diameter and an inch in thickness, which is connected with the negative pole of the battery ; the positive pole is a rod of carbon about 3 mm. in diameter, of any suitable length ; it slides vertically in a copper tube, which serves both as a guide and as a contact for it; this is pressed upwards against the centre by a weight passing over a pulley. The current can be passed adveast through as many as ten of such lamps, though it seems that the total illuminating’ power of this arrangement is not so great as when only two parallel lights are employed. The electrical arc has had a very useful application to the welding or autogenous soldering of metals, that is to say, joining them without the use of a solider; a method which is of great service, particularly in the case of iron. The two plates to be joined are placed in contact, and having been —860] Electric Lighting 859 connected with the negative pole, the positive carbon fixed in a suitable holder is held at such distance that the arc passes, which then melts one plate on the other. In other cases the two pieces of metal are pressed against each other, and the current passed through the line of contact. For these operations accumulators (872) are used charged by dynamos, which yield very powerful currents ; by means of a commutator the electro- motive force and the strength of the current can be varied within very wide limits at the will of the operator. Von Hefner’s differential lamp is represented in fig. 825; the current arriving by A divides at z (868); one portion passing through a fine wire coil, R, offering a large resistance, and the other through a short thick coil vy, whence it passes to a lever which turns about @; to this is connected at one end, 7, a soft iron core which plays in the two coils, and at the other end is the positive carbon C,. When the carbons are apart a great resistance is presented, and the current passes through R, so that the core is drawn within R, and the lever, and with it the carbon C, falls ; the fastening in the holder a@ is such that at a certain angle the carbon C, slips in the holder and touches the lower one, and the current passes by x d C, C, B; the iron core is then drawn down, but the holder a moves up, grips the carbon, which it moves with it, and the arc is reproduced ; when its normal length is attained its resistance in- creases to an amount such that the currents passing through the two coils now balance themselves, and their attraction on the iron being equal the core is stationary. Several such lamps may be arranged in a circuit, and the extinction of one of them does not affect the others. Schwendler devised a new unit of luminous intensity, which he calls the platinum light standard, specially for use with the electric Fig. 825 light. It is the incandescence pro- duced by a current of known strength passing through a (J-shaped strip of platinum foil 36:28 mm. in length, 2 mm. in breadth, and o-o17 mm. in thick- ness. The circuit contains a rheostat and a aananomeree by which the constancy of the current can be observed and ensured. When the strength of the current is constant the intensity of the light, radiated by the platinum, is constant also, and fulfils all the conditions of a standard measure of light, as it can always be reproduced in exactly the same form from pure platinum. The standard of light adopted by the International Congress of Electri- cians in 1884 is the light emitted by a square centimetre of melted platinum when on the point of solidifying. According to Rossetti the Bee Rae AA: of the positive carbon in the electric arc is between 2400° and 3900° C. ; it is higher the smaller is the radiating surface. The temperature of the negative electrode lies between 2138° and 2530°. It appears that the temperature of the positive carbon does not rise 860 Dynamical Electricity | [860— above a certain limit. Violle considers this to be the temperature of evapo- ration of carbon, and has indirectly determined it at 3500°. The resistance of the heated air in the arc is from I to 12 ohms (1000). Incandescent lamps, though not so economical! as arc lights, lend them- selves best to the distribution of the electric light. We have seen that when a strong current of electricity is passed through a wire of small conductivity (851), its temperature is raised to incandescence ; if the strength of the current is increased, the brightness of the light increases, but in a greater ratio than the strength of the current. At such high temperatures, however, wires even of the most difficultly fusible metals fuse or are disintegrated ; and the only material which does not fuse at the highest temperature is carbon. ‘The first lamps in which this material was applied were constructed independently by Edison in America and Swan in this country. Fig. 826 is a representation of Swan’s lamp. Inside the neck of a globular glass vessel, and fused to it, is a glass rod, through which pass two platinum wires, bent outside in loops. These loops can be easily fitted in the two bent wires in the holder (fig. 827), which are in contact with the binding screws, and thus allow a current to be transmitted. The spring-wire exerts an upward pres- sure, so as to always ensure good contact. To the other ends of the platinum is fixed the characteristic part, the carbon filament ; this is about 0°25 mm. in diameter, and is bent in the form of a double loop. It is prepared by im- mersing crochet cotton in sulphuric acid of a certain strength, by which it is converted into what is known as vegetable parchment, and then carbonising it by heating it to a high temperature in a closed vessel. The bulb, before being sealed, is exhausted of air by means of a Sprengel pump, and the vacuum is made so perfect that electricity does not pass init. The carbon of such a lamp, which is a thread about 12°7 cm. in length and o’013 cm. in diameter, has a resistance of 143 ohms in its normal incan- descence. . In Edison’s lamp the carbon filament is made of a special: kind of bamboo carbonised at high temperatures in closed nickel moulds. In the Maxim lamp, and in that of Lane Fox, the carbon filaments, after being carbonised and mounted, are heated by the current itself in an atmosphere of coal gas or the vapour of a hydrocarbon ; in this way carbon is deposited on the thinner and there- fore hotter parts of the filament, which is thus rendered more uniform and durable. If we surround an electric light in one case by an opaque calorimeter, which therefore absorbs the entire radiation, and then by a transparent one, which allows the light to pass, it will be found that the luminous radiation —861] Mechanical Lffects of the Battery 861 is about Io per cent. of the total in the case of arc lamps and 5 in that of incandescent lamps. The relation between lighting power and strength of current varies in different lamps according to the strengths of the currents. Edison’s lamp, giving 16-candle power, requires a current of o°6 ampere; taking its resist- ance when hot at 170 ohms, the potential difference at the connections would be from Ohm’s law (847) 0°6 x 170 = 102 volts. For the same standard of light, Swan’s lamp requires a current of 1°28 amperes, its resistance is 40, and hence the potential difference is 52 volts. The power absorbed bya lamp or other conductor through which a current flows is equal to C E, where C is the current and E the difference of potential at the terminals. The unit of power is the watt. Thus 1 watt =I ampere x I volt. A horse-power is equal to 746 watts. A kilowatt = 1,000 watts = 1°34 h.p. An incandescent lamp may be taken to absorb about 4 watts per candle. Lamps are usually classed according to the number of volts they require. Asa rule, the greater this number the more brilliant is the light. Whatever care may be exerted in their manufacture, the carbons at last give way ; their life, however, ought to be from 1,000 to 2,000 hours. The temperature of the carbon in a Ioo volt lamp is 1290°, and at 1330° it begins to volatilise. 861. Mechanical effects of the battery.—Under this head may be in- cluded the motion of solids and liquids effected by the current. An example of the former is found in the voltaic arc, in which there is a passage of the molecules of carbon from the positive to the negative pole (855). The mechanical action of the current may be shown by means of the following experiment (fig. 828). A glass tube, AB, bent at the two ends, about 50 cm. in length and I cm. in diameter, is almost filled with dilute sulphuric acid, and a globule of mercury, 7z, is introduced. The whole is fixed in a support, and the level of the tube can be adjusted by the screw z, the drop of mercury itself serving as index. When the two poles of a battery of 4 or 5 cells are introduced into the two ends, the globule of mercury elongates and moves towards the negative pole with a velocity which in- creases with the number of elements. With 24, a long column of mercury can be moved through a tube a metre in length; with 50, the velocity is greater and the mercury divides into globules, all moving in the same direction. If the direc- tion of the current is reversed, the mercury first remains ‘5 stationary, and then moves — = in the opposite direction. If the tube is gently in- clined towards the positive pole, the mercury is still moved with the current ; and a moment is at length reached at which there is equilibrium between = tL <= My. 862 Dynamical Electricity [861- the force due to the current and the weight of the mercury. The component of this weight parallel to the plane may then be taken as representing the mechanical action of the current which traverses the globule of mercury. A similar phenomenon, known as électrical endosmose, is observed in the following experiment, due to Porret. Having divided a glass vessel into two compartments by a porous diaphragm, he poured water into the two com- partments to the same height, and immersed two platinum electrodes in connection with a battery of 80elements. As the water became decomposed, part of the liquid was carried in the direction of the current through the diaphragm, from the positive to the negative compartment, where the level rose above that in the other compartment. A solution of copper sulphate is best for these experiments, because then the disturbing influence of the dis- engagement of gas at the negative electrode is avoided. A porous vessel is necessary, for otherwise the transport by the liquid would be at once hydrostatically equalised. The converse of these phenomena, that is, the production of electrical currents, when a liquid is forced through a diaphragm by mechanical means, has also been observed. Such currents, which were discovered by Quincke, are called diaphragm currents. A porous diaphragm, 7, is fixed ina glass tube (fig. 829), in which are also fused two platinum wires terminating in platinum electrodes, a and 6; on forcing a liquid through the diaphragm the existence of a current is evidenced by a galvanometer with which the wires are connected, the direction of the current being that of the flow of the liquid. The difference of potential due to this flow is proportional to the pressure. According to Zollner, all circulatory motions in liquids, especially when they take place in partial contact with solids, are accompanied by electrical currents, which have gene- rally the same direction as that in which the _ liquid flows. And he regards earth currents as analogous to dia- phragm currents ; there are currents in the liquid mass in the interior of the earth, and these currents coming in contact with the solidified masses produce electrical currents. Wertheim found that the elasticity of metal wires is diminished by the current, and not by the heat alone, but by the electricity ; he has also found that the cohesion is diminished by the passage of a current. To the mechanical effects of the current may be assigned the sounds produced in soft iron when submitted to the magnetising action of a discon- tinuous current—a phenomenon which will be subsequently described. 862. Electrocapillary phenomena.—If a drop of mercury be placed in dilute sulphuric acid containing a trace of chromic acid, and the end of a bright iron wire be so fixed that it dips in the acid and just touches the edge of the mercury, the latter begins a series of regular vibrations which may last for hours. The explanation of this phenomenon, which was first ob- served by Kiihne, is as follows :—When the iron first touches the mercury, an iron-mercury couple is formed, in consequence of which the surface of the mercury is polarised by the deposition of an invisible layer of hydrogen ; —862] Electrocapillary Phenomena 863 this polarisation (827) increases the surface-tension of the mercury (139), it becomes rounder, and contact with the iron is broken ; the chromic acid present depolarises the mercury, its original shape is restored, the couple is again formed, and the process repeats itself continuously. Lippmann was led by the observation of this phenomenon to a series of interesting experimental results, which have demonstrated a relation between capillary and electrical phenomena. Of these results the most important is the construction of a capillary electrometer. A glass tube, A (fig. 830), is drawn out to a fine point, and is filled with mercury: its lower end dips in a glass vessel, B, containing mercury at the bottom and dilute sulphuric acid at thetop. Platinum wires are fused in the tubes A and B, and terminate in the binding screws a and 6 respectively. At the beginning of the experiment, the position of the mercury in the drawn-out tube is such that the pressure due to the surface-tension at the surface of separation of the mercury in the tube and the liquid is: suff- cient to counterbalance the pressure of the column of mercury, A. This position is observed by means of a microscope, the focus of which is at the fiducial mark on the glass at which the mercury stops. If now a difference of potential be established between a and 4, 6 being at the higher potential, the surface-tension is increased, the mercury ascends in the capillary tube, and in order that the meniscus may be brought to its former position the pressure on A must be increased. ‘This increase is most simply effected by means of a thick caout- chouc tube, T, connected with the top of A, and with a manometer, H, and capable of more or less compression by means of a screw, E. The difference in level of the two legs of the manometer is thus a measure of the increase of the surface-tension, and therewith of the difference of potential. Lippmann found by special experiments, that this increase is almost directly proportional to the electromotive force, up to about o9 of a Daniell’s element. Each electrometer requires a special table of gradua- JZ #5 tion, but when once this ww wommTmmT mn 0w°iw0 AO WiN00000 ii Ai is constructed it can be Fig. 830 directly used for deter- mining electromotive forces. It should not be used for greater electro- motive forces than 06 of a Daniell ; but it can estimate the one-thousandth => nisl — — 864 Dynamical Electricity [862- part of this quantity, and, as its electrical capacity is very small, it shows rapid changes of potential, which ordinary electrometers cannot do. For very small electromotive forces, the pressure is kept constant, and the dis- placement of the meniscus is measured by the microscope. Its use is especially convenient with zero methods. 863. Chemical effects.—The first decomposition effected by electricity was that of water, in 1800, by Carlisle and Nicholson, by means of a voltaic pile. Water is rapidly decomposed by 4.or 5 Bunsen’s cells ; the apparatus (fig..831) is convenient for the purpose. It consists of a glass vessel fixed on a wooden base. In the bottom of the vessel two platinum electrodes, # and m, are fitted, communicating by means of copper wires with the binding screws. The activity of these electrodes is increased by covering them by electrolysis with a deposit of pulverulent platinum. The vessel is filled with water to which some sulphuric acid has been added to increase its conduc- tivity, for pure water is a very imperfect conductor (867) ; two glass tubes filled with water are inverted over the electrodes, and on interposing the apparatus in the circuit of a battery, decomposition is rapidly set up, and gas bubbles rise from the surface of each pole. The volume of gas liberated at the negative electrode is about double that at the positive, and on examina- tion the former gas is found to be hydrogen and the latter gas oxygen. This experiment accordingly gives at once the qualitative and quanti- tative analysis of water. The oxy- gen thus obtained has the peculiar and penetrating odour observed when an electrical machine is worked (815), which is due to ozone. The water contains at the same time peroxide of hydrogen, in producing which some oxygen Fig. 831 is consumed. Moreover, oxygen is somewhat more soluble in water than hydrogen. Owing to these causes the volume of oxygen is less than that required by the composition of water, which is two volumes of hydrogen to one of oxygen. Hence voltametric measurements are most exact when the hydrogen alone is determined, and when this is liberated at the surface of a small electrode (827). 864. Electrolysis.—The term electrolyte was applied to those substances which, like water, are resolved into their elements by the voltaic current, by Bacay, to whom the principal discoveries in this subject and the nomen- clature are due. /ectrolysts is the decomposition by the voltaic battery ; the positive electrode, or that by which positive electricity enters, Faraday called the azode, and the negative electrode the Zathode. The products of . decomposition are zoms; kation, that which appears at the kathode ; ; and anion, that which aipeare at he anode. By means of the battery, the compound nature of several substances which had previously been considered as elements has been determined. By means of a battery of 250 couples, Davy, shortly after the discovery of the —864] Electrolysis 865 decomposition of water, succeeded in decomposing the alkalies potass and soda, and proved that they were the oxides of the hitherto unknown metals potasstum and sodium. The decomposition of potass may be demonstrated, with the aid of a battery of 4 to 6 elements, in the following manner: a small cavity is made in a piece of solid caustic potass, which is moistened, and a drop of mercury placed in it (fig. 832). The potass is placed on a piece of platinum connected with the positive pole of the battery. The mercury is then touched with the negative pole. When the current passes, the potass is decomposed, oxygen is liberated at the positive electrode, while the potassium liberated at the negative pole amalgamates with the mercury. On distilling this amalgam out of contact with air, the mercury passes off, leaving the potassium. A very convenient arrangement for the preparation of metallic magnesium and some of the rarer metals consists of an ordinary clay tobacco pipe (fig. 833), in the stem of which an iron wire is inserted just extending tothe bowl, which is nearly filled with a mixture of the chlorides of potassium and magnesium. This is melted by a Bunsen’s burner, and a piece of graphite connected by a wire with the positive electrode of a battery is dipped in it, the wire in the stem forming the negative electrode. When the current passes, chlorine gas is liberated at the positive electrode, while metallic magnesium collects about the end of the iron wire in the bowl. The decomposition of binary compounds—that is, bodies containing two elements—is quite analogous to that of water and of potass; one of the elements goes to the positive and the other to the negative electrode. The bodies separated at the positive electrode are called electronegative ele- ments, because at the moment of separation they are considered to be charged with negative electricity, while those separated at the negative electrode are called electrofositive elements. One and the same body may be electronegative or electropositive, according to the body with which it is associated. For instance, sulphur is electronegative towards hydrogen, but is electropositive towards oxygen. The various elements may be arranged in such a series that any one in combination is electronegative to any following, but electropositive towards all preceding ones. This is called the electrochemical series, and begins with oxygen as the most electro- negative element, terminating with potassium as the most electropositive. The decomposition of solution of hydrochloric acid into its constituents, 3K 866 Dynamical Electricity [864- chlorine and hydrogen, may be shown by means of the apparatus represented in fig. 834. Carbon electrodes must, however, be substituted for those of platinum, this metal being attacked by the liberated chlorine: a quantity of common salt also must be added to the hydrochloric acid, in order to ; diminish the solubility of the liberated chicane. he decomposition of potassium iodide may be demon- strated by means of a single element. For this purpose a piece of bibulous paper is soaked with a solution of starch, to which potassium iodide has been added. On touching this paper with the elec- trodes, a blue spot is produced at the positive pole, due to the action of the liberated iodine on the starch. One of the best methods of determining whether a liquid is, or is not, an electrolyte, is to immerse in it the two platinum electrodes connected with a battery, and then, disengaging the electrodes from the battery, connect them with a detaching galvano- meter, and observe whether a reverse current, due to polarisation of the electrodes (827), passes through the galvanometer. Such a current, being due to the accumulation of different substances on the two electrodes, is a proof that the substance has been electrolytically decomposed by the original current from the battery. This method can often be applied when it is difficult, by direct chemical methods, to establish the presence of products of decomposition at the electrodes. 865. Decomposition of salts.—Ternary salts in solution are decomposed by the battery, and then present effects varying with the chemical affinities and the intensity of the current. In all cases the acid, or the body which is chemically equivalent to it, is electronegative in its action towards the other constituent. The decomposition of salts may be readily shown by means of the bent tube represented in fig. 834. This is nearly filled with a saturated solution of a salt, say sodium sulphate, coloured with syrup of violets. Platinum electrodes connected with a battery of four Bunsen’s elements are then placed in the two legs of the tube. After a few minutes the liquid in the positive leg, A, becomes of a red, and that in the negative leg, B, of a green colour, showing that the salt has been resolved into acid which has passed to the positive, and into a base which has gone to the negative pole, for these colours are the effects whicha free acid and a free base respectively produce on syrup of violets. In a solution of copper sulphate free acid and oxygen gas appear at the positive electrode, and metallic copper is deposited at the negative electrode. In like manner, with silver nitrate, metallic silver is deposited on the nega- tive, while free acid and oxygen appear at the positive electrode. This decomposition of salts was formerly explained by saying that che acid was liberated at the positive electrode and the base at the negative. Thus potassium sulphate, K,OSO,, was considered to be resolved into sulphuric acid, SO,, and potash, K,O. This view regarded salts composed of three elements as different in their constitution from binary or haloid salts. Their electrolytic deportment has led to a mode of regarding the constitution of —————— Eee —867] Transmissions effected by the Current 867 salts which brings all classes of them under one category. In potassium sulphate, for instance, the electropositive element is potassium, while the electronegative element is a complex of sulphur and oxygen, which is regarded as a single group, SO,,and to which the name oxy-su/phion may be assigned. The formula of potassium sulphate would thus be K,SO,, and its decom- position would be quite analogous to that of potassium chloride, KCl, lead chloride, PbCl,, potassium iodide, KI. The electronegative group: SO, corresponds to a molecule or two atoms of chlorine or iodine. In the decomposition of potassium sulphate, the potassium liberated at the negative pole decomposes water, forming potash and liberating hydrogen. In like manner the electronegative constituent SO,, which cannot exist in the free state, decomposes into oxygen gas, which is liberated, and into anhydrous sulphuric acid, SO,, which immediately combines with water to form ordi- nary sulphuric acid, H,SO,. In fact, where the action of the battery is strong, oxygen and hydrogen are liberated at the corresponding electrodes ; in other cases they combine in the liquid itself, reproducing water. The constitution of copper sulphate, CuSO,, and of silver nitrate, AgNO,, and their decomposition, will be readily understood from these examples. 866. Transmissions effected by the current.—In chemical decompositions effected by the battery there is not merely a separation of the elements, but a passage of the one to the positive and of the other to the negative electrode. This phenomenon was demonstrated by Davy by means of several experi- ments, of which the following two are examples :— i. He placed solution of sodium sulphate in two capsules connected by a thread of asbestos moistened with the same solution, and immersed the positive electrode in one of the capsules, and the negative electrode in the other. The salt was decomposed, and at the expiration of some time all the sulphuric acid was found in the first capsule, and the soda in the second. ii. Having taken three glasses, A, B, and C (fig. 835), he poured into the first solution of sodium sulphate, into the second dilute syrup of violets, and into the third pure water, and connected rise them by moistened threads of asbestos. The current was then passed in the direction from C to A. The sulphate in the vessel A was decomposed, and in the course of time there was nothing but soda in this glass, which formed the negative end, while all the acid had been transported to the glass C, which was positive, B con- taining only pure water. If, on the contrary, the current passed from A to C, the soda was found in C, while all the acid remained in A; but in both cases the remarkable phenomenon was seen that the syrup of violets in B became neither red nor green by the passage of the acid or base through its mass, a phenomenon the explanation of which is based on the hypothesis enunciated in the following paragraph. 867. Grothiiss’s hypothesis.—Grothiiss gave the following explanation of the chemical decompositions effected by the battery. Adopting the SK 868 Dynamical Electricity [867— hypothesis that in every binary compound, or body which acts as such, one of the elements is electropositive, and the other electronegative, he assumes that, under the influence of the contrary electricities of the electrodes, there is effected, in the liquid in which they are immersed, a series of successive decompositions and recompositions from one pole to the other. Hence it is only the elements of the terminal molecules which do not recombine, but, remaining free, appear at the electrodes. Water, for instance, is formed of one atom of oxygen and two atoms of hydrogen ; the first gas being electro- negative, the second electropositive. Hence when the liquid is traversed by a sufficiently powerful current, the molecule a in contact with the positive pole arranges itself as shown in fig 836—that is, the oxygen is attracted and the hydrogen repelled. The oxygen of this molecule is then given off at the positive electrode, the liberated hydrogen immediately unites with the oxygen of the molecule 4, the hydrogen of this with the oxygen of the molecule c, and so on, to the negative electrode, where the last atoms of hydrogen become free and appear on the poles. The same theory applies to the metallic oxides, to the acids and salts, and explains why in the experiment mentioned in the preceding paragraph the syrup of violets in the vessel B becomes neither red nor green. The reason why, in the fundamental ex- periment, the hydrogen is given off at the negative pole when the circuit is closed will be readily understood from a consideration of this hypothesis. Clausius objected that, according to this theory, a very great force must be required for overcoming the affinity for each other of the oppositely electrolysed particles of the com- if = : | pound ; and that below a certain minimum strength of current no decomposition could occur. Now - Buff showed that the action of even the feeblest currents, sy455 of an ampere, for instance, con- tinued fora long time can produce decomposition. Again, when the necessary potential is obtained, it should be sudden and complete ; whereas we know that it is proportional to the strength of the current. To overcome this difficulty Clausius applied the theory now generally admitted of the constitution, of liquids (296), which was originally pro- pounded by Williamson on the basis of purely chemical considerations. On this theory the particles of a compound liquid have not the rigid un- alterable condition of a solid body ; they are in a perpetual state of separa- tion and reunion, so that we must suppose compound bodies and their elementary constituents to coexist with each other in a liquid. Water, for instance, contains particles of water, together with particles of oxygen and of hydrogen ; the former are being continually decomposed and the latter continually reunited. The theory of Van’t Hoff on the nature of solutions (141), and the experimental researches to which it has led, support the present explanation of electrolytic phenomena, which is due to Arrhenius. In the case of a solution of potassium chloride, KCl, in water, a certain proportion, probably considerable, of the molecules of the salt is in a state of dissociation. (395), which proportion increases with the dilution of the solution ; so that along \ SSS Fig. 836 —868] Laws of Electrolysis 8€9 with molecules of the undecomposed salt there are present the free ions potas- sium and chlorine. These latter are exclusively the carriers of the positive and negative electricity respectively. They may in this respect be regarded as performing a function analogous to that of the pith ball in the convective discharge (792). When the voltaic current passes, it acts on the motion of the ions in such a manner that the negatively electrical ions of chlorine pass to the positive electrode, and the positively electrical ions of potassium to the negative electrode, and there give up their charges and are liberated in the free state. Hence the current does not bring about the decomposition, but utilises it, to give definite direction to the particles which are already separated. These considerations explain why the conductivity of a liquid increases with the temperature (990) ; for this increases the velocity of the molecules (298) and also the dissociation, that is, the number of partial molecules. It also shows that the conductivity should increase with the concentra- tion of the liquid, seeing that an increase in the number of decomposable molecules must be favourable to the movement of electricity. On the other hand, an increase in the number must give rise to an increased number of collisions ; hence it is that, though for very dilute solutions the conductivity increases with the concentration, it does so more slowly than in direct ratio, and it is not difficult to understand that for some liquids there is a concentra- tion which corresponds to a maximum conductivity, and this in a great many cases is below the point of saturation of the solution. This also explains why chemical compounds, such as water and pure acids, which within the ordinary range of temperatures are not subject to dissociation (395), are not electrolysed and therefore not decomposed, while mixtures of acids and water, and solutions of salts, which may be re- garded as chemical compounds in a state of dissociation, are easily electro- lysed and conduct well. In dealing with molecular magnitudes, theoretical investigations make it probable that the electrolytic resistance, which the ions experience in being moved by the current, is of the same order of magnitude as the capillary resistance which results from their friction in the liquid (149). Nothing is opposed to the idea that electrolysis is a purely mechanical process. Decomposition occurs in the first place by dissociation ; the difference of potential is the force in virtue of which the previously united ions are urged in contrary directions. The moving ions are the carriers of the motion of electricity and produce the current ; the resistance which they thereby experience is the electrical resistance of the liquid. This, therefore, is the cause of the development of heat in the liquid. 868. Laws of electrolysis.—The laws of electrolysis were discovered by Faraday ; the most important of them are as follows :— I. Electrolysis cannot take place unless the electrolyte ts a conductor. Hence ice is not decomposed by the battery, because it is a bad conductor. Other bodies, such as lead oxide, silver chloride, &c., are only electrolysed in a fused state—that is, when they can conduct the current. The converse of this is true ; if a liquid transmits a current it must be an electrolyte. From the fact that he was able to obtain a current in liquids which deflected a galvanometer without producing any visible decomposition, Faraday inferred 870 Dynamical Electricity [868—- that liquids had a slight conductivity like that of metals independently of their electrolytic conductivity. This apparent conductivity is, however, to be assigned to electrolytic convection (854). Il. The energy of the electrolytic action of the current is the same in all its parts. For if a number of voltameters, V, V’, V” (vzde inf.), are arranged in series so that they are all traversed by the same current (fig. 837), itis found that the weight of hydro- v’ vie gen in each of them in the same time is the same, whatever may be the nature and distance apart of the electrodes, the pro- portion and nature of the acid. ul If the current from the vy: battery divides at A into two branches (fig. 838), in which are two equal / voltameters V, and V.,, Fig. 838 then the quantities of gas liberated in V and V” will still be equal to each other ; and the quantities in V, and V, will be equal to each other, but each will be only half that quantity which passes in either of the voltameters V and V”. Ill. Zhe same quantity of electrictty—that ts, the same electric current— decomposes chemically equivalent quantities of all the bodies which tt tra- verses ; from which it follows, that the weights of elements separated in these electrolytes are to each other as their chemical equivalents. In a circuit containing a voltameter, V, Faraday introduced a tube, AB, containing tin chloride kept in a state of fusion by the heat of a spirit lamp V2 (fig. 839).. In the bottom of the tube a platinum wire was fused, which served as the negative electrode, while the positive electrode consisted of a rod of a graphite; when the current passed chlorine was liberated at the —868] as Of Electrolysis 871 positive, while tin collected at the negative pole ; lead oxide contained in a similar tube was also electrolysed and yielded lead at the negative and oxygen at the positive pole. Comparing the quantities of substances liberated, they are found to be in a certain definite relation. Thus for every 18 parts of water decomposed in the voltameter there will be liberated two parts of hydrogen, 207 parts of lead, and 117 of tin at the respective negative electrodes, and 16 parts of oxygen and 71 (or 2 x 35°5) parts of chlorine at the corresponding positive electrodes. Now these numbers are exactly as the equivalents (not as the atomic weights) of the bodies. It will further be found that in each of the cells of the battery 65 parts by weight of zinc have been dissolved for every two parts by weight of hydrogen liberated ; that is, that for every equivalent of a substance decom- posed in the circuit one equivalent of zinc is dissolved. This is the case whatever be the number of cells. An increase in the number only has the effect of overcoming the great resistance which many electrolytes offer, and of accelerating the decomposition. It does not increase the relative quantity of electrolyte decomposed. If in any of the cells more than 65 parts of zinc are dissolved for every two parts of hydrogen liberated, the excess arises from a disadvantageous local action (837) ; and the more perfect the battery, the more nearly is the ratio 65:2 satisfied. Chemistry takes account of the valency of an element, and divides elements into monads, dyads, triads, and tetrads—a classification based on their equiva- lence to and their power of replacing other elements ; thus one atom of the monad hydrogen (H = 1), the basis of this classification, or one atom of monad silver (Ag = 108), would combine with one atom of chlorine (Cl = 35°5) or one atom of iodine (I=127). One atom of oxygen (O = 16) unites with two atoms of hydrogen to form water, or with two atoms of silver to form silver oxide, Ag,O; one atom of the dyad zinc (Zn=65) unites with one atom of the dyad oxygen to form ZnO, or with the dyad sulphur (S = 32) to form ZnS. Again, gold is a triad, and one atom (Au=196) can combine with three atoms of chlorine to form AuCl,, and, accordingly, one monad is equivalent to one-third of the atom of the triad. Now electrolysis proceeds according to the eguzvalence ; that is, the same quantity of electricity which liberates one atom of a monad liberates half an atom of a dyad, and a third of an atom of a triad. This remark applies also to the compound groups, such as NO., which acts as a monad, and SO,, which acts as a dyad. Thus the same current which decomposes 200 grammes Hg in HgNO., decomposes I1oo grammes Hg(CN),. IV. It follows from the above law, that the guantity of a body decomposed in a given time ts proportional to the strength of the current. On this is founded the use of Faraday’s voltame¢er, in which the strength of a current is ascertained from the quantity of water which it decomposes in a given time. A convenient form of this instrument is that represented in fig. 840. The vessel a is that in which the water is decomposed, and contains two platinum plates, and is in connection with the flask 4, which contains water. In this is a lateral delivery tube, c, which is inclined until the level of the liquid in it is the same as inthe funnel tube 7. The air is then under the same pressure as the atmosphere. When the battery is connected with the decomposing 872 Dynamical Electricity [868- cell a, the gases disengaged expel a corresponding volume of water through the delivery tube ¢ ; at the conclusion of the experiment, this tube is inclined until the liquid is at the same level as in the tube z and in the flask. The weight of the liquid expelled is then a direct measure of the volume of the disengaged gases. The use of this voltameter appears simple and convenient ; Jacobi pro- posed as unit of the strength of current, that current which in one minute yields a cubic centimetre of mixed gas reduced to the temperature 0° and the pressure 760 mm. This is equal to 009567 ampere, that is, an ampere liberates 10°44 ccm. mixed gas in a minute. Yet, for reasons mentioned before (863), the measurements should be based on the volume of hydrogen liberated. niki Si DTN Au | My =| . 3 = ‘ i} y Poggendorff’s silver voltameter (fig. 841) is an instrument for measuring the strength of the current. A solution of silver nitrate of known strength is placed in a platinum dish which rests on a brass plate that can be con- nected with the negative pole of the battery by means of the binding screw * 6. In this solution dips the positive pole, which consists of a rod of silver wrapped round with muslin, and suspended to an adjustable support. When the current passes, silver separates at the negative pole, and is washed, dried, and weighed ; and the weight thus produced in a given time is a very accurate measure of the strength of the current. Some silver particles which are apt to become detached from the positive pole are retained in the muslin. Edison has used a zznc voltameter for measuring the powerful currents employed for technical purposes. It has been found by experiment that, when water is decomposed, a current of 1 ampere liberates 0:000010386 granime of hydrogen in a second ; this, then, is the electrochemical equivalent of hydrogen, and from this we can —869] Migration of the Ions 873 deduce the weight of any element liberated in the same time by unit current, if we multiply it by the equivalent weight of the element referred to hydrogen. The equivalent of silver is usually taken at 108 ; hence, if any of its salts are decomposed, the weight of silver liberated by an ampere in a second is O‘OOII217 gramme; this is the electrochemical equivalent of silver, and similarly that of copper is 0'0003271 and that of zinc 0'0003375. According to the best direct determinations the electrochemical equiva- lent of silver is:o‘oo11181. The electrochemical equivalent of hydrogen deduced from this is 0°000010353. The quantity of electricity which passes through a conductor with a current of one ampere is called a coulomb (1000), and thus we may say that a coulomb of electricity in traversing an electrolyte carries with it a weight of a metal which is represented by its electrochemical equivalent. The quantity of electricity which is thus associated with each valency represents a minimum quantity of electricity—the electrical atom or e/ectron as it has been called by Johnstone Stoney. By various theoretical considerations it has been attempted to estimate its amount; Richarz obtained the number 1:29, Ebert 1:4, and Stoney 3 x 10!° CGS. units:; numbers which thus arrived at independently agree very well as to the order of their magnitude. It was calculated by Weber that if the quantity of positive electricity required to decompose a grain of water were accumulated on a cloud at a distance of 3,000 feet from the earth’s surface, it would exert an attractive force upon the earth of upwards of 1,500 tons. Helmholtz estimated that if the+E attached to the atoms of 1 milligramme of water could be transferred without loss to a sphere, and the—E similarly to another sphere at a distance of a kilometre, the two spheres would attract each other with a force equal to the weight of 26,800 kilogrammes. 869. Migration of the Ions.—From what has been said, it would seem that when a solution of copper sulphate is electrolysed between copper elec- trodes, for every equivalent of copper deposited at the negative electrode an equivalent weight should be dissolved at the positive, and, the transfer taking place as described, the concentration of the solution should remain unchanged. This, however, is not the case; when the operation takes place without any agitation of the solution, the liquid about the negative pole becomes lighter in colour, indicating that the solution there is weaker. This phenomenon, which was investigated by Hittorf, is ascribed by him to the fact that in electrolysis both electricities, associated with their zoms or products of electrolytical decomposition, travel in the liquid towards their respective electrodes, but with unequal velocities, and this transference is called the mzgration of the tons. Each ion has a special velocity in the liquid independently of the compound of which it forms part; thus in CuSO, solution SO, travels twice as fast as Cu. The number which expresses this rate of travel is called 7, and has this meaning : let us conceive a vertical layer in the liquid the concentration of which remains unchanged by what takes place on each side ; then, if after electrolysis we determine the quantity of the constituents on each side, there is an increase of the positive on one side and of the negative on the other. These increases correspond to the quantities of the two constituents which have been driven through. 874 Dynamical Electricity [869- The number 7 expresses the ratio of the number of molecules of the anion which passes through the imaginary layer in a given time to that of the electrolyte decomposed. If £ is the velocity of the kation, and a that of the anion, then a R I-”_k vii Bee ee pi Fer Wyk Bode Hittorf has shown that z is a constant independent of the strength of the current, but varying with the concentration of the liquid. 870. Comparison between the tangent galvanometer and the voltameter. There are several objections to the use of the voltameter. In the first place, it does not indicate the current strength at any given moment, for in order to obtain measurable quantities of gas the current must be continued for some time. Again, the voltameter gives no indications of the changes in the current strength which may take place in this time, but only the mean strength. It offers also great resistance, and can thus only be used in the case of strong currents ; for weak currents either do not decompose water, or only yield quantities too small for accurate measurement. In addition to this, the indications of the voltameter depend not only on the strength of the current, but on the acidity of the water, and on the distance and size of the electrodes. But although it does not measure the strength of the current at any one time, it does, apart from accidental influences, give a measure of the total quantity of electricity that has passed within the period of observation. Magnetic measurements are preferable to chemical ones. Not only are they more delicate, but they give the current strength at any moment. On the other hand, indications furnished by the tangent galvanometer hold only for one special instrument. They vary with the diameter of the ring and the number of turns ; moreover, one and the same instrument will give different indications on different places, seeing that the force of the earth’s magnetism varies from one place to another (712). The indications of the two instruments may, however, be readily com- pared with one another. For this purpose the voltameter and the tangent galvanometer are szwzul/faneously inserted in the circuit of a battery, and the deflection of the needle and the amount of gas liberated in a given time are noted. In one set of experiments the following results were obtained :— Number of elements Deflection | Gas liberated in three minutes | 12 2055 4 | 125 CC 8 24°8 106 6 22H 93 | 9 - 1 3 PS he | 56 2 6'9 | a | | If we divide the tangents of the angles into the corresponding volumes of gas liberated in ove minute, we should obtain a constant magnitude which represents how much gas is developed in a minute by a current which could —871] Polarisation 875 produce on the tangent ygalvanometer the deflection 45°, for tang. 45°=1. Making this calculation with the above observations, we obtain a set of closely agreeing numbers the mean of which is 76:5. The gas was measured under a pressure of 737 mm. and at a temperature of 15°, and therefore under normal conditions (339) its volume would be 70 cubic centimetres. That is to say, this is the volume of gas which corresponds to a deflection of 45°. Hence in chemical measure the strength C of a current which pro- duces in Z/zs particular tangent galvanometer a deflection of $° is C= 70 tang. @. For instance, supposing a current produced in this tangent galvano- meter a deflection of 54°, this current, if it passes through a voltameter, would liberate in a minute 70x tang. 54°= 70x 1°376=96°32 cubic centi- metres of gas. If once the reduction factor for a tangent galvanometer has been deter- mined, the strength of any current may be readily calculated in chemical measure by a simple reading of the angle of deflection. This reduction factor of course only holds for one special instrument, and for experiments in the same place, seeing that the force of the earth’s magnetism varies in different places. The indications of the sine-compass may be compared with those of the galvanometer in a similar manner. 871. Polarisation.—When the platinum electrodes, which have been used in decomposing water, are disconnected from the battery, and connected with a galvanometer, the existence of a current is indicated which has the opposite direction to that which had previously passed. This phenomenon is explained by the fact that oxygen has been condensed on the surface of the positive plate, and hydrogen on the surface of the negative plate, analogous to what has been already seen in the case of the non-constant batteries (828). The effect of these is to set up an electromotive force e opposed to that of the battery (827) and called ¢he electromotive force of polarisation. The polarisation is not instantaneous, but may increase continuously from zero to a certain maximum limit which may be considerable ; it increases with the strength of the current, attaining the force of about 1°5 volts with platinum plates in dilute sulphuric acid. It constitutes a negative electro- motive force, and must be allowed for in Ohm’s formula (847), which then becomes _E-e eae The quantity of electricity required to produce a given state of polarisa- tion depends on the condition and dimensions of the plate, and is often called the capacity of polarisation relative to the given system. When the electrodes consist of plates of the same metal as that of the salt decomposed, there is practically no polarisation. Thus the polarisation is negligible when a copper salt is electrolysed between copper electrodes or a silver salt between silver electrodes. If a test tube containing mercury is placed in a vessel of mercury, and the electrodes of a voltaic battery are connected with the two masses of 876 Dynamical Electricity [871- mercury separated by the glass, no current passes at the or dinary tempera- ture. But if the arrangement is gradually heated a current is set up which increases with the temperature, while the physical condition of the glass appears quite unchanged. If the battery is removed and the electrodes connected with a galvanometer, a polarised current in the opposite direction to the primary one is observed. The surfaces of the glass are thus polarised, and the electricity must have been transmitted by the hot glass. 872. Secondary batteries. Accumulators.---Ritter was the first to show that on this principle batteries might be constructed of pieces of metal of the same kind—for instance, platinum-- which otherwise give no current. A piece of moistened cloth is interposed between a pair of metal plates, and the ends of this system are connected with the poles of a battery. After some time the apparatus has received a charge, and if separated from the battery can itself produce all the effects of a voltaic battery. Such batteries are called secondary batteries or, also, accumulators. Their action depends on an alteration of the surface of the metal produced by the electric current, the constituents of the liquid with which the cloth is moistened having become accumulated on the opposite plates of the secondary circuit. Planté first showed the practical importance of these batteries. His ele- ment (fig. 842) is constructed as follows : A broad strip of sheet lead with a tongue is laid upon a second similar sheet, contact being prevented by narrow strips of felt; and two similar strips having been laid on the upper piece, the sheets are rolled together so as to form a compact cylinder. This is placed in a vessel containing dilute sulphuric Fig. 842 acid, and, being connected by wires attached to the tongues with a battery of two Grove’s cells, a current (the primary current) is passed through it. The effect of this is that water is decomposed, oxygen being liberated at the anode, or plate, which serves as positive pole, and there unites with the lead, forming peroxide of lead, while hydrogen is accumulated at the other plate. If now the plates are detached from the charging battery and are connected with each other, a powerful polarisation current is produced in the opposite direction to the primary; the oxygen of the peroxide at the anode decomposes the dilute acid, combining with its hydrogen, and so travels through to the other plate, where it combines with the lead. When these operations are repeated several times the activity of the element increases, owing in great measure to the alteration in the — surfaces which is thereby produced. The element does, in fact, require a considerable expenditure of energy and time to form it, which is a source of expense, even when the energy of the discharge is expended in forming new plates. Faure made a great improvement in this direction. It consists in coating the lead plates with a thick paste of red lead, Pb,O,, soas to have about one 872] Secondary Batteries. Accumulators O77 gramme to the square centimetre. This is kept in its place by a sheet of parchment paper and slips of felt, and is then coiled up as in Planté’s (fig. 843). When the current is passed, the ultimate effect is that the red lead at the one electrode is oxidised to Pb,O,, while the other is reduced to granular porous grey metallic lead, both which coatings present a large sur- face. Such coatings, however, are liable to become detached, and a con- siderable advance was made in the introduction of gvzds, or gratings of lead in which square or round holes are filled with com- pressed lead oxide; the object being to store firmly as much of the porous material as possible, consis- tently with strength, lightness, and compactness. There are many plans by which this may be effected. Fig. 844 represents one of the batteries of the Electric Power Storage Company ; it will be seen that the whole of one set of six plates, forming the negative electrode, are fixed together, and a corre- sponding set of five plates, also joined together, can be placed between the other set, being kept from touching each other by staples or studs of some insulating material. Each set of plates forms in effect a single large plate, which is thus placed with its coated face opposite the coated faces of the other plate. The object of bringing the plates near each other is to diminish the internal resistance. The inverse electromotive force of such a cell while it is being charged rises to about 23 times that of a Daniell’s cell, so that three Daniell’s or two Grove’s cells are required to charge it. In charging, a considerable number of elements are joined together by their similar poles, and connected with the respective electrodes of the charging battery or of the dynamo ; the effect is the same as that of using a single element of a surface equal to the sum of the surfaces of all the elements. By means of a specially contrived com- mutator a given number of such batteries may be combined so as to produce at will the effects either of high potential or of quantity. So long as such batteries could be charged only from a voltaic battery they could never be economical; but the fact that after having been once charged they retain the charge for a considerable time, has led to their use in what is called ‘storing electricity’ produced by mechani- cal power through the agency of powerful dynamo and magneto-electrical machines. What they do is to store the products of chemical decomposition, and that in a form in which they are immediately available for electrical effects. Fig. 844 878 Dynamical Electricity [872- They are usually charged by shunt wound dynamos (944), whereby about 75 per cent. of the. energy is available. An accumulator of a given size can only consume in each interval of time a definite quantity of gas for its formation by oxidation and reduction. If more gas is developed it escapes uselessly. The charging current must be neither too strong nor too weak, For each accumulator there is a special rate of charge, which is most advan- tageous. An accumulator of great capacity is obtained by placing a zinc plate ina solution of sodium or potassium zincate, and a porous plate of copper obtained by compression. During the charge the zinc in the solution is precipitated on the zinc plate, and the copper absorbs an equivalent quantity of oxygen. During the discharge the copper is reduced and the zinc redissolves. This accumulator, however, does not retain its charge, and is only suitable for cases in which the discharge rapidly succeeds the charge. So far accumu- lators with lead plates have alone proved to be of practical utility. Figure 845 represents the course of charging an accumulator from an actual experiment in which a steady current of 22 ampere-hours (vzd. zu/f.) was used. In the first hour or so the E.M.F. rose rapidly until it was about 2,00 ENouas 2 Fig. 845 2:08 volts, when it was almost stationary for about 1o hours when 220 ampere- hours had been put in, and the E.M.F. was 2°13 volts ; from this point there was a rapid rise until 2°53 volts were reached. The maximum usually obtained is 2°5 volts, at which the liquid becomes milky owing to a disengage- ment of gas in the body of the liquid itself, which indicates that the charge is complete. A charged accumulator gradually loses its charge by leakage, and the efficiency of an accumulator depends on the power of retaining its charge. In this respect great improvement has been made by attention to a number of minute points ; the durability now extends to years, whereas it was formerly measured by months or weeks. The efficiency further depends on the cafaczty, which is the quantity of electrical energy which can be stored for unit weight of the accumulator, and which must not be confounded with the electrostatic capacity. It is usually represented by the number of amzfere-hours ; that is, a current of an ampere maintained for an hour, or 3,600 coulombs of electricity, for each kilogramme of plates. —872] Secondary Batteries. Accumulators 879) Of perhaps greater importance in judging of an accumulator is the éffictency, by which is meant the ratio of the electrical work which is accu- mulated in order to charge it to that which it gives out in sinking to its initial condition. The energy stored up in an accumulator is measured by the potential at the terminals during the charging, multiplied by the strength of the current and by the time. The product gives the energy in volt-amperes-seconds. In like manner the energy given out in the discharge is the potential into the current strength into the time of discharge. The whole charge which can be imparted to an accumulator cannot be advantageously utilised, for the accumulator is injured if this is done, and in practice the charge is only allowed to run down until the potential is 10 per cent. less than at starting. Thus a given accumulator was charged for 10°16 hours with a current of 5 amperes, the average potential being 2°15 volts; hence the energy stored is 10°I6x 2°15 x 5=109 watt-hours. In the discharge, which lasted 7°35 hours, the average potential was 1°88, and the current 6°5 amperes, repre- senting therefore 90 watt-hours ; the ratio of the two is o'826—that is, the efficiency of the accumulator is 82:6 per cent. ; a number which is now required for a good accumulator. It cannot be said that the reactions which take place during the charge and discharge of an accumulator are thoroughly understood ; they are undoubtedly more complicated than has been represented above, in which no account has been taken of the sulphuric acid. During the charge, the strength of the dilute sulphuric acid, and therewith its conductivity, gradually diminish, while during the discharge both increase. Hence a determination of the specific gravity of the solution at any time is a convenient practical method of measuring the state of the charge. This is effected by flat densi- meters (131) which float between the plates. The density may vary between I'I2 and 1°22, representing respectively about 16 and 30 per cent. of sul- phuric acid, SH,O,. As an example, one cell of the Electric Power Storage Company had an internal resistance of o‘oo12 ohm at the beginning, and 0'0028 at the end, and weighed 50 kilos. In such a cell 880 watt-hours could be accumu- lated, and 680 watt-hours, or about 79 per cent., obtained in the discharge. Thus each kilo represents 13°6 watt-hours of available energy, or »; of a’ horse-power ; that is, it could yield »; H.P. for an hour, or 1 H.P for 1°1 minute. As a horse power is equal to 270,000 kilogrammetres per second (482), this gives 5,000 kilogrammetres for each kilo, sufficient, therefore, to raise the battery itself through a height of 5,000 metres. In accumulators which are to be used to work motors, as in tram- cars, electrical boats, &c., the cafaczty is of first importance, while with stationary accumulators, as in electric lighting, the efficiency is the chief point. Many instructive comparisons may be made between a secondary bat- tery and a charged Leyden jar. Thus, for instance, when the poles of a secondary battery have been connected until no current passes, and are then disconnected for a while, a current in the same direction as the first is obtained on again cgnnecting them ; this is the ves¢dual discharge. The capacity of asecondary battery depends on the area of the electrodes, on their 880° Dynamical Electricity [872- nature, and on that of the interposed liquid, but not on the distance between them. The energy of the Leyden jar is stored in that state of mechanical strain which is called polarisation of the dielectric ; in the secondary battery the energy consists in the products which are stored up on the surface of the electrodes in a state ranging from chemical combination to mechanical adherence or simple juxtaposition. A dry pile which has become inactive may be used ¢7; a secondary battery. When a current is passed through it, in a direction contrary to that which the active battery would itself yield, it regains its activity. 873. Grove’s gas battery.—On the property, which metals have, of con- densing gases on their surfaces, Sir W. Grove constructed his gas battery (fig 846). A single cell consists of two glass tubes, B and A, in each of which is fused a platinum electrode, provided on the outside with binding screws. These electrodes are made more efficient by being covered with finely divided platinum. One of the tubes is partially filled with hydrogen, and the other partially with oxygen, and they are inverted over dilute sulphuric acid, so that half the platinum is in the liquid and half in gas. On connecting the electrodes with a galvanometer, the existence of a current is indicated whose direction in the connecting wire is from the platinum in oxygen to that in hydrogen ; so that the latter is negative towards the former. As the current passes through water this is decomposed : oxygen is separated at the positive plate and hydrogen at the other. These gases unite with the gases con- densed on their surface, so that the volume of gas in the tubes gradually diminishes, but in the ratio of one volume of oxygen to two volumes of hydrogen. These elements can be formed into a battery (fig. 792) by joining the dissimilar plates with one another just as they are joined in an ordinary battery. One © element of such aa si Se —~ a battery is suf- Cn ficient to decom- a — iz pose potassium iodide, and four will decompose water. Mond and Langer have constructed a battery on this principle. On each side of a plate of plaster is a lead grid, the holes of which are filled with platinum black. Air and hydrogen are forced through these holes and combine, forming water, and alsoan electric current, the electromotive force of which is one volt. 874. Passive state of iron.—With polarisation is probably connected a very remarkable chemical phenomenon, which many metals exhibit, but 876] Arbor Saturni.. Arbor Diane 881 more especially iron. When this is immersed in concentrated nitric acid it is unattacked. This condition of iron is called the fasszve state, and upon it depends the possibility of the zinc-iron battery (831). It is probable that in this experiment a thin superficial layer of iron protosesquioxide is formed ; on the one hand this protects the iron from further attack, and on the other itacts as an electromotor, like the layer of lead peroxide in Planté’s element (872).. The position of passive iron in the electromotive series is near that of platinum. 875. Nobili’s rings.—When a drop of copper acetate is placed on a silver plate, and the silver is touched in the middle of a drop with a piece of zinc, there are formed around the point of contact a series of copper rings alternately dark and light. These are /Vodzli’s coloured rings. They may be obtained in beautiful iridescent colours by the following process : A solu- tion of lead oxide in potash is obtained by boiling finely powdered litharge in a solution of potash. In this solution is immersed a polished plate of silver or of German silver, which is connected with the positive electrode of a battery of eight Bunsen’s elements. With the negative pole is connected a fine platinum wire fused in glass, so that only its point projects ; and this is placed in the liquid at a small distance from the plate. Around this point lead peroxide is separated on the plate in very thin concentric layers, the thickness of which decreases from the middle. They show the same series of colours as Newton’s coloured rings in transmitted light (664). The lead peroxide owes its origin to a secondary decomposition ; by the passage of the current some lead oxide is decomposed into metallic lead, which is deposited at the negative pole, and oxygen which is liberated at the positive ; and this oxygen combines with some lead oxide to form peroxide, which is deposited on the positive pole as the decomposition proceeds. This process is used for the metallic coloration of objects of domestic use and ornamentation. The effects are also well seen if a solution of copper sulphate is placed on a silver plate, which is touched with a zinc rod, the point of which is in the solution ; for then a current is formed by these metals and the liquid. 876. Arbor Saturni, or lead tree. Arbor Dianz.—When in a solu- tion of a salt is immersed a metal which is more oxidisable than the metal of the salt, the latter is precipitated by the former, while the immersed metal is substituted, equivalent for equivalent, for the metal of the salt. This pre- cipitation of one metal by another is attributable partly to the difference in their affinities, and partly to the action of a current which is set up as soon as a portion of the less oxidisable metal has been deposited. The action is promoted by the presence of a slight excess of acid in the solu- tion. A remarkable instance of the precipitation of one metal by another is the Arbor Saturnt. This name is given to a series of brilliant ramified crystallisations obtained by zinc in solutions of lead acetate. A glass flask is filled with a clear solution of this salt, and the vessel closed with a cork, to which is fixed a piece of zinc in contact with some copper wire. The flask, being closed, is left to itself. The copper wire at once begins to be covered with a moss-like growth of metallic lead, out of which brilliant att 882 Dynamical Electricity [876- crystallised laminze of the same metal continue to form ; the whole pheno- menon has great resemblance to the growth of vegetation, from which indeed the old alchemical name is derived. For the same reason the name A7vbor Diane has been given to the metallic deposit produced in a similar manner by mercury in a solution of silver nitrate. | If a rod of zinc is dipped in an acid solution of stannous chloride, crystallised tin is formed upon it ; the experiment is rendered more beautiful by dipping the platinum electrodes of a battery in the solution ; if the poles are reversed, the crystallised laminz disappear at one pole to reappear at the other. ELECTROMETALLURGY 877. Electrometallurgy.—The decomposition of salts by the battery has received a most important application in e/ectrometallurgy, or galvano- plastics, or the art of precipitating certain metals from their solutions by the action of a voltaic current. The processes are twofold ;in the one, e/ectro- typing or galvanoplasiics proper, a mould is used, on which a metal, usually copper, is more or less thickly deposited ; the deposit can afterwards be de- tached, and gives a copy of the original object ; in the other, which is known as electroplating, a thin coherent coating of metal—gold or silver, for instance —is deposited on objects and remains adherent to them. The art was dis- covered independently by Spencer in England and by Jacobi in St. Petersburg. In order to obtain a galvanoplastic reproduction of a metal or any other object, a mould must first be made, on which the layer of metal is deposited by the electric current. For this purpose several substances are in use, and one or another is preferred according to circumstances. For medals and similar objects which can be submitted to pressure, gutta-percha may be used with advan- tage. The gutta-percha is softened in hot water, pressed against the object to be copied and allowed to cool, when it can be detached without difficulty. For the reproduction of engraved wood blocks or type, wax moulds are now commonly used. They are prepared by pouring into a narrow flat pan a suitable mixture of wax, tallow, and Venice turpentine, which is allowed to set, and is then carefully brushed over with very finely powdered graphite. While this composition is still somewhat soft, the wood block or type is pressed upon it either by a screw press or, still better, by hydraulic pressure. If plaster-of-Paris moulds are to be made use of, it is essential that they be first thoroughly saturated with wax or tallow, so as to become impervious to water. 6 In all cases, whether the moulds be of gutta-percha or wax, or any non- conducting substance, it is of the highest importance that the surface be brushed over very carefully with graphite, and so made a good conductor. The conducting surface thus prepared must also be in metallic contact with a wire or a strip of copper by which it is connected with the negative elec- trode. Sometimes the moulds are made of a fusible alloy (344), which may consist of 5 parts of lead, 8 of bismuth, and 3 of tin. Some of the melted alloy is poured into a shallow box, and just as it begins to solidify, the medal is placed horizontally on it in a fixed position. When the alloy has become cool, a slight shock is sufficient to detach the medal. A copper wire is then -877] Electrometallurgy 883 bound round the edge of the mould, by which it can be connected with the negative pole of the battery, and then the edge and the back are covered with a thin non-conducting layer of wax, so that the deposit is formed only on the mould itself. The most suitable arrangement for producing an electro-deposit of copper consists of a trough of glass, slate, or wood, lined with india-rubber or coated with marine glue (fig. 847). This contains an acid solution of copper sulphate, and across it are stretched copper rods, B and D, connected respectively with the negative and positive poles ofa battery. By their copper conductors the moulds, #z, are suspended in the liquid from the negative rod B, whilst a sheet of copper, C, presenting a surface about equal to that of the moulds to be covered, is suspended from the positive rod D, at the distance of about two inches, directly opposite to them. The copper plate suspended from the positive pole not only acts as an electrode, but keeps the solution in a state of concentration, for the acid liberated at the positive pole dissolves the copper, and reproduces a quantity of copper sulphate equal to that decomposed by the current. The battery employed for the electric deposition of metals ought to be one of great constancy, and—on the small scale—-Daniell’s and Smee’s are mostly in use. These batteries have in large establishments been supplanted by accumulators or by dynamo machines (939), which furnish the electricity at one quarter the expense, and which are specially constructed so as to furnish currents which have small E.M.F. and small internal resistance. The density of a current is its strength divided by the surface of the electrodes, or the number of amperes per square decimetre, and a statement of this density in conjunction with a knowledge of the composition and strength of the bath is a succinct way of defining the conditions of electric deposition. The density at the electrodes has a great influence on the form in which the ions are separated out ; thus with a moderate density silver separates in a crystallised form, and at a greater one in the form of a black powder. Another, and very simple, process for producing the electric deposit of copper consists in making use of what is in effect a Daniell’s cell. A porous pot or a glass cylinder,covered at the bottom with bladder or with vegetable parchment, is immersed in a vessel of larger éapacity, con. 7) mm a i taining a con S==2S ate — a centrated solu- Be tion of copper sulphate. The porous vessel contains acidu- . lated water, and in it is suspended a piece of amalgamated zinc of suitable cassee 884 Dynamical Electricety [877— form, and having a surface about equal to that of the mould. The latter is: attached to an insulated wire connected with the zinc, and is immersed in the solution of copper sulphate in such a position that it is directly opposite to the diaphragm. The action commences by the mould becoming covered with copper, commencing at the point of contact with the conductor, and gradually increasing in thickness in proportion to the action of the Daniell’s. element thus formed. It is, of course, essential in the process to keep the: solution of copper sulphate at a uniform strength, which is done by agi- tating.the liquid and suspending in it bags filled with crystals of this salt. How great is the delicacy which such electric deposits can attain appears. from the fact that galvanoplastic copies can be made of daguerreotypes,. which are of the greatest accuracy. An important industrial application is made of electrolysis in the refinzng of copper. The metal is extracted by the ordinary metallurgical processes. so as to obtain plates containing 95 per cent. of pure copper. These plates are then used as positive electrodes in a bath of copper sulphate, and the metal is deposited in a state of perfect purity on thin sheets of pure copper, which form the negative electrode, while the impurities fall to the bottom. As the electrodes are practically identical, there is no polarisation (827), and the work of the current is solely employed in overcoming the resistance of the baths. The application of electrolysis to the extraction of metals was of limited use until the powerful currents of dynamos became available. In mountainous countries, where water-power can be had, it may in many cases be practicable to deal zz sztuz with the extraction of metals from their ores. 878. Electrogilding.—The old method of gilding was by means of mercury. It was effected by an amalgam of gold and mercury, which was applied on the metal to be gilded. The objects thus covered were heated ina furnace, the mercury volatilised, and the gold remained in a very thin layer on the objects. The same process was used for silvering ; but they were expensive and unhealthy methods, and have now been entirely replaced by electrogilding and electrosilvering. Electrogilding only differs from the process described in the previous paragraph in that the layer is thinner and adheres more firmly. Brugnatelli, a pupil of Volta, appears to have been the first, in 1803, to observe that a body could be gilded by means of the battery and an alkaline solution of gold ; but De la Rive was the first who really used the battery in gilding. The methods both of gilding and silver- ing owe their present high state of perfection principally to the improve- ments of Elkington, Ruolz, and others. The pieces to be gilded have to undergo three processes before gilding. The first consists in heating them so as to remove the fatty matter which. has adhered to them in previous processes. As the objects to be gilded are usually of what is called g7/ding metal or red brass, which is a special kind of brass rich in copper, and their surface during the operation of heating becomes covered witha layer of cupric or cuprous oxide, this is removed by the second operation. For this purpose the objects, while still hot, are immersed in very dilute nitric acid, where they remain until the oxide is removed. They are then rubbed with a hard brush, washed in distilled water, and dried in gently heated sawdust. To remove all spots they must undergo the third process, which consists: ~880] Llectric Deposition of Iron, Nickel, Cobalt, ete. 885 in rapidly immersing them in ordinary nitric acid, and then in a mixture of nitric acid, bay salt, and soot. When thus prepared, the objects aré attached to the negative pole of a battery consisting of three or four Bunsen’s or Daniell’s elements. They are then immersed in a bath of gold as previously described. They remain in the bath for a time, which depends on the thickness of the desired deposit. There is a great difference in the composition of the baths. The most in use consists of I part of gold chloride and Io parts of potassium cyanide, dissolved in 200 parts of water. In order to keep the bath in a state of con- centration, a piece of gold is suspended from the positive electrode, which dissolves in proportion as the gold dissolved in the bath is deposited on the objects attached to the negative pole. The density of the current should not exceed o°8 ampere for each square decimetre of the surface of the kathode. The method which has just been described can also be used for silver, bronze, German silver, &c. But other metals, such as iron, steel, zinc, tin, and lead, are very difficult to gild well. To obtain a good coating, they must first be covered with a layer of copper, by means of the battery and a bath of copper sulphate ; the copper with which they are coated is then gilded as in the previous case. The tint of the deposit is modified by adding solutions of copper or of silver to the gold bath ; the former gives a reddish and the latter a greenish tint. 879. Electrosilvering.—What has been said about gilding applies exactly to the process of electrosilvering. The difference is in the composition of the bath, which consists of 2 parts of silver cyanide and 2 parts of potas- sium cyanide, dissolved in 250 parts of water. To the positive electrode is suspended a plate of silver, which prevents the bath from becoming poorer ; its surface should be equal to the total. surface of the objects to be silvered ; the pieces to be silvered, which must be well cleaned, are attached to the negative pole. It may here be observed that these processes succeed best with hot solutions, and when the baths are old. The density of the current should be one-third of an ampere per square decimetre. Knowing the weight of any given metal which is transported by unit of electricity (868), it is easy to calculate the weight deposited in a given time by a current of known strength. Thus the current just specified would deposit 1°46 gramme of silver in an hour. A deposit of one ounce of silver on a square foot of surface gives a good coating ; its thickness, ;4; inch or 0°03 mm., is about half that of thin writing paper. 880. Electric deposition of iron, nickel, cobalt, and platinum.—One of the most valuable applications of the electric deposition of metals is to what is called the steeling (acterage) of engraved copper plates. The bath required for this purpose is obtained by suspending a large sheet of iron, connected with the positive pole of a battery, in a trough filled with a satu- rated solution of sal-ammoniac ; whilst a thin strip of iron, also immersed, 1s connected with the negative polé. By this means iron from the large plate is dissolved in the sal-ammoniac, while hydrogen is given off on the surface of the small one. When the bath has thus taken up a sufficient quantity of iron, an engravedscopper plate is substituted for the small negative strip. A bright deposit of iron begins to form on it at once, and the plate assumes 886 Dynamical Electricity [880- the colour of a polished steel plate. The deposit thus obtained in the course of half an hour is exceedingly thin, and an impression of the plate thus covered does not seem different from one obtained from the original copper plate ; it possesses, however, an extraordinary degree of hardness, so that a very large number of impressions can be taken from such a plate before the thin coating of iron is worn off. When, however, this is the case, the film of iron is dissolved off by dilute nitric acid, and the plate is again covered with the deposit of iron. An indefinite number of perfect impressions may, by this means, be obtained from one copper plate, without altering the original sharp condition of the engraving. The covering of metals by a deposit of zckel has of late come into use. The process is essentially the same as that just described. The bath used for the purpose can, however, be made more directly by mixing, in suitable proportions, salts of nickel with those of ammonia. The positive pole con- sists of a plate of pure nickel. A special difficulty is met with in the electric deposition of nickel, owing to the tendency of this metal to deposit in an un- even manner, and then to become detached. This difficulty is overcome by frequently removing the articles from the bath and submitting them toa polishing process. / Objects coated with nickel show a highly polished surface of the charac- teristic bright colour of this metal ; the surface layer is moreover very hard and durable, and is not affected either by the atmosphere or even by sulphu- retted hydrogen. A deposit of 2 grammes of nickel on the square decimetre represents a coating 0’023 mm. in thickness. | The deposit of cobalt has a brighter tint than that of nickel. Professor Silvanus Thompson uses a bath of cobalt sulphate or chloride, to which magnesium sulphate is added. To obtain a deposit of Alatznum, the hydrate of this metal is dissolved in syrupy phosphoric acid, and this solution diluted with water so that it contains I°2 to 1°5 per cent. of the hydrate. An anode of platinum or of carbon is used, and the strength of the bath is kept constant by the addition of the hydrate. Objects made of iron, nickel, and zinc must previously be coated with copper. —881] Electrodynamics 887 CHAPTER Lv. ELECTRODYNAMICS. ATTRACTION AND REPULSION OF CURRENTS BY CURRENTS 881. Electrodynamics.—By the term electrodynamics are understood the laws of electricity in a state of motion, or the action of electric currents upon each other and upon magnets, while e/ectrostatics deals with the laws of elec- tricity in a state of rest. The action of one electrical current upon another was first investigated by Ampére, shortly after the discovery of Oersted’s celebrated fundamental warmed ||) ©) Fig. 848 experiment (841). All the phenomena, even the most complicated, follow from two simple laws, which are— I. Zwo currents which are parallel, and in the same direction, attract one another. Il. Zwo currents parallel, but in contrary directions, repel one another. In order to demonstrate these laws, the circuit which the current traverses must consist of two parts, one fixed and the other movable. This is effected $38 Dynamical Electricity [881— by the apparatus (fig. 848), which is a modified and improved form of one originally devised by Ampére. It consists of two brass columns, A and D, between which is a shorter one. The column D is provided with a multiplier (842) of 20 turns, MN (fig. 850), the sensitiveness of the instrument increasing with the number of turns. This frame can be adjusted at any height, and in any position, by means of a universal screw clamp (see figs. 850-85 3). The short column is hollow, and in its interior slides a brass tube termi- nating in a mercury cup, ¢, which can be raised or lowered. On the colunin A is another mercury cup represented in section at fig. 849 in its natural size. In the bottom is a capillary aperture through which passes the point of a-sewing-needle fixed to a small copper .ball. This point extends as faras the mercury, and. turns freely in the hole. The movable part of the circuit consists of a copper wire proceeding from a small ball, and turning in the direction of the arrows from the cup a to the cup c. The two lower branches are fixed to a thin strip of wood, and the whole system is balanced by two copper balls, sus- pended to the ends. These details being known, the current of a Bunsen’s battery of 4 or 5 cells ascending by the column A (fig: 850) tolthe ‘cup re, traverses the circuit BC, reaches the cup c, descends the central column, and thence passes by a wire, P, to the multiplier MN, whence it returns to the bat- tery bythe wire Q. Now, if, before the current passes, the movable = circuit has been.arranged in the plane of the multiplier, with the sides B and M_ opposite each other, ‘when the cur- Figsgee rent passes, the side B is re- pelled, which demonstrates the second law; for in the branches B and M the currents, as indicated by the arrows, are proceeding in opposite directions. To demonstrate the first law the experiment is arranged as in fig. 850— that is, the multiplier is reversed ; the current is then in the same direc- tion both in the multiplier and in the movable part ; and when the latter is removed out of the plane of the multiplier, so long as the current passes it tends to return to it, proving that there is attraction between the two parts. 882. Roget’s vibrating spiral.—The attraction of parallel currents may also be shown by an experiment known as that of Roget’s vibrating spiral, fig. 851. A copper wire about 0:7 mm. in diameter is coiled in a spiral of ~$83] Laws of Angular Currents 889 about 30 coils of 25 mm. in diameter. At one end it is hung vertically from a binding screw, while the other just dips in a mercury cup. On passing the current of .a batter) of 3 to 5 ; Grove’s cells through the spiral by means of the mercury cup and the binding screw, its coils are tra- versed by parallel currents; they therefore attract one another, and rise, and thus the contact with the mercury is broken. The current having thus ceased, the coils no longer attract each other, they fall by their own weight, contact with the mercury is re-established, and the series of phenomena is inde- finitely reproduced. The experi- ment is still more striking if a magnetised rod the thickness of a pencil is introduced into the interior. This will be intelligible if we consider the action between the parallel Amperian currents (890) of the magnet and of the helix. Fig. 851 883. Laws of angular currents. I. Two rectilinear currents, the directions of which form an angle with each other, attract one another when both approach or recede from the apex of the angle. Il. They repel one another tf one approaches and the other recedes from the apex of the angle. These two laws may be demonstrated by means of the apparatus above de- scribed, replacing the movable circuit by the circuit BC (fig. 852). If then the multiplier is placed horizontally, so that its current is in the same direc- tion as in the moy- able current, on re- moving the latter it quickly approaches the multiplier, which verifies the first law. To prove the second law, the multiplier is turned so that the currents are in opposite direce _ tions, and then repulsion ensues (fig. 852). 890 Dynamical Electricity [883- Both laws are included in the statement that the two circuits tend to become parallel to each other with their currents in the same direction. In a rectilinear current each element of the current repels the succeeding one, and ts ttself repelled. This is an important consequence of Ampére’s law, and may be experi- mentally demonstrated by the following arrangement, which was devised by Faraday. A U-shaped piece of copper wire, the ends of which dip in two separate deep mercury cups, is suspended from one end of a delicate balance and suitably equipoised. When the mercury cups are connected with the two poles of a battery, the wire rises very appreciably, and sinks again to its original position when the current ceases to pass. The current passes into the mercury and into the wire ; but from the construction of the apparatus the former is fixed, while the latter is movable, and is accord- ingly repelled. 884. Laws of sinuous currents.—Zhe action of a sinuous current ts equal to that of a rectilinear current of the same length in projection. This principle is demon- strated by arranging the multiplier vertically and placing near it a movable circuit of insulated wire half sinuous and_ half rectilinear (fig. 853). It will be seen that there is neither attraction nor repulsion, showing that the action of the sinuous portion m2 is equalled by that of the rectilinear portion. An application of this principle will presently be g. 853 “met with in the appara- tus called solenoids (896), which are formed of the combination of a sinuous with a rectilinear current. 885. Action of an infinite current on a current perpendicular to its direction.—From the action exerted between two angular currents (883) the action of a fixed and infinite rectilinear current, PQ (fig. 854), on a movable current, KH, perpendicular to its direction can be determined. Let OK be the perpendicular common to KH and PQ, which is null if the two lines PQ and KH meet. The current PQ flowing from Q to P in the direction of the arrows, let us first consider the case in which the current KH approaches the current QP. From the first law of angular currents (883) the portion OQ of the current PQ attracts the current KH, because they both flow towards the summit of the angle formed by their directions. The portion PO, on the con- trary, will repel the current KH, for here the two currents are in opposite directions at the summit of the angle. If then sg and mp stand for the two forces, one attractive and the other repulsive, which act on the current KH, and which are necessarily of the same intensity, since they are symmetrically a i Q —885] Action of an Infinite Current 89OL arranged in reference to the two sides of the point O, these two forces may be resolved into a single force, #7, which tends to move the current KH parallel to the current QP, but in a contrary direction. A little consideration will show that when the current KH is below the current PQ, its action will be the opposite of what it is when above. On considering the case in which the current KH moves away from PQ (fig. 855), it will be readily seen from similar considerations that it moves parallel to this current, but in the same direction. H H Acad wn Be ee Ae ee zane a, } a aS & vb f K IK P Pout e : . a ) <— <— 0 <— Fig. 854 Fig. 855 Hence follows this general principle. A /finzte movable current which approaches a fixed infinite current ts acted on so as to move tn a atrection parallel and opposite to that of the fixed current; of the movable current tends from the fixed current, tt ts acted on so as to move parallel to the current and in the same direction. It follows from this, that if a vertical current is movable about an axis, XY, parallel to its direction (figs. 856 and 857), any horizontal current PQ will have the effect of turning the movable current about its axis, wafzl the x acd | ae: : : so la Vatiwey diva td“ Bo Mle i ae 'y P Q P :) Q oa <— +— a gna ee Fig. 856 Fig. 857 plane of the axis and of the current have become parallel to PQ ; the vertical current stopping, in reference to its axis, o7 the stde from which the current PQ comes (fig. 856), or on the side towards which it ts directed (fig. 857), according as the vertical current descends or ascends—that is, according as it approaches or moves from the horizontal axis. : It also follows from this principle that-a system of two vertical currents rotating about a vertical axis (figs. 858 and 859) is directed by a horizontal current, PQ, in a plane parallel to this current when one of the vertical 892 Dynamical Electricity [885— currents is ascending and the other descending (fig. 858); but that if they are both ascending or both descending (fig. 859), they are not directed. sapere. Jatt | Ki baa, ne oy ima faa fiat | choles Pp my! Bh Pp Yio a Fig. 858 Fig. 859 886. Action of an infinite rectilinear current on a rectangular or circular current.—It is easy to see that a horizontal infinite current exer- cises the same directive action on a rectangular current movable about a vertical axis (fig. 860) as that which has been above stated. For from the direc- tion of the currents indicated by the arrows, the part QY acts by attraction not only on the horizontal portion YD (/aw of angular currents), but also on the vertical portion AD (daw of perpendicular currents). The same action evidently takes place between the part PY and the parts CY and BC. Hence, the fixed current PQ tends to direct the movable rectangular current ABCD into a position parallel to PQ, and such that in the wires CD and PQ the direction of the two currents ts the samte. This principle is readily demonstrated by placing the circuit ABCD on the apparatus with two supports (fig. 860), so that at first it makes an angle with the plane of the supports. On passing a somewhat powerful current below the circuit in the same plane as the supports, the movable part passes into that plane. It is best to use the circuit in fig. 850, which is astatic, Fig. 860 _ while that of fig. 860 is not. What has been said about the rectangular current in fig. 860 applies also to circular currents, and is demonstrated by the same experiments. 887. Rotation of a finite horizontal current by an infinite horizontal rectilinear current.—The attractions and repulsions which rectangular currents exert on one another ae am a a R may readily be transformed i wley ‘ va into a continuous circular mo- 1 yA \ tion. Let ni es roa ie ae Sei fm current movable about the Ax we fr point O in a horizontal plane, pc ied ont ai and let PQ be a fixed infinite Se eee 7 current also horizontal. As these two currents flow in the is : direction of the arrows, it fol- lows that in the position OA_the movable current is attracted by the current Fig. 861 Fig. 862 -888] Rotation of a Vertical Current 893 PQ, for they are in the same direction. Having reached the position OA’, the movable current is attracted by the part NQ of the fixed current, and repelled by the part PN. Similarly in the position OA”, it is attracted by MQ and repelled by PM, and so on; from which follows a continuous rota- tory motion in the direction AA’A”A”’. If the movable current, instead of being directed from O towards A, were directed from A towards O, it is easy to see that the rotation would take place in the contrary direction. Hence, by the action of a fixed infinite current, PQ, the movable current OA tends to a continuous motion 27 a direction opposite to that of the fixed current. If, both currents being horizontal, the fixed current were circular instead of being rectilinear, its effect would still be to produce a continuous circular motion. For, let ABC (fig. 852) be a fixed circular current, and mz a rec- tilinear current movable about the axis #, both currents being horizontal. These currents, flowing in the direction of the arrows, would attract one another in the angle 7AC, for they both flow towards the summit (883). In the angle 7AB, on the contrary, they repel one another, for one goes towards the summit and the other moves from it. Both effects coincide in moving the wire 7772 in the same direction ACB. 888. Rotation of a vertical current by a horizontal circular current.— A horizontal circular current, acting on a rectilinear vertical, also imparts to it a continuous rotatory motion. In order to show this, the apparatus represented in fig. 863 is used. _ It consists of a brass vessel, round which are rolled several coils of in- sulated copper wire, through which a current passes. In the centre of the vessel is a brass support, a, terminated by a small cup containing mercury. In this dips a pivot supporting a copper wire, 44, bent at its ends in two ver- tical branches, which are soldered to a very light copper ring immersed in acidulated water contained in the vessel. A current entering through the wire 2, reaches the wire A, and, having made several circuits, terminates at B, which is connected by a wire underneath with the lower part of the column a. Ascending in this column, it passes by the wires 46 into the copperring, into the acidu- lated water, and into the sides of the vessel, whence it re- turns to the battery by the strip Jae ue circuit being thus closed, the wire 066 and the ring tend to turn ina direction contrary to that of the fixed current, a motion due to the action of the circular current on the current in the vertical branches 64; for, as follows from the two laws of angular currents, the branch 6 on the right is attracted by the portion A of he fixed current, and the branch 4 on the left is attracted in the contrary direction by the opposite Fig. 863 894 Dynamical Electricity [888— part, and these two motions coincide in giving the ring a continuous rotatory motion in the same direction. The action of the circular current on the horizontal part of the circuit 64 would tend to turn it in the same direction ; but from its distance the effect due to it may evidently be neglected. 889. Rotation of magnets by currents.—Faraday proved that currents impart the same rotatory motions to magnets that they do to currents. This may be shown by means of the apparatus represented in fig. 864. It consists of a large glass vessel, almost filled with mercury. In the centre of this is immersed a magnet, A, about eight inches in length, which projects a little above the surface of the mercury, and is loaded at the bottom with a platinum cylinder. At the top of the magnet is a small cavity containing mercury ; the current ascending the column 7 passes into this cavity by the rod C. From the magnet it passes by the mercury to a copper ring, G, when it emerges by the column #7. When the current flows the magnet begins to rotate round its own axis with a velocity depending on its magnetic power and on the intensity of the current. Instead of making the magnet rotate on its axis, it may be caused to rotate round a line parallel to its axis by arranging the experiment as shown (fig. 861). ; This rotatory motion is readily intelligible on Ampére’s theory of mag- netism (gor), according to which, magnets are traversed on their surface by an infinity of circular currents in the same direction, in planes perpen- dicular to the axes of the magnet. At the moment at which the current passes from the magnet into the mercury, it di- vides on the surface of the mercury into an infinity of rec- | tilinear currents proceeding from the axis of the magnet to the circumference of the glass. Figs. - 866 “and? $67, which corre- = = spond respec- Fig. 854 Fig. 865 tively to figs. 864 and 865, give on a larger scale, and on a horizontal plane passing through the surface of the mercury, the direction of the currents to which thé rotation is due. In fig. 864, the north pole being at the top, the Amperian currents pass round ‘the magnet in the reverse direction to that of the hands of a watch, as indi- ‘cated by the arrow? (fig. 865), while the currents which radiate from the rod C towards the metal ring GG’, have the direction CD, CE. Thus (883) any ‘given element ¢ of the magnetic current of the bar A is attracted by the -890] Directive Action of Magnets on Currents 895 current CE and repelled by the current CD; hence results a rotation of the bar about its axis in the same direction as the hands of a watch. In fig. 867 the currents CD, CF, being in the oppo- site direction to those of the bar, would repel the latter, which would be attracted by the eurrents. CE; GH: Pence. pithee bar rotates in a circular direction, shown by the arrow s, about the vertical axis which passes through the rod C. | If the north pole is below, or if the direction of the current is altered, the rotation of the magnet is in the opposite direction. Fig. 866 Fig. 867 ACTION OF THE EARTH AND OF MAGNETS ON CURRENTS 890. Directive actions of magnets on currents.—Not only do currents act upon magnets, but magnets also act upon currents. In Oersted’s funda- mental experiment (fig. 848), the magnet being movable while the current is fixed, the former is directed and tends to set at right angles to the current. If, on the contrary, the magnet is fixed and the current movable, the latter is directed and sets across the direction of the magnet. This may be illus- trated by the apparatus represented in fig. 868. This is the original form uy IT TTT TATU cc | fi ii Ce m7 il) ie of Ampére’s stand, and is frequently used in experimental demonstration. It needs no explanation. The circuit which the current traverses is movable, 896 : — Dynamical Electricity [890— and below its lower branch a powerful bar magnet is placed ; the circuit immediately begins to turn, and stops after some oscillations in a plane perpendicular to the axis of the magnet. For demonstrating the action of magnets upon currents, De la Rive’s floating battery (fig. 869) is well adapted. It consists of plates of zinc and copper which are immersed in dilute sulphuric acid contained in a glass bulb slightly loaded with mercury to keep it upright, and which can float freely on water. With the plates can be connected either circular or rect- angular wires, coils, or solenoids ; they are then traversed by a current, and can be subjected to the action either of magnets or of currents. 891. Rotation of currents by magnets.—Not merely can currents be directed by magnets, but they may also be made to rotate, as is seen from the following experiment, devised by Faraday (fig. 870). On a base with levelling screws, and resting on an ivory support, is a copper rod, BD. It is surrounded in part of its length by a bundle of magnetised wires, AB, and at the top of it isa mercury cup. A copper circuit, EF, balanced on a steel point, rests in the cup, and the other ends of the circuit, which terminate in steel points, dip in an annular trough full of mercury. The apparatus being thus arranged, the current from 4 or 5 Bunsen’s elements enters at the binding screw 4; it thence rises in the rod D, descends by the two branches, reaches the mercury by the steel points, whence it passes by the framework, which is of copper, to the battery by the binding screw a. If now the magnetised bundle is raised, the circuit EF rotates, either in one direction or the other, according to the pole by which it is influenced. This rotation is due to currents assumed to circulate round mag- nets ; currents which act on the vertical branches EF in the same way as the circular current on the branches 44 in fig. 863. In this experiment the magnetised bundle | may be replaced by a solenoid (898) or by an electromagnet, in which case the two binding screws in the base of the apparatus on the left give entrance to the current which is to traverse the solenoid or electro- magnet. 892. Electrodynamic and electromagnetic rotation of liquids.—The condition of a linear current assumed in the previous experiments is not necessary. This may be illustrated by a simple form of experiment devised by Clerk Maxwell.. At the bottom of a small beaker, a copper disc is placed with an insulated tongue bent at right angles, and connected with a similar zinc disc supported about an inch above the copper. Dilute acid is placed so as to cover both discs, and, some fine sawdust having been added to Fig. 870 893] Directive Action of the Earth on Vertical Currents 897 the liquid, the whole is placed on the pole of an electromagnet. The rotation of the liquid is then shown by that of the sawdust. 893. Directive action of the earth on vertical currents.—The earth, which exercises a directive action on magnets (703), acts also upon currents, giving them in some cases a fixed direction, in others a continuous rotatory motion. The first of these two actions may be thus enunciated: Avery vertical current movable about an axis parallel to ttself, places ttself under the direc- tive action of the earth in a plane through this axis perpendicular to the magnetic meridian, and stops after some oscillations, on the east of tts axts of rotation when it 7s descending, and on the west when tt ts ascending. This may be demonstrated by means of the apparatus represented in fig. 872, which consists of two brass vessels of somewhat different diameters. ’ The larger, a, about 13 inches in diameter, has an aperture in the centre, through which passes a brass support, 4, insulated from the vessel a, but communicating with the vessel K. This column terminates in a small cup, Fig. 872 in which a light wooden rod rests on a pivot. At one end of. this rod a fine wire is coiled, each end of which dips in acidulated water, with which the two vessels are respectively filled. The current arriving by the wire 7z passes to a strip of copper, which is connected underneath the base of the apparatus with the bottom of the column 6. Ascending in this column, the current reaches the vessel K and the acidulated water which it contains ; it ascends from thence in the wire ¢, redescends by the wire e, and, traversing the acidulated water, it reaches the sides of the vessel a, and so back to the battery through the wire 7. The circuit being thus closed, the wire e moves round the column 4, and stops to the east of it, when it descends, as is the case in the figure ; but if it ascends, which is effected by transmitting the current by the wire z, the wire e stops to the west of the column 4, in a position directly opposite to that which it assumes when it is descending. If the rod with a single wire, in fig. 872, is replaced by one with two 3M 898 Dynamical Electricity — -[893- wires as in fig. 872, the rod will not move, for as each wire tends to place itself on the east of the column a, two equal and contrary effects are produced which counterbalance one another. 894. Action of the earth on horizontal currents movable about a vertical axis.—The action of the earth on horizontal currents is not direc- tive, but ezves them a continuous rotatory motion. This may be illustrated by means of the apparatus represented in fig. 873 which only differs from that of fig. 872 in having but one vessel. The current, ascending by the column a, traverses the two wires cc, and descends by the wires 04, from which it regains the battery ; the circuit ccd then begins a continuous rotation anti-clockwise or clock- wise, according as in the wires cc the current goes from the centre, as is the case in the figure, or goes towards it, which is the case when the current enters by the wire m instead of by z But we have seen (893) that the action of the earth on the vertical wires 46 is destroyed ; hence the rotation is that produced by the action on the horizontal branches cc. This rotatory action of the earth on horizontal currents is an instance of the rotation of a finite horizontal by an infinite horizontal current (885). The motion of a movable current in a magnetic field is also illustrated by Barlow's wheel, represented in fig. 874. It consists of a light toothed metal wheel which can rotate about a horizontal axis, and is so arranged that one or more teeth dip in a mercury trough. The two branches of a horseshoe Fig. 875 magnet are on opposite sides of the trough, and when the poles of a battery are connected with the axis and mercury respectively, the wheel at once rotates. If the current flows from the centre to the circumference of the wheel, and the north pole is in front, the wheel rotates in a UifeCHon opposite that bf the hands of a watch. ~896]| Structure of a Solenoid 899 Faraday’s disc (fig. 875) is similar ; the current arrives and departs by two springs, one B which presses against the axis, and the other A against the cir- cumference of the wheel. H represents the direction of the lines of force of the field. 895. Directive action of the earth on closed currents movable about a vertical axis.—If the current on which the earth acts is closed, whether it be rectangular or circular, the result is not a continuous rotation, but a directive action, as in the case of vertical currents (893), in virtue of which the current places ttself in a plane perpendicular to the magnetic meridian, so that tt ts descending on the east of tts axts of rotation, and ascending on the west. This property, which can be shown by the apparatus represented in fig, 876, is a consequence of what has been said about horizontal and vertical currents. For in the closed circuit BA, the current in the upper and lower parts tends to turn in oppo- site directions, from the law of horizontal currents (894), and hence is in equilibrium ; while in the lateral parts the current on the one side tends towards the east, and on the other side to the west, from the law of vertical currents. From the directive action which the earth Fig. 876 exerts on currents, it is necessary, in many experiments, to neutralise this action. This is effected by arranging the movable circuit symmetrically about its axis of rotation, so that the directive action of the earth tends to turn the two branches in opposite directions. This condition is fulfilled in the circuit in fig. 876. Such circuits are hence called astatic circutts. 896. Structure of a solenoid.—A solenoid or electromagnetic cylinder is a system of equal and parallel circular currents formed of the same piece of covered copper wire and coiled in the form of a helix or spiral, as represented in fig. 877. A solenoid or electromagnetic cylinder, however, is only complete when part of the wire BC passes in the direction of the axis in the interior of the helix. With this arrangement, when the circuit is traversed bya current it follows from what has been said about sinuous currents (884) that the action of a solenoid in a longitudinal direction, AB, is counterbalanced by that of the rectilinear-current BC. This action is accordingly null in the direction of the length, and the action of a solenoid in a direction perpendicular to its axts is equivalent to that of a series of equal parallel currents. A solenoid as defined by Ampére is only a mathematical conception, being an arrangement of zzfinztely small closed equal currents all perpendicular to the same line called the avectrix, which passes through their centres This cannot be realised any more than can the simple pendulum, and we must. 3M2 Fig. 877 goo Dynamical Electricity [896- regard the above apparatus as bearing much the same relation to the ideal solenoid, as the compound does to the simple pendulum. 897. Action of currents on solenoids.—What has been said of the action of fixed rectilinear currents on finite rectangular or circular currents (885) applies evidently to each of the circuits of a solenoid, and hence a rectilinear current must tend to direct these circuits parallel to itself. To demonstrate this fact experi- mentally, a solenoid is con- structed as shown in fig. 878, so that it can be suspended by two pivots in the cups @ and ¢ of the apparatus repre- sented in fig. 876. The sole- noid is then movable about a vertical axis, and if a recti- linear current QP be passed beneath it, which at the same time traverses the wires of the solenoid, the latter is seen Fig. 878 to turn and tends to set at . right angles to the lower cur- rent—that is, in such a position that its circuits are parallel to the fixed current ; and, further, the current in the lower part’of each of the circuits is in the same direction as in the rectilinear wire. If, instead of passing a rectilinear current below the solenoid, it is passed vertically on the side, an attraction or repulsion will take place, according as the two currents in the vertical wire, and in the nearest part of the solenoid, are in the same or in contrary directions. . 898. Directive action of the earth on solenoids.—If a solenoid is suspended in the two cups (fig. 879), not in the direction of the magnetic Fig. 879 meridian, and a current is passed through the solenoid, the latter will begin to move, and will finally set in such a position that its axis is in the direction of the magnetic meridian. If the solenoid is deflected from its —901] Ampéere’s Theory of Magnetism gol position of equilibrium, it will, after a few oscillations, return, so that its axis is in the magnetic meridian. Further, it will be found that in the lower half of the coils of which the solenoid consists the direction of the current is from east to west ; in other words, the current is descending on that side of the coil turned towards the east and ascending on the west. The directive action of the earth on solenoids is accordingly a consequence of that which it exerts on circular currents. In this experiment the solenoid is directed like a magnetic needle, and the zorth pole, as in magnets, is that end which points towards the north, and the south fole that which points towards the south. This experiment may be made by means of a solenoid fitted on a De la Rive’s floating battery (890). 899. Mutual action of magnets and solenoids.—The same phenomena of attraction and repulsion exist between solenoids and magnets as between magnets themselves. For if one of the poles of a magnet is presented to a movable solenoid, traversed by a current, attraction or repulsion will take place, according as the poles of the magnet and of the solenoid are of contrary or.of the same name. The same phenomenon takes place when a solenoid traversed by a current and held in the hand is presented to a movable magnetic needle. If one pole of a long bar magnet is presented to the centre of the floating coil (fig. 869), then if the direction of the current in the coilis the same as that of the Ampérian current (901) in that pole of the magnet, the coil will be attracted to the magnet, and, encircling it, will move towards the middle, where it is stationary ; if the currents are opposite, then the coil will first of all be repelled, it will then turn round, and proceed as before. 900. Mutual action of solenoids.—When two solenoids traversed by a powerful current are allowed to act on each other, one of them being held in the hand and the other being movable about a vertical axis, as shown in fig. 879, attraction and repulsion will take place just as in the case of two magnets. These phenomena are easily explained by reference to what has been said about the mutual action of the currents, bearing in mind the direction of the currents in the extremities presented to each other. gor. Ampére’s theory of magnetism.— Ampére propounded a theory based on the analogy between solenoids and magnets, by which all magnetic phe- nomena may be referred to electrodynamical principles. Instead of attributing magnetic phenomena to the existence of two fluids Ampére assumed that each individual molecule of a magnetic substance is traversed by an electric current, and further that these molecular cur- rents are free to move about their centres. The coercive force, however, which is little or nothing in soft iron, but considerable in steel, opposes this motion, and tends to keep the molecular currents in any position in which they happen to be. When the magnetic substance is not magnetised, these currents, under the influence of their mutual attractions, occupy such positions that their total action on any external substance is null. Magnetisation consists in giving to these molecular currents a parallel direction, and the stronger the magnetising force the more perfect the parallelism. The /mzt of mag- netisation 1s attained when the currents are completely parallel. 902 Dynamical Electricity [901— The resultant of the actions of all the molecular currents is equivalent to that of a single current which traverses the outside of a magnet. For by inspection of fig. 880, in which the molecular currents are re- presented by a series of small internal circles in the two ends of a cylindrical bar, it will be seen that the adjacent parts of the currents oppose one another and cannot exercise any external electrodynamic action. ' This is not the case with the surface ; there the molecular currents at ab are not neutralised by other currents, and as the points adc are infinitely near, they form a series of elements in the sare direction situated in planes perpendicular to the axis of the magnet, thus constituting a true solenoid. The direction of these currents in magnets can be ascertained by con- sidering the suspended solenoid (fig. 878). If we suppose it traversed by a current, and in equilibrium in the magnetic meridian, it will set in such a position that in the lower half of each coil the current flows from eas¢ zo west. We have then the following rule :— When the north pole of a magnet zs looked at, the direction of the Amperian currents ts opposite to that of the hands of a watch; and when the south pole ts looked at, the direction ts the same as that of the hands. go2. Terrestrial current.—In order to explain terrestrial magnetic effects on this supposition, the existence of electrical currents is assumed, which continually circulate round our globe from east to west perpendicular to the magnetic meridian. The resultant of their action is a single current travers- ing the magnetic equator from east to west. They are supposed by some to be thermo-electric currents due to the variations of temperature caused by the successive influence of the sun on the different parts of the globe from east to west. | These currents direct magnetic needles; for a suspended magnetic needle comes to rest when the molecular currents on its under-surface are parallel and in the same direction as the terrestrial currents. As the molecular currents are at right angles to the direction of its length, the needle places its greatest length at right angles to east and west, or north and south. Natural magnetisation is probably imparted in the same way to iron minerals. 903. Hall’s experiment.-—In the action of magnets on currents which has been described in the foregoing sections, we have been concerned with the action of the magnet on the body which conveys the current. Professor Hall of Baltimore has made the following experiment to determine whether the path of a current itself in the body of a conductor is or is not deflected when it is exposed to the direct action of a magnetic field. A strip of gold leaf A B, 9 centimetres in length by 2 centimetres broad (fig. $81), is fastened on a glass plate, placed between the poles of an electro- Fig. 880 —$03] Hall's Experiment 903 magnet in such a manner that the plane of the strip is at right angles to the lines of force of the magnetic field. The ends of this strip A and B are in connection with the poles of a Bunsen’s cell. Two wires leading to a galvanometer @ and 6 are connected with two equipotential points at the opposite edges of the strip ; that is to say, at two points, found by trial, in which there is no deflection in the galvanometer (760). Fig. 882 shows the general direction of the lines of flow of the current when the electro- Fig. 882 Fig. 882 magnet is not excited, the dotted lines being equipotential lines. When the electromagnet is excited by passing a current through it, a distinct deflection is produced in the galvanometer, showing that the position of the equipoten- tial lines is varied (fig. 883), and that the paths of the current in the conducting strip have been deflected. This deflection is permanent, and cannot there- fore be due to induction, and its direction is reversed when the current in the electromagnet is reversed (fig. 884). Fig. 883 Fig. 884 The magnetic field acts thus upon the current in the gold leaf in sucha manner as to displace it towards one edge or the other, and to cause a small portion to pass through the circuit of the galvanometer. The electricity is displaced in the direction of the electromagnetic force, due to the magnet, from a to 4 through the galvanometer in the case of iron, zinc, and cobalt, but from 4 to a through the galvanometer, with nickel, gold, and bismuth. Of all metals, bismuth shows the phenomenon in far the highest degree. 904 Dynamical Electricity [904— CHAPTER V MAGNETISATION BY CURRENTS. ELECTROMAGNETS. ELECTRIC TELEGRAPHS 904. Magnetisation by currents.—A wire conveying a current creates about it a magnetic field. The existence of this field may be conveniently shown by a vertical wire forming part of a voltaic circuit which passes at right angles through a piece of cardboard. When iron filings are sprinkled on the cardboard they are seen to arrange themselves in circles con- centric with the wire as represented in fig. 885. If the direction of the current in the wire xy is that shown by the arrow, the direction of the lines of force is from right to left for an observer placed in the current. The direction of the par- ticles of iron is that which an in- Fig. 885 finitely small magnet would have if placed there. When a wire tra- versed by a current is immersed in iron filings, they adhere to it in large quantities (fig. 886), each particle setting perpendicularly to the wire ; they become detached as soon as the current ceases, and there is no action on any non-magnetic metal. In like manner an iron or steel bar is magnetised when placed at right angles, and near to a current ; the effect is increased by coiling an insulated copper wire round a glass tube, in which there is an unmagnetised steel rod. If a current is passed through the wire, even for a short time, the bar be- comes strongly magnetised. If, as we have already seen (813), the discharge of a Leyden jar be trans- mitted through the wire, by connecting one end with the outer coating, and the other with the inner coating, the bar is also magnetised. This is a convenient way of illustrating the identity between the effects of frictional and voltaic electricity. If in this experiment the wire is coiled on the tube in such a manner -905] Magnetisation by Currents 905 that when it is held vertically the downward direction of the coils is from right to left on the side next the observer, this constitutes a 7ight-handed or dextrorsal sptral or helix (fig. 887), of which the ordinary screw is an example. In a /e/¢t-handed or sinistrorsal helix the coiling is in the opposite direction—that is, from left to right (fig. 888). In a right-handed spiral the north pole is at the end at which the current emerges, and the south pole at the end at which it enters ; the reverse is the case in a left-handed spiral. But whatever the direction of the coiling, the polarity is easily found by the following rule: lf a person swimming in the current looks at the axts of the spiral, the north pole is always on his left. If the wire is not coiled regularly, but if its direction is reversed, at each change of direction a consequent pole (696) is formed in the magnet. The simplest method of remembering the polarity produced is as follows : What- ever be the nature of the helix, whether right or left handed, if the end facing the observer has the current flowing in the direction of the hands of a watch it is a south pole, and vice versd. The same polarity is produced whether or not there is an iron core within the helix. In order to magnetise a steel bar by means of electricity, it need not be placed in a tube, as shown in figs. 887 and 888. It is sufficient to coil round it a copper wire, covered with silk, cotton, or gutta-percha, in order to in- sulate the circuits from one another. go5. Electromagnets.—The ar- rangement which has been described above of a long length of insulated wire coiled on a bar or core of soft iron, and traversed by a current, forms what is called an electromagnet. In the case of soft iron the magnetisation is only temporary ; when the current ceases the magnetisation of the bar ceases also, and the iron reverts almost wholly to its ordinary magnetic but unmagnetised condition. Fig. 889 906 Dynamical Electricity [905- From its property of producing a powerful magnetic field, the coil in this experiment constitutes a magnetising coil or spiral; and the mag- netisation of the iron by its means is an application of the principle of magnetic induction. From the fact that electromagnets are far more powerful than permanent magnets, and, still more, that their magnetisation can be instantaneously evoked and destroyed, they have met with a host of applications of the very greatest importance ; and the form, dimensions, and strength of such electromagnets vary greatly with the purpose for ree they are intended. Fig. 890 Fig. 891 There are, however, two principal types ; dar magnets, as in fig. 894, or horseshoe magnets, either in one piece, as shown in fig. 889, or else formed of two straight electromagnets, each joined to a cross-piece of soft iron or yoke, T, as shown in fig. 891. It is better to have theiron in one piece, but the bending of large masses is difficult, and is apt to increase the coercive force, so that the other plan is generally adopted, great care being taken that the surfaces in contact be very accurately fitted to each other. In order that the poles at the two ends may be of opposite kinds, the wire must go round each branch in the same direction as it would do if the core had been bent after the winding had been finished. The windings ought to appear in opposite directions on the SO Soe & . two legs to an observer who is looking at the \ _ two ends (fig. 890), the current going like the \ WZ? hands of a watch round the south pole, and in == the opposite direction round the north pole. aN} Fig. 892 represents a compact form of electromagnet devised by Joule, the core and armature of which may be constructed Hig? foe by sawing a piece of wrought iron tubing | lengthwise. There must be space enough to contain the wire necessary. The volume of the wire is determined by the condition of not exceeding a certain temperature. The magnetisation in the core depends on the strength of the field due to the magnetising coil, and on the nature ee dimensions of the core ; it is represented by the formula I = «H, I being the magnetisation, H-the magnetic force producing it and « the coefficient of susceptibility ; for a long bar placed inside a long coil, the actual magnetic force H is nearly 4niit the same as that due to the coil alone, namely - where # is the number of turns per unit length, and z the current in amperes. Similarly the mag- ~905] Electromagnets 907 netic induction (number of lines of force per sq. cm.) B, in the core depends Ampere mia) If a soft iron ring or Zore be coiled round with insulated wire through which a current is passed, it is the seat of a very powerful magnetic in- duction, though it has no poles, and therefore no external action. Such a system forms a closed magnetic circuit; the arrangement represented in fig. 889, where the two poles of an electromagnet are connected by an arma- ture, also forms such a circuit, and an interesting analogy may be made between it and a closed electrical circutt. upon the magnetising force, and we have the equation B = »H = : ‘ ; Z ; If for z in the above expression we write — , where z is the total number n of turns of the wire, and / the length of the bar, and consider the total in- duction through the cross section s, the formula may be put ieee Annet is ps in which it is quite analogous to Ohm’s formula for an electric current (847) 4nnz being the magnetic equivalent of the electromotive force, and may accordingly be called the szagnetomotive force ; while is the analogue of pS electric resistance. It is called the magnetic resistance or reluctance. Its value, it will be seen, is directly as the length of the bar, and inversely as the cross section, and the permeability » being the equivalent in magnetism of conductivity in electricity (726); it represents conductivity for lines of magnetic force. This analogy also holds if we consider the magnetic circuit as made up of bodies of different permeabilities, and also in the case of divided magnetic circuits. The analogy fails, however, in one important respect ; electrical resist- ance is quite independent of electromotive force, while permeability differs in value with the value of the magnetising force. Hence the analogy is rather formal than real ; it is, however, useful in dealing with calculations about electromagnets. The expression 4772 shows that we get the same magnetic effect whether we have a small number of turns of wire with a strong current, or a great number of turns with a weak current. Thus, with a given bar the same effect is produced by one turn conveying a current of one ampere as by ten turns with a current of one-tenth of an ampere. In the case of electro- magnets the magnetising force is usually defined by the number of ampere turns used. With a given battery the greatest magnetising force is obtained when the resistance in the magnetising spiral is equal to the other resistances in the circuit, those of the battery included, and the length and diameter of the wire must be so arranged as to satisfy these conditions. Taking the permeability of air as unity, that of iron is many hundred times as great ; hence the introduction of a layer of air in a magnetic circuit is analogous to the introduction of a bad conductor in an electric circuit. Iron being the most permeable of all substances, a magnetic circuit should 908 Dynamical Electrectty (905- have as much iron as possible. The junctions also should be made close and true, since each joint increases the magnetic reluctance. If we take a given magnetising spiral, at right angles to the magnetic meridian, and place at some distance from it, and in the line of its axis, a small magnetic needle, on passing a current through the spiral the needle is deflected, and this deflection (or, more strictly, its tangent) is a measure of the magnetic moment acquired by the spiral; if the current be gradually increased the deflection will also be increased, and in proportion to the strength of the current. . If, however, the spiral contains a bar of soft iron, the case is not so simple. If we plot the curve which represents the ratio of the magnetising force to the magnetisation, as measured by the deflection jof the needle, it will be found that at first the magnetisation is proportional to the magnetising force, then a stage is reached when the magnetisation increases more rapidly than in direct proportion to the magnetising force, but the rate of increase gradu- ally becomes less, and the magnetisation ultimately approaches a limit which is not materiaily exceeded, even by a considerable increase in the magnetising force. This represents a state of saturation (737), and it corresponds to the case in which the axes of the molecular magnets (gor) are all strictly parallel to the axis of the spiral. The intensity of the magnetisation which can be imparted toa bar is about 1,700 C.G.S. units in the case of wrought iron, 1,240 with cast iron, and 515 in the case of nickel. Steel can acquire pretty much the same intensity of magnetisation as wrought iron, and retains about one half in the form of permanent or residual magnetism. Soft iron almost wholly loses its mag- netisation when the current ceases, and the more so the purer the iron, and the more carefully it is annealed. In many applications it is of great importance that the cessation of the magnetisation with the current should be as complete as possible. Perxmanent and residual magnetism are in fact the same, but the former expression is used when it is desired to retain the magnetism, and the latter when its presence is objectionable. Residual magnetism is greater in long magnets, that is to say, those in which the diameter is small in comparison with the length. Hence for rapid demagnetisation the cores should. be short and thick. A bundle of soft iron wires is more rapidly demagnetised than a massive bar of the same size. Residual magnetism is greater when the magnetising current is not stopped suddenly, as is usually the case, but is gradually brought back to zero by successively introducing increasing resistances. By suddenly stopping the current it has sometimes been found with thick rods of very soft iron, that a reversed magnetisation is met with which is called abnormal magnetisation. ‘This is easily understood from the tendency of molecular magnets to revert to their primitive condition (744\. In doing this they experience a certain friction or resistance, and when the magnetisation gradually diminishes, this hinders any reversal of the molecules ; but when the cessation is sudden, the molecules, from the greater vis véva of their reversal, will sooner come back to their original position, or even pass it, and come to rest on the opposite side. The effects of residual magnetism are lessened by preventing the —905] Electromagnets 909 armature from coming in direct contact with the magnet, either by inter- posing a thin sheet of paper or by providing the cores with brass studs. With uniform magnetisation the portative force of a magnet may be readily calculated. It is expressed by the formula ¢P =27B?S, where P is the mass in grammes, ¢=981, Bis the induction (726) and S the available surface. If 800 is the value of B in C.G.S. units, we get for the portative force about 4 kilos. per square centimetre, which is what is looked for in good specimens of permanent magnets. With soft iron in a strong field values of Io to 12 kilos. are obtained. When an armature is not in contact with the poles the attraction di- minishes very rapidly with the distance ; for in the first place the attraction is inversely proportional to the distance, and then the effect of this distance is to introduce a layer of air which from its very great reluctance greatly lessens the induction in the magnetic circuit. According to the researches of Bidwell, it appears that for low degrees of magnetisation the portative force increased less rapidly than the current strength up to a certain point, at which the field was about 240 units and the load supported 14,000 grammes per square centimetre. From this point the magnetising current and the load increased in the same ratio. When the field had an intensity of 585 units, the greatest weight supported was 15,900 grammes per sq. cm., or 226 pounds per square inch. Joule found that under a magnetising force which he considered sufficient to saturate the iron, but which appears to have been less than Ioo units, the length of an iron bar was increased by g7j4g5- When the bar with its coil was placed in a sort of water thermometer consisting of a glass flask provided with a capillary tube, Joule found, using the same magnetising force as before, that allowing for the expansion of water due to the heat of the current, there was no motion in the capillary tube ; from this he con- cluded that the volume of the iron was un- altered by magnetisation, and also that.since its length was increased, its diameter must have diminished. In Shelford Bidwell’s investigation of these phenomena, a far higher magnetising force was employed (up to nearly 1,500 units), and the results showed that Joule’s conclusions required modification. It was found that if the magnetising force is increased beyond the point at which the magnetic elongation of the A rod is greatest a further change takes place ; the length of the rod, instead of remaining un- aie altered, steadily diminishes. Fora certain value of the magnetising force, the rod resumes its original length, and on further increase of the magnetising force becomes shorter. The diameter of the rod is also changed ; with small forces it is diminished, and with large forces increased, but the longitudinal and transverse changes of dimensions are not often related in such a manner as to leave the volume of the bar unaltered. A magnetising force of 80 or go units has indeed generally no effect upon the volume ; with a smaller ee oe ~QIo Dynamical Electricity [905- force, however, the volume is diminished, while with a larger one it is increased. He also found that as regards magnetic changes of length, the behaviour of a cobalt rod is the reverse of that of an iron one, contracting under small and lengthening under great magnetic forces. A nickel rod is always shortened whether the magnetising force is great or small. In fig. 893 the abscissz represent magnetising forces,and the ordinates the corresponding magnetisations in a soft iron bar. The curve O A repre- sents the magnetisations starting from the magnetising force O and rising to F. The curve ACA’ represents decreasing values of the force from F to —F’, that is, an equal current in the opposite direction ; and, lastly, the curve A’BA represents increasing values from —F to + F. It will thus be seen that the magnetisation of a bar for a given force depends not only on its existing condition, but also on its previous state. The magnetisation is greater in the descending than in the ascending period for the same value of the magnetising force. This is due to residual mag- netisation ; there is a retardation or lag of the magnetisation in respect of the magnetising force to which Prof. Ewing has applied the term Aysteresis. The hysteresis is greater the wider the difference in the two curves. Hys- teresis 1s diminished if the body is submitted to vibrations during the pro- cess of magnetisation. If the circuit be broken while a horseshoe electro- magnet Is supporting even a heavy weight attached to the keeper, it frequently happens that the keeper does not at once become detached ; if now the magnet is gently tapped so as to set the molecules in vibration, the keeper immediately drops, and is no longer attracted when again placed in contact. To destroy residual magnetism, as, for instance, in a watch spring which has accidentally become magnetised by having been under the influence of a strong magnetic field, near a powerful dynamo for example, it should be submitted to a series of magnetising forces in alternate directions gradually decreasing to zero. A bar may also be rendered neutral by being heated to redness and cooled in a horizontal position at right angles to the magnetic meridian. When a soft iron bar is submitted to magnetisations and demagnetisations in rapid succession, its temperature rises. This represents the work of mag- netisation converted into heat. If in the above curve the magnetising force and the magnetisation are expressed in C.G.S. units, the area AB A’C repre- sents the value in ergs of the work so transformed per unit of volume of the iron. The loss may attain 15,000 ergs per cubic centimetre of soft iron for’ each complete cycle. One erg represents 4°17 x 10“ calories (456), and since the density of iron is 7°8, and its specific heat o:11 (467), the calorific capacity of a cubic centimetre is 0'°858. So that, taking the above number, we have 0°0004° as the rise in temperature for each complete cycle. If a bar magnet is suspended by a spring so that its axis is in the prolon- gation of that of the spiral, and the current is now passed, it will be seen that the magnet will be attracted or repelled according as the direction of the current is the same as that of the current in the spiral or not. In the case of attraction, ana if the magnet be not too long and be sufficiently free to move, it will be drawn within the spiral. The force with which the magnet is drawn in is nearly proportional to the strength of the current and to the number of turns of the wire. -907] Vibratory Motion and Sounds produced by Currents git Magnetism is not uniformly distributed in the section of electromagnets ; the external layer exhibits a stronger magnetisation than the inner ones, and with feeble forces there is only a magnetic excitation in the outer layer. The magnetism in solid and in hollow cylinders of the same diameters is the same, provided in the latter case there is sufficient thickness of iron for the development of the magnetisation. With currents below a certain strength, wide tubes of sheet-iron are far more powerfully magnetised than solid rods of the same length and weight ; but with more powerful currents the magnetism of the latter preponderates. 906. Vibratory motion and sounds produced by currents.—When a rod of soft iron is magnetised by a strong electric current, it gives a very distinct sound, which, however, is only produced at the moment of closing or opening the circuit. This phenomenon is due to a vibratory motion of the molecules of iron in consequence of a rapid succession of magneti- sations and demagnetisations. When the circuit is broken and closed at very eNore intervals, De la Rive observed that, whatever be the shape or magnitude of the iron bars, two sounds may always be distinguished ; one, which is musical, corresponds to that which the rod would give by vibrating transversely ; the other, which consists of a series of harsh sounds, corresponding to the interruptions of the current, was compared by De la Rive to the noise of rain falling on a metal roof. The most marked sound is that obtained by stretching, on a sounding-board, pieces of soft iron wire, well annealed, from I to 2 mm. in diameter and Ito 2 yardslong. These wires, being placed in the axis of one or more bobbins traversed by powerful currents, send forth a number of sounds, which produce a surprising effect, and much resemble that of a number of church bells heard at a distance. Rods of zinc, copper, or brass give no note even with strong currents. Wertheim also obtained the same sounds by passing a discontinuous. > w Fig. 894 current through the wires themselves. The musical sound is then stronger and more sonorous in general than in the previous experiment. The hy- pothesis of a molecular movement in the iron wires at the moment of their magnetisation and demagnetisation is confirmed by the researches of Wertheim, who found that their elasticity is then diminished. 907. Reis’s telephone.—The essential features of this instrument (fig. gI2 Dynamical Electricity [907 894) are a sort of box, B, one side of which is closed by a membrane C, while there is a mouthpiece, A, in another side. On the membrane is a piece of thin metal-foil C, which is connected with a wire leading to one pole of the battery G, the other pole of which is put to earth. Just above the foil, and almost touching it, is a metal point D, which is connected by the line wire (908) with one end of a coil of insulated wire surrounding an iron rod, the other end of the wire being put to earth. When the mouthpiece is spoken or sung into, the sounds set the mem- brane in vibration ; this coming into contact with the point D causes a rapid succession of currents to pass into the line and through the electromagnet in which the corresponding sounds are produced. ELECTRIC TELEGRAPH 908. Electric telegraphs.—These are apparatus by which signals can be transmitted to considerable distances by means of voltaic currents propa- gated in metallic wires. Towards the end of the last century, and at the beginning of the present, many philosophers proposed to correspond at a distance by means of the effects produced by electrical machines when pro- pagated in insulated conducting wires. In 1811, Semmering invented a telegraph, in which he used the decomposition of water for giving signals. In 1820, at a time when the electromagnet was unknown, Ampére proposed to correspond by means of magnetic needles, above which a current was sent, as many wires and needles being used as letters were required. In 1834, Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic current transmitted by a wire acted on a magnetised bar, the oscillations of which under its influence were observed by a telescope. They succeeded in thus sending signals from the Observatory to the Physical Cabinet in Got- tingen, a distance of a mile and a quarter, and to en belongs the honour of having first demonstrated experimentally the possibility of electrical communication at a considerable distance. In 1837, Steinheil in Munich, and Wheatstone in London, constructed telegraphs in which several wires each acted on a single needle; the current, in) the first (case being produced by an: electromagnetic machine, and in the second by a constant battery. Every electric telegraph consists essentially of three parts: I, a cévcuit consisting of a metallic connection between two places, and an electromotor for producing the current; 2, a transmitter for sending the signals from the one station ; and, 3, an z#- dicator for receiving them at the other station. The manner in which these objects, more especially the last two, are effected can be greatly varied, and we shall limit ourselves to a description of the three principal methods. On the larger circuits dynamos or accumulators or combinations of the two are used ; on smaller ones where there is constant work some form of a : DD ~909] Electric Telegraph 913 Daniell’s battery is used, and for other circuits Leclanché’s cell is coming into more extended use. In France, Daniell’s battery i used for telegraphic purposes. The connection between two stations is made by means of galvanised i iron wire suspended by porcelain supports (fig. 895), which insulate and protect them against the rain, either on posts or against the sides of buildings. In England and other moist climates special attention is required to be aid to the perfection of the insulation. In towns, wires covered with gutta-percha are placed in tubes laid in the ground. Submarine cables, where great strength is required combined with lightness and high conducting power, are formed on the general type of one of the Atlantic cables, a longitudinal view of which is given in fig. 896, while fig. 897 represents a cross section. Fig. 896 In the centre is the core, which is the conductor ; it consists of seven copper wires, each I mm. in diameter, twisted in a spiral strand and covered with ' several layers of gutta-percha, separated from each other by a coating of Chat- terton’s compound—a mixture of tar, resin, and gutta-percha. This forms the zzsw/ator proper, and it should have great resistance to the passage of electricity, combined with low specific inductive capacity (769). Round the insulator is a coating of hemp, and on the outside is wound spirally a pro- tecting sheath of steel wire, spun round with hemp. At the station which sends the despatch, the line is connected with the positive pole of a battery, the current passes by the line to the other station, and if there were a second return line, it would traverse it in the opposite direction to return to the negative pole. In 1837, Steinheil made the very important discovery that the earth might be used for the return conductor, thereby saving the expense of the second line. For this purpose the end of the conductor at the one station, and the negative pole of the battery at the other, are connected with large copper plates, which are sunk to some depth in the ground. The action is then the same as if the earth acted as a return wire. The earth is, indeed, far superior to a return wire; for the added resistance of such a wire would be considerable, whereas the resist- ance of the earth beyond a short distance is absolutely zz7. The earth really dissipates the electricity, and does not actually return the same current to the battery. 909. Wheatstone and Cooke’s single-needle telegraph. —Phis' . con- sists essentially of a vertical multipher (842) with an astatic needle, the arrangement of which is seen in fig. 899, while fig. 898 gives a front view of the case in which the apparatus is placed. A (fig. 899) is the bobbin, consisting of about 4oo feet of fine copper wire, wound in a frame in two 3.N 914 Dynamical Electricity [909— connected coils. Instead of an astatic needle, Mr. Walter has found it ad- vantageous to use a single needle formed of several pieces of very thin steel strongly magnetised ; it works with the bobbin, and a light index joined to: it by a horizontal axis indicates the motion of the needle on the dial. — SSS —— SS SaS5ssse SSE The signs are made by transmitting the current in different directions through the multiplier, by which the needle is deflected either to the nght or left, according to the will of the operator. The instrument by which this is effected is a commutator or key, G, fig. goo ; its action is shown in fig. 9o1, which also shows on a large scale how two stations are connected. It con- sists of a cylinder of boxwood with a handle, which projects in front of the case (fig. 898). On its circumference parallel to the axis are seven brass strips (fig. 900), the spaces between which are insulated by ivory; these strips are connected at the end by metallic wires, also insulated from each other, in the following manner: @ with 6 and ¢, fwith d,andewithg. Four springs press against the cylinder ; 2 and y are connected with the poles of the battery, #z, with the earth plate, and z with one end of the multiplier, N. When not at work the cylinder and the handle are in a vertical position, as seen on the left of the diagram. The circuit is thus ofem, for the pole springs, x and y, are not connected with the metal of the commutator. But -910] Wheatstone and Cooke's Single-Needle Telegraph 915 if, as in the figure on the right, the key is turned to the right, the battery is brought into the circuit, and the current passes in the following direc- SN tion: + pole, 2’a0’7’M’g’N’, line gf/MuacmE#, earth p’E’m’e’g’y’, — pole. The coils N and N’ are so arranged that by the action of the current the motion of the needle corresponds to the motion of the handle. By turn- ing the handle to the left the current would have the following direction : + pole «’dfm’E’p’, earth PEmcabnMg, p~’9’M’n’'b’a’y’, —pole, and thus the needle would be deflected in the opposite direction. The signs are given by differently combined deflections of the needle as represented in the alphabet on the dial (fig. 898). \. denotes a deflection of the upper end of the needle to the left, and “ a deflection to the right ; I, for instance, is indicated by two deflections to the left, and M by two to the right. D is expressed by right-left-left, and C by right-left-right-left, &c. These signs are somewhat complicated, and require great practice : usually not more than 12 to 20 words can be sent ina minute. The single- needle telegraph was formerly sometimes replaced by the double-needle one, which is constructed on the same principle, but there are-two needles and two wires instead of one, gio. Morse’s telegraph.—The telegraph just described leaves no trace of the despatches sent, and if any errors have been made in copying the signals there is no means of remedying them. These objections are met in the case of the writing telegraphs, in which the signs themselves are printed on a strip of paper at the time at which they are transmitted. Of the numerous printing and writing telegraphs which have been devised, that of Morse, first brought into use in North America, is best known. It 3N 2 Q1Goen yee a Dynamical Electricity “) «[ones has been almost universally adopted on the Continent. In this instrument there are three distinct parts: the vecezver, the sender, and the relay ; figs. QO1, 902, 903, and 904 represent these apparatus. Recetver.—We will first describe the receiver (figs. 901 and go2), leaving out of sight for the moment the accessory pieces, G and T, placed on the right of the figure. The current which enters the indicator by the wire, C, passés into an electromagnet, E, which when the circuit is closed attracts an armature of soft iron, A, fixed at the end of a horizontal lever movable about Fig. gor an axis, x; when the circuit is open the lever is raised by a spring. By means of two screws, # and 7, the amplitude of the oscillations is regulated. At the other end of the lever there is a pencil which writes the signals. For this purpose a long band of strong paper, 4/, rolled round a drum, R, passes between two copper rollers with rough surfaces, w and ¢, and turning in contrary directions. Drawn in the direction of the arrow, the band of paper becomes rolled on a second drum, Q, which is turned by hand. A clockwork motion placed in the box, BD, works the rollers, between which the band of paper passes. The paper being thus set in motion, whenever the electromagnet works, the point strikes the paper, and, without perforating it, produces an inden- tation the shape of which depends on the time during which the point is in contact with the paper. If it only strikes it instantaneously, it makes a dof (-).or short stroke ; but if the contact has any duration, a dash (—) of corre- sponding length is produced. Hence, by varying the length of contact of the transmitting key at one station, the operator produces a combination of dots and dashes at another station, and it is only necessary to give a definite meaning to these combinations. ~-910] Morse’s Telegraph QI7 In order to make an indentation a considerable pressure is required, which necessitates the employment of a strong current, and the newer instruments _ (fig. go2) are based on the use of z7k- writers. The paper band passes close to, but not touch- ing, a metal disc with a fine edge, c, which turns against a small z7zg- voller, a, all pee being rotated by He same mechanism. When the end A is attracted, the bent plate at the other end presses the paper against the disc, which is inked by contact with the ink-roller, and thus produces a mark on the SINGLE NEEDLE. SINGLE | eat Oe ee NEEDLE. | PRINTING. PRINTING. paper, which is either short or long according to the duration of the con- tact. The signs are thus more legible, and are produced by far weaker currents. The same telegraphic alphabet is now universally used wherever tele- graphic communication exists ; and the signals for the single-needle instru- ment (fig. 898) as well as those used for printing have been Fovarliaed so that they now correspond to each other. Thus a Beat of the top of the needle to g18 | Dynamical Electricety [910- the left \_ is equivalent to a dot: and a beat to the right / toa dash. The figure on the preceding page gives the alphabet. The flag signals used in military operations are similarly used. A swing of the flag from its upright vertical position to the right or left has the same bcos as the corresponding motion of the top end of the needle. So, too, long or short obscurations of the limelight used in signalling by night, or of the heliograph (535), correspond to dashes and dots. Sender or key. This consists of a small mahogany base, which acts as support for a metal lever aé (fig. 903), movable about a horizontal axis which passes through its middle. The end @ of this lever is always pressed upwards by a spring beneath, so that it is only by pressing with the finger on the key B that the lever strikes the button x Round the base are three binding screws, one connected with the wire P, which comes from the positive pole of the battery; the second connected with L, the line wire ; and the third with the wire A, which passes to the indicator ; for of course two places in communica- tion are each provided with an indicator and communicator. These details known, there are two cases to be considered. 1. The key arranged so as to receive a message from a distant station ; the end @ is then down, as represented in the figure, so that the current which arrives by the line wire L, and ascends in the metal piece m, descends in the wire a, which leads it to the indicator of the station at which the apparatus is placed. 2. A message is to be transmitted ; in this case the key B is pressed so that the lever comes in contact with the button x. The current of the local battery which comes by the wire P, ascending then in the lever, descends by # and joins the wire L, which conducts it to the station to which the despatch is addressed. According to the length of time during which B is pressed, a dot or dash 1s produced in the receiver to which the current proceeds. ' Relay. In describing the receiver we have assumed that the current of the line coming by the wire C (fig. 902) entered directly into the electro- magnet, and worked the armature A, producing a despatch ; but when the circuit consists of many miles of wire, the current may be too weak to act upon the electromagnet with sufficient force to print a despatch. Hence it is necessary to have recourse to a ve/ay—that is, to an auxiliary electromagnet which is still traversed by the current of the line, but which serves to intro- duce into the communicator the current of a Jocal battery of four or five elements placed at the station, and which is only used to print the signals transmitted by the wire. For this purpose the current entering the relay by the binding screw, L (fig. 905), passes into an electromagnet, E, whence it passes into the earth by the binding screw T. Now, each time that the current of the line $10] Working of Morse’s Telegraph 919 passes into the relay, the electromagnet attracts an armature, A, fixed at the bottom of a vertical lever, 4, which oscillates about a horizontal axis. At each oscillation the top of the lever # strikes against a button 2, and at this moment the current of the local battery, which enters by the binding screw ¢, ascends the column wv, passes into the lever ~, descends by the rod 0, which transmits it to the screw Z: thence it enters the electromagnet of the indicator, and returns to the local battery from which it started. Then, when the circuit of the line is open, the electromagnet of the relay does not act, and the lever Z, drawn by a spring 7, leaves the button A”, as shown in the drawing, and the local current no longer passes. Thus Fig. 904 the relay transmits to the indicator exactly the same phases of passage and intermittence as those effected by the manipulator in the station which sends the despatch. With a general battery of 25 Daniell’s elements the current is usually strong enough at upwards of 90 miles from its starting-point to work a relay. For a longer distance a new current must be taken, as will be seen in the paragraph on the change of current (vzde zz/fra). Working of the three apparatus. The three principal pieces of Morse’s apparatus being thus known, the following is the actual path of the current. The current of the line coming by the wire L (fig. 902) passes at first to the piece T intended to serve as lightning-conductor, when, from the in- fluence of atmospheric electricity in time of storm, the conducting wires become so highly charged with electricity as to give dangerous sparks. This apparatus consists of two copper discs, d@ and f, provided with teeth on the sides opposite each other, but not touching. The disc d is connected with the earth by a metal plate at the back of the stand which supports this lightning-conductor, while the disc fis in the circuit. The current coming by the line L enters the hghtning-conductor by the binding screw fixed at the lower part of the stand on the left ; then rises to a commutator, 7, which conducts it to a button, c, whence it reaches the disc f by a metal plate at the back of the stand ; in case a lightning discharge should pass along the wire, it would now act inductively on the disc d, and emerge by the points without danger to those about the apparatus. Moreover, from the disc f, the 920 Dynamical Electricity [910- current passes into a very fine wire insulated ona tube, ¢. As the wire is melted when the discharge is too strong, it acts as a safety catch (851) ; the electricity does not pass into the apparatus, which still further removes any: danger. Lastly, the current proceeds from the foot of the support to a screw on the right, which conducts it to a small galvanometer, G, serving to indicate by the deflection of the-needle whether the current passes. From this galvanometer the current passes to a key (fig. 903), which it enters at L, emerging at A to go to the relay (fig. 904). Entering this at L, it works the electromagnet, and establishes the communication necessary for the passage of the current of the local battery, as has been said in speaking of the relay. Change of current. To complete this description of Morse’s apparatus, it must be observed that in general the current which arrives at L, after having traversed several miles, has not sufficient force to register the despatch, or to proceed to a new distant point. Hence in each telegraphic station a new current must be taken, that of the Jostal battery, which consists of 20 to 30 Daniell’s elements, and is not identical with the local battery. This new current enters at P (fig. 901), reaches a binding screw which conducts it to the column H, and thence only proceeds further when the armature A sinks. A small contact placed under the lever then touches the button z ; the current proceeds from the column H to the metallic mass BD, whence by a binding screw and a wire, not represented in the figure, it reaches, lastly, the wire of the line, which sends it to the following station, and so on from one point to another. 911. Cowper’s writing telegraph.—This remarkable invention is a true telegraph, in that it faithfully reproduces at a distance an exact facsimile of a person’s handwriting. The following gives a general idea of the principle of the instrument. Two line wires are required, which are severally connected at the re- ceiving station with two galvanometers, whose coils are at right angles to each other. At the sending station is a vertical pencil with two light rods, jointed to it at right angles to each other. One of these contact rods guides a contact piece which is connected by a wire with one pole of a battery, the other pole of which is to earth. This contact piece slides over the edges of a series of contact plates insulated from each other, between each of which and the next a special resistance is interposed, and the last of the contact plates is connected with one line wire. The other contact piece slides over a second series of such plates connected with the other line wire. Let us consider one contact piece alone ; as it moves over the contact ‘plates in one direction or the other, it brings less or more resistance into the circuit, and thereby alters the strength of the current. The effect of this is that the needle of the corresponding galvanometer is less or more deflected. Now the end of this needle is connected by a light thread with a receiving pen, which is a capillary tube full of ink. An oscillation of the needle would produce an up and down motion of the pen, and if simultaneously a band of paper passed under the pen, being moved regularly by clockwork, there would be produced on it a series of up and down strokes. A corresponding effect would be produced by the action of the needle of the other galvano- ~912]} Induction in Telegraph Cables 921 meter, except that its strokes would be backwards and forwards instead of up and down. Now the action of the writing pen is that it varies simultaneously the strengths of the two currents, and they produce a motion of the receiving pen which is compounded of the two movements described above, and which is an exact reproduction, on a smaller scale, of the original motion. The following line is a facsimile. ___ Rowil—socety—Prurkinyton owe — x Fig. 905 Both the paper written in pencil at the sending station and that written in ink at the receiving station move along as the writing proceeds, and the messages have only to be cut off from time to time. Experiments made with this instrument show that it will write through resistances equal to 36 miles of telegraph wire. 912. Induction in telegraph cables—In the earliest experiments on the use of insulated subterranean wires for telegraphic communication it was found that difficulties occurred in their use which were not experienced with overhead wires. This did not arise from defective insulation, for the:better the insulation the greater the difficulty. It was suspected by Siemens and others that the retardation was due to statical induction, taking place be- tween the inner wire through the insulator and the external moisture ; and Faraday proved that this was the case by the following experiments among others. A length of about 100 miles of gutta-percha-covered copper wire was immersed in water, the ends being led into the observing-room. When the pole of a battery containing a large number of cells was momen- tarily connected with one end of the wire, the other end being insulated, and a person simultaneously touched the wire and the earth contact, he obtained a violent shock. When the wire, after being in momentary contact with the battery, was placed in connection with a galvanometer, a considerable deflection was observed ; there was a feebler one 3 or 4 minutes after, and even as long as 20 or 30 minutes afterwards. When the insulated galvanometer was permanently connected with one end of the wire, and then the free end of the galvanometer wire joined to the pole of the battery, a rush of electricity through the galvanometer into the wire was perceived. The deflection speedily diminished and the needle ultimately came to rest at zero. When the galvanometer was detached from the battery and put to earth, the electricity flowed as rapidly out of the wire, and the needle was momentarily deflected in the opposite direction. These phenomena are not difficult to explain. The wire with its thin insulating coating of gutta-percha becomes statically charged with electricity from the battery like a Leyden jar. The coating of gutta-percha through which the inductive action takes place is only 4, of an inch in thickness, and the extent of the coatings (copper wire on the one side, and water on the other side of the dielectric gutta-percha) is very great. The surface of the copper wire amountsso 8,300 square feet and that of the outside coating is four times as much. The potential can only be as great as that of the 922 Dynamical Electricity — [912- battery, but from the enormous surface the capacity, and therefore the quantity (804), is very great. Thus the wires, after being detached from the battery, showed all the actions of a powerful electric battery.. These effects take place, but to a less extent, with wires in air; the external coating is here the earth, which is so distant that induction and charge are very small, more especially i in the long lines. Hence the difficulty in submarine telegraphy. The electricity which enters the insulating wire must first be used in charging the large Leyden jar which it constitutes, and only after this has happened can the current reach the distant end of the circuit. The current begins later at the distant end, and ceases later. The electricity is not projected like the bullet from a gun, but rather hke a quantity of water flowing from a large reservoir into a canal in connection with large “basins which it has to fill as well as it- self. If the electrical currents follow too rapidly, an uninterrupted current will appear at the other end, which in- dicates small differences in strength, but not with sufficient clearness differ- ences in duration or direction. Hence in submarine wires the signals must be slower than in air wires to obtain clear indications. Ther retardation €eia directly as the length and the self- Fig. 906 induction (930) of the line. Bythe use of alternating currents sent bya special form of key—that is, of currents which are alternately positive and negative (933)—these disturbing influences may be materially lessened, and communi- cation be accelerated and made more certain, but they can never be entirely obviated. In the Atlantic Cable, instruments on the principle of Thomson’s reflect- ing galvanometer (844) are used for the reception of signals ; the motions of the spot of light to the right and left forming the basis of the alphabet. 913. Syphon recorder.—Lord Kelvin invented an extremely ingenious instrument called the syAhon recorder, by which the very feeble signals transmitted through long lengths of submarine cable are observed and also recorded. A light rectangular coil of iron s (fig. 906), connected with the line wire by the screws # and g, hangs by a bifilar suspension between the two poles of a powerful electromagnet AB, so that its plane is parallel to the lines of force between the poles. The space inside the coil is occupied by a mass of soft iron f, by which the strength of the fluid is greatly increased. Whena current is passed this coil tends to place itself perpendicular to the lines of force, and is deflected either to the right or the left according to the direction of the current ; its movements are almost dead-beat (843), as the damping is considerable. —914] Duplex Telegraphy 923 A very light capillary tube ¢ dips with its short end in a reservoir of ink, while the other end is in front of a paper ribbon which is moved along at a uniform rate like the ribbon in a Morse’s recorder. In order to get rid of friction against the paper, this ink is electrified, and spurts out in a continuous series of fine drops against the paper, marking on it a straight line so long as no current passes in the coil. The syphon is, however, connected by a system of silk threads with the coil, and according as this is deflected to the right or the left the end of the syphon is deflected too, and traces a wavy line (fig. 907) on the paper, which represents deflections right or left of the central line, that are, in short, the Morse signals (910). Ney fee io aa YU yp a b Cc a € | MWe h z 7 k Z Mm Sk eae hem oct all Foow? oat PY cen 8 Vega co Phe 0 2p g x Ss t ut uv zu ie y z Fig. 907 The electrification of the ink is effected bya small electrostatic induction machine ; this is worked by clockwork, which at the same time pays out the paper ribbon. 914. Duplex telegraphy.—By this is meant a system of telegraphy by which messages may be simultaneously sent in opposite directions on one and the same wire, whereby the working capacity of a line is practically doubled. Several plans have been devised for accomplishing this very important improvement ; no more can here be attempted than to give a general account of the principle of the method in one or two cases. Let m (fig. 908) represent the electromagnet of a Morse’s instrument which is wound round with two equal coils in opposite directions ; these coils are represented by the full and dotted lines, and one of them, which may be called the “ve cozl, is joined to the line LL’, which connects the two stations. The other coil, that represented by the dotted line, which may be called the equating cotl, is in connection with the earth at E by means of an adjustable resistance, or artificial line, R. By this means the resistance of the branch aRE may be made equal to that of the branch aLL’a’. The battery 6 has one pole to earth at E, and the other pole, by means of a Morse key, c, can be connected at a, where the two oppositely wound coils bifurcate. The back contact of the key is also connected with earth. The station at B is arranged in a similar manner, as is represented by corresponding dashed letters. Now when B depresses his key and sends a current into the line, inasmuch as the electromagnet of his instrument is wound with equal coils in opposite directions, the armature is not attracted, for the core is not magnetised be- cause the currents in the two coils counteract one another. Thus, although a current passes from ‘B, there is no indication of it in his own instrument— a condition essential in all systems of duplex telegraphy. 924 Dynamical Electricety [914- But with regard to the effect on A, there are two cases, according as he is or is not sending a message at the same time. If A’s key 1s not down, . then the current will circulate round the core of the electro- magnet and will reach the earth by the ‘path LacE ; the core will therefore become magnet- ised, the arma- ture attracted, and asignal pro- duced in the or- dinary way. Ea If, however, — at the moment at which B has his key down, A also depresses his, then it will be seen that, as the batteries 3’ are exactly alike, their electromotive forces neutralise one another, and no current passes in the line aLL’a’: it is, as it were, blocked. But though no current passes in the line coil, a current does pass at each station to earth, through the equating coil, which, being no longer counterbalanced by any opposite current in the line coil, magnetises the core of the electromagnet, which thus attracts the armature and produces a signal. We have here supposed that A and B both send, for instance, the same currents to line: the final effect is not different if they send opposite currents at the same time. For then, as they neutralise each other in the line LL’, the effect is the same:as if the resistance of the line were diminished. More electricity flows to line from each station through the line coil being no longer balanced by the equating coil ; the current of the line coil preponderates and then works the electromagnet. Hence, in both these cases, each station, so to speak, produces the signal which the other one wishes to send. Another method is based on the principle of Wheatstone’s bridge (986). At each station is a battery P (fig. 909), one pole of which is to earth while the other is connected with the key M. The wire from M bifurcates at A into the two branches AB and AC, between B and C is connected the galvano- meter or the receiving instrument. The branch AB goes to line and AC to earth. There are exactly corresponding parts at the other station. Now, from the principle of the bridge, the resistances AB and AC may be adjusted in such a manner that the potentials at the points B and C are equal when the key is depressed and the current sent ; accordingly, no current passes in the bridge, and the galvanometer is at rest ; but the current from A passing to line bifurcates at B’, traversing the galvanometer and going to earth; hence a signal is received at that station. ~ Sa ee er, -— sw eis ~ aot RERNSS WS an Ais SS SSS Ko. ee Fig. 908 ~917] Bain’s Electrochemical Telegraph 925 Other methods of duplex telegraphy are based on the principle of leakage ; but for these as well as for quadruplex telegraphy, special manuals must be consulted. B Re eae eee 915. Earth currents.—In long tele- graph circuits more or less powerful cur- rents are produced, even when the battery is not at work. This arises from a differ- ence of potential being established in the earth at the two places between which the communication is established. These cur- rents are sometimes in one direction and sometimes in another, and are at times SO powesmlanturrepuianvas: qiite to in- | ee terfere with the working of the lines. “8ser* Senay Lines running NE and SW are most ee frequently affected ; lines running NW and SE are less so, and the currents are far weaker. Their strength often amounts to as much as 4o millamperes (1000), which isa stronger current than is required for working ordinary tele- graph instruments. These currents do not seem to be due to atmospheric electricity, for they cease if a wire is disconnected at one of its ends, and they appear in under- ground wires. According to Wild, they are the prime cause of magnetic storms, but not of the periodical variations in the magnetic elements. 916. Bain’s electrochemical telegraph.—If a strip of paper is soaked in a solution of potassium ferrocyanide and is placed on a metal surface connected with the negative pole of a battery, on touching the paper with a steel pointer-connected with the positive pole, a blue mark due to the forma- tion of some Prussian blue will be formed about the iron, so long as the current passes. The first telegraph based on this principle was invented by Bain. The alphabet is the same as: Morse’s, but the despatch is first composed at the departure station on a long strip of ordinary paper. The paper is per- forated successively by small round and elongated holes, which correspond respectively to the dots and marks. The strip so prepared is interposed between a small metal wheel and a metal spring, both forming part of the circuit. The wheel, in turning, carries with it the paper strip, all parts of which pass successively between the wheel and the plate. If the strip were not perforated, it would, not being a conductor, constantly offer a resistance to the passage of acurrent ; but, in consequence of the holes, every time one of them passes, there is contact between the wheel and the plate. Thus the current works the relay of the station to which it is sent, and traces in blue, on a paper disc, impregnated with potassium ferrocyanide, the same series of points and marks as those on the perforated paper. 917. The sounder.—The sound produced when the armature of the electro- magnet in a Morse’s instrument is attracted by the passage of the current is so distinct and clear that many telegraph operators have been in the habit of reading the messages by the sounds thus produced, and at most of checking their reading. by comparison with the signs produced on the paper. 926 Dynamical Electricity [917— Based on this fact a form of instrument invented in America has come into use for the purpose of reading by sound. The sounder, as it is called, is essentially a small electromagnet on an ebonite base, resembling the relay in fig. 905. The armature is attached to one end of a lever, and is kept at a certain distance from the electromagnet by a spring. When the current passes, the armature is attracted against the electromagnet with a sharp click, and when the current ceases it is withdrawn by the spring. Hence the interval between the sounds is of longer or shorter duration according to the will of the sender, and thus in effect a series of short or long intervals which represent short and long sounds can be produced which correspond to the dots and dashes of the Morse alphabet. Such instruments are simple, easily adjusted, and portable, not occupying more space than an ordinary field-glass. They are coming into extended use, especially for military telegraph work. 918. Electric alarum.—One form of these instruments is represented in fig. gio. On a wooden board arranged vertically is fixed an electromagnet, E ; the line wire is connected with the bind- ing screw, #z, with which is also connected one end of the wire of the electromagnet ; the other end is connected with a spring, ¢, to - which is attached the armature, @; this again is pressed against by a spring, C, which in turn is connected with the binding screw 2, from which the wire leads to earth. Whenever the current passes, which is effected by a small contact-maker called a push, the armature a is attracted, carrying with it a hammer, P, which strikes against the bell Tand makes it sound. The moment this takes place, contact is broken between the armature @ and the spring C, and the current being stopped the electromagnet does not act ; the spring c, however, in virtue of its elasticity, brings the armature in con- tact with the spring C, the current again passes, and so on as long as the current con- tinues to pass. g19. Electrical clocks.—Electrical clocks are clockwork machines, in which an electromagnet is both the motor and the regulator, by means of an electric current regularly interrupted, in a manner resembling that de- scribed in the preceding paragraph. Fig. 911 represents the face of such a clock, and fig. 912 the mechanism which works the needles. An electromagnet, B, attracts an armature of soft iron, P, movable on a pivot, a. The armature P transmits its oscillating motion to a lever, s, which by means of a ratchet, 7, turns the wheel A. This, by the pinion, D, turns the wheel C, which by a series of wheels and pinions moves the hands. The small one marks the hours, the large one the minutes ; but as the latter does not move regularly, but by sudden starts from second to second, it follows. that it may also be used to indicate the seconds. Fig. g1o —920}] | Electromagnetic Motors » O27 It is obvious that the regularity of the motion of the hands depends on the regularity of the oscillations of the piece P. For this purpose, the oscil- lations of the current, before passing into the electromagnet B, are regulated by a standard clock, which itself has been previously regulated by a seconds. iy | ih iH | ! ieee i | iy . i s 1) 4y5 of a degree between the two resistances. It has been used by the inventor to measure the distribution of heat in the solar spectrum. By its means he has been able to map the dark heat of the spectrum, and to extend it far beyond the limits which were previously known. It has also been used in the investiga- tion of electrical vibrations (1002). 996. Divided or branch circuits.—In fig. 1021 the current from a Bunsen’s cell passes from the point g to the point , by two paths, the resistances of which are # and x. By applying Ohm’s law we see at once that the currents in these two branches (¢ in gf and c’ in gx) are inversely proportional to the resistances and x. For, the difference of potential between g and x must be independent of the path by which the electricity travels from the one to the other. Hence if the PD =e, by Ohm’s law ¢ =c x p=c' x x, and therefore:C|c= 9: Fig. 1025 Fig. 1026 —998] Use of Shunts 1035 Let C be the strength of the current in the undivided part of the circuit, there Cacre Eyl ad LE, Epre _ vp prr zat ce AisoeG=c+<¢ Tei 2 = é (3 +=): If # and x are removed and replaced by a single wire of resistance R, such that the value of C, and therefore of e, SSeS qu Fig. 1027 . I is not altered, we must have C= : , therefore ne bed slind generally if two R ee 2 et points are connected by a number of conductors whose resistances are ~, 7, r., &c., the resistances R of all of them taken together, that is the resistance which might replace them, are such that DL ODM SURRY ase Ta hs 997. Use of shunts.—The principle of divided or branch circuits has an important application in shumd¢s, by which any given proportion of even a powerful current may be transmitted through delicate galvanometers, and thus their range is greatly extended.- They consist of a set of resistances usually 4, s4, and géz, of that of the galvanometer, arranged as represented in fig. 1028. G and G’ are in connection with the ter- minals of the galvanometer, and P, P’ with those of the battery. The gaps, O, A, B, C, can be closed by plugs, and thus the corresponding resistances introduced. When they are all open, the entire current would pass through the galvanometer. By plugging O the currentis short-circuited, and none of it passes through the galvanometer. If 2 is the resistance of the galvanometer, s that of the shunt, C the total current, and ¢ that which passes p through the galvanometer and produces the deflection, 4 we may deduce from the laws of branch circuits a+ S ge=s (C—c) or C et oe Ge Fig. 1028 The expression & oe =m is Called the multiplying power of the shunt ; it is the value by which the observed current must be multiplied to obtain the principal current. In the above cases the muitiplying powers are 10, 100, and 1,000 respectively. 998. Blectrieai measuring instruments.—The numerous and important technical applications of electricity have given rise to the invention of 1036 Dynamical Electricity [998— a number of instruments for the direct measurement of electrical currents. ‘The amperemeter, or briefly ammeder, for instance, gives at once the strength of a current in amperes. As a type of these instruments we may take a recent form of that invented by Professors Ayrton and Perry; it depends on the principle that when a portion of an iron core is partly within and partly without a magnetising coil, it is drawn inwards when a current is passed through the coil. The essential feature of the apparatus is a coil of insulated wire, in the axis of which is a spiral attached at one end to an index moving over a graduated scale. At the other end of the spiral is a brass cap to which is attached a thin cylinder of sheet iron, which is in fact the core; it encircles the spiral and projects outside the coil. The spiral itself is formed of a ribbon of thin phosphorus bronze coiled so as to form a very narrow cylinder. This construction gives it the property that unlike ordinary spirals, when its length increases the free end rotates through a considerable distance. Accordingly, when the current passes through the coil, the iron tube is drawn within the spiral to an extent vary- ing with the strength of the current ; this thereby elongates the spiral to which it is attached, and the index attached to the latter moves over the scale, finally taking up a position which depends on the strength of the current. Such instruments are graduated empirically and within any desired range by observing the deflection caused by passing through them currents of known strength. The voltmeter, which is not to be confounded with the voltameter (868), measures the difference of potential between any two points of a circuit. It consists essen- tially of a coil such as the above, but with a great length of long fine wire, offering, therefore, between two points in a circuit a great resistance. This can be inserted as a shunt without appreciably altering the resistance of the circuit. It is empirically graduated like the ammeter. Cardew’s voltmeter depends on the heating effect pro- duced when a current traverses a wire, and consists essen- tially of a long fine platinum wire, stretched by a spring or a weight to which is attached a multiplying motion and an index. This wire, being introduced between the points of the circuit to be measured, becomes heated to an extent proportional to the square of the difference of potentials, and the motion of the index is a measure of this heating. The principle of the electrodynamometer is that of measuring attraction and the repulsion between parallel currents, one of them being fixed and the other movable. Fig. 1029 represents the main features of a form devised by Siemens for measuring the strength of the powerful currents used in electric lighting ; w is a coil of stout copper wire, and w’ a single wire ; m# are mercury cups, and £% binding screws, by which connection is made with the main circuit LL. The wire w’ is surmounted by a stout spiral spring, which is connected at one end with this wire, and at the other with a screw, s; the latter is pro- Fig. 1029 ~999] Absolute Electrical Units 1037 vided with an index, z, which moves over a graduated scale, S. An index, 22’, is also fixed to the wire w’. At the outset both indexes point to zero ; when the current passes it will be seen from the direction of the arrows that it traverses the fixed and movable coils in opposite directions, and the point z’ is displaced along the scale. By turning the screw s it is brought back to zero, in doing which the index ¢ is moved through an angle which is a measure of the torsion of the spiral spring f, and this angle is proportional to the square of the strength of the current by which the movable coil is deflected. This electrodynamometer has by no means the sensitiveness which can be readily obtained with ordinary galvanometers ; but it has the advantage that its indications are independent of the external magnetic field, and when the two coils are traversed by the same current they are also independent of the direction of the current, and can accordingly be used with advantage in measuring alternating currents. An electrodynamometer devised by Giltay on a principle first introduced by Bellati is remarkable for its great sensitiveness. A bundle of fine iron wires hangs by a bifilar suspension inside the coil of a multiplier, the plane of which is at an angle of 45° with the magnetic meridian. The bundle itself is at an angle of 45° with the plane of the coils, and is thus at right angles to the magnetic meridian. When alternating currents are passed through the coil they magnetise the wires with alternate poles, so that the bundle is always deflected in the same direction. The deflections are read off by a mirror and scale, and when small are directly proportional to the square of the current. The apparatus is so sensitive that deflec- tions of 18 cm. on the scale are produced by the currents of an ordinary telephone. 999. Absolute electrical units——The great importance of having a uniform system of measurements of physical magnitudes which should be universally adopted is at once obvious, and has been more especially felt in the applications of electricity. The first step in this direction was taken by the British Association, which adopted the system of absolute units known as the C.G.S. system, of which mention has already been made (62, 729), and which this account is intended to supplement. The essence of an absolute system of physical measurements is that the various units may be directly expressed in terms of the fundamental units (62) of length, time, and mass. A system of absolute electrical units may be based on either the electrostatic the electromagnetic, or again on the electrodynamic actions. There is no theoretical reason why one should be preferred to another of these, but in practice only the former two are used. Of these the electrostatic system is perhaps the simpler, but that based on electromagnetism is most convenient, and best lends itself to the practical determination of the most important standards, such as those of electromotive force and resistance. Electrostatic Units We shall distinguish these units by small letters placed in brackets. Quantity of Electricity. g. Coulomb’s law gives for the repulsive force Loss Dynamical Electricety [999- 9 ~ between two equal quantities g, of electricity at the distance 7, f= a (756), from which g=/,/f Hence we have for the dimensions of unit quantity of electricity [g]=Z*#= L2M!T-. Potential. v. The potential at a point distant / from g,a quantity ‘of electricity, is the quotient of the quantity by the distance. Hence [v] =7 os L?M?T}. Capacity. c. The capacity of a conductor is the quotient of the quantity of electricity with which it is charged, by the potential which this quantity produces in it; [<]=% from which [¢]=L. Accordingly the capacity of a conductor is expressed by a length. Unit capacity is thus that of a body which is raised by unit quantity to unit potential. An insulated conducting sphere which has a radius of one centimetre has unit capacity. Current. t. The strength of a current is the quantity of electricity which passes in a given time; [‘]=2 =L3M?T*. Therefore unit current is that which conveys unit quantity of electricity in a second. Resistance. ry From Ohm’s law (847), the resistance of a conductor is the quotient of difference of potentials at the two ends of a wire by the strength of a current. Hence [7] =” —L-'T, which shows that the dimen- 2 sions of resistance are the inverse of a velocity. Electromagnetic Units 2 ‘ “ Quantity of magnetism. From Coulomb’s law /= - , where M equals'a quantity of magnetism at a point, or strength of magnetic pole, from which [M]=L? ®M!T-+—that is, the same as that of quantity of electricity on the electrostatic system. Unit magnetic pole is that which repels an equal pole at a distance of a centimetre with a force of a dyne. Magnetic Field. H. Unit magnetic fluid is that field in which unit quantity magnetism is acted on by unit force. Hence F = HM, from which he) =e Current. 1. The unit of electrical current in the electromagnetic system is that which, traversing unit length of an arc of a circle of unit radius, exerts unit force on unit pole, or unit magnetism at its centre. Its dimensions are Pie Mr, Quantity of electricity. Q. The quantity of electricity conveyed by a con- ductor is the product of the current by the time that it lasts. Hence unit quantity is that which passes in a second in a conductor in which unit current is flowing, [Q]=IT = L3Mé. Resistance. ®. The resistance of a conductor may be defined by Joule’s law, W=l?RT. Hence [R]=<—that is, the resistance of a conductor is expressed by a velocity. Electromotive force. Difference of potentials [E]. From Ohm’s law, E=IR=L3MiT~. 1000] Practical Untts 1039 1000. Practical units.—The values of the absolute units in the C.G.S. system are not convenient for measuring the magnitudes which ordinarily occur. Thus the absolute unit of resistance is that represented by the twenty-thousandth part of a millimetre of pure copper wire a millimetre in diameter. It has therefore been necessary to choose units better suited for practical uses, and at the International Congress of Elec- tricians at Paris in 1881 an International Commission was formed for the purpose 9f deciding on such units and deter- mining their value. In 1892 a Committee of the Board of Trade agreed to recommend the following, which are in the main those originally introduced by the British Association. The practical unit of resistance is equal to 10° absolute electromagnetic C.G.S. units of resistance, and 1s called the Ohm. It has been decided to represent it by a column of pure mercury of uniform section 106°3 cm. in length at 0° C., and with a mass of 14°521 grammes. Copies of this standard may be made either in mercury (fig. 1030) or in wire (fig. 1029), and each copy-has the value marked upon it, which is correct for a certain temperature. A wire of pure copper, a millimetre in diameterand 46°25 metres in length, has a resistance of one ohm. Siemens’s unit (983) has a resistance of 0°94339 ohm. The copper conducting wire of an ordinary submarine cable has a resistance of about 11 ohms per mile. In order to express multiples and submultiples the prefixes mega and micro are used, which are respectively a million times as great or as small. Thus a megohm is 10° ohms—that is, 10 absolute units of resistance. In like manner a microhm is 10° ohm—that is, 10? = 1,000 such units. The Volt is the practical unit of electromotive force or of difference of potentials, and is equal to 10° absolute units. From the difficulty of getting an element which is perfectly constant, more especially when it is closed, the standard of E.M.F. is best derived from measurements of resistance and of strength of current, which are both convenient and very accurate. Com- pared with the electrostatic unit of potential the volt is very small, being only 34,5 of such a unit. The Board of Trade Committee takes the Clark cellstandard of electromotive force as equal to 1°434 volt ; so that ies electromotive force of Clark cell at 15° C. 1°434 The Amfere is the unit of current, and is the current produced by the electromotive force of a volt in a circuit having a resistance of an ohm. It is therefore equal to 10! C.G.S. units. It is equal to the current that can deposit o‘001118 gramme of silver per second from a neutral solution of silver nitrate. A mzllampere is the thousandth of an ampere. The resistance of a Daniell’s element with an external cylinder of zinc, 8 inches high and 34 in diameter, surrounding the porous pot, is about 1°3 ohm, and taking its E.M.F. at 1°08 volt, its current when on short circuit is about o°8 ampere. In like manner a medium-sized Bunsen has a resistance of about o'r ohm, and as its E.M.F-. is 1°8 volt, the current on short circuit is 18 amperes. A Brush machine the current of which ignited 16 arc lamps in series had an E.M.F. of 839 volts ; its internal resistance was 10°55, and 1040 Dynamical Electricety {1000- the external, including the lamps, was 73 ohms. Accordingly the current was 10°64 amperes. A Holtz machine has in electromagnetic measurement an E.M.F. of 90,000 volts ; its internal resistance, when it makes two turns — in a second, is calculated at 27 x 10° ohms ; thus its current is sg4y55 of an ampere, or ;'5 of a millampere. Sucha current is too weak for telegraph work ; the currents used with the ordinary Morse receivers have a strength of 14 to 16 millamperes. The Coulomé is the unit of quantity of electricity, and is that quantity which traverses the section of a conductor in a second, when a current of an ampere is passing through it. A coulomb of electricity in traversing an electrolyte decomposes a weight of the body expressed by 000001038 of its chemical equivalent. The electric energy expended when a coulomb of electricity falls in potential by one volt is a called a Joule. _ Its value in C.G.S. units is 107 x 10° = 10/.ergs. The Farad is the unit of capacity, and is such that in a condenser of that capacity the quantity of a coulomb produces a difference of potential of a a volt. It is 10% C.G.S. units. The farad is far too large a unit for practical use ; thus the capacity of the globe is only 0:000636 of a farad, that of the Sun does not amount to a farad. Accordingly the technical unit of capacity is the millionth part of the farad, and p is called the mzcrofarad. This is to” absolute units. A Leyden jar with a total coated surface of a square metre, the glass of which is 1 mm. thick, has a capacity of »+; of a microfarad. The capacity of an ordinary submarine cable may be taken at about 4 of a microfarad per £vzof or nautical mile of 1852 metres. A sphere nine kilometres in radius has a capacity of a microfarad. The practical standards consist of circular or square sheets of tinfoil with projecting tongues, a and a’ (fig. 1031), fastened on thin sheets of mica. Be- tween each such coated sheet is placed an uncoated one of mica, the two sets of tongues being severally connected with each other, and thus the coatings represent the coated surfaces of a condenser. The whole is en- closed in a box ; a condenser having a capacity of a microfarad will repre- sent a coated surface of over 6 square yards. Wati.—The energy, W, of an electrical current in unit time may be 2 variously expressed ; thus W =C?R= = =CE. This latter expression is the al a th ua Fig. 1031 most convenient for practical purposes ; if the factors which express the watt are given in practical units, it represents the work done per second by unit current (ampere) when impelled by an E.M.F. of a volt. It is thus a wolt- ampere, and on the proposal of the late Sir W. Siemens has been called a watz. If the factors are given in absolute units, V A is equal to 107 ergs per second. It may also be defined as the work done by the quantity of electricity of a coulomb falling through a difference of potentials equal to a volt, and in this form the definition is closely analogous to that of a kilogramme metre. The watt is -4, of an English horse-power, or one horse-power = 746 watts. -1001] Relation of Electrostatic to Electromagnetic Unit 1041 The French cheval-vapeur of 75 kilogramme-metres or 542°4 foot-pounds per second is equal to 736 watts. In addition to the above, a practical unit of inductance has been adopted, and is called the hezry. The self-inductance of a circuit is one henry, if an opposing electromotive force of one volt results from a variation of the strength of current in the circuit at the rate of one ampere per second. The mutual inductance of two circuits is one henry if an electromotive force of one volt in one of them results from a variation of the strength of current in the other at the rate of one ampere per second. The value of the henry in C.G.S. measure is consequently 10°. 1001. Relation of the electrostatic to the electromagnetic unit.—If we compare the dimensions of the units of quantity and of the other electrical magnitudes in the electrostatic with those of the corresponding dimensions as expressed in the electromagnetic system, we find that the ratios are independent of the unit of mass, and that = that is, the expression of a velocity, always enters into the ratio between them. Now the ratio of the two sets of units may be determined experimentally. Suppose’ that a con- denser is charged with electricity. Its dimensions being known, the quantity, g, of the charge may be determined in electrostatic measure, by measuring, for instance, the repulsion which a given proportion of the total charge produces in a torsion balance of known dimensions. The same con- denser, being charged to the same extent, may be discharged through a galvanometer, and by measuring the deflection produced, and knowing the constants of the instrument, we may obtain the quantity in electromagnetic units, and thus the ratio of the quantity expressed in the two sets of units may be deduced. Or, again, the E.M.F. of a Daniell’s cell may be measured first by the aid of an absolute electrometer (803), which will give in electro- static units of potential about 070036. On the other hand, the potential determined in electromagnetic measure has the value 1°088 x 10°, Hence it would thus be found that in round numbers the electromagnetic unit of quantity is equal to 3 x 10° electrostatic units of quantity. This can be understood if we consider that the latter is the quantity of electricity which attracts or repels another equal quantity at a distance of I cm. with a force of a dyne, while the former is the quantity which traverses the wire in a second when the current has unit intensity. Similarly, by making deter- minations of the ratio in all cases in which the same magnitude may be determined in electrostatic as well as in electromagnetic measure, it is found that the agreement in the numbers found is very close, and that the mean of the best results is 2.9857 x 10'°. As the ratio between the units is always of the dimensions of a velocity, and holds under the condition that the centi- metre is the unit of length, and the second is the unit of time, this velocity is 298,570 kilometres, or 185, 530 milesinasecond. Nowthis ee agrees very closely with that which has been experimentally found for the velocity of light—185,420 miles (519). We may illustrate the relation between the two units as follows. Suppose a ring with a uniform charge of one electrostatic unit on each unit of length, the centimetre ; if this is rotated about its own axis, it carries with it a certain ‘ 3x 1042 Dynamical Electricity [1001— charge of electricity in the same way as a current in a ring at rest would do ; this has been shown by Rowland by direct experiment. The number wv expresses the velocity with which the unit of length of ring must be rotated so as to produce the electromagnetic unit of quantity. This, as we have seen, is practically equal to that of light, namely 300,000 kilometres per second. It expresses the number of electrostatic units which the electromagnetic unit carries through each section of the conductor in unit time. Hence the quantity of electricity represented by the electro- magnetic unit is exceedingly great in comparison with the electrostatic unit, and thus the current of a Holtz machine, for instance, produces very slight action on the galvanometer. 1002. Electromagnetic theory of light.—Faraday, discarding the idea of action at a distance, considered that electrical forces are transmitted through an elastic medium, and that this was the luminiferous ether (651) Maxwell, starting from these ideas, was led to the development of his electromagnetic theory of light ; this theory requires that an electromagnetic wave motion must be transmitted with a velocity represented by the ratio of the electrostatic to the electromagnetic unit of quantity of electricity ; this, as we have seen, is equal to the velocity of light. Now, if luminous and electromagnetic waves are transmitted in one and the same medium and with the same velocity, it is natural to suppose that they are identical in kind. The theory also requires the relation between the refractive index of a body and the dielectric constant which we have already found to exist (769). These theoretical previsions of what is known as the ‘ Faraday-Maxwell’ theory received a striking confirmation in a most remarkable and beautiful series of experiments by the late Professor Hertz, of which we can only give an outline of some of the principal results. . In order to demonstrate that light is essentially an electromagnetic phenomenon, it would be necessary to produce, with a vibratory motion of a purely electromagnetic origin, the same class of phenomena as can be produced with ordinary light, such, more especially, as interference and re- fraction. The difficulty is the great length of the waves with which we have to deal; for from the laws of wave motion (256), if the frequency of the electrical oscillations were even as great as ten thousand in a second, that would represent a wave-length of 30 kilometres, and for a wave-length of 3 metres the duration should not be greater than the hundred-millionth of a second. Now in the discharge of a Leyden jar, or the still more rapid one which takes place between the ends of the secondary wire of a Ruhmkorff’s coil, the duration of the oscillation is comprised within the ten-thousandth and the hundred-thousandth of a second. Hertz devised an apparatus which he calls a wzébrator or discharger for obtaining by continuous but very rapid electrical oscillations, true vays of electrical energy. "Two spheres or plates of metal, AA’ (fig 1032), are pro- vided with straight metal rods with small knobs at the end, the distance, C, of which can be adjusted. The rods are in connection with the poles of a small Ruhmkorff’s coil B, which charges the two spheres to different potentials, and a spark passes at C. This spark, by heating the air, forms, as it were, a path for the subsequent oscillations, and the vibrator now -1002] Electromagnetic Theory of Light 1043 discharges itself independently, as if it were detached from the coil, forming between the discharges of the Ruhmkorff a series of oscillations of ex- treme rapidity. Theory shows that if the resistance of the circuit is so small as to be neglected, the period, Zz, of such an oscillation is proportional to the square root of the capacity, and the coefficient of self-induction, ¢= 27./ LC ; and accord- ingly by suitably choosing the dimen- sions of the apparatus it has been pos- sible to obtain electrical oscillations with a frequency of 5 x Io! in a second, re- presenting a wave-length of 6cm. This is still 12,000 times that of light. If a wire frame is connected with one of the spheres, as shown on the right of the figure, the potentials are equal at a and 8, and no spark passes between them. But if the connection is made asymmetrically, as shown in the left —that is to say, is nearer one knob than the other—there is a difference of potential, and very minute sparks pass continuously. If we have a vibrating tuning-fork producing sound waves therefore, and we approach to it a body tuned in unison with the fork, the body in question begins to vibrate also; such bodies, as we have seen, are called resonators (259). In order to investigate the distribution of electrical waves inthe region about a vibrator, Hertz used what he calls an electrical resonator. This consists (fig. 1033) of a wire ring, one end terminating in a point and the other in a knob, which by a micrometric arrangement, not shown in the figure, may be kept at any desired distance. The dimensions of the frame are adjusted—czuned as it were—so that its oscillations synchronise with those of the vibrator. If now the resonator is placed with its axis parallel to the axis of the vibrator—that is, to the line joining a and 8—positions are found in which a flow of minute sparks passes between the ends of the resonator; their quantity and strength diminish as the distance from the vibrator increases, but are per- ceptible at even 50 or 60 feet. These waves are transverse to the direction of propagation, as appears from the fact that when in a given position the resonator is giving sparks, it ceases to do so when turned at right angles. When the vibrator works well the whole room is pervaded by electrical waves, and by varying the position and distance of the resonator in reference to the vibrator, it is possible to plot out the exact form of the wave motion in the field. Sparks can be taken between any two pieces of metal ; by presenting a penknife to a gaspipe and the like. These electrical waves pass through ordinary conductors, such as a door or a wall, but are reflected from a conducting surface. If the vibrator is ° eye swe pAL B0G a Fig. 1033 1044 Dynamical Electricity [1002-- placed at a suitable distance in front of a large sheet of metal, the waves are reflected from the wall, and interfering with incident rays give rise to stationary waves made up of nodes and loops at regular intervals, quite analogous to the corresponding acoustical phenomenon. This may be demonstrated by means of the resonator, which gives no spark if placed at a node, but does so if in a loop. If the metal is a perfect conductor, there is formed a node at the reflecting surface and others at equal distances. This is analogous to the case of a stopped pipe. | If the vibrator is placed in front of a tall cylindrical metal reflector with a parabolic section (fig. 1034), the effects produced are more pronounced, and can be per- ceived at a greater distance than before. A mass of = = electrical rays parallel to the focal line is formed, and —- the experiment of the conjugate mirrors (427) may be repeated. An insulating screen placed between the two mirrors does not stop the action, but a conducting screen does. It forms an électrical shadow. The electrical rays undergo a refraction on passing from one medium to another. This Hertz demonstrated by means of a huge prism of pitch, weighing about half a ton, 5 feet in height, with a refracting angle of 30°, and with a face of over a square yard. When the rays, rendered parallel by the mirror, fell on this, they were deflected towards the base, and by means of the resonator the position of minimum deviation could be obtained, and thus the refractive index was found to be 1°69 ; the optical refractive index is between 1°5 and 1°6. _ By allowing electrical rays to fall on a plane reflecting surface, part are absorbed and part reflected, and it is readily shown that the angle of reflec- tion, as with light and heat, is equal to the angle of incidence (523). If the electrical rays concentrated by a mirror fall on a grating formed of parallel copper wires, it is found that when the grating is in the direction of the rays—that is, when the wires are parallel to the focal line of the mirror —they are transmitted, but are stopped when the wires are turned at right angles to the direction. This is a phenomenon of polarisation ; the grating acts in regard to the rays like a tourmaline in respect of plane polarised light (680). In another experiment Hertz reproduced the phenomena of diffraction (660). He also showed that electrical waves can exert a mechani- cal action by causing them to strike against a small tube of gold paper very delicately suspended. A straight insulated wire fixed perpendicularly to the centre of a metal plate placed close to one of the knobs of the discharger is traversed by waves which, reflected from the end of the wire, also give rise to stationary vibrations. The distance from one node to another is constant, whatever be the nature of the wire, and this value is the same as for air. It follows from this that the propagation takes place through the air, and not through the wire. We might infer from the extreme rapidity of the oscillations that the phenomenon does not penetrate beyond the surface of the wire. Hertz demonstrated this directly by the following arrangement (fig. 1035). The Fig. 1034 -1002] Electromagnetic Theory of Light 1045 wire is cut at A, and the gap is enclosed in a kind of cage made of metal wires stretched between two discs, a and. The disc a is in contact with the wire ; the disc 8 is supported by a tube yé, which surrounds the wire, but does not touch it. As the waves arrive in the direction of the arrow, there is no spark at A if the tube is connected at 6 with the wire ; the electrical action stops at the outer surface. The sparks reappear, however, if the tube is insulated at 6; the oscillations travel through the dielectric between the wire and the inner surface of the tube. Hertz’s experiments have been reproduced by many observers, and with other resonators.and modifications in the way of experimenting. Dragoumis found that Geissler’s tubes were well fitted for this purpose. Lecher’s method of investigation is convenient. The vibrator is formed of two metal plates, rf & g E | ! iS yr" Ae Fig. 1036 ab (fig. 1036), connected with the terminals of a Ruhmkorff’s coil as in fig. 1032, opposite which are two similar ones, a’d’; from these pass long wires, s¢ s’/’, parallel from s to 4, which are tightly stretched by means of strings. If a Geissler’s tube g with or without electrodes is placed across the wires, it becomes luminous. If now a metal wire, xx’, is placed across, the luminosity ceases, but by moving the cross wires backwards or forwards, positions are found in which it again appears. These positions represent the nodes. According to Lecher, this is a phenomenon of electrical resonance ; a principal vibration is formed from a@ sxx’s’b’, which by induction produces secondary vibrations in the rest of the wire. If a portion of each of the wires is cut off, the resonance is disturbed, the tube is dark, and to restore the luminosity the bridge xv’ must be moved nearer to F’; the amount of displacement’ is half the length of the pieces thus cut off. “i 1046 Dynamical Electricity [1002- If a sheet of tinfoil is attached to each end, this increases the capacity ; the period of the vibration is increased, the wave-length greater, and to keep the tubes luminous the cross wires must be moved nearer the ends ¢#’.. This leads to a method of determining capacities and dielectric constants by means of very rapid vibrations. The apparatus furnishes also a ready means of determining the electrical wave-length. In certain experiments with a period of vibration of the hundred-thousandth of a second, the distance of two consecutive nodes, or half a wave-length, was found to be 1°4 m., so that from the formula (256) this gives for the velocity of electricity 280,000 kilometres—that is, virtually the same as that of light (519). The velocity is the same whatever be the nature of the wires used, from which it follows that the transmission is effected by the surrounding medium and not by the wire itself. All these experiments show that the analogy is complete between the waves of light and of electricity, and we are led to the conclusion that elec- trical, thermal, and luminous phenomena have one and the same origin, which is a vibratory motion of the ether, and that they only differ in the length of the waves. The wave-length of the longest visible rays is about o’00005 cm., that of the longest dark thermal ray hitherto observed is 0°003 cm., while the shortest electrical wave is 50cm., or a million times that of light. These experiments lead to a fundamental change in our views as to the way in which the electrical current is transmitted. It has hitherto been considered that when the circuit is closed the wire itself is the agency by which the current is transmitted. We must for the future consider that the surrounding medium, the ether, transmits the electrical energy, and that this energy enters the wire from the outside; it is there destroyed as electro- magnetic energy, but is converted into heat, which heat travels by radiation from layer to layer like changes of temperature in a conductor. The less rapidly electrical forces change their direction in the medium the more com- pletely does heat penetrate the wire ; when the change takes: place many million times in a second the interior of the wire is not affected by the current. This is analogous to the case of a body which is subject to excessively rapid alternations of heat and cold. 1003. Telegraphing without wires.—In connection with these researches some account may be given of recent experiments on establishing telegraphic communication between two places without employing connecting wires. These experiments depend on using Hertz waves to produce signals accord- ing to a conventional code, and the practical arrangements consist simply of convenient means of producing waves at one station, and of detecting their arrival at the other. The ¢vansmitter or sender (910) is an ordinary Morse signalling key interposed in the circuit with a battery and the primary of an induction coil, the secondary terminals of which are connected with two carefully insulated metal balls at a small distance from each other. By depressing the signalling key for a longer or shorter period, series of sparks of corresponding duration pass between the balls, these longer or shorter intervals representing the ordinary signals of the Morse telegraph (910). The vecezver is an application of an experiment made by Branley. He formed a circuit of a Daniell’s cell, a glass tube containing iron filings with -1003] Telegraphing without Weres 1047 suitable connections, and a galvanometer: on closing the circuit no current passed. When, however, the spark of an electrical machine or of a Leyden jar was produced in the neighbourhood of the tube, the needle of the galvano- meter was powerfully deflected, indicating the passage of a current. When the tube containing the iron filings is gently tapped the current ceased to pass, but did so when a spark was again produced, and so on. What is the action of the spark cannot perhaps be exactly stated ; the effect is as though it enormously diminishes the resistance of the tube: the particles of iron in the original condition being separated by a non- conductor, air, the resistance is very great, but if the minute film of air between the neighbouring particles is broken down by the passage of an infinitesimal spark a permanent current can pass. Lodge supposes that the effect of the spark is to bring the particles in actual electrical contact, and to make them cohere, and the term coherer by which he designates this apparatus is that by which it is now known. In signalling, the coherer is placed in the focal line of such a mirror as that represented in fig. 1034, and is connected up with a battery and a Morse or other receiving instrument. When the key is depressed and sparks produced between the balls, the electromagnetic waves, falling on the coherer, affect it so that the current passes and a signal is produced. In order to interrupt this current and to restore the coherer to its original condition so that it may be ready to receive another signal, the tube must each time be gently tapped ; this is done by the tongue of an electromagnetic arrangement worked automatically by the current itself. In this way distinct signals have been sent through such great distances as nine miles. 1048 Dynamical Electricity [1004— Cot Ad lx. ANIMAL ELECTRICITY 1004. Muscular currents.—The existence of electrical currents in living muscle was first indicated by Galvani, but his researches fell into oblivion after the discovery of the voltaic pile, which was supposed to explain all the phenomena. Since then, Nobili, Matteucci, Du Bois Reymond, and others, have shown that electric currents do exist in living muscles and nerves. For investigating these currents it is necessary to have a delicate gal- vanometer, and also electrodes which will not become polarised or give a current of their own, and which will not in any way alter the muscle when placed in contact with it ; the electrodes which satisfy these conditions best are those of Du Bois Reymond, as modified by Donders. Each consists of a glass tube, one end of which is narrowed and stopped by a plug of paste made by moistening china-clay with a solution of common salt ; the tube is then partially filled with a saturated solution of zinc sulphate; and into this dips the end of a piece of thoroughly amalgamated zinc wire, the other end of which is connected by a copper wire with the galvanometer; the moistened china-clay is a conducting medium which is perfectly neutral to the muscle, and amalgamated zinc in solution of zinc sulphate does not become polarised. 7 1005. Currents of muscle at rest.—In describing these experiments the surface of the muscle is called the zatural longitudinal section ; the tendon the watural transverse section; and the sections obtained by cutting the muscle longitudinally or transversely are respectively the artificial longitu- dinal and artificial transverse sections. If a living irritable muscle is removed from a recently killed frog, and the clay of one electrode is placed in contact with its surface, and of the other with its tendon, the galvanometer will indicate a current from the former to the latter ; showing, therefore, that the surface of the muscle is positive with respect to the tendon. By varying the position of the elec- trodes, and making various artificial sections, it is found— 1. That any longitudinal section is positive to any transverse section. 2. That any point of a longitudinal section nearer the middle of the muscle is positive to any other point of the same section farther from the centre: 3. In any artificial transverse section any point nearer the periphery is positive to one nearer the centre. 4. The current obtained between two points in a longitudinal or in a transverse section is always much more feeble than that obtained between two different sections. 1005] Currents of Muscles at Rest 1049 5. No current is obtained if two points of the same section equidistant from its centre are taken. 6. To obtain these currents it is not necessary to employ a whole muscle, or a considerable part of one, but the smallest fragment that can be experi- mented with is sufficient. 7. If a muscle is cut straight across, the most powerful current is that from the centre of the natural longitudinal section to the centre of the arti- ficial transverse ; but if the muscle is cut across obliquely, as in fig. 1037, the most positive point is moved from c towards J,and the most negative from d towards a (‘currents of inclination’). To explain the existence and rela- tions of these muscular currents, it may be supposed that each muscle is made up of regularly disposed electromotor elements, which may be re- garded as cylinders whose axes are parallel to that of the muscle, and whose sides are charged with positive and their ends with negative electri- city ; and, further, that all are suspended and enveloped in a conducting medium. In such a case (fig. 1037) it is clear that throughout most of the muscle the positive electricities of the opposed surfaces would neutralise one another, as would also the negative charges of the ends of the cylinders ; so that, so long as the muscle was intact, only the charges at its sides and ends would be left to manifest themselves by the production of electromotive phenomena; the whole muscle being enveloped in a conducting stratum, a current would constantly be passing from the longitudinal to the transverse section, and, a part of this being led off by the wire circuit, would manifest itself in the galvanometer. This theory also explains the currents between two different points on the same section ; the positive charge at 4, for instance (fig. 1038), would have more resistance to overcome in get- ting to the transverse section than that at d@, therefore it has a higher potential ; andif éandd are connected by the electrodes, 6 will be found positive to d, and a current will pass from the former to the latter. What are called currents of tnclina- tion are also explicable on the above hypothesis, for the oblique section can be repre- sented as a number of elements arranged as in fig. 1039, so that both the longitudinal surfaces and the ends of the cylinders are laid bare, and it can thus be regarded as a sort of oblique pile whose positive pole is towards 6 and its negative at a, and whose current adds itself algebraically to the ordinary current and displaces its poles as above mentioned. A perfectly fresh muscle, very carefully removed, with the least possible contact with foreign matters, sometimes gives almost no current between its different natural sections, and the current always becomes more marked after Fig. 1038 IO50 Dynamical Electricity [1005- the muscle has been exposed a short time; nevertheless, the phenomena are vital, for the currents disappear completely with the life of the muscle, sometimes becoming first irregular or even reversed in direction. 1006. Rheoscopic frog. Contraction without metals.—The existence of the Sereculat currents can be manifested without a galvanometer, by using another muscle as a galvanoscope. Thus, if the nerve of one living muscle of a frog is dropped sud- denly on another living muscle, so as to come in contact with its longi- tudinal and transverse sections, a contraction of the first muscle will occur, due to the stimulation of its nerve by the passage through it of the electric current derived from the surface of the second. 1007. Currents in active muscle.—When a muscle is made to contract there occurs a sudden diminution of its natural electric current, as indicated by the galvanometer. This is so instantaneous that, in the case of a single muscular contraction, it does not overcome the inertia of the needle of the galvanometer ; but if the contractions are made to succeed one another very rapidly—that is, if the muscle is ¢e¢anzsed (849)—then the needle swings steadily back towards zero from the position in which the current of the resting muscle had kept it, often gaining such momentum in the swing as to pass beyond the zero point, but soon reverting to some point between zero and its original position. The negative variation in the case of a simple muscular contraction can, however, be made manifest by using another muscle as a rheoscope ; if the nerve of this second muscle is laid over the first muscle in such a position that the muscular current passes through it, and the first muscle is then made to contract, the sudden alteration in its strength of the current stimulates the nerve laid on it (849), and so causes a contraction of the muscle to which the latter belongs. The same phenomenon can be demonstrated in the muscles of warm- blooded animals ; but with less ease, on account of the difficulty of keeping them alive after they are laid bare or removed from the body. Experiments made by placing electrodes outside the skin, or passing them through it, are inexact and unsatisfactory. 1008. Electric currents in nerve.—The same electrical indications can be obtained from nerves as from muscles—at least, as far as their smaller size will permit ; the currents are more feeble than the muscular ones, but can be demonstrated by the galvanometer inasimilar way. Negative varia- tion has been proved to occur in active nerve as in active muscle. The effect of a constant current passed through one part of a nerve on the amount of the normal nerve-current, measured at another part, has already been described (849). 1009. Electrical fish.—Electrical fish are those fish which have the re- markable property of giving, when touched, shocks like those of the Leyden jar. Of these fish there are several species, the best known of which are the torpedo, the gymnotus, and the silurus. The torpedo, which is very common Fig. 1039 -1009] Electrical Fish 1051 in the Mediterranean, was carefully studied by Becquerel and Breschet in France, and by Matteucci in Italy. The gymnotus was investigated by Humboldt and Bonpland in South America, and in England by Faraday, who had the opportunity of examining live specimens. The shock which they give serves as a means both of offence and of defence. It is purely voluntary, and becomes gradually weaker as it is repeated and as these animals lose their vitality, for the electrical action soon exhausts them materially. According to Faraday, the shock which the. gymnotus gives is equal to that of a battery of I5 jars exposing a coating of 25 square feet, which explains how it is that horses frequently give way under the repeated attacks of the gymnotus. Numerous experiments show that these shocks are due to ordinary electricity. For if, touching with one hand the back of the animal, the belly is touched with the other, or with a metal rod, a violent shock is felt in the wrists and arms ; while no shock is felt if the animal is touched with an insulating body. Further, when the back is connected with one end of a galvanometer wire and the belly with the other, at each discharge the needle is deflected, but immediately returns to zero, which shows that there is an instantaneous current ; and, moreover, the direction of the needle shows that the current goes from the back to the belly of the fish. Lastly, if the cur- rent of a torpedo be passed through a helix in the centre of which is a small steel bar, the latter is magnetised by the passage of a discharge. By means of the galvanometer, Matteucci established the following facts :— 1. When a torpedo is lively, it can give a shock in any part of its body, but as its vitality diminishes, the parts at which it can give a shock are nearer the organ which is the seat of the development of electricity. 2. Any point of the back is always positive as compared with the correspond- ing point of the belly. 3. Of any two points at different distances from the electrical organ, the nearest always plays the part of a positive pole, and the farthest that of a nefative pole. With the belly the reverse is the case. The organ where the electricity is produced in the torpedo is double, and formed of two parts symmetrically situated on two sides of the head and attached to the skull-bone by the internal face. Each part consists of nearly parallel lamellze of connective tissue enclosing small chambers, in which lie the so-called electrical plates, each of which has a final nerve ramification distributed on one of its faces. The face, on which the nerve ends, is turned the same way in all the plates, and when the discharge takes place is always negative to the other. Matteucci investigated the influence of the brain on the discharge. For this purpose he laid bare the brain of a living torpedo, and found that the first three lobes could be irritated without the discharge being produced, and that when they were removed the animal still possessed the faculty of giving a shock. The fourth lobe, on the contrary, could not be irritated without an immediate production of the discharge ; but if it was removed, all dis- engagement of electricity disappeared, even if the other lobes remained untouched. Hence it would appear that the primary source of the electricity elaborated is the fourth lobe, whence it is transmitted by means of the nerves 1052 Dynamical Electricity [1009- to the two organs described above, which act as multipliers. In the silurus the head appears also to be the seat of the electricity ; but in the gymnotus it is found in the tail. 1o1o. Application of electricity to medicine.—The first applications of electricity to medicine date from the discovery of the Leyden jar. Nollet and Boze appear to have been the first who thought of the application, and soon the spark and electrical friction became a universal panacea ; but it must be admitted that the results of subsequent trials did not come up to the hopes of the early experimentalists. After the discovery of dynamic electricity Galvani proposed its applica- tion to medicine ; since which time many physicists and physiologists have been engaged upon this subject, and yet there is still much uncertainty as to the real effects of electricity, the cases in which it is to be applied, and the best mode of applying it. Practical men prefer the use of currents to that of statical electricity, and, except in a few cases, discontinuous to continuous currents. There is, finally, a choice between the currents of the battery and induction currents; further, the effects of the latter differ, according as induction currents of the first or second order are used. In fact, since induction currents, although very intense, have a very feeble chemical action, it follows that when they traverse the organs they do not produce the chemical effects of the current of the battery, and hence do not tend to produce the same disorganisation. Further, in electrifying the muscles of the face, induction currents are to be preferred, for these currents only act feebly on the retina, while the currents of the battery act energeti- cally on this organ, and may affect it dangerously. There is a difference in the action of induced currents of different orders ; for while the primary induced current causes lively muscular actions, but has little action on the cutaneous sensibility, the secondary induced current, on the contrary, in- | creases the cutaneous sensibility to such a point that its use ought not to be prescribed to persons whose skin is very irritable. Hence electrical currents should not be applied in therapeutics without a thorough knowledge of their various properties. They ought to be used with great prudence, for their continued action may produce serious acci- dents. Matteucci says: ‘In commencing, a feeble current must always be used. This precaution now seems to me the more important as I did not think it so before seeing a paralytic person seized with almost tetanic con- vulsions under the action of a current formed of a single element. Take care not to continue the application too long, especially if the current is energetic. Rather apply a frequently interrupted current than a continuous one, especially if it be strong ; but after twenty or thirty shocks, at most, let the patient take a few moments’ rest.’ Of late years, however, feeble continuous currents have come more into use. They are frequently of great service when applied skilfully, so as to throw the nerves of the diseased part into a state of katelectrotonus or anelectrotonus (850), according to the object which is wished for in any given case. ~1012] | Meteorograph 1053 ELEMENTARY FOU 1 LINES OF MBG BOROLOGY WAND SCIIMATOROGY METEOROLOGY 1011. Meteorology.—The phenomena which are produced in the atmo- sphere are called meteors ; and meteorology is that part of physics which is concerned with the study of these phenomena. A distinction is made between aerza/ meteors, such as winds, hurricanes, and whirlwinds ; agweous meteors, comprising fogs, clouds, rain, dew, snow, and hail ; and /wmdznous meteors, as lightning, the rainbow, and the aurora borealis. 1012. Meteorograph.—The importance of being able to make continuous observations of various meteorological phenomena has led to the construc- tion of various forms of automatic arrangements for this purpose, of which that of Osler in England may be mentioned. One of the most compre- hensive and complete is Secchi’s mmeteorograph, which consists of a base of masonry about 2 feet high (fig. 1040) ; on this are fixed four columns about 24 yards high, which support a table on which is a clockwork regulating the whole of the movements. The phenomena are registered on two sheets which move downwards on two opposite sides, their motion being regulated by the clockwork. One of them occupies ten days in so doing, and on it are registered the direction and velocity of the wind, the temperature of the air, the height of the barometer, and the occurrence of rain; on the second, which only takes two days, the barometric height and the occurrence of rain are repeated, but on a much larger scale ; this gives moreover the moisture of the air. Direction of the wind.—The four principal directions of the wind are re- gistered by means of four pencils fixed at the top of thin brass rods, a, 4, ¢, d (fig. 1040), which are provided at the bottom ends with soft iron keepers attracted by two electromagnets, E E’, for west and north, and by two other electromagnets lower down for south and east. These four electro- magnets, as well as all the others on the apparatus, are worked by a single battery of twenty-four elements. The passage of the current in one or 1054 Meteorology [1012- the other of these electromagnets is regulated by means of a vane (fig. 1041) consisting of two plates at an angle of thirty degrees with each other, by Sey a= wi Bee Pee. ang sa Pe] = 4| / al i =] | | | my A xy AL) PACT mm { | sy Hon wi NC I WANT ote || i} 1 I | th | B ee | 6! | — ! LU | ae ae rl | im | | a CEN | ten coe i \ i 5 a i Al [ A TTT : 1 Towns +. D 2 i Milpezia & IZ {0 } : i | on | i’ E i f | 1 f 3 Mm Whe ca ” | : if ee OMT ol La cam [ . W ih pl jee am Bb. Fa Ne ah TT l ATT i an = 2\\ £ = F | ae, aes — << ml pd i a av vii mrs which greater steadiness is obtained than with a single plate. In the rod of the vane is a small brass plate, 0; this part is in the centre of four metal = —__ San SS s= == eee = - ERE: te UL = net 7 = = == z —— = == | i 0 ; . g 0c é Te 09 02 08 05 OUl O11 O41 ol ZT OSt ff ‘9 ‘(ON UVAA AHL WOd SAMA LOSI . - P . as ; s ae) ee ee —1012] Velocity of the Wind 1055 sectors, insulated from each other, and each provided with a-binding-screw, by which connection is established with the binding-screw K, and the elec- tromagnets EE’. The battery current reaches the rod of the vane by the wire a, and thence the sliding contact 0, which leads it to the electro-magnet for the north, for instance. If the current passed constantly in this electromagnet, the pencil on the rod d would be stationary ; but from the electro- magnet E’ the current passes into a second electromagnet, 7, over the clockwork, and is thereby alternately opened and closed, as will be seen when we speak of the velocity of the wind. Hence the armature of the rod @, alternately free and attracted, oscillates ; and its pencil, which is always pressed against the paper AD by the elasticity of the rod, traces on it a series of parallel dashes as the paper descends, and so long as the wind is in the north. If the wind changes then to west, for in- stance, the rod a@ oscillates, and its pencil ie E HH re —————— HECLARO Fig. 1041 traces a different series of marks. The rate of displacement of the paper being known, we get the direction of the prevalent wind at a given moment. Velocity of the wind.—This is indi- cated by a Robinson’s anemometer, and is registered in two ways : by two counters which mark in decametres and kilometres the distance travelled by the wind ; and by a pencil which traces on a table a curve, the ordinates of which are proportional to the velocity of the wind. Robinson, who originally devised this form of anemometer (fig. 1042), proved that its velocity is proportional to that of the wind; in this apparatus the length of the arms is so calculated that each re- volution corresponds to a velocity of ten metres. The anemometer is placed at a considerable distance from the meteoro- graph, and is connected with it by a copper wire, @, which passes to the electro- magnet, 2, of the counter. On its rod there is, moreover, an excentric, which at each turn touches a metal contact in connec- tion with the wire @. The battery current Fig. 1042 reaches the anemometer by a wire a, the circuit is closed once at each rotation, and the current passes to the electromagnet 7, which moves the 1056 Meteorology [1012-- needle of the dial through one division. There are fifty such divisions, which represent as many turns of the vane, and therefore so many multiples of ten metres. The lower dial marks the kilometres. The curve of velocities is traced on the sheet by a pencil, z, fixed to a horizontal rod. This is joined at its two ends to two guide-rods, o and y, which keep it horizontal. The pencil and the rod are moved laterally by a chain which passes over two pulleys, 7’ and 7, and is then coiled over a pulley placed on the shaft of the counter, but connected with it merely by a ratchet- wheel ; and moved thus by the counter and the chain, the pencil traces every hour on the sheet a line the length of which is proportioned to the velocity of the wind. From hour to hour an excentric moved by clockwork detaches, from the shaft of the counter, the pulley on which is coiled the chain, and this pulley becoming out of gear, a weight, 2, connected with the pencil z, restores this to its starting point. All the lines, V, traced succes- sively by the pencil, start as ordinates from the same straight line, and their ends give the curve of velocities. The counters on the right and left are worked by electromagnets, 7 2’, and are intended to denote the velocity of special winds ; for instance, those of the north and south, by connecting their electromagnets with the north and south sectors of the vane (fig. 1041). Temperature of the atr.—This is indicated by the expansion and con- traction of a copper wire of 16 metres in length stretched backwards and forwards on a fir post 8 metres in length. The whole being placed on the outside—on the 1oof, for instance—the expansion and contraction are trans- mitted by a system of levers to a wire, v, which passes to the meteorograph, where it is jointed to a bent lever, 7 This is jointed to a horizontal rod, s, which supports a pencil, and at the other end is jointed to a guide-rod, x. Thus the pencil, sharing the oscillations of the whole system, traces the curve of the temperatures. Pressure of the atmosphere.—This is registered by the oscillations of a barometer, B, suspended at one end of a bent scale-beam, I F, playing ona knife-edge (fig. 1045). The arm F supports a counterpoise ; to the arm I is suspended the barometer B, which is wider at the top than at the bottom. A wooden flange or floater, Q, fixed to the lower part of the tube, plunges in a bath of mercury, so that the buoyancy of the liquid counterbalances part of the weight of the barometer. Owing to the large diameter of the barometric chamber, a very slight variation of level in this chamber makes the tube oscillate, and with it the scale-beam 1 F. To the axis of this is a triangle, . ghk, jointed to a horizontal rod, which in turn is connected with a guide-rod, g. In the middle of this rod is a pencil which, sharing in the oscillations of the triangle g/£, traces the curve H of pressure. A bent lever at the bottom of the barometer tube keeps this in a vertical position. Rainfall.—This is registered between the direction of the winds and the curve H by a pencil at the end of a rod, wz, which is worked by an electro- magnet, e¢. On the roof is a funnel which collects the rain, and a long tube leads the water to a small water-balance, with the cups placed near the meteorograph (fig. 1044). To the axis of the scale-beam one pole of the battery is connected ; the left cup being full, tips up, and a contact, a, closes the current, which passes then to one of the binding-screws, C, and ‘ —1012] Measurement of the Rainfall 1057 hence to the electromagnet, ¢. Then the right cup, being in turn full, tips in the opposite direction, and the contact 4 now transmits the current to the electromagnet. Thus, at each oscillation this latter attracts its armature, and with it the rod a, which makes a mark by means of a pencil at the end. If the rain is abundant, the oscillations of the beam are rapid, and the marks, being very close together, give a deep shade ; if, on the contrary, the oscilla- tions are slow, the marks are at a greater distance, and give a light shade. When the rain ceases the oscillations cease also, and the pencil makes no mark. To complete this description of the art face of the meteorograph: S is the alarum-bell of the clock- work ; OO a cord supporting a weight which moves the works of the hour-hand ; LZ is a second cord that supports the weight which works the alarum; the wheel U, placed below the clockwork, winds up the sheet AD when it is at the bottom of its course. The second sheet (fig. 1044) gives the barometric height and the rainfall like the first, but on a larger scale, since the motion of the sheet is five times as rapid. Its principal function is that of registering the moisture of the air. This is effected by means of the psychrometer (fig. 1043). T and T’ are two thermo- meters fixed on two plates. The muslin which covers the second is kept continually moist by water dropping on it. In each of the bulbs is fused a platinum wire; the stems of the thermometers are open at the top, and in them are two platinum wires, 7 and 7, suspended to a metal frame movable on four pulleys supported by a fixed piece, B. The frame A, in contact with the current of the battery, is suspended to a steel wire, L, which passes over a pulley to the meteorograph (fig. 1043) Here is a long triangular lever, W, which supports a small wheel, to which is, fixed the wire L. The lever W, which turns about an axis, f, is moved by a rod, a, by means of an excentric, which the clock works every quarter of an hour. At each oscillation the lever W transmits its motion to a small chariot, on which is an electromagnet, x, and at the same time to the steel wire L, which supports the frame A (fig. 1045). The chariot, moved towards the left by the rotation of the excentric, lets the frame sink. The moment the first platinum wire reaches the mercurial column of the dry- bulb thermometer, which is the highest, the circuit is closed, and the current passes into the electromagnet of the chariot. An armature at once causesa pencil to mark a point on the sheet which is the beginning of a line repre- senting the path of the dry-bulb thermometer. As the frame continues to descend, the second platinum wire touches the mercury of the wet bulb, and causes a current to flow in a relay, M, which opens the circuit of the electro- magnet, x The pencil is then detached ; then, returning upon itself, the chariot reproduces the closing and opening of the circuit in the opposite direction, the pencil making another mark, which is the end of the line. There are thus formed two series of dots arranged in two curves, one of which represents the path of the dry, and the other the path of the wet, bulb. The horizontal distance of the two points of these curves is proportional to the 3¥ Fig. re 1058 Meteorology [1012- difference 7—7, of the temperatures indicated at the same moment by the thermometers (fig. 1045). Bl | Lic cA ff ili} MUG ne Fig. 1044 Quantity of ratn.—The quantity of rain which falls in a given time is registered on a disc of paper on a pulley, R. On the groove of this is coiled a chain to which is suspended a brass tube, P. This is fixed at the 1013] Direction and Velocity of Winds 1059 bottom to a float, which plunges in a reservoir placed in the base of the meteorograph. On passing out of the water-balance (fig. 1041) the water passes into this reservoir, and as its section is one-fourth that of the funnel, the height of water which falls is quadrupled ; it is measured on a scale, G, divided into millimetres. As the float rises, a weight, Z, moves the pulley in the contrary direction, and its rotation is proportional to the height of water which. has fallen. A pencil moves at the same time from the centre to the circumference of the paper disc with a velocity of 5 mm. in 24 hours: hence the quantity of rain which falls every day is noted on a different place on the paper disc. 1013. Direction and velocity of winds.— Wznds are currents moving in the atmosphere with vari- ‘able directions and velocities. There are eight principal directions in which they blow—vorth, north-east, east, south-east, south, south-west, west, and zorth-west. Mariners further divide each of the distances between those eight directions into four others, making in all 32 directions, which are called points or rhumbs. A figure of 32 rhumbs on a circle, in the form of a star, is known as the mariners cara. Velocity is determined by means of the anemometer (fig. 1042), a small vane with _ fans, which the wind turns ; the velocity is deducted from the number of turns made in a given time. In our climate the mean velocity is from 18 to 20 feet ina second. With a velocity of less than 18 inches in a second no movement is perceptible, and smoke ascends straight ; with a velocity between 13 and 2 feet per second the wind is perceptible and moves a pennant ; from 13 to 22 feet it is moderate, it stretches a flag and moves the leaves of trees ; with from 23 to 36 feet velocity it is fresh, and moves the branches of trees ; with 36 to 56 feet it is strong, and moves the larger branches and the smaller stems ; with a velocity of 56 to 9o feet it is a storm, and entire trees are moved; and from 90 to 120 it is a hurricane. To measure the pressure of the wind a plate is used, which by means of a vane is always kept in a direction opposite that of the wind. Behind the plate are one or more springs, which are the more pressed the greater is the pressure of the wind against the plate. Knowing the distance through which the plate is pressed, we can calculate the pressure which the wind exerts on the plate in question. With some degree of approximation, and for low velocities, the pressure may be taken as proportional to the square of the velocity. Thus, if the pressure on the square foot is 0005 pound with a velocity of 1°5 foot in a second, it is 0.02 pound with a velocity of 3 feet, and 0°123 with a velocity bfo7-33 feet, . Fig. 1046 ge: 1060 Meteorology [1014- 1014. Causes of winds.—Winds are produced by a disturbance of the equilibrium in some part of the atmosphere ; a disturbance always resulting from a difference in temperature between adjacent countries. Thus, if the temperature of a certain extent of ground becomes higher, the air in contact with it becomes heated, expands and rises towards the higher regions of the atmosphere ; whence it flows, producing winds which blow from hot to cold countries. But at the same time the equilibrium is destroyed at the surface of the earth, for the barometric pressure on the colder adjacent parts is greater than on that which has been heated, and hence a current will be produced with a velocity dependent on the difference between these pressures ; thus two distinct winds will be produced—an upper one setting outwards from the heated region, and a lower one setting zzzwards towards it. Ioi5. Regular, periodical, and variable winds.—According to the more or less constant directions in which winds blow, they may be classed as regular, periodical, and variable winds. i. Regular winds are those which blow all the year through in a virtually constant direction. These winds, which are also known as the frade winds, are uninterruptedly observed far from the land in equatorial regions, blowing from the north-east to the south-west in the Northern Hemisphere, and from the south-east to the north-west in the Southern Hemisphere. They prevail on the two sides of the equator as far as 30° of latitude, and they blow in the same direction as the apparent motion of the sun—that is, from east to west. The air above the equator being gradually heated, rises as the sun passes round from east to west, and its place is supplied by the colder air from the north or south. The direction of the wind, however, is modified by this fact, that the velocity which this colder air has derived from the rotation of the earth—namely, the velocity of the surface of the earth at the point from which it started—is less than the velocity of the surface of the earth at the point at which it has now arrived: hence the currents acquire, in reference to the equator, the constant direction which characterises the trade winds. i. Periodical winds are those which blow regularly in the same direction at the same seasons and at the same hours of the day: the monsoon, simoom, and the land and sea breeze are examples of this class. The name monsoon is given to winds which blow for six months in, one direction and for six months in another. They are principally observed in the Red Sea and in the Arabian Gulf, in the Bay of Bengal and in the Chinese Sea. These winds blow towards the continents in summer, and in a contrary direction in winter. The sz700m 1s a hot wind which blows over the deserts of Asia and Africa, and which is characterised by its high temperature and by the sands which it raises in the atmosphere and carries with it. During the prevalence of this wind the air is darkened, the skin feels dry, the respiration is accelerated, and a burning thirst is experienced. This wind is known under the name of szvocco in Italy and Algiers, where it blows from the great desert of Sahara. In Egypt, where it prevails from the end of April to June, it is called amsin. The natives of Africa, in order to protect themselves from the effects of the too rapid perspiration occasioned by this wind, cover themselves with fatty substances. A wind characteristic of Switzerland and known as the Fv/m, originates as -1017] Law of the Rotation of Winds 1061 follows: a mass of air coming from the south-east being impelled over a mountain ridge becomes rarefied as it ascends ; the temperature falls, and it deposits its moisture on the other side as rain or snow. Being driven still forward into the valleys, the superincumbent pressure being greater, the air is condensed and its temperature rises, and having parted with its moisture it appears as a wind which is at once hot and dry. One observation gave the temperature at 31°4° C., while it only contained 20 per cent. of moisture. The Zand and sea breeze is a wind which blows on the sea-coast, during the day from the sea towards the land, and during the night from the land to the sea. For during the day the land becomes more heated than the sea, in .consequence of its lower specific heat and greater conductivity, and hence, as the superincumbent air becomes more heated than that upon the sea, it ascends and is replaced by a current of colder and denser air flowing from the sea towards the land. During the night the land cools more rapidly than the sea, and hence the same phenomenon is produced, but in a contrary direction. The sea breeze commences after sunrise, increases up to three o’clock in the afternoon, decreases towards evening, and is changed into a land breeze ‘after sunset. These winds are only perceived at a slight distance from the shores. They are regular in the tropics, but less so in our climates ; traces of them are seen as far as the coasts of Greenland. The proximity of mountains, and also of forests, likewise gives rise to periodical daily breezes. 1. Variable winds are those which blow sometimes in one direction and sometimes in another, alternately, without being subject toanylaw. In mean latitudes the direction of the winds is very variable ; towards the poles this irregularity increases, and under the arctic zone the winds frequently blow from several points of the horizon at once. On the other hand, in approach- ing the torrid zone they become more regular. The south-west wind prevails in England, in the north of France, and in Germany ; in the south of France the direction inclines towards the north, and in Spain and Italy the north wind predominates. 1016. Law of the rotation of winds.—Notwithstanding the great irregu- larity which characterises the direction of the winds in our latitude, it has been ascertained that the wind has a preponderating tendency to veer round according to the sun’s motion—that is, to pass from north, through north-east- south-east to south, and so on round in the same direction from west to north ; that it often makes a complete circuit in that direction, or more than one in succession, occupying many days in doing so, but that it rarely veers, and very rarely or never makes a complete circuit in the opposite direction. This course of the winds is most regularly observed in winter. According to Leverrier, the displacement of the north-east by the south- west wind arises from the occurrence of a whirlwind formed upon the Gulf Stream. For a station in south latitude a contrary law of rotation prevails. This law, though more or less suspected for a long time, was first formally enunciated and explained by Dove, and is known as Dove's law of rotation of winds. 1017, Weather charts.—A considerable advance has been made in weather forecasts by the frequent and systematic publication of weather charts ; that is to say,smaps in which the barometric pressure, the tempe- 1062 M eleorology [1017- rature, the force of the wind, &c., are expressed for considerable areas in an exact and comprehensive manner. A careful study of such maps renders possible a forecast of the weather for a day or more in advance. We can here do no more than explain the meaning of the principal terms in use. If lines are drawn through those places on the earth’s surface where the corrected barometric height at a given time is the same, such lines are called zsobarometric lines, or, more briefly, zsobaric lines, or zsobars. Between any two points on the same isobar there is no difference of pressure. Isobars are usually drawn for a difference of 2°5 mm. or of 34, of an inch. If we take a horizontal line between two isobars, and at that point at which the pressure is greatest draw a perpendicular line on any suitable scale, which shall represent the dzference in pressure between the two places, the line drawn from the top of this perpendicular to the lower isobar will form an angle with the horizontal, and the steepness of this angle is a measure of the fall in pressure between the two stations, and is called the barometric gradient. Gradients are usually expressed in England and America in hundredths of an inch of mercury for one degree of sixty nautical miles, and on the Continent in millimetres for the same distance. The closer are the isobars the steeper is the gradient, and the more powerful the wind ; and though no exact numerical relationship can be proved to exist between the steepness of the gradient and the force of the wind, it may be taken that a gradient of about 6 represents a strong breeze; and a gradient of 10, or a difference in pressure of ;4, of an inch for 60 miles, is a stiff gale. The direction of the wind is from the place of higher pressure to that of lower, and in this respect the law of Buys Ballot may be mentioned, which has been found to hold in all cases of the Northern Hemisphere, where local configuration does not come into play. //f we stand with our back to the wind, the line of lower pressure is on the left hand. ¥or places in the Southern Hemisphere exactly the opposite law holds. If within any area the pressure is lower, the wind blows round that area, the place of lowest pressure being on the left. The direction of the wind is, in short, contrary to that of the hands of a watch. Such acirculation is called cyclonic ; it 1s that which is characteristic of the West Indian hurricanes, which are known as cyclones. Conversely, the wind blows round an area of higher pressure in the same direction as the hands of a watch ; and this cir- culation is called azte-cyclonic. Cyclonic systems are by far the most frequent, and are characterised by steep gradients ; the air in them tends to move in towards the centre, and thence to the upper regions of the atmosphere. They bring with them over the greater part of the region which they cover much moisture, an abundance of cloud, and heavy rain. An anti-cyclonic system has the opposite charac- teristics : the gradients are slight, the wind is light, and moves with the hands of a watch. The air is dry, so that there is but little cloud, and no rain. Cyclonic systems, from the dampness of the air, produce warm weather in winter, and cold wet weather in summer. Anti-cyclonic systems bring our hardest frosts in winter and greatest heat in summer, as there is but little moisture in the air to temper the extremes of climate. Both systems travel over the earth’s surface—the cyclones rapidly, but the anti-cyclones more slowly. ~1019] fogs and Mists 1063 1018. Fogs and Mists.—When aqueous vapour rising from a vessel of boiling water diffuses in the colder air, it is condensed ; a sort of cloud is formed, consisting of a number of small vesicles of water, which remain suspended in the air. These are usually spoken of as vapour, yet they are not so—at any rate, not in the physical sense of the word, for in reality they are condensed vapour. When this condensation of aqueous vapour is not occasioned by contact with cold solid bodies, but takes place throughout large spaces of the atmo- sphere, it constitutes fogs or mzs¢s, which, in fact, are essentially the same, the appearance seen over a vessel of hot water. A chief cause of fogs consists in the moist soil being at a higher tem- perature than the air. The vapours which then ascend condense and become visible. In all cases, however, the air must have reached its point of satura- tion before condensation takes place. Fogs may also be produced when a current of hot and moist air passes over a river at a lower temperature than its own ; for then, the air being cooled as soon as it is saturated, the excess of vapour present is condensed. The distinction between mists and fogs is one of degree rather than of kind. A fog is a very thick mist. By observations based on diffraction phenomena (660), the diameter of fog vesicles has been found to vary from o’0154 to o’0521 mm.; the longer the continuance of fine weather, the smaller are the vesicles ; before rains they increase rapidly. Dines, by direct microscopic measurement, found that the diameter of fog particles varied with the same fog from o'o15 to 0127 mm. ; the larger occur in dense fogs, in lighter fogs they sink to 070033. Kamtz found from ool 4 to 0°035 mm. When water is coated with a layer of coal-tar, it is prevented from evaporating. Sir Edward Frankland ascribes the dry fog met with in London to the large quantities of coal-tar and paraffine vapour which are sent into the atmosphere, and which, condensing on the vesicles of fog, pre- vent their evaporation. Aitkin has shown that aqueous vapour never condenses unless some liquid or solid is present on which it is deposited. Particles of dust in the air are the nuclei for clouds and fogs. This he showed by passing steam into filtered air; it remained quite clear, while a turbidity was produced under the same circumstances in unfiltered air. The density of the cloud was found to depend on the number of particles of dust in the air. A most abundant source of dust is the combustion of coal. ‘The sulphur in the coal in burning also forms sulphurous acid, which, though a gas, is found to act as a nucleus. 1019. Clouds.—C/ouds are masses of vapour condensed into little drops or vesicles of extreme minuteness, like fogs. There is no difference of kind between fogs and clouds. Fogs are clouds resting on the ground. Toa person enveloped in it, a cloud on a mountain appears like a fog. They always result from the condensation of vapour which rises from the earth. The horizontal base of a cloud denotes the layer of air in which the ascending current of air has attained the dew-point. According to their appearance, clouds were divided by Howard into four principal kinds : the zzdéus, the stratus, the cumulus, and the cirrus.’ These four kinds are represented in 1064 Meteorology [1019— fig. 1047, and are designated respectively by one, two, three, and four birds on the wing. The cirrus consists of small whitish clouds, which have a fibrous or wispy appearance, and occupy the highest regions of the atmosphere. The name of mares’ tails, by which they are generally known, well describes. their appearance. From the low temperature of the spaces which they occupy, it is certain that cirrus clouds consist of frozen particles ; and hence it is that halos, coronz, and other optical appearances, produced by refraction and reflection from ice-crystals, appear almost always in these clouds and their derivatives. Their appearance often precedes a change of weather. The czzziZus are rounded spherical forms which look like mountains of cotton wool piled one on the other. They are more frequent in summer Fig. 1047 than in winter, and after being formed in the morning, they generally dis- appear towards evening. If, on the contrary, they become more numerous, and especially if surmounted by cirrus clouds, rain or storms may be expected. Any such cumulus is nothing more than an ascending current of air which makes its path visible by condensed aqueous vapour. Stratus clouds consist of very large and continuous horizontal sheets, which form chiefly at sunset and disappear at sunrise. They are frequent in autumn and unusual in spring-time, and are lower than the preceding. The wzmbus, or rain clouds, which are sometimes classed as one of the fundamental varieties, are properly a combination of the three preceding kinds. They affect no particular form, and are solely distinguished by a uniform grey tint and by fringed edges. They are indicated on the right of the figure by the presence of one bird. -1020] formation of Clouds 1065 The fundamental forms pass into one another in the most varied manner. Howard classed these transitional forms as c7rro-cumulus, ctrro-stratus, and cumulo-stratus, and it is often very difficult to tell, from the appearance of a cloud, which type it most resembles. The cirro-cumulus is most cha- racteristically known as a ‘mackerel sky ;’ it consists of small roundish masses, disposed with more or less irregularity. It is frequent in summer, and attendant on warm and dry weather. Czrro-stratus appears to result from the subsidence of the fibres of cirrus to a horizontal position, which at the same time approach laterally. The form and relative position when seen in the distance frequently give the idea of shoals of fish. The tendency of cumutlo-stratus is to spread, settle down into the zzméus, and finally fall as rain. The height of clouds varies greatly ; in the mean it is from 1,300 to I,500 yards in winter, and from 3,300 to 4,300 yards in summer. But they often exist at greater heights ; Gay-Lussac, in his balloon ascent, at a height of 7,030 yards, observed cirrus clouds above him, which appeared to be at a considerable height. In Ethiopia, D’Abbadie observed storm-clouds whose height was only 230 yards above the ground. In order to explain the suspension of clouds in the atmosphere, Halley first proposed the hypothesis of vesicular vapours. He supposed that clouds are formed of an infinity of extremely minute vesicles, hollow, like soap- bubbles filled with air, which are hotter than the surrounding air, so that these vesicles float in the air like so many small balloons. Others assume that clouds and fogs consist of extremely minute droplets of water, which are retained in the atmosphere by the ascensional force of currents of hot air, just as light powders are raised by the wind. Ordinarily, clouds do not appear to descend, but this absence of downward motion is only apparent. In fact, clouds do usually fall slowly, but then the lower part is continually dissipated on coming in contact with the lower and more heated layers ; at the same time the upper part is always increasing from the condensation of new vapours, so that from these two actions clouds appear to retain the same height. 1020. Formation of clouds.—Many causes may concur in the formation of clouds.. The usual cause of the formation of a cloud is the ascent, into higher regions of the atmosphere, of air laden with aqueous vapcur ; it thereby expands, being under diminished pressure; and in consequence of this expansion it is cooled, and this cooling produces a condensation of vapour. Hence it is that high mountains, stopping the currents of air and forcing them to rise, are an abundant source of rain. If the air is quite dry, its temperature would be one degree lower for every 300 metres. The case is different with moist air ; for when the air has ascended so high that its temperature has fallen to the dew-point, aqueous vapour is condensed, and in consequence of this heat is liberated ; when the dew-point is thus attained, and the air is saturated, the cooling due to the ascent and expansion of air is counteracted by this liberation of latent heat, so that the diminution of temperature with the height 1s considerably slower in the case of moist than of dry air. About one-half of the entire quantity of moisture in the air is contained in the first six or seven thousand feet upon the ground. The following calculation will give us the quantity of water separated 1066 Meteorology [1020— in a given case: Suppose air at a temperature of 20° to be saturated with aqueous vapour at that temperature ; the pressure of the vapour will be 17:4 mm., and the weight contained in one cubic metre of air 17°1 grammes. If the air has risen to a height of 3,500 metres, it has come under a pressure which is only % of what it was: its temperature is 4°, and its volume about r$ times what it originally was. As it remains saturated the pressure will be 6:1 mm., and the quantity of vapour will be 6:4 grammes in a cubic metre—that is to say, 6°4 x 15 =9°6 grammes in the whole mass of what was originally a cubic metre. The pressure of aqueous vapour has sunk during the ascent from 17°4 mm. to 6°I mm., and its weight from 17°! grammes to 9°6 grammes; that is, a weight of 7°5 grammes has been deposited from the mass of air which at the sea-level occupied a space of one cubic metre. These 7°5 grammes are in the form of the small droplets which constitute fogs or clouds. If the mass of air has risen to a height of 8,500 metres, where the pres- sure is only one-third that on the sea-level, the temperature is — 28°, and the space it occupies three times. as great as at first. The prescure of aqueous vapour is 0’°5 mm., and its weight o°6 gramme ina cubic metre. Hence there is now only 1°8 gramme left of the entire quantity of aque- ous vapour originally present, and the remaining 15°3 grammes would be separated as water orice. A similar calculation will show that at a height of 4,200 metres, where the temperature is zero and the pressure 2, the quan- tity of water present in the original cubic metre is only 0°82 gramme, the rest being deposited. Thus, a mass of air which, at the sea-level, occupies a space of a cubic metre, and is saturated with aqueous vapour at 20°, and then contains 17°1 grammes, will contain only 9°6 grammes at a height of 3°500 metres, 8°2 grammes at 4,200 metres, and 1°8 gramme at 8,500 metres. Hence, while a mass of air rises from the sea-level to a height of 4,200 feet, 8-9 grammes of aqueous vapour are separated as cloud-vesicles ; at 8,500 metres, or about double the height, 6:4 grammes are separated in the form of ice. A hot moist current of.air mixing with a colder current undergoes a cooling, which brings about a condensation of the vapour. Thus, the hot and moist winds of the south and south-west, mixing with the colder air of our latitudes, give rain. The winds of the north and north-east tend also, in mixing with our atmosphere, to condense the vapours ; but as these winds, owing to their low temperature, are very dry, the mixture rarely attains saturation, and generally gives no rain. The formation of clouds in this way is thus explained by Hutton. The pressure of aqueous vapour, and therewith the quantity present in a given space when saturated, diminishes according to a geometrical progression, while the temperature falls in arithmetical progression, and therefore the elasticity of the vapour present at any time is reduced by a fall of tempera- ture more rapidly than in direct proportion to the fall. Hence, if a current of warm air, saturated with aqueous vapour, meets a current of cold air also saturated, the air acquires the mean temperature of the two, but can retain only a portion of the vapour in the invisible condition, and a cloud or mist is formed. Thus, suppose a cubic metre of air at 10° C. mixes with a cubic metre of air at 20° C., and that they are respectively saturated with aqueous -1021} Rain 1067 vapour. By formula (408) it is easily calculated that the weight of water contained in the cubic metre of air at 10° C. is 9,397 grammes, and in that at 20° C. is 17°153 grammes, or 26°559 grammes in all. When mixed they produce two cubic metres of air at 15° C.; but as the weight of water required to saturate this is only 2 x 12°8=25°6 grammes, the excess, 0°95 gramme, will be deposited in the form of mist or clouds. 1021. Rain.—When the individual vapour-vesicles become larger and heavier by the condensation of aqueous vapour, and when, finally, individual vesicles unite, they form regular drops, which fall as raz. The quantity of rain which falls annually in any given place, or the annual rainfall, is measured by means of a vatu-gauge, or pluviometer. Ordinarily it consists of a cylindrical vessel, M (figs. 1048 and 1049), closed at the top by a funnel-shaped lid, in which there is a very small hole, through which the rain falls. At the bottom of the vessel is a glass tube, A, in which the water rises to the same height as inside the rain- gauge, and is measured by a scale on the side, as shown in the figures. The apparatus being placed in an exposed situation, if at the end of a month the height of water in the tube is two inches, for example, it shows that the water has attained this height in the vessel, and, conse- quently, that a layer of two inches in depth expresses the quantity of rain which this extent of surface has received. It has been noticed that the quantity of rain indicated by the rain-gauge is greater the nearer this instrument is to the ground. This has been ascribed to the fact that the raindrops, which are generally colder than the layers of air which they traverse, condense the vapour in these layers, and therefore constantly increase in volume. Hence more rain falls on the surface of the ground than at a certain height. But it has been objected that the excess of the quantity of rain which falls, over that at a certain height, is six or seven times that which could arise from condensation, even during the whole course of the raindrops from the clouds to the earth. The difference must therefore be ascribed to purely local causes, and it is now assumed that the difference arises from eddies produced in the air about the rain-gauge, which are more perceptible the higher it is above the ground : as these eddies dis- perse the drops which would otherwise fall into the instrument, they diminish the quantity of water which it receives. In any case it is clear that, if raindrops traverse moist air, they will, from their lower temperature, condense aqueous vapour and increase in volume. If, on the contrary, they traverse dry air, the drops tend to vaporise, and less rain falls than at a certain height; it might even happen that the rain did not reach the earth. From measurements of the coronze (1019), Delezenne determined the EZ ee YL ty Yj Fig. 1049 1068 Meteorology f1021- diameter of the globules in the case of rain-clouds just about to fall, and in the case of the cloud from a low-pressure steam-engine (481). The former was found to vary from 0°0565 to 070226 mm., and the latter from 0'0051 to 0'0042 mm. With the former, 5,500 droplets would be needed to make a drop of water a millimetre in diameter, and with the latter 50,000. According to the same author, there would be about 15 mgr. of globules in a cubic metre of a cloud which produced a rainfall of to mm. of water in an hour. With this number the mean distances of the vesicles with the above magnitudes are respectively 1°845, 0°706, 0°167, and o'148 mm. Many local circumstances may affect the quantity of rain which falls in different countries ; but, other things being equal, most rain falls in hot cli- mates, for there the vaporisation is most abundant. The rainfall decreases, in fact, from the equator to the poles. At London it is 23°5 inches; at Bordeaux it is 25°8; at Madeira it is 27°7; at Havannah it is 91°2; and at St. Domingo it is 107°6. The quantity varies with the season : in Paris, in winter, it is 4°2 inches ; 1n spring, 6°9 ; in summer, 6°3 ; and in autumn, 4°8 inches. The heaviest annual rainfall at any place on the globe is on the Khasi Hills, in Bengal, where it is 600 inches ; of which 500 inches fall in seven months. On July 1, 1851, a rainfall of 254 inches on one day was observed at Cherrapoonjee. At Kurrachee, in the north-west of India, the rainfall is only 7 inches. The rainfall diminishes with the height of a station above the sea-level at the rate of 3 or 4 per cent. for each 100 feet of altitude above the sea. The driest recorded place in England is Lincoln, where the mean rainfall is 20 inches ; and the wettest is Stye, at the head of Borrowdale, in Cumber- land, where it amounts to165 inches. The greatest average amount of rain- fall in any one day, taking the means of all stations, is 14 inch; though individual stations far exceed this amount, sometimes reaching 4 inches. An inch of rain on a square yard of surface expresses a fall of 46°74 pounds, or 4°67 gallons. On an acre it corresponds to 22,622 gallons, or 100°9935 tons. 100 dons fer inch per acre isa ready way of remembering this. 1022. Waterspouts.—On hot summer days, and when the weather is otherwise calm, we often notice sand and dust carried forward in a column with a whirling motion. As storms come on, larger whirlwinds of this kind are formed, which carry with them leaves, straw, and even small branches. When they are of larger dimensions they form real whirlwinds. They are probably due to the contact of two winds blowing in the upper regions of the atmosphere. When they pass over land they form large conical-shaped masses of dust, which make them visible at a distance; when they pass over rivers or the sea they present a curious phenomenon: the water is disturbed, and rises in the form of a cone, while the clouds are depressed in the form of an inverted cone; the two cones then unite and form a continuous column from the sea to the clouds (fig. 1050). Even, however, on the high seas the water of these waterspouts is never salt, proving that they are formed of condensed vapour, and not of sea-water raised by aspiration. 1023. Influence of aqueous vapour on climate.—Tyndall applied the property possessed by aqueous vapour of powerfully absorbing and radiating -1023]. lnfluence of Aqueous Vapour on Climate 1069 heat to the explanation of some obscure points in meteorology. He esta- blished the fact that in a tube 4 feet long the atmospheric vapour on a day of average dryness absorbs Io per cent. of obscure heat. With the earth warmed by the sun as a source, at the very least Io per cent. of its heat is intercepted within 10 feet of the surface. The absorption and radiation of aqueous vapour is more than 16,000 times that possessed by dry air. The radiative power of aqueous vapour may be the main cause of the torrent-like rains that occur in the tropics, and also of the formation of cumulus clouds in our own latitudes. The same property probably causes the descent of very fine rain, called sévezz, which has more the characteristics of falling dew, as it appears a short time after sunset, when the sky is clear ; its production has therefore been attributed to the cold resulting from the Fig. 1050 radiation of the air. It is not the air, however, but the aqueous vapour in the air, which by its own radiation chills itself, so that it condenses into SCrein. The absorbent power of aqueous vapour is of even greater importance. Whenever the air is dry, terrestrial radiation at night is so rapid as to cause intense cold. Thus, in the central parts of Asia, Africa, and Australia, the daily range of the thermometer is enormous; in the interior of the last- named continent a difference in temperature of no less than 40° C, has been recorded within 24 hours. In India, and even in the Sahara, ice has been formed at night, owing to the copious radiation. But the heat which aqueous vapour absorbs most largely is of the kind emitted from sources of low temperature ; it is to a large extent transparent to the heat emitted from the sun, whilst it is almost opaque to the heat radiated from the earth. Con- 1070 Meteorology [1023- sequently, the solar rays penetrate our atmosphere with a loss, as estimated by Pouillet, of only 25 per cent., when directed vertically downwards, but after warming the earth they cannot retraverse the atmosphere. Through thus preventing the escape of terrestrial heat, the aqueous vapour in the air moderates the extreme chilling which is due to the unchecked radiation from the earth, and raises the temperature of that region over which it is spread. In Tyndall’s words, ‘aqueous vapour is a blanket more necessary to the vegetable life of England than clothing is to man. Remove for a single summer night the aqueous vapour from the air which overspreads this country, and every plant capable of being destroyed by a freezing tempera- ture would perish. The warmth of our fields and gardens would pour itself unrequited into space, and the sun would rise upon an island held fast in the iron grip of frost.’ 1024. Tyndall’s researches.—Tyndall found that the action of the sun or of the electric light decomposed certain highly rarefied vapours. He used a glass tube, which could be exhausted and then filled with air charged with the va- pours of volatile liquids, by allowing the air to bubble through small Wolff bottles containing them. By mixing the air charged with vapour with differ- ent proportions of pure air, and by varying the degrees of exhaustion, it was possible to have a vapour under any degree of attenuation. The tube could also be filled with the vapour ofa liquid alone. The tube having been filled with air charged with vapour of amyl nitrite,a somewhat convergent beam from the electric lamp was passed intothe tube. Fora moment the tube appeared optically empty, but suddenly a shower of liquid spherules was precipitated on the path of the beam, forming a luminous white cloud. The nature of the substance thus precipitated was not specially investigated. This effect was not due to any chemical action between the vapour and the air, for when either dry oxygen or dry hydrogen was used instead of air, or when the vapour was admitted alone, the effect was substantially the same. Nor was it due to any heating effect, for the beam had been previously sifted by passing through a solution of alum, and through the thick glass of the lens. The unsifted beam produced the same effect ; the obscure calorific rays did not seem to affect the result. The sun’s light also effects the decomposition of amyl nitrite vapour ; and this decomposition was found to be mainly due to the more refrangible rays. When the electric light, before entering the experimental tube, was made to pass through a layer of liquid amy] nitrite an eighth of an inch in thickness, the luminous effect was not appreciably diminished, but the chemical action was almost entirely stopped. Thus, that special constituent of the luminous radiation which effects the decom- position of the vapour is absorbed by the liquid. The decomposition of liquid amyl nitrite by light, if it take place at all, is far less rapid and distinct than that of the vapour. The absorption is the same, whether the nitrite is in the liquid or in the vaporous state, showing that it is not the act of the molecule as a whole, but that it is atomic ; that is, that it is to the atoms that the peculiar rate of vibration is transferred which brings about the decomposition of the body. It was also found that a vapour which when alone resists the action of light may, by being associated with another gas or vapour, exhibit a vigorous action.. Thus, when the tube was filled with atmospheric air, mixed with —1024] Tyndall’s Researches 1071 butyl nitrite vapour, the electric light produced very little effect ; but with half an atmosphere of this mixture, and half an atmosphere of air which had passed through hydrochloric acid, the action of the light was almost instan- taneous. In another case, mixed air and butyl nitrite vapour were passed into the tube so that the mixture was under a pressure of 2°5 mm. Air passed through aqueous hydrochloric acid was introduced until the pressure was 3 inches. The condensed beam passed through at first without change, but afterwards a superb blue cloud was formed. In cases where the vapours are under a sufficient degree of attenuation, whatever otherwise be their nature, the visible action commences with the formation of a blue cloud. The term ‘cloud,’ however, must not be understood in its ordinary sense ; the blue cloud is invisible in ordinary daylight, and to be seen must be surrounded by darkness, z¢ a/ome being illuminated by a powerful beam of light. The blue cloud differs in many important particulars from the finest ordinary clouds, and may be considered to occupy an inter- mediate position between these clouds and true cloudless vapour. By graduating the quantity of vapour, the precipitation may be obtained of any required degree of fineness ; forming either particles distinguishable by the naked eye, or particles beyond the reach of the highest microscopic power. ‘The case is similar to that of carbonic acid gas, which, diffused in the atmosphere, resists the decomposing action of solar light, but is decom- posed when in contact with the chlorophyll in the leaves of plants. When the blue cloud produced in these experiments was examined by any polarising arrangement, the light emitted laterally from the beam—that . is, in the direction at right angles to its axis—was found to be perfectly polar- ised. This phenomenon was observed in its greatest perfection the more perfect the blue of the cloud. It is produced by any particles, provided they are sufficiently fine. This is quite analogous to the light of the blue sky. When this is examined by a Nicol’s prism, or any other analyser, it is found that the light emitted at mght angles to the path of the sun’s rays is polarised. The phenomena of the firmamental blue, and the polarisation of the sky-light, thus find definite explanations in these experiments. We need only assume the existence, in the higher regions of the atmosphere, of excessively fine particles of water; for particles of any kind produce this effect. It is easy to conceive the existence of such particles in the higher regions, even on a hot summer’s day. For the vapour must there be in a state of extreme attenuation ; and inasmuch as the oxygen and nitrogen of the atmo- sphere behave like a vacuum to radiant heat, the extremely attenuated particles of aqueous vapour are practically in contact with the absolute cold of space. ‘ Suppose the atmosphere surrounded by an envelope impervious to light but with an aperture on the sunward side, through which a parallel beam, of solar light could enter and traverse the atmosphere. Surrounded on all sides by air not directly illuminated, the track of such a beam would resemble that of the parallel beam of the electric light through an incipient cloud. The sunbeam would be blue, and it would discharge light laterally in the same condition as that discharged by the incipient cloud. The azure revealed by such a beam would be to all intents and purposes a blue cloud,’ 1072 Meteorology [1025- 1025. Dew. Hoarfrost.—Dew is aqueous vapour which has condensed on bodies during the night in the form of minute globules. It is occasioned by the chilling which bodies near the surface of the earth experience’ in consequence of nocturnal radiation. Their temperature having then sunk several degrees below that of the air, it frequently happens, especially in hot seasons, that this temperature is below that at which the atmosphere is saturated. The layer of air which is immediately in contact with the chilled bodies, and which has virtually the same temperature, then deposits a por- ' tion of the vapour which it contains (401) ; just as when a bottle of cold water is brought into a warm room it becomes covered with moisture, owing to the condensation of aqueous vapour upon it. According to this theory, which was first propounded by Dr. Wells, all causes which promote the cooling of bodies increase the quantity of dew. These causes are the emissive power of bodies, the state of the sky, and the agitation of the air. Bodies which have a great radiating power more readily become cool, and therefore ought to condense more vapour. In fact there is generally no deposit of dew on metals, whose radiating power is very small, especially when they are polished ; while the ground, sand, glass, and plants, which have a great radiating power, become abundantly covered with dew. The state of the sky also exercises a great influence on the formation of dew. If the sky is cloudless, the planetary spaces send to the earth an in- appreciable quantity of heat, while the earth radiates very considerably, and therefore, becoming very much chilled, there is an abundant deposit of dew. But if there are clouds, as their temperature is far higher than that of the planetary spaces, they radiate in turn towards the earth, and as bodies on the surface of the earth experience only a feeble chilling, no deposit of dew takes place. Wind also influences the quantity of vapour deposited. If it is feeble, it increases it, inasmuch as it renews the air; if it is strong, it diminishes it, as it heats the body by contact, and thus does not allow the air time to become cooled, Finally, the deposit of dew is more abundant according as the air is moister, for then it is nearer its point of saturation. Hoarfrost and rime are dew which has been deposited on bodies cooled below zero, and has become frozen. The flocculent form which the small crystals present of which rime is formed, shows that the vapour solidifies directly without passing through the liquid state. Hoarfrost, like dew, is formed on bodies which radiate most, such as the stalks and leaves of vege- tables, and is chiefly deposited on the parts turned towards the sky. We must distinguish between the dew formed in consequence of lowering of temperature by radiation, and the deposit formed by warm moist air passing over a cold wall ; in mild weather this deposit forms a liquid, and in severe weather a snow or icy coating. Unlike dew, a deposit of this kind is most abundantly found on good conductors, for they are the coldest. 1026, Snow. Sleet.—Svzow is water solidified in stellate crystals, vari- ously modified, and floating in the atmosphere. These crystals arise from the congelation of the minute vesicles which constitute the clouds, when the temperature of the latter is below zero. They are more regular when formed inacalm atmosphere. Their form may be investigated when they are collected —1028] Hail 1073 on a black surface and viewed through a strong lens. The regularity, and at the same time variety, of their forms are truly beautiful. Fig. 1051 shows some of these forms as seen through a microscope. Very roughly, a fall of one foot of snow may be taken as equal to an inch of rain. It snows most in countries near the poles, or lying high above the sea-level. By the limit of perpetual snow—or, briefly szow-/¢me—is meant that ‘height above the sea-level at which the snow does not melt, even in the hottest summers. It is lower nearer the poles than the equator : it does not depend solely on the latitude, but is influenced by many local circumstances. Steet is also solidified water, and consists of small icy needles pressed together in a confused manner. Its formation is ascribed to the sudden congelation of the minute globules of the clouds in an agitated atmosphere. Fig. 1051 When the ground is cooled below zero after severe frost and a thaw sets in, the moist air passing over the ground deposits its moisture, which is converted into a continuous sheet of ice ; this is known as glazed frost (the French verg/as) ; it may also occur when raindrops which have been cooled below zero in the higher regions of the air, and are accordingly in a state of superfusion (349), fall on the ground, which may even be above the freezing- point. 1027. Hail.—/az/ is a mass of compact globules of ice of different sizes which fall in the atmosphere. In our climate hail falls principally during spring and summer, and at the hottest times of the day; it rarely falls at night. The fall of hail is always preceded by a peculiar noise. Hail is generally the precursor of storms ; it rarely accompanies them, and follows them still more rarely. Hail falls from the size of a small pea to that of an egg or an orange, with a core of compressed snow which is sur- rounded by concentric layers of ice. While snowstorms may last for days, hailstorms do not last for more than a quarter of an hour. The formation of hailstones has never been altogether satisfactorily accounted for; nor, more especially, their great size. 1028. Ice. Regelation.—Ice is an aggregation of snow-crystals, such as are shown in fig. 105% The transparency of ice is due to the close contact 32 1074 Meteorology [1028— of these crystals, which causes the individual particles to blend into an un- broken mass, and renders the substance of¢ically, as well as mechanically, continuous. When large masses of ice slowly melt away, a crystalline form is sometimes seen by the gradual disintegration into rude hexagonal prisms ; a similar structure is frequently met with, but in greater perfection, in the ice-caves or glaciers of cold regions. An experiment of Tyndall shows the beautiful structure of ice. When a piece of ice is cut parallel to its planes of freezing, and the radiation from any source of light 1s permitted to pass through it, the disintegration of the substance proceeds in a remarkable way. By observing the plate of ice through a lens, numerous small crystals will be seen studding the interior of the block ; as the heat continues these crystals expand, and finally assume the shape of six-rayed stars of exquisite beauty. This is a kind of negative crystallisation, the crystals produced being composed of water; they owe their formation to the molecular disturbance caused by the absorption of heat from the source. Nothing is easier than to reproduce this phenomenon, if care be taken in cutting the ice. The planes of freezing can be found by noting the direction of the bubbles in ice, which are either sparsely arranged in striz at right angles to the surface, or thickly collected in beds parallel to the surface of the water. A warm and smooth metal plate should be used to level and reduce the ice to a slab not exceed- ing half an inch in thickness. A still more important property of ice remains to be noticed. Faraday discovered that when two pieces of melting ice are pressed together they freeze into one at their points of contact. This curious phenomenon is now known under the name of Regelatzon. The cause of it has been the subject of much controversy, but the simplest explanation seems to be that given by its discoverer. The particles on the exterior of a block of ice are held by cohesion on one side only: when the temperature is at o° C., these exterior particles, being partly free, are the first to pass into the liquid state, anda film of water covers the solid. But the particles in the interior of the block are bounded on all sides by the solid ice, the force of cohesion is here a maximum, and hence the interior ice has no tendency to pass into a liquid, even when the whole mass is at 0°. If the block is now split in halves, a liquid film instantly covers the fractured surfaces, for the force of cohesion on the fractured surfaces has been lessened by the act. By placing the halves together, so that their original position shall be regained, the liquid films on the two fractured surfaces again become bounded by ice on both sides. The film being excessively thin, the force of cohesion is able to act across it ; the consequence of this is, the liquid particles pass back into the solid: state, and the block is reunited by vegelation. Not only do ice and ice thus freeze together, but regelation also takes place between moist ice and any non-conducting solid body, as flannel or sawdust ; a similar explanation to that just given has been applied here, substituting another solid for the ice on one side. It must be remarked, however, that many eminent philosophers dissent from the explanation here given. Whatever may be the true cause of regelation, there can be no doubt that this interesting observation of Faraday’s explains many natural phenomena. For example, the formation of a snowball depends on the regelation of the -1030] Glaciers 1075 snow-granules composing it; and as regelation cannot take place at tem- peratures below o° C., for then both snow and ice are dry, it is only possible to make a coherent snowball when the snow is melting. The snow-bridges, also, which span wide chasms in the Alps and else- where, and over which men can walk in safety, owe their existence to the regelation of gradually accumulating particles of snow. We see an example of this formation of ice from pressure in the glazed appearance of the tracks in snow on roads over which heavy carts have passed. Bottomley has made a very instructive experiment which illustrates rege- lation. A block of ice is suspended on two supports, and a fine piano wire with heavy weights at each end 1s laid across it. After some time the wire has slowly cut its way through, but the cut surfaces have reunited, and, except- ing a few bubbles, show no trace of the operation ; the wire is below zero, as is proved by placing it in cold water, upon which some ice forms round it. 1029. Glaciers.—Tyndall applied this regelating property of ice to an explanation of the formation and motion of glaciers, of which the following is a brief description: In elevated regions, the szow-lime (1026) marks the boundary of eternal snow, for above this the heat of summer is unable to melt the winter’s snow. By the heat of the sun and the consequent percola- tion of water melted from the surface, the lower portions of the snow-field are raised to o°C. ; at the same time this part is closely pressed together. by the weight of the snow above ; regelation therefore sets in, converting the loose snow into a coherent mass. By increasing pressure the intermingled air which renders snow opaque becomes ejected and the snow becomes transparent ; ice is then formed. Its own weight and the pressure from behind urge downwards the glacier which has thus been formed. In its descent the glacier behaves like a river, passing through narrow gorges with a certain velocity, and then spreading out and moving more slowly as its bed widens. Further, just as the central portions of a river move faster than the sides, so Forbes ascertained that the centre of a glacier moves more quickly than its margin, and from the same reason (the difference in the friction encountered) the surface moves more rapidly than the bottom. To explain these facts Forbes assumed ice to be a viscous body capable of flexure, and flowing like lava ; but asice has not the properties of a viscous substance, the now generally accepted explanation of glacier motion is that supplied by the theory of regelation. According to this theory, the brittle ice of the glacier is crushed and broken in its passage through narrow channels, such as that of Trélaporte on Mont Blanc; and then, as it emerges from the gorge which confined it, becomes reunited by virtue of regelation ; in this instance forming the well-known Mer de Glace. By numerous experiments Tyndall established that regelation is adequate to furnish this explanation, and artificially imitated, on a small scale, the moulding of glaciers by the crushing and subsequent regelation of ice. 1030. Atmospheric electricity. | Franklin’s experiment.—The most frequent luminous phenomena, and the most remarkable for their effects, are those produced by the free electricity in the atmosphere. The first physicists who observed the electric spark compared it to the gleam of lightning, and its crackling to the sound of thunder. But Franklin, by the Ese: 1076 Meteorology | [1030- aid of powertul Leyden batteries, first established a complete parallelism between lightning and electricity; and indicated, in a memoir published in 1749, the experiments necessary to attract electricity from the clouds by means of pointed rods. The experiment was tried by Dalibard in France ; and Franklin, pending the erec- tion of a pointed rod on a spire in Philadelphia, had the happy idea of flying a kite, provided with a metal point, which could reach the higher regions of the atmosphere. In June, 1752, during stormy weather, he flew the kite in a field near Philadelphia. The kite was flown with ordinary packthread, at the end of which Franklin attached a key, and to the key a silk cord, in order to insulate the apparatus ; he then fixed the silk cord to a tree, and having presented his hand to the key, at first he obtained no spark. He was beginning to despair of success, when, rain having fallen, the cord became a good conductor, and a spark passed. Franklin, in his letters, describes his | emotion on witnessing the success of the experiment as being so great that he could not refrain from tears. Franklin imagined that the kite drew from the cloud its electricity ; it is, in fact, a simple case of induction, and depends on the inductive action which the thunder-cloud exerts upon the kite and the cord. 1031. Apparatus to investigate the electricity of the atmosphere.—To observe the electricity in fine weather, when the quantity is generally small, an ap- paratus may be used as devised by Saussure for this kind of investigation. It is an electroscope similar to that already described (774), but the rod to which the gold leaves are fixed is surmounted by a conductor 2 feet in length, and terminates in either a knob or a point (fig. 1052). To protect the apparatus against rain, it is covered with a metal shield 4 inches in diameter. The glass case is square instead of being round, and a divided scale on its inside face indicates the divergence of the gold leaves. This electrometer gives signs of atmospheric electricity only as long as it is raised in the atmosphere so that its pointed end is in layers of air of different electrical potential from its own. To ascertain the electricity of the atmosphere Saussure also used a covver ball, which he projected vertically with his hand. This ball was fixed to one end of a metal wire, the other end of which was attached to a ring, which could glide along the conductor of the electrometer. From the divergence of the gold leaves, the electrical condition of the air at the height which the ball attained could be determined. Becquerel, in ex- periments made on the St. Bernard, improved Saussure’s apparatus: by substituting for the knob an arrow, which was projected into the atmosphere by means of a bow. A gilt silk thread, 88 yards long, was fixed with one end to the arrow, while the other end was attached to the stem of an electro- -1031] Apparatus to investigate Atmospheric Electricity 1077 scope. Peltier used a gold-leaf electroscope, at the top of which was a somewhat large copper globe. Provided with this instrument, the observer places himself in a prominent position ; it is then quite sufficient to raise the electroscope even a foot or so to obtain signs of electricity. To observe the electricity of clouds, where the potential is very con- siderable, use is made of a long bar terminating in a point. This bar, which is insulated with care, is fixed to the summit of a building, and its lower end is connected with an electrometer, or even with electric chimes (fig. 738), which announce the presence of thunder-clouds. As, however, the bar can then give dangerous shocks, a metal ball must be placed near it, which is well connected with the ground, and which is nearer the bar than Fig. 1053 the observer himself; so that if a discharge should ensue, it will strike the ball, and not the observer. Richmann, of St. Petersburg, was killed in an experiment of this kind, by a discharge which struck him on the forehead. Sometimes also captive balloons or kites have been used, provided with a point, and connected by means of a gilt cord with an electrometer. A good collector of atmospheric electricity consists of a fishing-rod with an insulated handle which projects from an upper window. At the top is a bit of lighted tinder held in a metallic forceps, the smoke of which, being an excellent conductor, conveys the electricity of the air downa wire attached to the rod. A sponge moistened with alcohol, and set on fire, is also an excellent conductor. A convenient instrument for investigating atmospheric electricity was introduced by Lord Kelvin, one form of which, used in the Meteorological Observatory of Montseuris, is represented in fig. 1053. It consists of a large metal vessel, A, resting on three insulating glass legs fixed to the top 1078 Meteorology [1031- of a tall column of cast iron. A sheet-metal mantle, B, protects the supports from the rain. The apparatus is arranged in the open, and can be filled with water from a pipe, C. The water issues through a long lateral jet in A, in a stream so fine that the volume of the water is not appreciably altered. An insulated wire, z, passing through the column, connects the vessel A with an electrometer placed indoors. This plan of collecting the atmo- spheric electricity is adopted in balloons, where a flame, for instance, is out of the question. The manner in which the electricity of the atmosphere is registered is seen from fig. 1054, which represents the form in use at the above observatory. In a light-tight box is a band of sensitised photographic paper, stretched on the surface of a cylinder and moved by clockwork. AES ATT awa) Fig. 1054 In one side of the box is a long cylindrical glass lens, in front of which at E are two quadrant electrometers (802). Both of these are connected with the same collector of electricity, placed outside, and their sectors are charged by the same source of electricity, but one of them is ten times as sensitive as the other. Near one side of the box is a gas-burner with an opaque chimney, A, in two opposite sides of which are longitudinal slits, through which the light passes to two total-reflection prisms (557), # Z’, which are arranged so as to send two pencils of light on the mirrors, 7 mz’, of the electrometer. This is shown on a larger scale on the left of the figure: the two pencils fall upon the lens, L, which concentrates in a point the slices of light issuing from the chimney and reflected from the mirror. These follow 1032] Ordinary Electricity of the Atmosphere 1079 the motion of the mirror, and thus impress on the sensitive paper the curves of electrical potential of the air. There is also an arrangement by which an electromagnet puts the electrometers to earth for a few minutes at every hour, and thus discharges them. The mirrors revert then to their original position and commence a new trace. If we replace the electrometer with its mirror attached by a magneto- meter, we can easily see how the variations in the magnetic declination may be recorded (716). 1032. Ordinary electricity of the atmosphere.—-By means of the dif- ferent apparatus which have been described, it has been found that the presence of electricity in the atmosphere is not confined to stormy weather, but that the atmosphere always contains free electricity, in the vast majority of cases positive, but occasionally negative. When the sky is unclouded the potential is always positive, and it increases with the height above the ground. Its value is greatest in the highest and most isolated places. No trace of positive electricity is found in houses, streets, and under trees ; in towns, positive electricity is most perceptible in large open spaces, on quays, or on bridges. Lord Kelvin found in the Isle of Arran, at a height of 9 feet above the ground, a difference of potential equal to 200 to 400 Daniell’s elements, or from 216 to 432 volts. This represents a rise of potential of from 24 to 48 volts for each foot of ascent. This is subject to great varia- tion ; with winds from the north and north-east the potential was often six to ten times as much as the higher of these amounts. The change of potential is most rapid in cold dry weather, when the quantity of moisture in the air is at its lowest. Thus, at a temperature of —8° to —12° C., Exner found a change of 600 Daniells per metre in the direction of the vertical. Witha vapour-pressure of 2°3 mm. the change was 325, with 6°8 it was 116, and with 12°5 it was 68. Between 5 and 7°30 A.M. the positive electricity in the air is at a mini- mum ; it increases from 7 to 9.30 A.M., according to the season, and then attains its first maximum. It then decreases rapidly until from 2.30 to 4.39 P.M., and again increases till it reaches its second maximum, from 6.30 to 9.30 P.M. ; the remainder of the night the electricity decreases until sun- rise. Thus the greatest amount of electricity is observed when the baro- metric pressure is highest. These increasing and decreasing periods, which are observed all the year, are more perceptible when the sky is clearer and the weather more settled. The positive electricity of fine weather is much stronger in winter than in summer. It may, in short, be said that electricity of the air follows the opposite course to that of temperature and moisture. When the sky is clouded, the electricity is sometimes positive and some- times negative. According to Palmieri, the occurrence of negative electricity is a certain indication that within a distance of 4o miles it either rains, or snows, or hails. It often happens that the electricity changes its sign several times in the course of the day, owing to the passage of an electrified cloud. During storms, and when it rains or snows, the atmosphere may be positively electrified oneday, and negatively the next, and the numbers of the two sets of days are virtually equal. 1080 Meteorology [1032 - During a thunderstorm the changes in potential and sign of electricity are so rapid that the photographic method of registration fails. From a long series of observations on the electricity of the atmosphere made in the early morning, Dellman found that the electricity increased with the density of the fog, but in a far more rapid ratio. The electricity of the ground was found by Peltier to be always negative, and this seems to be the cardinal fact in reference to atmospheric electricity ; it is so, however, to different extents, according to the hygrometric state and temperature of the air. The density is, moreover, exceedingly small, being calculated at 0°00036 unit per square centimetre, from which it follows: that the electrical pressure (759) is o'o0000082 dyne per square centimetre, or less than the millionth of a milligramme in weight. Even if the pressure were ten times as great, it would be insufficient to raise even the lightest bodies. 1033. Causes of atmospheric electricity.—Although many hypotheses have been propounded to explain the origin of atmospheric electricity, it must be confessed that our knowledge is in an unsatisfactory state. Volta first showed that the evaporation of water produced electricity. Pouillet subsequently showed that no electricity is produced by the evapo- ration of distilled water ; but that if an alkali or a salt is dissolved, even in small quantity, the vapour is positively and the solution is negatively electrified. The reverse is the case if the water contains acid. Hence it has been assumed, that as the waters which exist on the surface of the earth and on the sea always contain salt dissolved, the vapours disengaged ought to be positively and the earth negatively electrified. The devolopment of electricity by evaporation may be observed by heating strongly a platinum dish, adding to it a small quantity of liquid, and placing it on the upper plate of the condensing electroscope (fig. 758), taking care to connect the lower plate with the ground. When the water of the capsule is evaporated, the connection with the ground is broken, and the upper plate raised. The gold leaves then diverge if the water contains salts, but remain quiescent if the water is pure. Reasoning from such experiments, Pouillet ascribed the development of electricity by evaporation to the separation of particles of water from the substances dissolved ; but Reich and Riess showed that the electricity disengaged during evaporation could be attributed to the friction which the particles of water carried away in the current of vapour exert against the sides of the vessel, just as in Armstrong’s electrical machine (780). By a series of experiments, Gaugain arrived at the same result. Sohncke recalls an experiment of Faraday which he has repeated, showing that the friction of minute vesicles of water against dry ice is an abundant source of electricity ; he ascribes atmospheric electricity to this origin, suggesting that in the upper regions particles of both water and ice may coexist. ‘The ice particles become positively electrified, while those of water are negative. When these fall in rain, they carry with them their negative electricity. A similar theory has been propounded by Luvini. 1034. Electricity of clouds.—Clouds are in general electrified usually positively, but sometimes negatively, and differ only in their higher or lower potential. The formation of positive clouds is by some ascribed to —1035] Lightning 1081 the vapour disengaged from the ground and condensed in the higher regions. Negative clouds are supposed to result from fogs, which, by their contact with the ground, become charged with negative electricity, which they retain on rising into the atmosphere ; or to have been separated from the ground by layers of moist air, and negatively electrified by induction from the positive clouds, which have repelled into the ground positive electricity. Thunder-clouds are sometimes as low as 700 to 1,000 feet ; but their usual height appears to be 3,000 to 6,000 feet. Whatever be the origin of atmospheric electricity, there can be no doubt that the invisible aqueous vapour is the carrier of it, and it is easy to explain the high potential of clouds from the condensation of this vapour. For suppose 1,000 vapour-particles, each possessing the same charge of electricity, coalesce to form a single droplet, the diameter of such a droplet will be ten times that of the individual particles—that is, its capacity is ten times as great, since the capacity is equal to the radius (762) ; but the quantity of electricity will be I,ooo times as great as on the small one, and therefore the potential will be 100 times as great. Now the number of vapour-particles which go to form a single droplet is rather to be counted by billions ; hence, however small be the finite value which we assign to the potential of the electricity of the vapour-particles, that of the drops will be enormously pico and sufficient to account for the high potential of clouds. 1035. Lightning.—This, as is well known, is the dazzling light emitted by the electric spark when it shoots from blonds charged with electricity. In the lower regions of the atmosphere the light is white, but in the higher regions, where the air is more rarefied, it takes a somewhat reddish tint ; as does the spark of the electrical machine in a rarefied medium (808). The flashes of lightning are often more than a mile, and sometimes extend to four or five miles, in:length ; they generally pass through the atmosphere in a zigzag direction—a phenomenon ascribed to the resistance offered by the air condensed by the passage of a strong discharge. The spark then diverges from a right line, and takes the direction of least resist- ance. In avacuum, electricity passes in a straight line. De la Rue and Miiller have calculated that the potential required to produce a flash a mile in length would be that of 3,516,480 of their cells (833). We cannot, however, regard the length of a lightning flash as the direct striking distance between two conductors. Owing to the number of droplets met on its path, the discharge is rather to be compared with that of the luminous tubes and panes (811). ‘The experiments of Mascart on the rela- tion between the striking distance (810) and the potential required to pro- duce it, show that the striking distance increases far more rapidly than the potential. Thus, while the potential required for a striking distance of 1 cm. is represented by 8°3, for 4 cm. it iS 15:9, for 8 cm. 20°5, and for 15 cm. 233. From this it is possible that a lightning discharge is produced by a difference of potentials between two clouds which is not greatly out of proportion with those obtained by our electrical machines. Several kinds of lightning flashes may be distinguished—1, the zigzag flashes, which move with extreme velocity in the form of a line of fire with 1082 Meteorology ay [1035- sharp outlines, closely resembling the spark of an electrical machine. The recent investigation of the shape of lightning discharges by means of extra rapid photographic dry plates (622) has shown that the path of a dis- charge is not so sharply zigzag as is usually represented, but has more the shape of the course of a river as shown on a map, and with frequent branch- ings; 2, the see¢ flashes, which, instead of being linear, like the preceding, fill the entire horizon without having any distinct shape. This kind, which is most frequent, appears to be produced in the cloud itself, and to illuminate the mass. According to Kundt, the number of sheet discharges is to the zigzag discharges as 11:6; and from spectrum observations it would appear that the former are brush discharges between clouds, while the latter are true electrical discharges between the clouds and the earth. Another kind, called heat lightning, is ascribed to distant lightning flashes which are below the horizon, but illuminate the higher strata of clouds, so that their bright- ness is visible at great distances ; they produce no sound, probably in con- sequence of the fact of their being so far off that the rolling of thunder cannot reach the ear of the observer. There is, further, the very unusual phenomenon of glode lightning, or the flashes which appear in the form of globes of fire 18 inches in diameter. These, which are sometimes visible for as much as ten seconds, descend from the clouds to the earth with such slowness that the eye can follow them. They often rebound on reaching the ground ; at other times they burst and explode with a noise like that of the report of many cannon. No adequate explanation has been given of these, though Planté with a large battery of his cells has imitated the phenomena. The duration of the light of the first three kinds does not amount to the millionth of a second, as was determined by Wheatstone by means of his rotating wheel, which was turned so rapidly that the spokes were invisible : on illuminating it by the lightning flash, its duration was so short that whatever the velocity of rotation of the wheel, it appeared quite stationary ; that is, its displacement is not perceptible during the time the lightning exists. The hight produced by a lightning flash must be comparable to the sun in brightness, though it does not appear to us brighter than ordinary moon- light. But considering its excessively brief duration, and that the full effect of any light on the eye is only produced when its duration is at least the tenth of a second, it follows that a landscape continuously illuminated by the lightning flash would appear 100,000 times as bright as it actually appears to us during the flash. Here also may be mentioned the phenomenon known as St. Elmo's fire, which occurs in a highly electrical state of the atmosphere when the clouds are low. It isa sort of brush discharge (809), appearing like small flames issuing from prominent point-objects such as masts, tops of trees, lightning- conductors ; it has also been observed on the points of helmets and lances, alpenstocks ; it is of course most easily seen in the dark, and is accompanied by a slight rustling noise. On the sea during thunder-storms it is not un- common on mastheads and yardarms. 1036. Thunder.— 7hunder is the violent report which succeeds lightning in stormy weather. The occurrence of lightning and thunder is practically simultaneous, but an interval of several seconds is generally observed -1037] Thunder 1083 between the perception of these two phenomena, which arises from the fact that sound travels at the rate of only about 1,100 feet in a second (235), while the passage of light is almost instantaneous. Hence an observer will hear the noise of thunder only five or six seconds, for instance, after the lightning, according as the distance of the thunder-cloud is five or six times 1,100 feet. The noise of thunder arises in some such manner as the crack of a whip or the report of a gun. The lightning discharge, whether by heating the air or by a purely mechanical action, such as is illustrated with Kinnersley’s thermometer (fig. 773), is expanded with explosive violence, which is only possible by a compression of the surrounding air. This com- pressed air rushes in to fill the partial vacuum, forming itself, in turn, a partial vacuum, and thus, giving rise to alternate condensation and rarefaction, constitutes the wave-motion producing the sound. The depth of the note represents a great wave-length, and shows that the disturbance must have a great length. Near the place where the lightning strikes the sound is sharp and of short duration. Ata greater distance a series of reports are heard in rapid succession. At a still greater distance the noise, feeble at first, changes into a prolonged rolling sound of varying intensity. If the lightning is at a greater distance than 14 or 15 miles, it is no longer heard, for sound is more imperfectly propagated through air than through solid bodies : hence there are lightning discharges without thunder ; these occur at times when the sky is cloudless. The rolling of thunder, the alternate rise and fall of the sound, occurs ordinarily with sheet lightning, less so with forked lightning, when the sound is short and crackling. Various causes contribute to produce the rolling ; one cause is the reflec- tion from the ground, from clouds, and even from layers of air of unequal density. Lightning, too, is not a single discharge, but a series of discharges, each of which gives rise to a particular sound, and which are variously reflected by objects which they meet on their path. If two waves reach the ear simultaneously they strengthen each other if they are in the same phase, but if in different ones they interfere partially or wholly and the sound sinks. Thus it may happen that the sound after sinking may rise again. This is the well-known phenomenon of beats (266). The phenomenon has finally been ascribed to the zigzags of lightning themselves, assuming that the air at each salient angle is at its greatest compression, which would produce the unequal intensity of the sound. The distance of the nearest point of a lightning flash is obtained in kilometres if we divide the time in seconds which elapses between the lightning flash and the beginning of the thunder by 3. This is evident since s = v¢ (233) and v the velocity found is 330 metres or 4 kilometre per second. 1037. Effects of lightning.—The lightning discharge is the electric discharge which strikes between a thunder-cloud and the ground. The latter, by the induction of the electricity from the cloud, becomes charged with contrary electricity ; and when the tendency of the two electricities to com- bine exceeds the resistance of the air, the spark passes, which is often ex- pressed by saying that ‘a thunderbolt has fallen. Lightning in general strikes from above, but ascending lightning is also sometimes observed ; 1084 Meteorology [1037— probably this is the case when the clouds being negatively the earth is positively electrified ; for experiments show that at the ordinary pressure positive electricity passes through the atmosphere more easily than negative electricity. The discharge usually falls first on the nearest and best conducting objects, and, in fact, trees, elevated buildings, metals, are particularly struck by the discharge. Hence it is imprudent to stand under trees during a thunderstorm. According to Hellman, the frequency with which trees are struck is: fir 5, beech 7, oak 18; in like manner of soils the ratio is : chalk 1, clay 7, sand 9g, and loam 22. The effects of lightning are very varied, and of the same kind as those of Leyden batteries (805), but of far greater power. The lightning discharge kills men and animals, ignites combustibles, melts metals, breaks bad con- ductors in pieces. When it penetrates the ground it melts the silicious substances on its path, and thus produces in the direction of the discharge those remarkable vitrified tubes called /ulgurztes, some of which are as much as 12 yards in length ; in most cases there are found to be accumulations of water below such fulgurites. When it strikes bars of iron it magnetises them, and often inverts the poles of compass needles. The action of lightning on trees is very singular. When struck by it they are sometimes stripped of their bark, either wholly or partially, or the wood is often split into thin laths, or intoa mass of fibres. Franklin ascribed this to the sudden evaporation of the water. After the passage of lightning a highly peculiar odour is frequently produced, like that perceived in a room in which an electrical machine is being worked. This is due to the formation of ozone, a peculiar allotro- pic modification of oxygen (815). An electrified cloud forms with the earth below a condenser, the intervening mass of air being the dielectric. This mass of air is therefore in a state of strain, like the dielectric in a charged Leyden jar, and it is to this state of strain which precedes the actual discharge, rather than to the discharge itself, that is due the production of ozone. Heated air conducts better than cold air, probably only owing to its lesser density. Hence it is that large numbers of animals are often killed by a single discharge, as they crowd together in a storm, and a column of warm air rises from the group. 1638. Return shock.—This is a violent and sometimes fatal shock which men and animals experience, even when at a great distance from the place where the lightning discharge passes. It is caused by the inductive action which the thunder-cloud exerts on bodies placed within the sphere of its activity. ‘These bodies are then, like the ground, charged with the opposite electricity to that of the cloud ; but when the latter is discharged by the recombination of its electricity with that of the ground, the induction ceases, and the bodies reverting rapidly from the electrical state to the neutral state, the concussion in question is produced—the return or back shock. A gradual decomposition and reunion of the electricity produces no visible effects ; yet it is alleged that such disturbances of the electrical equilibrium are perceived by nervous persons. 1039] Lightning-Conductor 1085 The return shock is always less violent than the direct one ; there is no instance of its having produced any inflammation, yet plenty of cases in which it has killed both men and animals ; in such cases no broken limbs, wounds, or burns are observed. | The return shock may be imitated by placing a gold-leaf electroscope connected by a wire with the ground near an electrical machine ; when the machine is worked, at each spark taken from the prime conductor the gold leaves of the electroscope suddenly diverge. It is stated that persons struck by lightning often lose their lives only by a temporary injury to the nerves which control the act of respiration ; so that under favourable circumstances such persons might probably be saved by producing artificial respiration. 1039. Lightning-conductor.—This was invented by Franklin in 1755. There are two principal parts in a lightning-conductor, the rod and the conductor. The vod (fig. 1055) is a pointed bar of iron, preferably galvanised, P, fixed vertically to a tube or rod of iron, which, by means of a collar aa, and tube g, is fitted on the roof of the edifice to be protected ; it is from 6 to Io feet in height, and its basal section is about 2 or 3 inches in diameter. The cov- ductor is best formed of a wire rope, C, attached to the rod by a metal collar, 4. The section of the metallic conductor ought to be about half a square inch, and the individual wires 0°04 to o'06 inch in diameter: they ought to be twisted in strands, like an ordinary cord. The conductor is usually led into a well, a pond, or other continuous mass of water, and to connect it better with the ground it should terminate in a plate called an earth plate, or if a strand of wires the separate wires should be spread out. This plate should be of the same metal as the conductor, so as to avoid the possibility of local galvanic action (837), by which one or the other metal would be eaten away and the continuity destroyed. If there is no well near, a hole is dug in the soil to the depth of 6 or 7 yards, or to where the earth is permanently damp ; where the ground is naturally dry it is advantageous to direct the rainfall from the roof towards where the plate is placed, and the ends of the conductor having been introduced, the hole is filled with powdered coke, which conducts very well. A good earth contact is obtained when it is possible to connect the wire conductors with large iron gas or water pipes. The action of a lightning-conductor is regarded as an illustration of the action of induction and of the property of points (758) ; when a storm cloud positively electrified, for instance, forms in the atmosphere, it acts inductively on the earth, repels the positive and attracts the negative electricity, which accumulates on bodies placed on the surface of the soil, the more abundantly as these bodies are at a greater height. The density is then greatest on the highest bodies, which are therefore most exposed to the electric discharge ; but if these bodies are provided with metal points, like the rods of conductors, the negative electricity, withdrawn from the soil by the influence of the cloud, 1086 | Meteorology [1039- flows into the atmosphere, and neutralises the positive electricity of the cloud. Hence the action of the lightning-conductor is twofold ; not only does it tend to prevent the accumulation of electricity on the surface of the earth, but it also tends to restore the clouds to their natural state, both which concur in preventing lightning discharges. This mode of action of lightning-conductors is often overlooked ; it is stated in reference to Pietermaritzburg that until lightning-conductors became common in that town it was constantly visited by thunderstorms at certain seasons. They come as frequently as ever, but cease to give flashes on reaching the town ; they do so, however, when they have passed over it. The quantity of electricity is, however, sometimes so abundant that the lightning-conductor is inadequate to discharge the elec- tricity accumulated, and the lightning strikes ; but the conductor receives the discharge, in consequence of the greater conductivity, and the edifice is preserved. A conductor, to be efficient, ought to satisfy the following conditions :— (i.) The rod ought to be so large as not to be melted if the discharge passes. (ii.) It ought to terminate in a point, or in several points, to give readier issue to the electricity disengaged by induction from the ground. (ii1.) Copper was formerly preferred to iron owing to its greater conductivity. But the lightning discharge is strictly analogous to the discharge of a Leyden jar, which according to circumstances may form either a continuous discharge like a steady current, or a series of oscillations (805). In the latter case the discharge is restricted to the surface owing to the effect of impedance (933), which may have a greater influence than the ohmic resistance, so that the advantage of the greater conducting power of copper disappears. The con- ductor must be continuous from the point to the ground, and the connection between the rod and the ground must be as intimate as possible; this is the most important of all, and the one point most frequently neglected in the older arrangements. A lightning-conductor with bad earth contact is not only useless but dangerous. In regard to this, it may be said that the best earth for contact is water. The continuity of the conductor may be tested by means of a voltaic cell and a portable form of galvanometer. (iv.) If the building which is provided with a lightning-conductor contains metallic surfaces of any extent, such as zinc roofs, metal gutters, or ironwork, these ought to be connected with the conductor, or, still better, have each a separate earth connection. If the last two conditions are not fulfilled, there is a great danger of lateral discharges—that is to say, that the discharge takes place between the conductor and the edifice, and then it increases the danger. Colladon concludes, from the observation of a series of lightning dis- charges, that a tall tree, such as a poplar, whose roots are in moist ground, may act as a good lightning-conductor, if on the other side of the house there does not happen to be a well or pool, towards which the electricity can spring through the house. The requirements above laid down are based on the older view of the protection of buildings. Another mode of protection is based on the screen- ing action of a closed conducting surface either continuous or formed of wire gauze. Suchan enveloping conductor, as we have seen (757), protects a body inside it from external electrical action, and probably does so also in the case of violent and sudden electrical discharges. If a building could be -1040] Rainbow 1087 surrounded by a wire cage which itself had good earth contact, this would be an efficient protection. Accordingly, an alternative plan aims at provid- ing all the ridges, eaves and corners, and chimneys of a building with abun- dance of galvanised iron wire, preferably barbed, and with wire netting, all in metallic connection with each other and with the earth. Copper conductors with a surface of 50 sq..mm. have been known to be raised to nearly a red heat by a lightning discharge, and such as have a section of 5 sq. mm. have frequently been melted. An estimate based on this fact gives for the quantity of electricity passing in such a discharge values of not less than 50 nor more than 290 coulombs. 1040. Rainbow.—The vazzdow is a luminous phenomenon which appears in the clouds opposite the sun when they are resolved into rain. It consists of seven concentric arcs, presenting successively the colours of the solar spectrum. Sometimes only a single bow is perceived, but there are usually two ; a lower one, the colours of which are very bright ; and an external or secondary one, which is paler, and in which the order of the colours is re- versed. In the interior rainbow the red is the highest colour ; in the other rainbow the violet is. It is seldom that three bows are seen ; theoretically a greater number may exist, but their colours become so faint that they can- not be perceived. The phenomenon of the rainbow is produced by decomposition of the white light of the sun when it passes into the drops, and by its reflection from their inside face. In fact, the same phenomenon is witnessed in dew- drops and in jets of water—in short, wherever sunlight passes into drops of water under a certain angle. The appearance and the extent of the rainbow depend on the position of the observer, and on the height of the sun above the horizon ; hence only some of the rays refracted by the raindrops, and reflected in their concavity to the eye of the spectator, are adapted to produce the phenomenon. Those which do so are called effective rays. To explain this let us suppose z (fig. 1056) to be a drop of water, into which a solar ray S a penetrates. At a point of incidence, a, part of the light is reflected from the surface of the liquid ; another, entering it, is de- composed and traverses the drop in the direction a 6. Arrived at 4, part of the light emerges from the raindrop, the other part is reflected from the concave surface, and tends to emerge at g. At this point the light is again partially reflected ; the remainder emerges in a direction gO, which forms with the incident ray, S a, an angle called the angle of deviation. It is such rays as gO, proceeding from the side next the observer, which produce on the retina the sensation of colours, provided the light is sufficiently intense. It can be shown mathematically that in the case of a series of rays which impinge on the same drop, and only undergo one reflection in the interior, the angle of deviation increases from the ray S’’7, for which it is zero, up toa certain limit, beyond which it decreases, and that near this limit rays passing parallel into a drop of rain also emerge parallel. From this parallelism a beam of light is produced sufficiently intense to impress the retina ; these are the rays which emerge parallel and are efficient. As the different colours which compose white light are unequally refran- 1088 Meteorology [1040-. gible, the maximum angle of deviation is not the same for all. For red rays the angle of deviation corresponding to the active rays is 42° 2’, and for violet rays itis 40° 17’. Hence, for all drops placed so that rays proceeding from the sun to the drop make, with those proceeding from the drop to the eye, an angle of 42° 2’, this organ will receive the sensation of red light ; this will be the case with all drops situated on the circumference of the base of a cone, the summit of which is the spectator’s eye; the axis of this cone is parallel to the sun’s rays, and the angle formed by the two opposed generating lines is 84° 4’. This explains the formation of the red band in the rainbow ; the angle of the cone in the case of the violet band is 80° 34’. The cones corresponding to each band have a common axis called the visual axts. As this right line is parallel to the rays of the sun, it follows that when this axis is on the horizon, the visual axis is itself horizontal, and the rainbow appears as a semicircle. If the sun rises, the visual axis sinks, and with it the rainbow. Lastly, when the sun is at a height of 42° 2’, the Fig. 1056 arc disappears entirely below the horizon. Hence the rainbow is never seen except in the morning and evening. What has been said refers to the interior arc. The secondary bow is formed by rays which have undergone two reflections, as shown by the ray S’id feO, inthe drop g. The angle S’IO formed by the emergent and incident rays is called the angle of deviation. The angle is no longer suscep- tible of a maximum, but of a minimum deviation, which varies for each kind of rays, and to which also efficient rays correspond. It is calculated that the minimum angle from violet rays is 54°7’, and for red rays only 50° 57’ ; hence it is that the red bow is here on the inside, and the violet arc on the outside. There is a loss of light for every internal reflection in the drop of rain, and therefore the colours of the secondary bow are always feebler than those of the internal one. The secondary bow ceases to be visible when the sun is 54° above the horizon. The moon sometimes produces rainbows like the sun, but they are very pale. 1o41. Aurora borealis.—The aurora borealis, or northern light, or more # . a ae iol Wi gtt sc ye o < —— 4 ¢ Fy, Fi at i SS oe TH. LONDON. SPOTTISWOCODE & Co —1041] Aurora Borealis 1089 properly folar aurora, is a remarkable luminous phenomenon which is fre- quently seen in the atmosphere in high latitudes. Fig. 1057 represents an aurora borealis observed at Bossekop, in Lapland, lat. 70°, in the winter of 1838-39. Plate III. represents a very beautiful aurora observed by Lemstrém on the north coast of Norway. The radial divergence of the aurora and the convergence towards a corona is due to an effect of perspective. The work of this author (Z’Auwrore Boréale, Gauthier Villars, Paris) is a storehouse of information on this subject. A French scientific commission to the North observed 350 aurore boreales in 200 days ; it appears that at the poles, nights without an aurora borealis are quite exceptional, so that it may be assumed that they take place every night, though with varying intensity: They are visible at a considerable distance from the poles, and over an immense area. Some- Fig. 1057 times the same aurora borealis has been seen at the same time at places so widely apart as Moscow, Warsaw, Rome, and Cadiz. The height of the aurora above the surface of the ground is probably lower than has generally been stated. Lemstrém holds that from 22 to 44 miles is a close approximation to the truth ; and it may be regarded as certain that even in more southern latitudes the aurora is often seen much lower—at a height of two or three miles, for instance. In polar countries certain forms of aurora, more especially those of weak flames, are seen to proceed from the ground on the tops of certain mountains. They are most frequent at the equinoxes, and least so at the solstices. The number differs in different years, attain- ing a maximum every II years at the same time as the sun-spots, and like these a minimum which is about five or six years from the maximum. The years 1844, 1855, 1866, and 1877 were poor in the appearance of the aurora. AA 1090 Meteorology [1041- There is, moreover, a period of about 60 years ; for the years 1728, 1780, and 1842 have been remarkable for the prevalence of the aurora. The last two periods are also remarkable for the occurrence of disturbances in the earth’s magnetism. Numerous hypotheses have been devised to account for the aurore boreales. As they share the rotation of the earth, they must have an atmo- spheric origin. Their direction is not due north and south, but is always parallel to that of the dipping-needle, pointing to the magnetic pole ; this, together with their action on the magnetic needle (708), seems to prove that they ought to be attributed to electric currents in the higher regions of the atmosphere. In high latitudes the aurora borealis acts powerfully on the wires of the electric telegraph; the alarums are for a long time violently rung, and telegraphic messages frequently interrupted, by the spontaneous abnormal working of the apparatus (915). In the lower discharges a crack- ling sound has been heard, and during balloon ascents a strong smell of ozone has been perceived when the balloon was among the luminous rays. The spectrum of the aurora borealis has been found to consist of several lines in the green, and of an indistinct line in the blue ; to which must be added a red line due to the red protuberances ; these lines are the same as those of nitrogen, greatly rarefied and at a low temperature ; one special line between the green and the yellow, and called the yellow line, is so characteristic of the aurora that it is visible even when the eye can discern no other trace of this light ; this line has not been produced in laboratory experiments. De la Rive held that aurore boreales were due to electric discharges which take place in polar regions between the positive electricity of the atmosphere and the negative electricity of the earth. The positively elec- trified aqueous vapours are supposed to be carried by the equatorial current in the higher regions of the atmosphere to the poles, where the neutralisa- tion takes place. These discharges produce luminous appearances of the same kind as are observed in Geissler’s tubes ; and De la Rive showed by means of an apparatus specially devised for the purpose (fig. 980) that the forms of the luminous phenomena are in accordance with this theory. By direct experiments Lemstrém has been able to imitate and reproduce a peculiar form of aurora observed in winter as a flame-like appearance on the tops of two mountains 800 and 1,100 metres in height, and to show that it is of electrical origin. He erected on the summit of a hill a system of pointed rods extending over a surface of nearly 4,000 square feet ; each rod was carefully insulated from the earth by means of a Mascart’s insulator (fig. 714), but was connected with the rest, and an insulated wire led down from this system into the valley, where it was connected with one ter- minal of a galvanometer, the other being put to earth. The existence of a positive current from the air to the earth was observed, and at the same time yellowish-white columns of light, reaching to a height of 120 metres, were observed to issue from the points. Observed with the spectroscope it gave the characteristic lines between D and E. Making similar experiments on even a larger scale in Lapland on a detached peak, he observed that the characteristic luminous phenomena were produced there, while the neighbouring peaks remained dark. -—1043] Mean Temperature 1OQI The investigations of Exner relative to the fall ot atmospheric electrical potential lend a further support to the view that the aurora is due to elec- tricity. In the polar regions the rate of fall of potential is 13 times greater in summer, and 18 times greater in winter than at the equator. Hence an electrical phenomenon, which depends on the magnitude of this fall of potential, must be more intense in winter and in high latitudes than in summer and in the torrid zones. The occurrence of irregular currents of electricity which manifest them- selves by abnormal disturbances of telegraphic communications is not in- frequent : such currents have received the name of earth currents. Sabine held that irregular magnetic disturbances are due to a peculiar action of the sun, and are probably independent of its radiant heat and light. It has also been ascertained that the aurora borealis as well as earth currents in- variably accompanies these magnetic disturbances. According to the late . Balfour Stewart, aurorz and earth currents are to be regarded as secondary phenomena due to small but rapid changes in the earth’s magnetism : he likened the body of the earth to the magnetic core of a Ruhmkorft’s coil (949) : the lower strata of the atmosphere forming the insulator, while the upper and rarer, and therefore electrically conducting, strata may be considered as the peony coil. On this analogy the sun may perhaps be likened to the primary current which performs the part of producing changes in the magnetic state of the core. Now in Ruhmkorff’s coil the energy of the secondary current is derived from that of the primary current. Thus, if the analogy be correct, the energy of the aurora borealis may in like manne: come from the sun ; but until we know more of the connection between the sun and terrestrial magnetism, these ideas are to be accepted with some reserve. CLIMATOLOGY 1042. Mean temperature.—The mean daily temperature is that obtained by adding together 24 hourly observations, and dividing by 24. A very close approximation to the mean temperature is obtained by taking the mean of the highest and lowest temperatures of the day and of the night, which are determined by means of the maximum and minimum ther- mometers. These ought to be protected from the sun’s rays, to be raised above the ground, and far from all objects which might influence them by their radiation. The temperature of a month is the mean of the temperature of 30 days, and the temperature of the year is the mean of those of 12 months. Finally, the temperature of a place is the mean of its annual temperatures for a great number of years. The mean temperature of London is 8:28° C., or 46°9° F. The temperatures in all cases are those of the air, and not those of the ground. 1043. Causes which modify the temperature of the air.—The principal causes which modify the temperature of the air are the latitude of a place, its height, the direction of the winds, and proximity of seas. Influence of the latitude——The influence of the latitude arises from the 4A2 1092 Meteorology [1048 - greater or less obliquity of the solar rays, for as the quantity of heat absorbed is greater the more perpendicular are the rays (421), the heat absorbed de- creases from the equator to the poles, for the rays become more oblique. This loss is, however, in summer, in the temperate and arctic zones, partially compensated by the length of the days. Under the equator, where the length of the days is constant, the temperature is almost invariable ; in the latitude of London, and in more northerly countries, where the days are very unequal, the temperature varies greatly ; but in summer it sometimes rises almost as high as under the equator. The lowering of the temperature produced by the latitude is small; thus, in a latitude 115 miles north of Paris, the temperature is only 1° C. lower. Influence of hetght.—The height of a place above the sea level has a much more considerable influence on the temperature than its latitude. The cooling on ascending in the atmosphere has been observed in balloon ascents, and a proof of it is seen in the perpetual snows which cover . the highest mountains. Itis due in part tothe greater rarefaction of the air, which necessarily diminishes its absorbing power ; besides which the air is at a greater distance from the ground, which heats it by contact ; and finally, dry air is very diathermanous. The law of the diminution of temperature corresponding to greater heights in the atmosphere has not been made out, in consequence of the numerous disturbing causes which modify it, such as the prevalent winds, the hygrometric state, the time of day, the season of the year, &c. The difference between the temperatures of two places at unequal heights is not proportional to the difference of level, but for moderate heights an approxi- mation to the law may be made. As the mean of a series of very careful observations made during balloon ascents, a diminution of 1° C. corresponded to an increase in height of 232 yards. It will thus be seen that at a certain height above the ground there must be a surface or layer where the temperature is uniformly zero. The height of this isothermal surface (1045) will vary materially with the time of the year, being lower in the cold months: it varies also with the time of day, rising rapidly about midday. In summer this height may be taken at from 3,400 to 3,700 metres above the sea-level. Direction of winds.—As winds share the temperature of the countries which they have traversed, their direction exercises great influence on the air in any place. In Paris, the hottest winds are the south ; then come the south-east, the south-west, the west, the east, the north-west, north, and lastly, the north-east, which is the coldest. The character of the wind changes with the seasons ; the east wind, which is cold in winter, is warm in summer. Proximity of the sea.—The neighbourhood of the sea tends to raise the temperature of the air, and to render it uniform. The average temperature of the sea in equatorial and polar countries is always higher than that of the atmosphere. With reference to the uniformity of the temperature, it has been found that in temperate regions—that is, from 25° to 50° of latitude— the difference between the highest and lowest temperature of a day does not exceed, on the sea, 2° to 3° ; while upon the continent this amounts to from 12° to 15°. Inislands the uniformity of temperature is very perceptible, even No. 5. ISOTHERMS- FOR JULY: | ———— yas Sa dit iat yi yp Ww TMK A via | | LS a a a Ea 70. 50 60 60 50 / : f fl | + > f) sy ae IN | Ne af n|| | |! Niso. 170 160 150 140 130 120° 110 100 90 80 70 == 4 | | —— aes Ses = | ] H I } -1046] Climase 1093 during the greatest heats. In continents, on the contrary, the winters for the same latitudes become colder, and the difference between the tempera- ture of summer and winter becomes greater. 1044. Gulf Stream.—A similar influence to that of the winds is exerted by currents of warm water. To one of these, the Gulf Stream,,the mildness of the climate in the north-west of Europe is mainly due. This great body of water, taking its origin in equatorial regions, flows through the Gulf of Mexico, whence it derives its name; passing by the southern shores of North America, it makes its way in a north-westerly direction across the Atlantic, and finally washes the coast of Ireland and the north-west of Europe generally. .Its temperature in the Gulf is about 28° C. ; and it is usually a little more than 5° C. higher than the rest of the ocean on which it floats, owing to its lower specific gravity. Toits influence is due the milder climate of West Europe as compared with that of the opposite coast of America ; thus the river Hudson, in the latitude of Rome, is frozen over three months in the year. It also causes the polar regions to be separated from the coasts ot Europe by a girdle of open sea; and thus the harbour of Hammerfest is open the year round. Besides this influence in thus moderating climate, the Gulf Stream is an important help to navigators. 1045. Isothermal lines.— When on a map all the points whose tempera- ' ture is known to be the same are joined, curves are obtained which Hum- boldt first noticed, and which he called zsothermal lines. If the temperature of a place only varied with the obliquity of the sun’s rays—that is, with the latitude—isothermal lines would all be parallel to the equator ; but as the temperature is influenced by many local causes, especially by the height, the isothermal lines are always more or less curved. On the sea, however, they are almost parallel. Maps 4, 5, and 6 represent these lines for the Year, for January, and for July. A distinction is made between zsothermal lines, tsotheral lines, and iso- chimenal lines, where the mean general, the mean summer, and the mean winter temperatures are respectively constant. An zsothermal zone is the space comprised between two isothermal lines. Kupffer also distinguishes Zsogeothermic lines where the mean temperature of the soil is constant. 1046. Climate.—By the climate of a place are understood the whole of the meteorological conditions to which the place is subjected ; its mean annual temperature, summer and winter temperatures, and the extremes within which these are comprised. Some writers distinguish seven classes of climates, according to their mean annual temperature: a hot climate from 30° to 25° C. ; a warm climate from 25° to 20° C.; a mild climate from 20° to 15° C.; a ¢emperate climate from 15° to 10° C. ; a cold climate from 10° to 5° C.;a very cold climate from 5° to zero C. ; and an arctic climate where the temperature is below zero. Those climates, again, are classed as constant climates where the dif- ference between the mean and summer and winter temperatures does not exceed 6° to 8°; variable climates, where the difference amounts to from 16° to 20° ; and extreme climates, where the difference is greater than 30°. The climates of Paris and London are variable ; those of Pekin and New York are extreme. Island climates are generally little variable, as the temperature of the sea is nearly constant ; and hence thedistinction between 1094 Meteorology [1046— land and sea climates. Marine climates are characterised by the fact that the difference between the temperature of summer and winter is always less than in the case of continental climates. But the temperature is by no means the only character which influences climate ; there are, in addi- tion, the moisture of the air, the quantity and frequency of the rains, the number of storms, the direction and intensity of the winds, and the nature of the soil. 1047. Distribution of temperature on the surface of the globe.—The temperature of the air on the surface of the globe decreases from the equator to the poles ; but it is subject to perturbing causes so numerous and so purely local, that its decrease cannot be expressed by any law. It has hitherto not been possible to do more than obtain by numerous observations the mean temperature of each place, or the maximum and minimum tempera- tures. The following table gives a general idea of the distribution of heat in the Northern Hemisphere. Mean temperature at different latitudes Abyssinia. : eo Om ebitesels., oh Oreagtee Calcutta : : aZo.s Strasburg : ; a OG Jamaica. : : Ame ORE Geneva . E27, Senegal. / : Beer ie) Boston . BP Sekt) Cairo ¢ : end London . : : Regs) Constantine . : ei yao Stockholm Me Be Naples . : ; SOME Ke Bee Moscow . , ; fe Beo Mexico . ; feel OO St. Petersburg A PR Marseilles. : Dn eb St; Gothard .o; : . -1°0 Constantinople. ai e7 Greenland ; ' Rene 6 | Pekin . . : SM Oty Melville Island ; .- 187 Paris. 44; : Fi LOus These are mean yearly temperatures. The highest temperature which has been observed on the surface of the globe is 47°4° at Esne, in Egypt, and the lowest is —75° in the Arctic Expedition of 1876 ; which gives a difference of 122° between the extreme temperatures observed on the surface ot the globe. The highest temperature observed at Paris was 38:4° on July 8, 1793, and the lowest — 23°5° on December 26,1798. The highest observed -at Greenwich was 35° C. in 1808, and the lowest —20° C. in 1838. No arctic voyagers have succeeded in reaching the poles, in consequence of the seas round them being completely frozen, and hence the temperature there is not known. In our hemisphere the existence of a single glacial pole —that is, a place where there was the maximum cold—has been long assumed. But the bendings which the isothermal lines present in the Northern Hemisphere have shown that in this hemisphere there are two cold poles— one in Asia, to the north of Gulf Tamour ; and the other in America, north of Barrow’s Straits, about 15° from the earth’s north pole. The mean temperature of the first of these poles has been estimated at —17°, and that of the second at —19°. With respect to the southern hemispheres, the ISOTHERMS FOR. JANUARY: Ss \4 {| i f TR i Ay mY, =i oN | Wi} | Hi \\ : esr | ill i y Wii} | 3 ae i I \ , | thf \ Pg VE: AW, xt | Wh "| I TTT i tI § fhe, mm sy K ? Re yyy bs iT} ties aN { I Het ety oof HOH di tbe, is ° i D & ue 1049] Temperatures of Lakes, Seas, and Springs 1095 observations are not sufficiently numerous to decide whether there are one or two poles of greatest cold, or to determine their position. 1048. Temperatures of lakes, seas, and springs.—In the tropics the temperature of the sea is generally the same as that of the air; in polar regions the sea is always warmer than the atmosphere. The temperature of the sea in the torrid zone is always about 26° to 27° at the surface : it diminishes as the depth increases, and in temperate as well as in tropical regions the temperature of the sea at great depths is between 2°5° and 3°5°. The low temperature of the lower layers is caused by submarine currents which carry the cold water of the polar seas towards the equator. The variations in the temperature of lakes are more considerable ; their surface, which becomes frozen in winter, may become heated to 20° or 25° in summer. The temperature of the bottom, on the contrary, is virtually 4°, which is that of the maximum density of pure water. Springs, which arise from rain water which has penetrated into the crust of the globe to a greater or less depth, necessarily tend to assume the tempera- ture of the terrestrial layers which they traverse. Hence, when they reach the surface their temperature depends on the depth which they have attained. If this depth is that of the layer of invariable temperature, the springs have a temperature of 10° or 11° in this country, for this is the temperature of this layer, or about the mean annual temperature. If the springs are not very copious, their temperature is raised in summer and cooled in winter by that of the layers which they traverse in passing from the invariable layer to the surface. But if they come from below the layer of invariable temperature their temperature may considerably exceed the mean temperature of the place, and they are then called thermal springs. The following list gives the temperatures of some of them :— Wildbad . ; ; : ; ‘ , : Unsyice Ae Vichy : ; : : ; : ; : : edo Bath , : ; ; : ; : ; ; AS Ems ; , : : ; : 3 : , oe 40 Baden-Baden . ‘ : 4 : , : : 075 Chaudes-Aigues ; : : : : : : oe) fete Trincheras , : ‘ : : : ' : hey: Great Geyser, in Iceland, at a depth of 66 feet : . 124 From their high temperature they have the property of dissolving many mineral ‘substances which they traverse in their passage, and hence form mineral waters. The temperature of mineral waters is not modified in general by the abundance of rain or of dryness; but it is by earthquakes, after which they have sometimes been found to rise and at other times to sink. 1049. Distribution of land and water.—The distribution of water on the surface of the earth exercises great influence on climate. The area covered by water is considerably greater than that of the dry land ; and the distribution is unequal in the two hemispheres. The entire surface of the globe occupies about 200 millions of square miles, nearly three-fourths of which are covered by water ; that is, the extent of the water is nearly three 1096 Meteorology [1049 times as great as that of the land. The surface of the sea in the Southern Hemisphere is to that in the Northern in about the ratio of 13 to 9. The depth of the open sea is very variable; the lead generally reaches the bottom at about 300 to 450 yards; in the ocean it is often 1,300 yards, and instances are known in which a bottom has not been reached at a depth of 4,500. it has been computed that the total mass of the water does not exceed that of a liquid layer surrounding the earth with a depth of about I,100 yards, PROBLEMS AND EXAMPLES IN PHYSICS I. EQUILIBRIUM 1. A body being placed successively in the two pans of a balance, requires 180 grammes to hold it in equilibrium in one pan, and 181 grammes in the other; poguitad the weight of the body to a milligramme. From the es v= yas we have = »/180 x 181 = 1808", 499. 2. What resistance does a nut offer when placed in a pair of nutcrackers at a distance of 3 of an inch from the joint, if a pressure of 5 pounds applied at a distance of 4 inches foe the joint is just sufficient to crack it? Ans, 262 pounds. 3. What force is required to raise a cask weighing 6 cwt. into a cart o°8 metre high along a ladder 2°75 metres in length ? Ans. 1954 pounds. 4. If a horse can move 30 cwt. along a level road, what can it move along a road the inclination of which is 1 in 80, the coefficient of friction on each road being | ? Ans, 26% ay ' 5, The piston of a force-pump has a diameter of 8 centimetres, and the arms of the lever by which it is worked are respectively 12:and 96 centimetres in length; what force must be exerted at the longer arm if a pressure of 12°36 pounds on a square cen- timetre is to be applied? Ans. 77°69 pounds. IL) (GRAVITATION 6. Astone is thrown from a balloon with a velocity of 50 metres in a second. How soon will the velocity amount to 99 metres ina second, and through what distance will the stone have fallen ? To find the time requisite for the Seely: to have acquired the velocity of 99 metres in a second, we have v= V+ gt; in which V is the initial velocity, g the acceleration of gravity, which, with sufficient approximation, is equal to 9'8 metres in a second, and #/ the time. Substituting these values, we have t= 99 — 5° = 49 = ¢ seconds. 9°8 9°8 For the space traversed we have S= Vit ket = 50 x5 + 46% 25 =972'5 metres, 7. A projectile was thrown vertically upwards to a height of 510™‘22, Disregard- ing the resistance of the air, what was the initial velocity of the body ? The velocity is the same as that which the body would have acquired on falling from a height of 510°22 metres. From the formula v = /2 5 we get = /2 x 98 x 510°22 = »/10000 = 100 metres 8. A stone is thrown vertically upwards with an initial velocity of Ioo metres. After what time would it return to its original position? 1098 Problems and Examples in Physics The time of rising and falling is the same, but the time of falling is _ (from the s formula v=g?) or ~~ =10'2, which is half the time required ; therefore ¢=20°4 sec. 9° 9. A stone is thrown vertically upwards with an initial velocity of 100 metres ; after x seconds a second stone is thrown with the same velocity. The second stone is rising 8°7 seconds before it meets the first. What interval separated the throws? The rising stone will have the velocity v = V — gt, whence v = 100 — 9‘8 x 8°7. On the other hand, the falling stone, at the moment the stones meet, will have the velocity given by the equation v = gt’, in which @’ is the time during which the stone falls before it meets the second one. This time is equal to 8°7 seconds + x — — Hence 9° its velocity is Equating the two values of v and reducing, we obtain x = 3 seconds. 10. A body moving with a uniformly accelerated motion traverses a space of 1000 metres in ro seconds. What would be the space traversed during the eighteenth second if the motion continued in the same manner ? The formula s = 4 gt? gives for the accelerating force g = 20 metres per second. The space traversed during the eighteenth second will be equal to the difference of the space traversed in 18 seconds and that traversed at the end of the seventeenth. ZORA 1G we cO nn 572 Bie 2 x= = 350 metres. 11. A cannon-ball has been shot vertically upwards with a velocity of 250 metres in asecond. After what interval of time would its velocity have been reduced to 54 metres under the retarding influence of gravity, and what space would have been traversed by the ball at the end of this time ? If ¢ be the time, then at the end of each second the initial velocity would be dimi- nished by 9™°8. Hence we shall have 54 = 250 — # x g'8, whence ¢ = 20 seconds; and for the space traversed 9°8 x 207 = 250 X 20 — 2 = 3040 metres. 12. Required the time in which a body would fall through a height of 2000 metres, neglecting the resistance of the air. From s = 3 g¢? and substituting the values, we have 8 2000 = 2° 72, whence ¢ = 20°2 seconds. 2 13. A body falls in air from a height of 4000 metres. Required the time of its fall and its velocity when it strikes the ground. From the formula s = 4 g¢? we have for the time ¢ = -—~; and, on the other hand, from the formula for velocity v = gt we have ¢ = — i OLA: Hence 2 = vA ae from whichv = »/ 2 5g, and substituting the values for s and e g, v = 280 metres. 14. A stone is thrown into a pit 150 metres deep and reaches the bottom in 4 seconds. With what velocity was it thrown, and what velocity had it acquired on reaching the ground? Azs. The stone was thrown with a velocity of 17°9, and on reaching the ground had acquired the velocity 57°r. 15. A stone is thrown downwards from a height of 150 metres with a velocity of 10 metres per second. How long will it require to fall ? The distance through which the stone falls is equal to the sum of the distances Gravitation 1099 through which it would fall in virtue of its initial impulse and of that which it would 28 traverse under the influence of gravity alone; that is, 150 = 107 + 2 Taking the positive value only we get ¢ = 4°61 seconds. 16. How far will a heayy body fallin vacuo during the time in which its velocity increases from 40°25 feet per second to 88°55 feet per second? Ans. Taking the value of g at 32°2 feet, the body falls through 96°6 feet. 17. Required the time of oscillation of a single pendulum whose length is 0°9938, and in a place where the intensity of gravity is 9°81. From the general formula ¢ = 7 a, 2 in which ¢ expresses the time of one & oscillation, 7 the length of the pendulum, and g the intensity of gravity, we have i= 3°1416 eee = I second. 9°81 18. What is the intensity of gravity in a place in which the length of the seconds pendulum is o™*ggi ? la U , In) this|case Za: ree and also z = 7 7 and therefore 2 = i from & Si & g which g’ = Bs Substituting in this latter equation the values of 2’, 7, and 7, we have g/ = 9™'782. 19, In a place at which the length of the seconds pendulum is 0’99384, it is required to know the length of a pendulum which makes one oscillation in 5 seconds. In the present case, as g remains the same in the general formula, and ¢ varies, the length 7 must vary also. We shall have, then, Ose eas Jak say & & from which, reducing and introducing the values, we have fem a5" X. 000304 = 24'S46, 20. A pendulum, the length of which is 1™’95, makes 61,682 oscillations in a day. Required the length of the seconds pendulum. Ans. 0°99385 metre. 21. A pendulum clock loses 5 seconds in a day. By how much must it be shortened to keep correct time ? Let s = the number of seconds in one day, and s’ the number indicated by the clock, then s:’=2:2'=t:t=r/1': /7 .*. 86400 : 86395=1: A/xx."..x = '9998843. Hence 1—x=0'0001157 Avs. 22, What is the normal acceleration of a body which traverses a circle of 42 metres diameter with a rectangular velocity of 3 metres? Ans. 4°286 metres, 23. An iron ball falls from a height of 68 cm. on a horizontal iron plate, and rebounds to a height of 27 cm. Required the coefficient of elasticity of the iron. If an imperfectly elastic ball with the velocity wv strikes against a plate, it rebounds with the velocity v, = — #v, from which, disregarding the sign, 4 = “4. Now we v have the velocity v, = “2 gh, and v = /2 gh, from which & Vt, Substitut- fh ing the corresponding values, we get & = 0°63. 24. Two inelastic bodies, weighing respectively 100 and 200 pounds, strike against each other with velocities of 50 and 20 feet ; what is their common velocity, after the impact? Ams. 30, or 3°3, according as they move in the same or in opposite directions before impact. I100 Problems and Examples in Physics III. ON LIQUIDS AND GASES 25. The force with which a hydraulic press is worked is 20 pounds ; the arm of the lever on which this force acts is 5 times as long as that of the resistance; lastly, the area of the large piston is 70 times that of the smaller one. Required the pressure transmitted to the large piston. If F be the power, and # the pressure transmitted to the smaller piston, we have from the principle of the lever x 1 = / x 5. Moreover, from the principle of the equality of pressure : FxiI= p~p* 7O = 5 X 20 X 70 = 7000 pounds. 26. The force with which a hydraulic press is worked being 30 kilos. and the arm of the lever by which this force is applied being ro times as long as that of the resist- ance, and the diameter of the small piston being two centimetres; find the diameter of the large piston, in order that a pressure of 2000 kilos may. be produced. Ans. 5°164 centimetres. 27. One of the limbs of a U-shaped glass tube contains mercury, to a height of o™*575 ; the other contains a different liquid to a height of o™42; the two columns being in equilibrium, required the density of the second liquid with reference to mer- cury and to water. If dis the density of the liquid as compared with mercury, and d, the density com- pared with water, then 1 x o'175 = 0°42 x d; and 136 x .0°'175 = 0°42 x @,; whence d@d = o'416andd, = 5°66. 28. What force would be necessary to support a cubic decimetre of platinum in mercury at zero? Density of mercury 13°6 and that of platinum 21°5. From the formula P = VD the weight of a cubic decimetre of platinum is I x er’s = 21*s and that. of a cubic decimetre of mercury 15 © x 13°65=13".0. From the principle of Archimedes, the immersed platinum loses part of its weight equal to that of the mercury which it displaces. Its weight in the liquid is therefore 21'5 — 13°6 = 7°9, and this represents the force required. 29. Given a body 4 which weighs 7°55 grammes in air, 5°17 gr. in water, and 6°35 gr. in another liquid, B ; required from these data the density of the body 4 and that of the liquid B. The weight of the body 4 loses in water 7°55 — 5°17 = 2°38 grammes; this repre- sents the weight of the displaced water. In the liquid B it loses 7°55 — 6°35 = 1'2 gr.; this is the weight of the same volume of the body B, as that of 4 and of the displaced’ water. The specific gravity of 4 is therefore ; TRV ene ey T2000 en scp 3°172, and that of B See 0°504. 30. A cube of lead, the side of which is 4 cm., is to be supported in water by being suspended to a sphere of cork. What must be the diameter of the latter, the specific gravity of cork being 0°24, and that of lead 11°35? The volume of the lead is 64 cubic centimetres; its weight in air is therefore 64 x 11°35, and its weight in water 64 x 11°35 — 64 = 662°4 gr. If ~ be the radius of the sphere in centimetres, its volume in cubic centimetres will 3 5 ; bets.) , and its weight in grammes is sas Tey Now, as the weight of, the 3 displaced water is obviously 47 in grammes, there will be an upward buoyancy 3 my represented by AMI 4.07 % O24 _ 477 x 0°76 3 5 3 477 x 0°76 which must be equal to the weight of the lead ; that is, = 662'5, from which x = 5°™‘o25 and the diameter = 11°85. On Liguids and Gases 1101 31. A cylindrical steel magnet 15 cm. in length and 1‘2 mm. in diameter is loaded at one end with a cylinder of platinum of the same diameter and of such a length that when the solid thus formed is in mercury, the free end of the steel projects 10 mm. above the surface. Required the length of this platinum, specific gravity of steel being 7°8 and of platinum 2r’s. The weight of the steel in grammes will be 15 7 7? x 7°8 and of the platinum “er? X% 21'S. These are together equal to the weight of the displaced mercury, which is a 72 (14 + x) 13°6, from which = 9‘29 cm. 32. A cylindrical silver wire o™‘oors in diameter weighs 3°2875 grammes; it is to be covered with a layer of gold o™‘ooo2 in thickness. Required the weight of the gold, the specific gravity of silver being 10°47 and that of gold 19°26. If vis the radius of the silver wire and & its radius when covered with gold, then yr = ofo75 and R = o%'095. The volume of the silver wire will be ™7?Z and its weight 7 7? 7 10°47, from which 7 = 17°768. The volume of the layer of gold is mw (R2 — rv?) 17°768, and its weight m (0'0952 — 0°075”) x 17°768 xX 19°26 = 3°656 nearly. 33. A kilogramme of copper is to be drawn into wire having a diameter of 0°16 centimetre. What length will it yield? Specific gravity of copper 8°88. The wire produced represents a cylinder 7 cm. in length, the weight of which is nw v2 7 8°88, and this is equal to 1000 grammes. Henced = 56™'0085. 34. The specific gravity of cast copper being 8°79, and that of copper wire being 8°88, what change of volume does a kilogramme of cast copper undergo in being 100 * 86617" 35. Determine the volumes of two liquids, the densities of which are respectively 1°3 and 0’7, and which produce a mixture of three volumes having the density og. If x and y be the volumes, then from 7? = VD,13% + o'7 y = 3 x 0o’9 and x +y = 3, from which = rand y = 2. drawn into wire? Ans 36. The specific gravity of zinc being 7 and that of copper 9, what weight of each metal must be taken to form 50 grammes of an alloy having the specific gravity 8s, it being assumed that the volume of the alloy is exactly the sum of the alloyed metals ? Let x = the weight of the zinc, and y that of the copper, then x + y = 50, and from the formula P = VD, which gives V = < the volumes of the two metals and of the alloy are respectively * 4+ i = a From these two equations we get x = 17°07 7 : and y = 32°93. 37. A platinum sphere 3 cm. in diameter is suspended to the beam of a very ac- curate balance, and is completely immersed in mercury. It is exactly counterbalanced by a copper cylinder of the same diameter completely immersed in water. Required the height of the cylinder. Specific gravity of mercury 13°6, of copper 8°8, and of platinum 21's. Ans. 2°'025 centimetres. 38. To balance an ingot of platinum 27 grammes of brass are placed in the other pan of the balance. What weight would have been necessary if the weighing had been effected in vacuo? The density of platinum is 21°5, that of brass 8°3, and air under a pressure of 760 mm. and at the temperature o° has 22 the density of water. 772 The weight of brass in air is not 27 grammes, but this weight minus the weight of a volume of air equal to its own. Since P = VD.", V = - and the weight of the air is —— = =f, x 770 83x 770 By similar considerations, if x is the weight of platinum in vacuo, its weight in air 1102 Problems and Examples in Phystcs will be x minus the weight of air displaced, that is x — ae ee Rene ae weight orc x 970 is equal to that of the true weight of the brass ; and we have Pe pains BED ARS 27___: from which x = 26'9c6. 21°5 X 770 ul Sc Sux e770 39. A body loses in carbonic acid 1°15 gr. of its weight. What would be its loss of weight in air and in hydrogen respectively ? Since a litre of air at o? and 760 mm. weighs 1'293 gramme, the same volume of carbonic acid weighs 1°293 X 1°524 = I’‘97gramme. We shall, therefore, obtain the volume of carbonic acid corresponding to 1°15 gr. by dividing this number by 1°97, which gives 0°5837 litre. This being then the volume of the body, it displaces that volume of air, and therefore its loss of weight in air is 0°5837 x 1'293 = 0°7547 gramme, and in hydrogen 0°5837 x 1°293 x 0°069 = 0°052076. 40. Calculate the ascensional force of a spherical balloon of oiled silk which, when empty, weighs 62°5 kilos, and which is filled with impure hydrogen, the density of which is * that of air. The oiled silk weighs 0'250 kilo. the square metre. 13 The surface of the balloon is 62°5 = 250square metres, This surface being that of 0°25 a sphere, is equal to 4 7 &?, whence 4 RX? = 250 and & = 4°459; therefore V = qa kK’ me) = 371°52 cubic metres. The weight of air displaced is 371°52 x 1°293 kilo. = 480°375 kilos. ; the weight of the hydrogen is 36°88 kilos., and therefore the ascensional force is 480°375 — (36°88 + 62°5) = 380°995. 41. A balloon 4 metres in diameter is made of the same material and filled with the same hydrogen as above. How much hydrogen is required to fill it, and what weight can it support? The volume is * 7 R35 = 33°51 cubic metres, and the surface 4 R? = 50°265 square metres. The weight of the air displaced is 33°51 x 1'293 = 43°328 kilos, and that of the hydrogen is from the above data 3°333 kilos, while the weight of the material is 12°566 kilos. Hence the weight which the balloon can support is 43°328 — (12°566 + 3°333) = 27°429 kilos. 42. Under the receiver of an air-pump is placed a balance, to which are suspended two cubes; one of these is 3 centimetres in the side,and weighs 26°324 gr. ; and the other is 5 centimetres in the side, and weighs 262597 grammes. When a partial vacuum is made these cubes just balance each other. What is the pressure ? Ans\'O™37a% 43. A soap-bubble 8 centimetres in diameter was filled with a mixture of one volume of hydrogen gas and 15 volumes of air. The bubble just floated in the air; required the thickness of the film. The weight of the volume of air displaced is 4 73 x 0001293 gramme, and that of the mixture of gases 4 on 73 x 0°00I293 X 320093 ; and the difference of I these will equal the weight of the soap-bubble. This weight is that of a spherical shell, which, since its thickness ¢ is very small, is with sufficient accuracy 4 7 7* 7s in grammes, where s is the specific gravity =‘1.. tilence 37 7 (001293 — ‘001293 xX Ie) = 4ig2et tz, Dividing each side by 4 + 72, and putting y = 4, we get 4 X ‘001293 (: as ios) =3°3¢; On Liquids and Gases 1103 or "001293 X ESE os 3°37: 4 whence ¢ = ‘00009116629 cm. 44. In a vessel whose capacity is 3 litres, there are introduced 2 litres of hydrogen under the pressure of 5 atmospheres ; 3 litres of nitrogen under the pressure of half an atmosphere, and 4 litres of carbonic acid under the pressure of 4 atmospheres. What is the final pressure of the gas, the temperature being supposed constant during the experiment ? The pressure of the hydrogen, from Dalton’s law, will be te 5, that of the nitro- gen will remain unchanged, and that of the carbonic acid will be 4 * 4. Hence the total pressure will be Lome Tyax6 = + —~ + — = go atmospheres. 3 2 3 45. A vessel containing ro litres of water is first exposed in contact with oxygen under a pressure of 78 cm. until the water is completely saturated. It is then placed in a confined space containing roo litres of carbonic acid under a pressure of 72 cm. Required the volumes of the two gases when equilibrium is established. The coeffi- cient of absorption of oxygen is o’042, and that of carbonic acid unity. The volume of oxygen dissolved is 0°42. Being placed in carbonic acid it will act as if it alone occupied the space of the carbonic acid, and its pressure will be Toux PGE 0°326 cm. 100°42 : Similarly the 1o litres of water will dissolve ro litres of carbonic acid gas, the total volume of which will be 110, of which 100 are in the gaseous state and ro are dissolved. Its pressure is therefore 72 x TOO = 65°454 cm. IIo Hence the total pressure when equilibrium is established is 0°326 + 65°454 = 65°78 cm. ; and the volume of the oxygen dissolved reduced to the pressure 65'78 is Naas olit‘o9208, and that of the carbonic acid 10 x oe Apeeee 9°95. 65°78 65°78 46. In a barometer which is immersed in a deep bath the mercury stands 743 mm. above the level of the bath. The tube is lowered until the barometric space, which contains air, is reduced to one-third, and the mercury is then at a height of 7o1 mm. Required the atmospheric pressure at the time of observation. Azs. = 764mm, 47. What is the pressure on the piston of a steam boiler of 8’ decimetres diameter if the pressure in the boiler is 3 atmospheres ? Ans. 10385'85 kilos. 48. What is the pressure of the atmosphere at that height at which an ascent of 21 metres corresponds to a diminution of 1™™ in the barometric height ? Azs. 378°9™™, olit-42 x 49. What would be the height of the atmosphere if its density were everywhere uniform ? Ans. 7954'1 metres, or nearly 5 miles. 50. How high must we ascend at the sea-level to produce a depression of 1 mm. in the height of the barometer ? Ans. Taking mercury as 10,500 times as heavy as air, the height will be 10°5 metres. 51. Mercury is poured into a barometer tube so that it contains 15 cc. of air under the ordinary atmospheric pressure. The tube is then inverted in a mercury bath and the air then occupies a space of 25 cc. ; the mercury occupying a height of 302 mm. What is the pressure of the atmosphere ? Let x be the amount of this pressure, the air in the upper part of the tube will have a pressure represented by en and this, together with the height of the mercurial 2 column 302, will be the pressure exerted in the interior of the tube on the level of the 1104 Problems and Examples in Physics mercury in the bath, which is equalto the atmospheric pressure ; that is TS¥ + 302 25 = x, from which x = 755 mm. 52. What effort is necessary to support a cylindrical bell-jar full of mercury immersed in mercury ; its internal diameter being 6 centimetres, its height 02 above the surface of the mercury (fig. 1) 18 centimetres, and the pressure of the atmosphere 0°77 centimetre? The bell-jar supports on the outside a pressure equal to that of a column of mercury the section of whose base is cd, and the height that of the barometer. This pressure is equal to Whee (aw CO pienek 3-0, The pressure on the inside is that of the atmosphere less the weight of a column of mercury whose base is cd and height 0d. Thisis equal tom R? x (0°77 —0°18) x 13°6 and the effort necessary is the difference of these two pressures. Making: # = 3, cm.,. this. is found \to ‘he 69'216 kilos. 53. A barometer is placed within a tube which is after- wards hermetically closed. At the moment of closing, the temperature is 15° and the pressure 750 mm. The ex- ternal space is then heated to 30°. What will be the height of the barometer ? The effect of the increase of temperature would be to raise the mercury in the tube in the ratio r + pies to 1 + fe) ™5_ and the height Z would therefore be S5Se este = 75(2 * 550 Tobit T5S_ Fig. I. 555° and since in the closed space the elastic force of the air increases in the ratio I + 30a :12 + 15a, we Shall have finally 2 = 301°74 mm. 54, The heights of two barometers 4 and B have been observed at — 109? and + 15°, respectively, tobe A = 737 and B = 763. Required their corrected heights BtiO-. Ans. A = 738°33. B = 760'94. 55. A voltaic current gives in an hour 840 cubic centimetres of detonating gas under a pressure of 760 and at the temperature 12°'5 ; a second voltaic current gives in the same time 960 cubic centimetres under a pressure of 755 and at the temperature 15°°5. Compare the quantities of gas given by the two currents, Ams. 1 : 1°129. 56. The volume of air in the pressure gauge of an apparatus for compressing gases is equal to 152 parts. jim By the working of the machine this is reduced to 7 parts, and the mercury is raised through 0°43 metre. What is the pressure of the gas? Here AB = 152, AC = 37 parts, and BC =o0™-48. |e The pressure of air therefore in AC is, from Boyle's law, both rs 4atm-ro8 = 3™°122, a 37 -— ee The pressure in the receiver is therefore 3°122 + 0°48 = °3™'602, which is equal to 4°74 atmospheres. 57. An airtight bladder holding two litres of | air at the standard pressure and temperature is | immersed in sea-water to a depth of too metres, | where the temperature is 49. Required the volume ~ of the gas. E E| ATT TEM NTT asi : Air Pump L105 The specific gravity of sea-water being 1‘026, the depth of 100 metres will repre- sent a column of pure water 102°6 metres in height. As the pressure of an atmo- sphere is equal to a pressure of 10°33 metres of pure water, the pressure of this column J) *r02°68 10°33 Hence, adding the atmospheric pressure, the bladder is now under a pressure of 10°94 = 9°94 atm. atmospheres, and its volume being inversely as the pressure will be aie De 0'183 litre, 10°94 if the temperature be unaltered. But the temperature is increased by 4°, and therefore the volume is increased in the ratio 277 to 273, and becomes o°183 x 277 = 0'18568 litre. 273 58. To what height will water be raised in the tube of a pump by the first stroke of the piston, thelength of stroke of which is o’5m., the height of the tube 6 metres, and its section zy that of the piston? At starting the air in the tube is under a pressure of ro metres. If we take the section of the tube as unity, that of the body of the pump is 10; and the volumes of the tube and of the body of the pump are in the ratio of 6 to s. Then if x is the height to which the water is raised in the pipe, the volumes of air in the pump before and after the working of the pumpare 6 at the pressure 10, and 5 + 6 — x at the pressure Io — x. Forming an equation from these terms, and solving, we have two values, x’ = 18™ 26 and x” = 2°74. ‘The first of these must be rejected as being physically impossible ; and the true height is x = 2°75 metres. 59, A receiver with a capacity of to litres contains air under the pressure 76 cm. It is closed by a valve, the section of which is 32 square centimetres, and is weighted with 25 kilogrammes. The temperature of the air is 30°; its density at o° and 76 cm, pressure is 1 that of water. The coefficient of the expansion of gases is 0°00366. Required hassel of air which must be admitted to raise the valve. The air already present need not be taken into account, as it is under the pressure of the atmosphere. Let x be the pressure in centimetres of mercury of that which is x 1.1316 nee admitted, will represent in kilogrammes its pressure on a square centi- metre; and therefore the internal pressure on the valve, which is equal to the ex- 2X 13 OK, Ge 1000 ternal pressure of 25 kilogrammes, is = 25k. Fromwhich x = 57°44. For the weight we shall have be ERC eadice piel ie 88055 grammes, I + 0'00366 x 30 =. 7600 60. A bell-jar contains 3°17 litres of air; a pressure gauge connected with it marks zero when in contact with the air (fig. 3). The jar is closed and the machine worked; the mercury rises to 65 cm. A second barometer stands at 76 cm, during the experiment. Required the weight of air withdrawn from the bell-jar and the weight of that which remains. Ato® and 76cm. the weight of air in the bell-jar is 1'293 X 3°17 = 4°'09881. At 0° and under the pressure 76 — 65 the weight of the residual air is 4°09881r x II 7a) and therefore the weight of that which is withdrawnis 4°0988 — 0°5932 = 3°5056 gr. 61. The capacity of the receiver of an air-pump = 0°5932, 1106 Problems and Exaniples in Physics is 7°53; it is full of air under the ordinary atmospheric pressure and at 0°. Re- quired the weight of air when the pressure is reduced to o'21; the weight with- drawn by the piston; and the weight which would be left at 15°. The weight of 7°53 litres of air under the ordinary conditions is 9'736 grammes. Under a pressure of o’2r it will be 2°69 grammes, and at the temperature 15° it will be pete 00 Bh ee 0255 gramme. Fret 'O'00300 xX 15 62. In a theoretically perfect air-pump, how great is the rarefaction after ro strokes, if the volumes of the barrel and the receiver are respectively 2 and 3? Ans, = 4°59™™; or about - & of an atmosphere. aa 63. What must be the capacity of the barrel of an air-pump if the air in a re- ceiver of q litres is to be reduced to 4 the density in two strokes? AUS. Zit: 64. The reservoir of an air-gun, the capacity of which is 4o cubic inches, contains air whose density is 8 times that of the mean atmospheric pressure. A shot is fired when the atmospheric pressure is 741 mm. and the gas which escapes occupies a volume of 80 cubic inches. What is the elastic force of the residual air? Azs, 6'05 atmospheres. 65. Suppose that at the limit of the atmosphere the pressure of the attenuated air is the —*— of a millimetre of mercury and the temperature — 135°, and that ina 1000 place at the sea-level, in latitude 45°, the pressure of the atmosphere is 760™™ and its temperature 159 C. Determine from these data the height of the atmosphere. From the formula 18400 { 1 + o'002{7 + ¢} | log oy we get for the height in metres 82237, which is equal to 51°1 miles. . 66. If water is continually flowing through an aperture of 3 square inches with a velocity of 10 feet, how many cubic feet will flow out in an hour? -Azs. 750 cubic feet. 67. With what velocity does water issue from an aperture of 3 square inches, if 37°5 cubic feet flow out every minute? Ans. 36 feet: 68. What is the ratio of the pressure in the above two cases ? LASTS TO: 69. What is the theoretical velocity of water from an aperture which is 9 feet below the surface of water ? Ans. 24 feet. 70. Ina cylinder, water stands 2 feet above the aperture and is loaded by a piston which presses with a force of 6 pounds on the square inch. Required the velocity of the effluent water. Ans, 32 feet. 71. How deep must the aperture of the longer leg of a syphon, which has a sec- tion of 4 square centimetres, be below the surface of the water in order that 25 litres may flow out in a minute? Ans. 5°535 cm, 72. Through a circular aperture having an area of o’196 square cm. in the bottom of a reservoir of water which was kept at a constant level, 55 cm. above the bottom, it was found that 98°5 grammes of water flowed in 22 seconds. Required the coeffi- cient of efflux. . Since the velocity of efflux through an aperture in the bottom of a vessel is given by the formula v =»/2 gh, it will readily be seen that the weight in grammes of water which flows ina given time, ¢, will be given by the formula w = aq tr/ 22h, where a is the area in square centimetres, a the coefficient of efflux, ¢ the time in seconds, and & the height in centimetres. Hence in this case a= 0699. 73. Similarly through a sgware aperture, the area of which was almost exactly the same as the above, and at the same depth, 104°4 grammes flowed out in 21°6 seconds, In this case 2 = 0'73. Sound 1107 IV, ON SOUND 74. A stone is dropped into a well, and 4 seconds afterwards the report of its striking the water is heard. Required the depth, knowing that the temperature of the air in the pit was 109°74. From the formula v = 333 4/1 + a¢ we get for the velocity of sound at the tem- perature in question 339°05 metres. Let ¢ be the time which the stone occupies in falling; then 4.72 = x will represent the depth of the well; on the other hand, the time occupied by the report will be 4 — 4, and the distance will be (4 — ¢) v = ~ (i); thus (4 — ¢) v = 3g? (ii), from which, substituting the values, (4 — 2) 3395 = 49 2 ¢ = 3°793 seconds, and substituting this value in either of the equations (i) or (ii), we have the depth = 72°6 metres nearly, 75. A bullet is fired from a rifle with a velocity of 414 metres, and is heard to strike a target 4 seconds afterwards. Required the distance of the target from the marks- man, the temperature being assumed to be zero. age Mee As Gan 730 e 76. At what distance is an observer from an echo which repeats a sound after 3 seconds, the temperature of the air being 109? In these 3 seconds the sound traverses a distance of 3 x 339 = 1017 metres ; this distance is twice that between the observer and the reflecting surface ; hence the dis- tance is IOI7 = 508'5 metres. 77. Between a flash of lightning and the moment at which the corresponding thunder is first heard, the interval is the same as that betweea two beats of the pulse. Knowing that the pulse makes 80 beats in a minute, and assuming the temperature of the air to be 15° C., what is the distance of the discharge? Ams.’ 454°I metres. 78. A stone is thrown into a well with a velocity of 12 metres, and is heard to strike the water 4 seconds afterwards. Required the depth of the well. Ans, About 110 metres. 79. What is the velocity of sound in coal gas at 0°, the density being 0°5? Ans. 470°9 metres. 80. What must be the temperature of air in order that sound may travel in it with the same velocity as in hydrogen at 0° ? Ans, About 3680° C. 81. What must be the temperature of air in order that the velocity of sound may be the same as in carbonic acid at 0°? Ans. — 10595 C. 82. Kendall, in a North Pole Expedition, found the velocity of sound at — 40° was 314 m. How closely does this agree with that calculated from the value we have assumed for 0° ? Ans, 6°64 metres too much. 83. The report of a cannon is heard 15 seconds after the flash is seen, Required the distance of the cannon, the temperature of the air being 22°, From the formula for the velocity of sound we have I5 X 333 »/1 + 0°003665 x 22 = 5190 metres. 84. If a bell is struck immediately at the level of the sea, and its sound, reflected from the bottom, is heard 3 seconds after, what is the depth of the sea ? Ans. 7140 feet. 4B2 1108 Problems and Examples in Physics 85. A person stands 150 feet on one side of the line of fire of a rifle range 450 feet in length and at right angles to a point 150 feet in front of the target. What is the velocity of the bullet if the person hears it strike the target * of a second later than the report of the gun? The temperature is assumed to be 16°°5. Azs. 2038 feet. 86. An echo repeats five syllables, each of which requires a quarter of a second to pronounce, and half a second elapses between the time the last syllable is heard and the first syllable is repeated. What is the distance of the echo, the temperature of the air being 10° C. ? Ans, 297'47 metres. 87. The note given by a silver wire a millimetre in diameter and a metre in length being the middle C, what is the tension of the wire? Density of silver 10°47. Ans, 22°67 kilogrammes. 88. The density of iron being 7°8 and that of copper 8°8, what must be the thickness of wires of these materials, of the same length and equally stretched, so that they may give the same note ? From the formula for the transverse vibration of strings we have for the number of vibrations 2 = — yas ey As in the present case, the tensions, the length of the strings, and the se if vibrations a are the same, we have at hich Spe Ly. i / a? ri aa eae drags é whence bee eh AN 8. hence os wf 3 oer obs. ad 4 7°38 89. A wire stretched by a weight of 13 kilos: sounds a certain note. What must be the stretching weight to produce the major third ? The major third having 5 the number of vibrations of the fundamental note, and as, all other things being the same, the numbers of vibrations are directly as the square roots of the stretching weight, we shall have x = 20°312 kilos. 90. The diameters of two wires of the same length and material are o’oo15 and 00038 m. ; and their stretching weights 400 and 1600 grammes respectively. Required the ratio of the numbers of their vibrations. Ans) 75 t =E 26608 91. A brass wire r metre in length stretched by a weight of 2 kilogrammes, and a silver wire of the same diameter, but 3°165 metres in length, give the same number of vibrations. What is the stretching weight in the latter case ? Since the number of vibrations is equal, we shall have I adi TP a ica rl na Ke Sz d, : from which, replacing the numbers, we get x = 25 kilos. 92. A brass and a silver wire of the same diameter are stretched by the weights of 2 and 25 kilogrammes respectively, and produce the same note. What are their lengths, knowing that the density of brass is 8°39, and of silver 10°47? Ans. The length of the silver wire is 3°16 times that of the brass, 93. A copper wire 1°25 mm. in diameter and a platinum one of 0°75 mm. are stretched by equal weights. What is the ratio of their lengths, if, when the copper wire gives the note C, the platinum gives F on the diatonic scale? Ans. The length of the copper is to the length of the platinum = 1°264 : I 94. An organ pipe gives the note C at a temperature 0°; at what temperature will it yield the major third of this note? Anspirsavc. 95. A brass wire a metre in length, and stretched by a weight of a kilogramme, yields the same note asa silver wire of the same diameter but 2'5 metres in length and stretched by a weight of 7°5 kilogrammes, Required the specific gravity of the silver. Ans. 10°068. 96. How many beats are produced in a second by two notes, whose rates of vibra- tion are respectively 340 and 354? Ans. 14. Fleat 1109 VoSON Hea Tt 97. Two mercurial thermometers are constructed of the same glass ; the internal diameter of one of the bulbs is 7™™:5 and of its tube 2's; the bulb of the other is 6°2 in diameter and its tube 1°5. What is the ratio of the length of a degree of the first thermometer to a degree of the second? Let 4: and B be the two thermometers, D and D the diameters of the bulbs, and d and a’ the diameters of the tubes. Let us imagine a third thermometer C with the same bulb as B and the same tube as 4, and let Z /’, and 7” denote the length of a degree in each of the thermometers respectively. Since the stems of 4 and C have the equal diameters, the lengths Z and 7” are directly as the volumes of the tubes, or what is the same, as the cubes of their diameters; and as Band C have the same bulk, the lengths 2’ and 2” are inversely proportionate to the sections of the stems, or what amounts to the same, to the squares of their diameters. We have then Z D5 d OT hae ee sy n Fie se hea Z D's Z a’ introducing the values and solving, we have l — = 0°638. 7 a 98. At what temperature is the number on the Centigrade and Fahrenheit thermometers the same ? Ans, — 40°. 99. The same question for the Fahrenheit and Réaumur scales. Ans, — 25'6. 100. A capillary tube is divided into 180 parts of equal capacity, 25 of which weigh 1’2 gramme. What must be the radius of a spherical bulb to be blown to it so that 180 divisions correspond to 150 degrzes Centigrade? Since 25 divisions of the tube contain 1'2 gramme, 180 divisions contain ED ouige) = 304, Fig. 4. ce And since these 180 divisions are to represent 150 degrees, the weight of mercury corresponding to a single degree is aoa But as the expansion corresponding to 150 8°64 a one degree is only the apparent expansion of mercury in glass, the weight - eaten 150 480 of the mercury in the reservoir, which is 4 7R3, From this R = 1°8755 centimetre. 3 101. By how much is the circumference of an iron wheel, whose diameter is 6 feet, increased when its temperature is raised 400 degrees? Coefficient of expansion of iron = 00000122, Ans. By 0'0g2 foot. 102. What must be the length of a wire of this metal which for a temperature of 1° expands by one foot? ins, 81967 feet. 103. A pendulum consists of a platinum rod, on a flattening at the end of which rests a spherical zinc bob. The length of the platinum is Z at 0°. What must be the diameter of the bob, so that its centre is always at the same distance from the point of suspension whatever be the temperature? Coefficient of expansion of platinum 0'0000088 and of zinc 0’0000294. Ans. The diameter of the bob must be 3 of the length of the platinum. 104. Two walls, which when perpendicular are 30 feet apart, have bulged out- wards to the extent of 2°4 inches. ‘They are to be made perpendicular by the contrac- IITIO Problems and Examples in Physics tion of an iron bar. By how much must its temperature be raised above that of the air, which is taken at 0°? Ans. 546°4. 105. An iron wire 4 sq. mm. in cross section is stretched ae its length by a weight of 1 kilogramme. What weet must be applied toa ae 9g sq. mm. in cross section, when it is heated from 0° to 20°, in order to prevent it from expanding ? Ans. 44°5 kilos. 106. At the temperature zero a solid is immersed 0'975 of its total volume in alcohol. At the temperature 25° the solid is wholly immersed. ‘The coefficient of _expansion of the solid being 0’000026, required the coefficient of expansion of the alcohol, Ans. O°OOI052. 107. Into a glass globe, the capacity of which at 0° is 250 cc., are introduced 25 cc. of air measured at 0° and 76cm. ‘The flask being closed and heated to 100°, required the internal pressure. Coefficient of cubical expansion of glass aay 38700 o At 100° the capacity of the flask is 250 (: + 02) ; again at 100? the volume of 38700 the free air under the pressure 76 is 25 (I + 100 X 0'00366). But.its real volume is 250 x a under a pressure x. Hence 3°7 WO 2 *% =. 250,x aS :25 x 1°366, from which x = 10°3548 cm. 3°97 108. The specific gravity of mercury at 0° being 13°6, required the volume of 3 kilogrammesat 85°. Coefficient of expansion ae : fo) The volume at 0° will be —*— and at 85° 3 x (: +e ey) = 0°22309 litre. 13°6 136 5550 109. A hollow copper sphere 20 cm. in diameter is filled with air at o° under a pressure of 14 atmosphere ; what is the total pressure on the interior surface when the enclosed air is heated to a temperature of 600° ? Ans, 6226'°5 kilogrammes. 110. Between the limits of pressure 700 to 780mm. the boiling-point of water varies. 0°'0375 C. for each mm. of pressure. Between what limits of temperature does the boiling point vary, when the height of the barometer is between 735 and 755 mm. ? Ans. Between 99°'0625 and 99°°8125. 111. Liquid phosphorus cooled down to 30°, is made to solidify at this tempera- ture. Required to know if the solidification will be complete, and if not, what weight will remain melted? The melting point of phos pneriad is 44°2; its latent heat of fusion 5°4, and its specific heat o°2. Let x be the weight of phosphorus which solidifies; in so doing it will give out a quantity of heat = 5°4 4%; this is expended in raising the whole weight of the phos- phorus from 30 to 44"2. Hence we have 5°4* = I x (44°2 — 30) o'2, from which x= 7 oe 0'526, so that 0°474 of phosphorus will remain liquid. 54 112. A pound of ice at oon is placed in two pounds of water at o°; required the weight of steam at 1009 which will melt the ice and raise the temperature of the mix- ture to 30°. The latent heat of the liquefaction of ice is 79’2, and that of the vaporisa- tion of water 536. Ans. °279 pound. 113. 65°5 grammes of ice at — 20° having been placed in x grammes of oil of turpentine at 13°3°, the final temperature is found to be 3°19. The specific heat of turpentine is 0°4, and it is contained in a vessel weighing 25 grammes, whose specific heat iso‘z. The specific heat of ice iso'5. Required the value of x. Ans, x = 1475 grammes. 114. In what proportion must water at a temperature of 30° and linseed oil (sp. heat = o'5) at a temperature of 50° be mixed so that there are 20 kilogrammes of the mixture at 40°? Ans. Water = 6°66 kilos. and linseed oil = 13°34. Fleat ox III1 115, By how much will mercury at 0° be raised by an equal volume of water at 100° ? wns) 68°19 Ga 116. The specific heat of gold being 0'03244, what weight of it at 45° will raise a kilogramme of water from 12°9°3 to 15°'7? Let x be the weight sought ; then x kilogrammes of gold in sinking from 45° to 15°°7 will give out a quantity of heat represented by x (459 — 15°°7) 00324, and this is equal to the heat gained by the water, that is to 1 (15°7 — 12°3) = 3°4, thatis x = 3°58. 117. The specific heat of copper sulphide is o‘r2r12, and that of silver sulphide 0'0746. 5 kilos. of a mixture of these two bodies at 40°, when immersed in 6kilos. of water at 7°669°, raises its temperature to 10°. How much of each sulphide did the mixture contain ? The weight of the copper sulphide = 2, and that of the silver sulphide 3. 118. Into a mass of water at 0°, 100 grammes of ice at — 12° are introduced; a weight of 7°2 grammes of water at 0° freezes about the lump immersed, while its temperature rises to zero. Required the specific heat of ice. Latent heat of water 79°2. Ans. 0°4752. 119, Four pounds of copper filings at 130° are placed in 20 pounds of water at 20°, the temperature of which is thereby raised 2 degrees. What is the specific heat, ¢, of copper ? AN S.s6i == 40" 0020s 120. Two pieces of metal weighing 300 and 350 grammes, heated toa temperature x, have been immersed, the former in 3351°6 grammes of water at 10°, and the latter in 1935'4 grammes at the same temperature. ‘The temperature in the first case rises to 2o~, and in thesecond to 30°. Required the original temperature and the specific heat of the metal. 475.2 the temperature = 10009 }/¢ the specific. heat =" orm. 121. In what proportions must a kilogramme of water at 50° be divided in order that the heat which one portion gives out in cooling to ice at zero may be sufficient to change the other into steam at 100° ? ARS AL =f O°0209- 122. Three mixtures are formed by mixing two and two together, equal quantities of ice, salt, and water at 0°. Which of these mixtures will have the highest and which the lowest temperature ? Ams. The mixture of ice and salt will produce the lowest temperature, while that of ice and water will produce no lowering of temperature. 123. In 25°45 kilogrammes of water at 12°°5 are placed 6'17 kilos. of a body at a temperature of 80° ; the mixture acquires the temperature 14°°r. Required the specific heat of the body. If ¢c isthe specific heat required, then mc (# — 9) represents the heat lost by the body in cooling from 80° to 149°1; and that absorbed by the water in rising from 12°'5 to 14°°r is m’ (9 — ¢), ‘These two values are equal. Substituting the numbers, we have ¢ = O'IOOT4. | 124. Equal lengths of the same thin wire traversed by the same electrical current are placed respectively in 1 kilogramme of water and in 3 kilogrammes of mercury. The water is raised 10° in temperature; by how much will the mercury be raised ? Ans. 100°'04. 125. How many cubic feet of air under constant pressure are heated through 1° C. by one thermal unit ? Ans. 55°3 cubic feet. 126. Given two pieces of metal, one x weighing 2kilos. heated to 80°, and the other y weighing 3 kilos., and at the temperature 50°. To determine their specific heats they are immersed in a kilogramme of water at 10°, which is thereby raised to 269°3. The experiment is repeated, the two metals being at the temperature roo? and 40° respectively, and, as before, they are placed in a kilogramme of water at 10°, which this time is raised to 289’4. Required the specific heats of the two metals. ASK =) O7LIS j Y= OLO535. 127. For high temperatures the specific heat of iron is o'1053 + 0’000017 #. What is the temperature of a red-hot iron ball weighing a kilogramme, which, plunged in 26 Lire Problems and Examples in Physics kilogrammes of water, raises its temperature from 12° to 249? What was the tempe- rature of the iron? (0'1053 + o'000017 Z) (¢ — 24) = 16 (24 — 12), or ‘oooo17 2% + ‘1048892 ¢ — 2°5272 = 192; transposing and dividing by the coefficient of 77, we get f@-+ 6176 t = |AT442770, #2 + 6170 ¢ + (3085)? = 20960001 hence ¢+ 3085 = 4578°3 nearly; .°. ¢ = 1493°3. 128. A kilogramme of the vapour of alcohol at 80° passes through a copper worm placed in 10°8 kilogrammes of water at 12°, the temperature of which is thereby raised to 36°. The copper worm and copper vessel in which the water is contained weigh together 3 kilogrammes. Required the latent heat of alcohol vapour. 10. A Siemens unit is equal to the resistance of a column of pure mercury a metre in length and a square mm. in cross section. It is equal to 0’9536 of an ohm or BA unit; ora BA unit equals 10485 Siemens unit, or equals a column of mercury 1°0485 metre in length and a square mm. in cross section. 194, A single thermo-electric couple deflects a galvanometer of roo ohms resist- ance 0° 30’; how much will a series of 30 such couples deflect it, the connections being made by short thick wires ? Ans, TA°*40": 195. Suppose a sine galvanometer had been used in the last question, and the first reading had been 09°30’, what would the second be? Ansei5 16h 196. The internal resistance of a cell is halfan ohm; when a tangent galvano- meter of 1 ohm resistance is connected with it by short thick wires it is deflected 15° ; by how much will it be deflected if for one of the thick wires a thin wire of 14 ohm resistance is substituted ? ANS]? t3Gh 197, What will be the deflection if each of the wires is replaced by a thin wire of 14 ohm resistance ? AAG SOs 198. A cell of one-third of an ohm resistance deflects a tangent galvanometer of unknown resistance 45°, the connection being made by two short thick wires. If a wire of 3 ohms resistance be substituted for one of the short wires the deflection is 30°. What is the resistance of the galvanometer? AMS, 3°75 ohms. 199. What would be the deflection if for the cell in the last question three exactly similar cells in series were substituted (2) when the galvanometer alone is in circuit ; (4) when both the galvanometer and the thin wire are in circuit ? Ans, & 68°48, 0 = B79*4r", 200. A galvanometer offering no sensible resistance is deflected 50° by a cell connected with it by short thick wires. Ifa resistance of 3 ohms be put in the circuit, the deflection is 20°. Find the internal resistance of the cell. Ans, 1°32; 201. Suppose the results in the last question were produced by two exactly similar cells in series, find the internal resistance of each. Ans, 0°659. 202. Suppose they were produced by two exactly similar cells placed side by side, find the internal resistance of each. Ans. 2°639. 203. If the resistance of 130 yards of a particular copper wire of an inch in I diameter is an ohm, express in that unit the resistance of 8242 yards of copper wire fee 12 of an inch in diameter. ; Ans. 35°66. 203. One form of fuse for firing mines by voltaic electricity consists of a platinum wire 2 of an inch long, of which a yard weighs 2 grains. Required its resistance in terms of a Siemens unit. Specific gravity of platinum 22, and its conducting power 11°25 that of mercury. Ans, 0°131. 205. Express in ohms the resistance of one mile of copper wire } of an inch in diameter of the same quality as that referred to in 203. Ans, 0'8461, 1118 Problems and Examples in Physics 206. The whole resistance of a copper wire going round the earth (24800 miles) is 221650 ohms. Find its diameter in inches. Ans. 0'0738. 207. What length of platinum wire 0’o5 of an incn in-diameter must be taken to get a resistance equal to 1 ohm, the specific resistance of platinum being taken at 5°55 that of copper ? Ans. 14'9 metres, 208. 660 yards of iron wire 0'0625 of an inch in diameter have the same electrical resistance as a mile of copper wire o’0416 of an inch in diameter. Find the specific resistance of iron, that of copper being unity. Ans, 6°02. 209. Ten exactly similar cells in series produce a deflection of 45° in a tangent galvanometer, the external resistance of the circuit being ro ohms. If arranged so that there is a series of 5 cells, of two abreast, a deflection of 33°42!’ is produced ; find the internal resistance of the cell. Ans. 4 ohm. 210. On the bobbins of the new Post Office pattern of a single needle instrument are coiled 225 yards of No. 35 copper wire 0°0087 inch in diameter, the resistance of which is about 92 ohms. Required the conducting power of the wire in terms of mercury. Ansiess 6. 211. Ten exactly similar cells each of § of an ohm resistance give, when arranged in 2 series of five each, a deflection of 239°57’; but when arranged in 5 series of 2 each a deflection of 33°°42’. Required the external resistance of the circuit including that of the galvanometer. Ans, 35. 212. A cell ina certain circuit deflects a tangent galvanometer 18° 26’; two such cells abreast in the same circuit deflect it 23° 57’; two such cells in series in the same circuit diminished by 1 ohm deflect it 29°°2’.. Find the internal resistance of one cell and that of the circuit. Ans. Ros 4 st 66, 213. What is the best arrangement of 6 cells, each of % of an ohm resistance, against an external resistance of 2 ohms? Ans. Indifferent whether in 6 cells of 1 each or in 3 cells of 2 each. 214. What is the best arrangement of 20 cells, each of 0’8 ohm resistance, against an external resistance of 4 ohms? Ans. to cells of 2 each. 215. Ina circuit containing a galvanometer and a voltameter, the current which deflects the galvanometer 45° produces 10°32 cubic centimetres of mixed gas in a minute. ‘The electrodes are put farther apart, and the deflection is now 20° ; find how much gas is now produced per minute. Ans. 3°757 cc. 216. 100 inches of copper wire weighing 100 grains has a resistance of 0'1516 ohm, Required the resistance of 50 inches weighing 200 grains. Ans. 0°0379. 217. A knot of nearly pure copper wire weighing one pound has a resistance of 1200 ohms at 15°’5 C.; what is the resistance at the same temperature of a knot of the same quality of wire weighing 125 pounds? Ans. 96 ohms, 218. Find the length in yards of a wire of the same diameter and quality as the knot pound in 217, having a resistance of 2 ohms. Ans. 3°38 yards. 219. Find the length in yards of a wire of the same quality and total resistance as the knot pound in 217, but of three times the diameter. Ans, 18261 yards. 220. The specific gravity of platinum is 2} times that of copper; its resistance 5% as great. What length of platinum wire weighing roo grains has the same resistance as roo inches of copper wire also weighing Ioo grains? Ans. 27, 221. Acell with a resistance of an ohm is connected by very short thick wires with the binding screws of a tangent galvanometer, the resistance of which is half an ohm, and the deflection is 45° ; if the screws of the galvanometer be also connected at the same time by a wire of 1 ohm resistance, find the deflection. Ans. 36° 52’. 222. The resistance of a galvanometer is half an ohm, and the deflection when Voltaic E lectricity : L119 the current of a cell is passed through it is 30°. When a wire of 2 ohms resistance is introduced into the circuit the deflection is 15°; find the internal resistance of the cell. ASS Toa 223. When the current of a cell, the resistance of which is $ of an ohm, is passed through a galvanometer connected with it by very short thick wires, the deflection is 45°; when the binding screws are also connected by a shunt having a resistance of 1 the deflection is 33°°42’. Find the resistance of the galvanometer. aoe 2 224. A cell whose internal resistance is 2 ohms has its copper pole connected with he binding screw A of a galvanometer formed of a thick band of copper. From the other screw Ba wire of 20 ohms resistance passes to the zinc pole, and the deflection read off is 79°8’. Find the deflection when B is at the same time connected with the zine pole by a second wire of 30 ohms resistance. ANS ei ie G 225. What would be the deflection in 224 if the second wire instead of passing from B to the zinc pole passed directly from the zinc pole to the copper pole? Ans, 6°°47'. 226. A Leclanché cell deflects a galvanometer 30° when 200 ohms resistance are introduced into the circuit, 15° when 570 ohms are introduced; a standard Daniell cell deflects it 30° when 100 ohms are in circuit, and 15° when 250 additional ohms are introduced. Required the electromotive force of the Leclanché in terms of that of the Daniell. Ans, 1°48. 227. A Bunsen and a Daniell cell are placed in the same circuit in the first case so that the carbon of the first is united to the zinc of the Daniell; and in the second case so that their currents oppose each other.. The currents are respectively 30°°2’, and in the second 10°°6’. Required the electromotive force of the Bunsen in terms of the Daniell. Ans. 1°89. 228. A telegraph line constructed of copper wire, a kilometre of which weighs 30°5 kilogrammes, is to be replaced by iron wire a kilometre of which weighs 135°6 kilo- grammes. In what ratio does the resistance alter? Avs. The resistance of the iron wire will be 1°18 times that of the copper wire for which it is substituted. 229. A telegraph line which has previously consisted of copper wire weighing 30°5 kilogrammes to the kilometre is to be replaced by an iron wire of the same length which shall offer the same resistance. What must be the section of the latter, and what its weight per kilometre ? Ans. The section of the copper wire is 3°4357 sq. mm., that of the iron by which it is replaced is 20°6 sq. mm., and its weight per kilometre is 160°4 kilogrammes. 230. When the poles of a voltaic cell are connected by a conductor of resist- ance 1, acurrent of strength 1°32 is produced ; and when they are connected by a conductor of resistance 5 the strength of the current is 0°33. Find from these data the internal resistance and the electromotive force of the cell. Ans. R=} H=1'76. 231. A silver wire is joined end to end to an iron wire of the same length, but of double the diameter, and six times the specific resistance; the other ends are joined to the battery, the current of which is transmitted for five minutes, during which time a total quantity of 45 units of heat is generated in the two wires. How is it shared between them ? Ans, Ag: Fe=18 : 27. 232. A window casement of iron faces the south, and the hinges which support it are on the east. What electrical phenomena are observed (a) when the window is opened, and (4) when it is closed ? 233. Two points 135° apart in a uniform circular conducting ring are connected with the opposite poles of a voltaic battery. Compare the strength of the current in the two portions of the ring. 234. A mile of cable with a resistance of 3°59 ohms was put in water, with the end B insulated ; its core having been pricked with a needle the resistance tested from the end 4 was found to be 2°81 ohms. 4 being insulated, a test from B showed the resistance to be 2°76. Required the distance from & to the injured spot. 217s. 867 yards, 7 7s ih ‘ t ; Sy F i - eves a an Gr je Ye 4qsile. ude ¢ Se Ph a BE eae Or i vet ‘ ' Fe yO atc & Pr ay ee eval be ty 7 4 iy 72) mie agus Te hes) , neha bee ‘ea a om, j 5 5 — : ‘ « Ball +250 U ' ? ; bone Aylin pes RO as a te ee... eatiauls y j id WP tb (ie of Cel aaa Te ei =. ¢ :* 4 >. ys) ‘ oe ? lis ¢ . sc} bay > a A fay « ke , j f ' ¢ oe. a i ’ ‘ * . ; J 5 , z@ 5 « ‘ lt v5 od 5 tlt P Me lata preg te Pie sreces tts 5 oe a! Pe ae | t » ) Jie oad they } oy Yet nd av pee Tee iy ys 9. red a Piviniet ; ' ae pif ‘leis uceeiel vh : t be | | Peed, isle baud it part ot ele 4 J 7 4 ny Sof yeiNt ad: ae hdd On, Wed hes bh Mey per Ee . , ’ fr 619 54 i 4 Jute pe 2. 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Ml ied sowie csi nite tne ban Re OG Leet NG a en ¥ . ‘ s / : ° ~ 5 € .* Brace ia.) eo Gol! aA Uyed ALIEN aE Gal, ae ees. e bial Al, Gla e 4sh aca, it pia} ty Pig's Ai cia eybeihent ail ‘| fy val) phi jet é ‘ 5 cme, ey he) beta 3 eRe ve) Wades pales ae Boy aie: ja bth vd heat i:'S rs ei "yoga Heme i? we ew a 1a YORE BAS ae aia rene Sale Be, hues ; pt i LF i bs\6 mu i‘ A * a3 * bo its ‘ anit alge Son. tne Pra sue ie el eahlan prea = enpnet Lansyeal, 3 wih (i Ait. iy «eon os el Dies sgt emegrtyh net) nee are wt OPh Aiea versa + Aaeeme v4 ere INDEX (THE NUMBERS REFER TO THE ARTICLES) ABE BERRATION, spherical, 545 Abnormal dispersion, 593 Absolute electrical units, 999 Absolute expansion of mercury, 326 Absolute measure of electrical resistance, 985; temperature, 508 Absorbent power of aqueous vapour, 1023 Absorbing power, 431 Absorption, electrical, 795; of gases by chromatic, 5953 solids, 196; of gases by liquids, 192; | of heat by liquids, 442; by vapours, 443; heat produced by, 492 Acceleration of a force, 27, 62, 78 Accidental haloes, 641; images, 640; magnetic variations, 706 Accommodation (of the eye), 634 Accumulator, hydraulic, 154 Accumulators, 788 Achromatism, 596 ; of the microscope, 604 | Achromatopsy, 646 Acidometer, 128 Acierage, 880 Aclinic lines, 712 Acoustic foci, 240 ; attraction and repul- sion, 294 Acoustics, 223-295 Actinic balance, 995 ; rays, 441, 585 Action and reaction, 39 Ader’s telephone, 960 Adhesion, 87 Aerial meteors, 10II ; perspective, 631 Aerolites, 490 #ésculine, 594 Affinity, 86 After action, elastic, 89 Agents, 6 Agonic line, 706 Air, aspirating action of currents of, 210; causes which modify temperature of, 1012, 1043 ; heating by, 503; thermo- meter, 338 ;resistance of, 48; trap, 170; velocity of, 25; gap, 951 ANI Air-balloons, 199 ; chamber, 220 Air-brake, 212; pump, 203, 477; Bian- chi’s, 206 ; condensing, 212; Deleuil’s, 207; gauges, 2Cc4; rarefaction in, 203 5 “receiver of, (203.50 Sprengel s; 208 ; uses of, 213 Ajutage, 148 Alarum, electric, 918 Alcarrazas, 377 Alcohol thermometer, 310 Alcoholic value of wines, 382 Alcoholometer, 129 ; Gay-Lussac’s, 129; centesimal, 129 | Allotropic states, 466 Alloys, 344 Alternate currents, 936 Amagat’s experiments, 98, 184 Amalgam, electrical, 777 Amalgamated zinc, 837 Amber, 745 Amici’s camera lucida, 615 Ammeter, 998 Ampere, 835 Ampere’s memoria technica, 841; stand, 890 ; theory of magnetism, 901 Amplitude of vibration, 55 Analogous pole, 754 Analyser, 670 Analysis, spectral, 587; of solar light, 437 Anamorphoses, 546 Anelectrics, 746 Anelectrotonus, 850 Anemometer, IO12 Aneroid barometer, 167, 190 Angle of deviation, 556; critical. 552; optic, 630; of polarisation, 668; of reflection and incidence, 523, 5483 of refraction, 548 ; visual, 630 Angular currents, laws of, 883 ; velocity, 53 Animal heat, 497 Anion, 864 La 22 ANN Annealing, 91, 95 Annual variations of magnetism, 707 Anode, 864 Anticyclone, 1017 Antilogous pole, 754 Anvil of an induction coil, 949 Aperiodic galvanometer, 843 Aperture of a lens, 570 Aplanatic lenses, 570 Aqueous humour of the eye, 625 Aqueous vapour, its influence on climate, 1023; tension of, 359-365 Arago’s experiment, 184 Arbor Dianz, 876; Saturni, 876 Arc lamps, 860 Arc of vibration, 55 ; voltaic, 855 Archimedes’ principle, 14; applied to gases, 198 , Area, unit of, 22 Argon, 160 Armatures, 739; drum, 941; Siemens’, 03% Arms of levers, 40 Armstrong’s hydro-electric machine, 780 Artesian wells, 112 Artificial magnets, 695 Ascension, angle of right, 612 Ascent of liquids in capillary tubes, 133 ; between surfaces, 134 Aspirating action of air currents, 210 Astatic needle and system, 714; circuits, 895 Astronomical telescope, 607 Athermancy, 442 Atmolysis, 193 tmosphere, its composition, 160; crush- ing force of, 162 ; amount of, determi- nation of, 166; electricity in the, 10323 moisture of, 407 Atmospheric electricity, causes of, 1033, 1034 $ pressure, 161, 166, 1012 Atomic heat, 468 ; weight deduced from specific heat, 468 Atoms, 3 Attraction, capillary, 132; and repulsion produced by capillarity, 138; mole- cular, 84 ; universal, 67 Attraction, magnetic, laws electrical, laws of, 756 Atwood’s machine, 78 Audiometer, 962 Audiphone, 243 Aura, electrical, 787 Aurora borealis, 708, 1041 Aurum musivum, 777 Austral pole, 703 Avoirdupois, 23 O17 ET: Index BER Axis of crystal, 654 ;- electric; 7545 lenses, 567; optic, 654 ; of a magnet, 696 ; of oscillation, 80 Azimuth circle, 709 AD conductors, 411 Bain’s telegraph, 916 Balance, 72 ; actinic, 995; beam of, 73; compensating, 324; delicacy of, 74; hydrostatic, 114, 121; induction, 962 ; knife-edge of, 72 ; physical and chemi- cal, 75; spring, 89 ; torsion, 90, 717, 756 Ballistic galyanometer, 843; pendulum, 82 Balloons, 199-202; Montgolfier, 199; weight raised by, 202 Bands of spectrum, 586 Barker’s mill, 151 Barlow’s wheel, 894 Barometers, 167 ; aneroid, 167, 1005 Bunten’s, 170; cistern, 168 ; corrections in, 172 ; determination of heights by, 181; differential, 189; fixed, 178; Fortin’s, 169; Gay-Lussac’s, 170; glycerine, 179; Huyghen’s, 180; pre- cautions with, 171; wheel; 177; variations of height of, 174 Barometric formula, Laplace’s, 181 ; gradients, 1017; height, corrected for heat, 331; manometer, 189; va- riations, 175 Baroscope, 198 Bassoon, 276 Battery, Bunsen’s, 831; Callan’s, 831; chemical effects of, 863; Daniell’s, 829; electric, 796; floating, 38090; gas, 873; gravity, 833; Grove's, $304 Leclanché’s, 834; Leyden, 796; con- stant, 828 ; luminous effects, 855 ; mag- netic, mechanical effects of, 861 ; Mi- notto’s, 833; Marié Davy’s, 833; secondary, 872; Smee’s, 832 ; mercury sulphate, 833; thermo-electric, 972 ; voltaic, 825, 826; Wollaston’s, 826 Beam of a balance, 73; of a steam- engine, 477 Beats, 266 Beaume’s hydrometer, 128 Becquerel’s pyrometer, 979; electric battery, 974 Bell of a trumpet, 242 Bell’s telephone, 960 ; photophone, 966 Bellows, 246; hydrostatic, 102; water, 210 Bells, 286 Berthelot’s calorimetrical bomb, 495 thermo- Index BER Berthollet’s experiment, 191 Bianchi’s air-pump, 206 Biaxial crystals, double refraction in, 658; rings in, 681 Bidwell’s experiments, 905 Binnacle, 711 Binocular vision, 635 Biot’s apparatus, 691 Biquartz, 692 Black’s experiments 479 Bladder, swimming, 118 Blagden’s law, 347 Block and tackle, 41 Blood-globules, 12 Blue cloud, 1024 Bodies, properties of, 7, 88 Bohnenberger’s electroscope, 839 Boiler, 476 Boiling, 367; by cooling, 371 Boiling-point, influence of dissolved sub- stances on, 369; of nature of vessel, 370 ; of pressure on, 371 ; in a. ther- mometer, 306; measurement of heights by, 373 Bolometer, 995 Bomb, calorimetrical, 495 Borda’s method, 76 Boreal pole, 703 Bottomley’s experiment, 1028 Boutigny’s experiments, 391 Boxes, resistance, 984 Boyle’s law, 183-185 Boys’s radiomicrometer, 976; threads, go Brake, friction, 483; air, 212 Bramah’s hydraulic press, 109 Branch currents, 996 Breaking weight, 92 Breezes, land and sea, 1015 Breguet’s thermometer, 313 Bridge, Wheatstone’s, 986 British imperial yard, 22; and French system of weights and measures, 126 Brittle bodies, 94 Browning’s regulator, 858 Brush discharge, 809; dynamo-electrical machine, 942 Brushes, displacement of, 943 Bulbs, specific gravity. 124 Bunsen’s Sprengel-pump, 209 ; battery, 831;. burner, 58%; ice calorimeter, 460 ; photometer, 521 Bunsen and Kirchhoff’s researches, 588 Bunten’s barometer, 170 Buoyancy of liquids, ror Burning mirfors, 427 on latent heat, CHE ABLE telegraph, 912 Ceesium, 590 Cagniard-Latour’s sirene, 2453 experi- ments on formation of vapour, 374 Cailletet’s and Pictet’s researches, 386 Calibration, 302 Callan’s battery, 831 Calorescence, 441 Calorie, 456 Calorific effects of electrical discharge, Si2; of currents electricity S01 of Ruhmkorff’s coil, 949, 9513; of the spectrum, 585 Calorimeter, 459; Bunsen’s ice, 460; Black’s, 459; Favre and Silbermann’s, 4/73; Lavoisier and Laplace’s, 459 Calorimetry, 456 Camera lucida, 615; Amici’s, Wollaston’s, 615 ; obscura, 614 Campani’s eyepiece, 604 Capacity, error of barometric, 168; elec- trical, 762; specific inductive, 769 Capillarity, 132; attraction and repulsion produced by, 1383; correction for, 172 Capillary phenomena, 132-140; electro- meter, 862 ; tubes, 133 Capsule, of the eye, 625 Carbon, 831 Cardan’s suspension, 169 Cardew’s voltmeter, 998 Carré’s mode of freezing, 378 Carriage lamps, 547 Cartesian diver, 117 Cascade, charging by, 798 Cataracts of a steam engine, 477 Cathetometer, 89 Catoptric telescopes, 610 Caustics, 545 Cauterisation, galvanic, 851 Celsius’ scale, 307 Centesimal alcoholometer, 129 Centigrade scale, 307 Centimetre, 126 Centre, optical, 567; of gravity, 69; of parallel forces, 38; of pressure, 103 Centrifugal force, 53 Centripetal force, 53 Charge of a Leyden jar, penetration of, 7953; measurement of, 799; residual, 125 Charging by cascade, 798 Charles’s law, 335 Chatterton’s compound, 908 Chemical affinity, 86; combination, 493: decomposition, 863 ; effects of electrical discharge, 815; of voltaic currents, 863; of Ruhmkorff’s coil, 951 ; har- AN GEZ 615 5 I124 CHE monicon 282; hygrometer, 400 ; pro- perties of the spectrum, 585 Chemistry, I Cheval-vapeur, 1000 Children’s experiment, 852 Chimes, electrical, 786 Chimney, 500 Chladni’s experiments, 286 Chlorophane, 649 Chlorophyl, 592 Chords, major and minor, 250; physical constitution of, 268 ; tones dominant and subdominant, 251; vocal, 263 Choroid, 625 Chromatic scale, 253; aberration, 595 Chromium, magnetic limit of 741 Ciliary processes, 625 Circle, azimuthal, 709 Circular polarisation, 683 Cirrocumulus, 101g Cirrostratus, 1019 Cirrus, 1019 Cistern barometer, 168 Clamond’s thermo-electric battery, 975 Clarinet, 276 Clarke’s magneto-electrical machine, 934 Cleavage, electricity produced by, 753 Clef, 255 Clément-Désorme’s experiment, 210 Climate, 1046; constant, 1046 ; influence of aqueous vapour on, 1023 Climatology, 1042-1049 Clocks, «823° ‘erutelyof, 9525 velectrical, 919 Clouds, 1019 ; electricity of, 1034 ; forma- tion of, 1020 Coatings, 769 ; Leyden jar with movable, 793 Cobalt, 741 Coercive force, 701 Coefficients of linear expansion, 317-320; conductivity, 412 ; Poisson’s, 89 Cohesion, 85 Coil, primary, 921; Ruhmkorff’s, 949 ; effects produced by, 951; resistance, 984; secondary, 921 Cold, apparent reflection of, 429 ; pro- duced by evaporation, 377 ; expansion of gases, 506; by nocturnal radiation, 507 ; sources of, 505 Colladon and Sturm’s experiments, 237 Collecting plate, 801i Collimation, 607 Collision of bodies, 58 Colloids, 142 Coloration produced by rotatory polari- sation, 689 Index CON Colour. 7 ; of bodies, 581; of heat, 444 ; of thin plates, 664 Colour discs, 579 Colour disease, 646 Colours, contrast of, 641; mixed, 582; simple, 578; complementary, 582 ; produced by polarised light, 676- 682 Combustion, 493 ; heat disengaged dur- Ing, 494 Comma, musical, 251! Common reservoir, 748 Commutator, 929, 950 Compass, correction of errors, 736; de- clination, 709; mariner’s, 711 ; incli- nation, 713; sine, 846; tangent, 845 Compensation, method of magnets, 730 ; pendulum, 324; balance, 324; grid- iron, 324; strips, 324 Complementary colours, 582 Component forces. 32 Composition of velocities, 52 Compound microscope, 602 ; dynamo, 944 Compressed glass, colours produced by, 682 Compressibility, 7, 16; of gases, 157, 183 ; of liquids, 08 Concave mirrors, 426, 537 Concert pitch, 254 Concordant tones, 250 Condensation of vapours, 379 Condensed gas, 196, 212; wave, 228 Condenser, ’ electrical; 755 >>" “ot wim engine, 477 ; limits to charge of, 790; of Ruhmkorff’s coil, 950; Liebig’s, 381 Condensing engine, 481 ; air-pump, 212 ; electroscope, 801 ; plate, 819 ; hygro- meters 401 Conduction of heat, 411; of electricity, 747; lightning, 1039 Conductivity of bodies for heat, 411 ; co- efficient of, 412; of gases, 416; of liquids, 414 ; for electricity, 989 Conductors, 747; equivalent, 987 ; good and bad, 411; lightning, 1039; resist- ance of, 983 Congelation, 347 Conjugate mirrors, 427; focus, 537 Conservation of energy, 6 Constant currents, 828 Contact theory of electricity, 819 Contractile force, 323 Contraction, coefficient of, 89 Convection, 415 ; currents, 453 ; electro- lytic, 854 wound Lundex CON Convective discharge, 792 Convex meniscus, 132 ; mirrors, 536, 538 Cooling, method of, 464 ; Newton’s jaw of, 423 Corliss engine, 481 Cornea, 625 Cornet-a-piston, 284 Cornish engine, 477 Corona, 1041 Corpuscular theory of light, 511 Corti’s fibres, 264 Cosine, law of the, 421, 520 Coulomb, 835, 1000 Coulomb’s law, 756 Couple, 37; terrestrial magnetic, 704; voltaic, 822; thermo-electric, 972 Couronne des tasses, 826 Cowper’s writing telegraph, 911 Coxwell’s balloon, 199 Crab winch, 42 Crane, 42 Critical angle, 552; current, 945; tem- perature, 374 Crookes’s radiometer, 453; vacuum, 208, 4543 experiments, 956 Cross-wire of a telescope, 607 Crutch of a clock, 82 Cryohydrate, 352 Cryophorus, 377 Crystal, hemihedral, 754 Crystalline, 625 Crystallisation, 348 Crystalloids, 142 Crystals, 348; expansion of, 320; doubly refracting, 653, 673; uniaxial, 654; positive and negative, 657 Cumulostratus, 1019 Cumulus, 1019 Current electricity, 821 Currents, action on currents, 881 ; action of magnets, 890 ; action of earth on, 895; action on solenoids, 897 ; con- stant, 828 ; divided, 986 ; diaphragm, 861; direct and inverse, 921; effects of enfeeblement of, 827; extra, 930 ; intensity of, 847 ; induction by, 921 ; laws of angular, 883 ; laws of sinuous, 884; local, 827; magnetisation by, 904 ; motion and sounds produced by, 906 ; muscular, 1004; rotation of mag- nets by, 889; secondary, 827; terres- trial,),9G2.¢ thermal effects’ of,” $51; transmissions by, 866 Curves, magnetic, 720 Cut-out, 851 Cyclones, 1017 Cymbal, 286 DIE Oye eee 620 Daltonism, 646 | Dalton’s laws on gases and vapours, 389; method of determining the tension of aqueous vapour, 360 Damper, 283, 843, 929 Daniell’s battery, 829 ; hygrometer, 402 ; pyrometer, 315 Dark lines of the spectrum, 586; of solar spectrum, 591 Day, apparent, 21 Dead-beat galvanometer, 843; -point, 480 Decimetre, 126 Declination compass, 709; errors of, 7iO; magnetic, 705; ‘of needle, 705% variations in, 706; of a star, 612 Decomposition, chemical, 863 ; of white light, 576 Decrement, logarithmic, 843 Degrees of a thermometer, 307 De la Rive’s floating battery, 890; ex- periments, 957 De la Rue and Miiller’s experiments, Deleuil’s air-pump, 207 Delezenne’s circle, 929 Delicacy of balance, 743; of thermo- meter, 311 Densimeter, 131 Density, 24; of an electrical current, 877; of the earth, 68 ; electric, 755; gravimetrical, 188; of gases, 339- 341; maximum of water, 334; of vapours, Gay-Lussac’s method, 392 ; Dumas’s, 394 ; Deville and Troost’s, 394 ; Hofmann’s, 393 Depression of liquids in capillary tube, 132; between surfaces, 134; coefh- cient of, 347 Derived currents, 996 Descartes’ laws of refraction, 549 Developer, 620 Deviation, angle of, 556 Deville and Troost’s method, 394 Dew, 1025; point, 401 Dewar’s experiments, 388 Diabetic urine, analysis of, 693 Diagram indicator, 483 Dialyser, 142 Dialysis, 142 Diamagnetism, 968 Diapason, 254 Diaphanous bodies, 512 Diaphragm, 603; currents, 861 Diathermancy, 442 Diatonic scale, 251 Dielectric polarisation, 770 1126 DIE Dielectrics, 769 Differential barometer, 189; galvano- meter, 842 ; lamp, 860; thermometer, S127 note, 207 Diffraction, 515; spectra, 662; fringes, 660 Diffusion of gases, 193; of heat, 445 ; of liquids, 142 Digester, Papin’s, 375 Dimensions of units, 62 Dioncea muscipula, 849 Dioptric telescopes, 610 Diosmose, I4I Dip, magnetic, 712 Diplopia, 645 Dipping needle, 712 Direct vision spectroscope, 5&9 Directrix of a selenoid, 896 Disc, Newton’s, 579; Maxwell’s colour, 582 Discharge, convective, 792; electrical, effects of the, 805; lateral, 1039; silent, 815; slow and instantaneous, 789 Discharging rod, 789 Dispersion, 556; abnormal, 593 Dispersive power, 576 Displacement, 46 Disruptive discharge, 805 Dissipation of energy, 510 Dissociation, 395, 496, 867 Dissolving views, 617 Distance, estimation of, 631; adaptation of eye to, 634 Distillation, 380 Distribution of free electricity, 757 ; of magnetism, 742; of temperature, 1047 ; of land and water, 1049 Diurnal variations of magnetism, 707 Diver, Cartesian, 117 Divided currents, 996 Dividing machine, II Divisibility, 7, 12 Dobereiner’s lamp, 492 Dolbear’s experiments, 960 Dominant chords, 251 Doppler’s principle, 236 Double refraction, 653, 666 Double-weighing, 76 Doublet, Wollaston, 598 Dove’s law of storms, 1016 Draught of fire-places, 500 Drawplate, 93 Dredging machines, 152 Driving wheels, 480 Drum, 287 Drum armature, 941 Index ELE Drummond’s light, 618 Dry batteries, piles, 838 ; plates, 622 eae microscope, 618; regulator, Ds Ductility, 7, 93 Duhamel’s graphic method, 248 Dulong and Arago’s experiments on Boyle’s law, 184; method of deter- mining the tension of aqueous vapour, 361 Dulong and Petit’s determination of ab- solute expansion of mercury, 326; method of cooling, 464 ; law, 467 Dumas’s method for vapour density, 394 Duplex telegraphy, 914 Duration of electric spark, 816 Dutroche’s endosmometer, 141 Dynamic radiation and absorption, 450 Dynamical theory of heat, 436 Dynamo-electrical machine, 939, 941,942. Dynamo-magnetic machine, 939 Dynamometer, 91, 433 Dyne, 62 AR, the, 264 Ear trumpet, 242 Earth, density of, 68; its action on currents, 895 ; action on solenoids, 898; current, 915, 1041; flattening of, by rotation, 83; magnetic poles of the, 703 ; magnetisation by, 735 Earth’s magnetism, 705 Ebullition, 354 ; laws of, 367 Eccentric, 479 Echelon lenses, 619 Echoes, monosyllabic, trisyllabic, mul- tiple, 240 Eclipses, 515 Eddy currents, 959 Edelmann’s hygrometer, 401 Edison’s phonograph, 295 ; 963; telephone, 964 Efficiency ot an accumulator, 872; of a machine, 152, 483, 945; of. heat engines, 484 Effluvium, electrical, 815 Efflux, velocity of, 144; quantity of, 147; influence of tubes on, 148 Effusion of gases, 194 Elastic bodies, 58; after action, 89 Elastic force of gases, 155; of vapours, tasimeter, ci) Elasticity, 7, 17 ; limit of, 17, S05q08 traction, 89 ; modulus of, 89 ; of tor- sion, 90; of flexure, QI. Electric alarum, 918; batteries, 796 ; charge, 799; chimes, 786; clocks, Index ELE 919; density, 758; discharge, 805 ; egg, 810; fish, 1009 ; lamp, 860 ; light, 856-860 ; pendulum, 746; poles, 754; residue, 794 ; shock, 805 ; spark, 785; telegraphs, 908-920; tension, 759; whirl, 737 Electric endosmose, 861; field, 761; potential, 760; capacity, 762, mea- surement of, 763; machines, 775- 7843 precautions In, 7773 resistance, unit of, 984; conductivity, 747, 989; quantity, 762; units, 999 Electricity, 6, 745; application of, to medicine, 1012; atmospheric, 1030- 1039; contact theory, 819; current, 821; communication of, 772; de- velopment of, by friction, 746; by pressure and cleavage, 753; distribu- tion of, 7573; disengagement of, in chemical’ actions, 820; loss of, 766; mechanical effects, 814; power cf points, 765; velocity of, 817; theories of, 750; work required for production of, 783 Electrocapillary phenomena, 862 Electrochemical equivalent, 868 ; series, 864 Electrodes, 824; polarisation of, $27 Electrodynamics, 881 Electrodynamometer, 998 Electrogilding, 878 Electrolysis, 864 ; laws of, 868 Electrolyte, 864 Electrolytic convection, $54 Electromagnetic motors, 920 ; 999 ; theory of light, 1002 Electromagnets, 905 Electrometallurgy, 877 Electrometer, 774; Lane’s, 799; quad- rant, 779; Thomson’s, 803 Electromotive series, 822; force, 823 ; determination of, 993; force of ele- ments, 835 Electron, 868 Electrophorus, 775 ; work of an, 783 ‘Electropyrometer, 979 Electroscope, 746 ; Bohnenberger’s, 839 ; Volta’s condensing, 801 ; gold leaf, 774 Electrosilvering, 879 Electrostatic units, 999 Electrostriction, 814 Electrotonus, 850 Elliptical polarisation, 683, 686 Emission theory, 511 Emissive power, 432 Emmetropic eye, 643 Emulsions, 142; gelatine, 622 units, 1127 EYE Endosmometer, 141 Endosmose, 141; electrical, 861; of gases, 193 Endosmotic equivalent, 141 Endothermic reactions, 496 Energy, 63; conservation of, 66; dissi- pation of, 510; transformations of, 65 ; varieties of, 64 Engines, gas, 486; steam, 475; low and high pressure, 481 ; single action, 479; locomotive, 480; fre, 222 ; Cornish, 477; horizontal, 478 ; work of, 482 ; hot air, 485 Equator, 696; magnetic, 712 Equilibrium of forces, 35; of floating bodies, 1163; of heavy bodies, 70; of liquids, 105; mobile of temperature, 422 5 euiiaet7 basta ple.. 7 kta ins stable, 71 Equivalent, electrochemical, 868; en- dosmotic, 141 ; conductors, 987 Erg, 62 Escapement, 82; wheel, 82 Ether, 436; luminiferous, 511 Eustachian tube, 264 Evaporation, 354; causes which accele- rate it, 366; cold due to, 377 ; latent heat of, 376 Evaporation and ebullition, 368 Ewing’s experiments, 744 Exchanges, theory of, 422 Exhaustion, produced by air-pump, 204 ; by Sprengel’s pump, 208 Exosmose, 141 Exothermic reactions, 496 Expanded wave, 228 Expansibility of gases 156 Expansion, 300 ; apparent and real, 325 ; absolute, of mercury, 326; apparent, of mercury, 327; of liquids, 330; of gases, 335-337 ; linear and cubical, coefficients of, 317; measurement of linear, 318; of crystals, 320; applica- tions of, 323 ; force of, 323 Expansion of gases, cold produced by, 506 ; problems on, 336 Expansive force of ice, 350 Experiment, Berthollet’s, 191; Frank- lin’s;,. 3723. Florentine, 98); Pascal’s, 165; Torricellian, 164 Extension, 7, 9 Extra current, 930 Eye, 625 ; accommodation of, 634; not achromatic, 642; refractive indices of media of, 626; path of rays in, 628 dimensions of various parts of, 627 Eye lens, 604 ; Campani’s, 604 Ties FAH AHRENHEIT’S hydrometer, 124 ; scale, 307 Falling bodies, laws of, 77 Falsetto notes, 263 Farad, 1000 Faraday’s experiments, 768 ; disc, 894; theory of induction, 770; voltameter, 868 ; wheel, 639 Fatigue, elastic, 89 Favre and Silbermann’s calorimeter, 473 ; determination of heat of com- bustion, 494 Fibres, Corti’s, 264 Field, electric, 761 ; magnetic, 721 ; of a microscope, 604; of view, 605 Field lens and glass, 605 Field magnets, 938 Figures, Lichtenberg’s, 794 Filament, solenoidal, 724 Filter-pump, 209 Filters, 15 Finder, 607 Fire-ball, 1035; -engine, 222; -places, 499 ; -works, 151 Firmamental blue, 1024 Fish, electrical, 1009 Fishes, swimming bladder of, 118 Fizeau’s experiments, 320, 519 Flag signals, 910 Flame, 493 ; sensitive, 282 Flask, specific gravity, 122 Flattening of the earth, 83 Fleming’s rule, 928 Flexure, elasticity of, 91 Floating bodies, 116 Florentine experiment, 13, 98 Fluid, 4; imponderable, 6 ; elastic, 155 ; magnetic, 699 Fluidity, 7 Fluorescence, 594 Flute, 284 Flux of magnetic force, 723 Fluxes, 344 Focal distance, 426 Foci, acoustic, 240; of convex mirrors, 538 ; in double convex lenses, 564 Focus, 426, 537; of a parabola, 145; con- jugate, 537; determination of the prin- ciple, 539 ; of aspherical concave mirror, 537 3 in double convex lens, 564 Focussing the microscope, 599, 603 Fog-signal, 245 Fogs, 1018 Fon, I015 Foot, 22 Foot-pound, 61, 482 Force, 26; acceleration of, 78; centri- Lndex GAL fugal, 53; condensing, of electricity, 804; conservation of, 66; coer- Cive, 701; direction of, 305 elastic, of gases, 155; lines of magnetic, 722 ; of expansion and contraction, 323; electromotive, 823, 835 ; representation of, 30 ; parallelogram of, 33 ; of liquids, 3333 portative, 740 Forces, 6; along the same line, che equilibrium of, 35; impulsive, 57 ; magnetic, 722; molecular, 84 ; mo- ments of, 36; polygon of, 34 ; triangle of, 35 Formulz for expansion, 322; barome- tric, 181; for sound, 234; for spheri- cal mirrors, 542 ; for lenses, 571 Fortin’s barometer, 169 Foucault’s currents, 959 ; determination of velocity of light, 518; experiment, 856,959 Fountain in vacuo, 213; at Giggleswick, 217 ; intermittent, 215 ; Hero’s, 214 Fovea centralis, 625 Franklin’s experiment, 372, 1030; plate, 791; theory of electricity, 750 Fraunhofer’s lines, 586 Freezing, apparatus for, 378 Freezing mixtures, 351; point in a ther- mometer, 306 French weights and measures, 126 Fresnel’s experimentum crucis, rhomb, 685 Friction, 43, 47; heat of, 488; hy- draulic, 149; internal, of liquids, 48, 149 ; of gases, 454; development of elec- tricity by, 746 Friction wheels, 78 Frigorific rays, 429 Fringes, 660 Frog, rheoscopic, 1006 Frost, 1025 Frozen mercury, 377, 385, 391 Fulcrum, 40 Fulgurites, 1037 Fulminating pane, 791 Furnace, electrical, 946 Fuse, Schaw’s, 851 Fusing point, 342 Fusion, laws of, 342; vitreous, 342; latent heat of, 470; of ice, 459 659; ALILEO’S telescope, 609 Galleries, whispering, 240 Gallium, 590 Gallon, 126 Galvani’s experiment, 818 Index GAL Galvanometer, 842, 979; differential, 842 ; sine, 846; Thomson’s, 844 Galvanoscope, 842 Galvano-thermometer, 852 Gas battery, 873 ; engines, 486 Gaseous state, 4 Gases, absorption of, by liquids, 192; by solids, 196; by vapours, 443; application of Archimedes’ principle to, 198 ; cold produced by expansion of, 506; compressibility of, 157, 183; condensed, 196, 212; conductivity of, 416; diamagnetism of, 968; density of, 339; dynamical theory of, 297; expansion of, 156, 3353; endosmose of, 193; effusion, 194; transpiration of, 195 ; index of refraction of, 562 ; laws of mixture.of, 191 ; permanent, 384; liquefaction of, 384; physical properties of, 155; pressure exerted by, 159; radiation of, 4493; specific heat of, 469; velocity of sound in, 234; viscosity of, 454; weight of, 158 Gauge, air-pump, 204 ; rain, 1021 Gay-Lussac’s alcoholometer, 129 ; baro- meter, 170; determination of the ex- pansion of gases, 335; of vapour-. density, 392 ; stopcock, 389 Geissler’s tubes, 208, 590, 954 Geographical meridian, 705 Geometrical shadows, 515 Germanium, 590 Giffard’s injector, 210 Gilding metal, 878 Gimbals, 711 Glacial pole, 1047 Glaciers, 1029 Glashier’s balloon ascents, 199 ; factors, VU Ge compressed, 682 ; expansion of, 329; magnifying, 598; object, 602; opera, 609 ; unannealed, 682 Glasses, weather, 177 Globe lightning, 1035 Glow, electrical, 809 ; worm, 649 Glycerine barometer, 179 Gold-leaf electroscope, 774 Goldschmid’s aneroid, 190 Gong, 286 Goniometers, 546 Good conductors, 411 Governor of a steam engine, 478 Gradient, barometric, 1017 Gramme, 24, 126 Gramme’s magneto-electrical machine, 940 Graphic method, Duhamel’s, 248 ; Fos- ter’s, 853 HEF Graphite, 831 Graphophone, 295 Gratings, 661 Grave harmonic, 267 Gravesand’s ring, 300 Gravimetrical density, 188 Gravitation, 6, 83; terrestrial, 68, 83 ; accelerative effect of, 27 Gravity, battery, 833 Gravity, centre of, 69; Jolly’s determina- tion of constant of, 76 Gregorian telescope, 611 Gridiron pendulum, 324 Grimaldi’s experiment, 659 Grotthiiss’ hypothesis, 867 Grove’s battery, 830; gas, 873 Guard ring, 803 Guericke’s air-pump, 203 Guide-blades of a turbine, 152 Guitar, 283 Gulf Stream, 1044 Guthrie’s researches, 352 Gymnotus, 1009 AlL,F1027 Hair hygrometer, 406 Haldat’s apparatus, 102 Hall’s experiment, 903 Hallstrom’s experiments, 334 Haloes, 641, 660, 1019 Hammer, oscillating, 949 ; ofa piano, 283 Harceurt’s pentane lamp, 521 Hardening, 91 Hardness, 7; scale of, 94 Harmonie triad, 251; grave, 267 Harmonicon, chemical, 282 Harmonics, 257, 277 Harp, 283 ; Marloye’s, 285 Harris’s unit jar, S00 Heat, 296; animal, 497; absorption of, by vapour, &c., 443, 448; atomic, 468 ; conduction of, 4113; diffusion of, 445; developed by induction, 959 ; dynamical theory of, 436; hypothesis on, 296; latent, 345 ; mechanical equi- valent of, 509; polarisation of, 694 ; produced by absorption and imbibi- tion, 492; radiated, 410; radiant, ANS, AZ Ined SSyerenection of; (424 ; scattered, 4313; sources of, 487-497 ; specific, 457-469; transmission of, 410 ; terrestrial, 491 Heaters, 476 Heating, 498; by steam, 502; by hot air, 503; by hot water, 504 Hefner Alteneck lamp, 521 1130 HEI Height of barometer, 168; variations | in, 174 Heights of places, determination of, by barometer, 181 ; by boiling point, 373 Heliograph, 535 Heliostat, 546 Helium, 590 Helix, 45, 896, 904 Helmholtz’s analysis of sound, 259 ; re- searches, 262 Hemihedral crystal, 754 Hemispheres, Magdeburg, 163 Henley’s electrometer, 779 Henry, 1000 Herapath’s salt, 672 Hero’s fountain, 214 Heroult’s electrical furnace, 946 Herschelian rays, 437; telescope, 613 Her'z’s experiments, 1002 Hirn’s experiments, 509 Hoar-frost, 1025 Hofmann’s density of vapours, 393 Holtz’s electrical machine, 781 Homogeneous light, 584 ; medium, 514 Hope’s experiments, 334 Horizontal line, 68 ; plane, 68 Horn, 284 Horse-power, 61, 482 Hot-air, engines, 485; heating by, 503 Hotness, 301 Hot-water, heating by, 504 Houre2t Howard’s nomenclature of clouds, 1019 Hughes’s microphone, 961; induction balance, 962 Humour, aqueous, of the eye, 625 Huyghens’ barometer, 180; eyepiece, 604 Hyaloid membrane, 625 Hydraulic press, 109 ; engine, 154 ; fric- tion, 149 ; lift, 109 ; power, application of, 109; ram, 153; tourniquet, 151 Hydraulics, 96 Hydrodynamics, 142 Hydro-electric machine, 780; currents, 969 Hydrometers, 120; Nicholson’s, 121 ; Fahrenheit’s, 124 ; with variable im- mersion, 127 ; Beaumé’s, 128 ; of con- stant immersion, 127; specific gravi- ties, 120; uses of tables of, 126 Hydrostatic bellows, 102; paradox, 104 ; balance, 114, I2I Hydrostatics, 96 Hygrometers, 399, 406 ; chemical, 400; condensing;* gor 5’ ‘Daniell’s;» 402 ; wet-bulb, 4o ; Regnault’s, 403 Index INS Hygrometric state, 398 ; substances, 397 Hygrometry, 397 ; problem on, 408 Hygroscope, 406 Hypermetropia, 643 Hypothesis, 5 Hypsometer, 373 Hysterisis, 905 CE, 1028; method of fusion of, 459 Ice calorimeter, 460; Bunsen’s, 460; expansive force of, 350; ma- chine, 506 Iceland spar, 673 Ideal gas, 296; solution, 141 Idioelectrics, 746 - Image and object, magnitudes of, 573 Images, accidental, 640; condition of distinctness of, 599; formation of, in concave mirrors, 540; in convex mir- rors, 541; in plane mirrors, 525; of multiple, 528; magnitude of, 544; produced by small apertures, 516; virtual and real, 526; inversion of, 629 Imbibition, 196 ; heat produced by, 492 Impedance, 933 Impenetrability, 7, 8 Imperial British yard, 22 Imponderable matter, 6 Impulsive forces, 57 Incandescent lamps, 860 Inch, 526 Incident ray, 424, 548 Inclination, 712 ; compass, 713 Inclined plane, 43 ; motion on, 50 Index of refraction, 550; measurement of, in solids, 560; in liquids, 561; in gases, 562 Indicator, 908 ; diagram, 483 Indices, refractive, table of, 562 Indium, 590 Induced currents, 921-932 Induction, © balance,’ 96253 “by the? earth, 929.3. of ‘a’ current om itsely 930; electrical, 767; in telegraph cables, 912 ; Faraday’s theory of, 770 ; heat developed by, 959; by magnets, 925; magnetic, 700 Inductive capacity, specific, 769 Inductorium, 949 Inelastic bodies, 58 Inertia, 7, 19 ; applications of, 20 Influence, magnetic, 700; electrical, 777 Ingenhaus’s experiment, 411 Injector, Giffard’s, 210 Insects, sounds produced by, 245 Insolation, 650 Index INS Instruments, optical, 597; polarising, O70 en OOUuL, 2758 reed 27.0 stringed, 283 ; wind, 274 Insulating bodies, 748; stool, 785 Insulators, 747 Intensity of the current, 847; of the electric light, 859; of reflected light, 5215 OL asamusical @ note,’ 249.3" of radiant heat, 421; of sound, causes which influence, 229; of terrestrial magnetism, 715; of terrestrial gravity, 3 Interference of light, 659; of sound, 265 Intermittent fountain, 215; springs, 217 ; syphon, 217 - Intervals, musical, 250 Intrapolar region, 850 Inversion, of images, 629; thermo- electric, 970 Ions, 864 Iris, 625 Iron, passive state of, 874; electrical deposition of, 880 Iron ships, rhagnetism of, 736 Irradiation, 641 Irregular reflection, 530 Isobars, 1017 Isochimenal line, 1045 Isoclinic lines, 712 Isodynamic lines, 715 Isogeothermic lines, 1045 Isogonic lines, 706 Isotheral lines, 1045 Isothermal lines, 413, 1045 ; zone, 1045 ABLOCHKOFF candle, 860 Jar, Harris’s unit, 800 Jar, Leyden, 792-800 Jet, lateral, 145; height of, 146; form of, 150 Jew’s harp, 276 Jolly’s spring balance, 89; air thermo- meter, 338; determinaticn of gravity, 76 Jordan’s glycerine barometer, 179 Joule’s experiment on heat and work, 509 ; equivalent, 509 ; law, 852 ; elec- tromagnet, 905 Jupiter, 517 Jurin’s laws of capillarity, 133 ALEIDOPHONE, 639 Kaleidoscope, 528 Kamsin, I015 Kater’s pendulum, 80 Kathelectrotonus, 850 hist LEN Kathode, 864 Kation, 864 Keepers, 739 Kelvin, Lord (see Thomson) Kerr’s electro-optical experiments, 967 Keynote, 252 Kienmayer’s amalgam, 777 Kilogramme, 126 Kilogrammetre, 61, 482 Kilowatt, 945 Kinemetograph, 640 Kinetic energy, 63, 509 Kinnersley’s thermometer, 814 Knife-edge, 72 Knot, 1000 Konig’s apparatus, flames, 292 Kundt’s velocity of sound, 281 260; manometric ABYRINTH of the ear, 264 Lactometer, 130 Lag, magnetic, 905 Lalande and Chapercn’s element, 833 Lambert’s method, 582 Lamps, incandescent, 860; Dobereiner, 402; differential, 860 Land and water, distribution of, 1049 Lane’s electrometer, 799 Langley’s observations on the spectrum, 439 Lantern, magic, 616 Laplace’s barometric formula, 181 Laryngoscope, 575 Larynx, 263 Latent heat, 345; of fusion, 470; of vapours, 376, 471 Lateral jet, 145 Latitude, magnetic, 712: influence of, on the temperature of the air, 1047 ; parallel of, 83 Lavoisier and Laplace’s calorimeter, 459 ; method of determining linear expan- sion, 318 Law, 5 Laws of mixture of gases and liquids, 389 Lead, angle of, 943 Lead tree, 876 Leads of a voltaic battery, 851 Lechatellier, the:mopile, 979 Leclanche’s elements, 834 Ledger lines, 255 Leidenfrost’s phenomenon, 391 Lemniscate, 681 | Lenard’s experiments, 958 p Length, unit of, 22 ; of undulation, 228 Lens, axis of, 563 E32 LEN Lenses, 56325 72'; achromatic, 500% aplanatic, 570; centres of curvature, 563; combination of, 572; echelon, 619; foci in double convex, 564; in double concave, 565; formation of images in double convex, 568; in double concave, 569; formule relat- ing to, 5713; lighthouse, 619 ; optical centre, secondary axis of, 567 Lenz’s law, 923 Leslie's cube, 430; thermometer, 312 Level, water, 1103 spirit, 111 Level surface, 68 Levelling staff, 110 Lever, 40 Leyden discharge, inductive action of, 924 Leyden jars, 792-799; charged by Ruhmkorff’s coil, 951; potential of, 804 ; work by, 806 Lichtenberg’s figures, 794 Liebig’s condenser, 381 Lift, hydraulic, 10g Ligament, suspensory, 625 Light, 511; diffraction of, 660; homo- peneous, 5645; imvensity, of, . 5203 interference of, 659; laws of reflec- tion of, 523 ; oxyhydrogen, 618 ; polar- isation of, 666; relative intensities of, 522; sources of, 648 ; theory of polar- ised light, 675; undulatory theory of, 511, 651; velocity of, 517-520 Lighthouse lenses, 557, 619 Lighting, electric, 855 Lightning, 1035; effects of, 1037; 3 con- ductor, 1039 Limit of elasticity, 17; magnetic, 741; of perceptible sounds, 247 Linde’s ice-machine, 506 ; apparatus, 388 Line, aclinic, 712; of collimation, 607 ; isoclinic, 712 ; agonic, 706; isogonic, 700 ; isodynamic, ibe tol sight, 607 Linear expansion, coefficients of, 317 Lines of magnetic force, 722; of elec- trical force, 761 Lippmann’s capillary electrometer, 862 Liquefaction of gases, 384; of vapours, 379 Liquids, 97; buoyancy of, 101; com- pressibility of, 98; conductivity of, 414; calculation of density of, 108; diffusion of, 142; diamagnetism of, 968 ; expansion of, 330; equilibrium of, 105; manner in which they are heated, 4153; pressure on sides of vessel, 103; refraction of, 561; rota- tory power of, 691 ; spheroidal form experiment, Bil 3 Index. MAG of, 85; spheroidal state off 3913 specific heat of, 465; volatile and fixed, 353; tensions of vapours of, 363 ; of mixed liquids, 364 Lissajous’s experiments, 288-290 Litre, 24, 126 Local action, 837 ; attraction, 736; bat- tery, 910 Locatelli’s lamp, 435 Locomotives, 480 Lodestar, 695 Lodestone, 695 Long sight, 643 “Loop circuit, 960 Loops and nodes, 273 Loss of electricity, 766 ; of weight in air, correction for, 409 Loudness of a musical tone, 249 Lullin’s experiment, 814 Luminiferous ether, 511 Luminous bodies, 512; effects of the electric discharge, 808, 855 ; of Ruhm- korff’s coil, 949 ; heat, 442 ; meteors, IOIIL; paint, 650; pane, 789; pencil, 513; radiation, 440; ray, 513; tube, SII; square, 811 ACHINE, Atwood’s, 78; trical, 775-782 Mackerel-sky, 1019 Macleod’s gauge, 208 Magazine magnetic, 738 Magdeburg hemispheres, 163 Magic lantern, 616 Magnetic attraction and repulsion, 717 ; battery, 738; couple, 704; curves, 720; declination, . 7053 dip. 71 am effects of the electrical discharge, 813 ; equator, 712; field, 721 ; fluids, 699 ; induction, 700 ; influence, 700 ; limit, 740.5 \meridian, 705 7a neediew.7oam observatories, 716; poles, 7123; satu- ration, 737; storms, 706, 708 Magnetisation, 731; by the action of the earth, 735; by currents, 904; single touch, 732 Magnetism, 6, 695; determination of, in absolute measure, 729 ; earth’s, 703 ; of iron ships, 736; Ampere’s theory elec- of, QOI ; remanent, 905; theory of, 699; terrestrial, 703; distribution of free, 742 Magneto and dynamo-electrical machines, 934-945 ve Magneto-electrical apparatus, 934 Magnetomotive force, 905 Index MAG Magnets, artificial and natural, 695 ; broken, 698 ; action of earth on, 703 ; floating, 743 ; heat developed by, 959 ; north and south poles of, 696 ; normal, 741; portative force of, 740 ; saturation of, 737 ; influence of heat, 741 ; induc- tion by, 925 ; inductive action on moy- ing bodies, 926; action on currents, 890; on solenoids, 899; rotation of induced currents by, 957; optical effects of, 965; total action of two, 727 Magnification, linear and _— superficial measure of, 601, 606 ; of a telescope, 607 Magnifying power, 606 Magnitude, 9; apparent, of an object, 600 ; of images in mirrors, 544 Major chord, 250; triads, 251 Malleability, 7, 93 Mance’s heliograph, 535 ; method, 988 Manganese, magnetic limit of, 741 Manhole, 476 Manometer, 98, 186; with compressed air, 187; Regnault’s barometric, 189 Manometric flames, 292 Mares’ tails, 1019 Marie-Davy battery, 833 Marine barometer, 168; engines, 476; galvanometer, 844 Mariner’s card, 1013 ; compass, 711 Mariotte and Boyle’s law, 183 Mariotte’s tube, 183 Marloye’s harp, 285 Mascart’s insulator, 766 Maskelyne’s experiment, 68 Mason’s hygrometer, 405 Mass, measure of, 23 ; unit of, 23 Matter, 2 Matteucci’s experiment, 924 Matthiessen’s thermometer, 312 ; electri- cal conductivity, 989 Maxim’s lamp, 860 Maximum and minimum thermometers, 314 Maximum current, conditions of, 848 Maxwell’s electromagnetic theory of light, 770, 1002; colour discs, 582 Mayer’s floating magnets, 743 Mean temperature, 1042 Measure of force, 29 ; of work, 60 Measure of magnification, 601, 606 ; of mass, 225. ol/space,) 22 5 ofitime; 21; of velocity, 25 Measurement of small angles by reflec- tion, 534 Mechanical equivalent of heat, 509; ELB4 MIS effects of electrical discharge, 814; battery, 861 Melloni’s researches, 435; thermomul- tiplier, 419, 976 Melting point, influence of pressure on, 343 Membranes, semipermeable, 141; sensi- tive, 232; vibrations of, 287 Memoria technica, Ampere’s, 841 Meniscus, 132; convex, 1323 in baro- meter, 172; Sagitta of, 172 Mensbrugghe’s experiment, 135 Mercury, frozen, 377, 385,391; pendulum, 324; coefficient of apparent expan- sion, 327 ; expansion of, 326; pump, 2113 purification of, 171 Meridian, 21; geographical and mag- netic, 705 Metacentre, 116 Metal, lRose’s 344 Metals, conductivity of, 989 Meteoric stones, 490 Meteorograph, 1012 Meteorology, 101i Meteors, aerial, IOII Metre, 22, 126 Metronome, 82 Mica, 678 Microfarad, 1000 Micrometer, 606 ; screw, II Microphone, 961 Microscope, 12; achromatism of, 604 ; Duboscq’s, 618 ; compound, 602 ; field of, 604; focussing, 599; magnifying - powers of, 601 ; photo-electric, 618 ; simple, 598; solar, 617 Microspectroscope, 592 Microvolt, 1000 Migration of the ions, 869 Mill, Barker’s, 151 Milliampere, 1000 Millimetre, 126 Mineral waters, 1048 Mines, firing, by electricity, 851 Minimum thermometer, 314 ; deviation, and Wood’s fusible, 559 Minor chord, 250 Minotto’s battery, 833 Minute, 21 Mirage, 553 Mirrors, 524; applications of, 546; burn- ing, 427 ;concave, 426, 537, 540 ; con- jugate, 427; convex, 538; glass, 527; parabolic, 547; rotating, 532, 816; spherical, 536 Mists, 1018 1134 MIX Mixture of gases, 191; of gases and liquids, 192 ; laws of, 389 Mixtures, freezing, 351 ; method of, 461 Mobile equilibrium, 422 Mobility, 7, 18 Modulus of elasticity, 88 Moisture of the atmosphere, 407 Molecular forces, 3; attraction, 84 ; sieve, 1413; state of bodies, 43 state, relation of absorption to, 451; velocity, 295 Molecules, 3 Moments of forces, 36 Momentum, 28 “Monochord, 270 Monochromatic light, 584 Monosyllabic echo, 240 Monsoon, 1015 Montgolfier’s balloon, 199; ram, 153 Moon, 522 Morin’s apparatus, 79 Morren’s mercury pump, 211 Morse’s telegraph, 910 Moser’s images, 196 Motion, 18; on an inclined plane, 50; curvilinear.) 25 ; inva cinele,,/5 3,545 rectilinear, 25; resistance to, in a fluid, 48; uniformly accelerated rec- tilinear, 49; quantity of, 28; of a pendulum, 55; of projectile, 51 Mouth instrument, 275 Multiple battery, 848 Multiple echoes, 240; images formed by mirrors, 527 Multiplication, method of, 929 Multiplier, 842 Muscular currents, 1004-1008 Music, 223; physical theory of, 249-268 Musical boxes, 285; comma, 251 ; intervals, 250; scale, 251; tempera- ment, 253; note, properties of, 249; intensity, 249; notation, 255 ; pitchand timbre, 249; sound, 224; range, 255 Myopia, 643 ASCENT state, 86 Natterer’s apparatus, 385 Natural magnets, 695 Needle, declination of, 705; dipping, Vis s\"astatic, Vids magnelic,.2705); thermoelectric, 981 Negative plate, 822 Negatives on glass, 621. Neumann’s law, 468 Nerve-currents, 1008 Neutral line, 767; equilibrium, point, 767 ; temperature, 970 71; Index OSC | Newton’s disc, 579 ; law of cooling, 423 ; rings, 664, 665; theory of light, 580 Newtonian telescope, 612 ' Niaudet’s element, $33 Nicholson’s hydrometer, 121 Nickel, electrical deposition of, 880;. magnetic limit of, 741 Nicol’s prism, 674 Nimbus, 1019 _ . Nobert’s lines, 606 Nobili’s battery, 973; rings, 875; ther- momultipliers, 976; thermo-electric pile, 973. Nocturnal radiation, 507 Nodal points, 273, 278, 659 Nodes and loops, 273 ; of an organ pipe, 278 ; explanation of, 280 Noises, 223 Nonconductors, 747 Normal magnets, 741 Norremberg’s apparatus, 671 Northern hight, 1041 Norwegian stove, 417 Notation, musical, 255 Notes in music, 249 ; musical, of women and boys, 263 ; wave-length of, 256 Nut of a screw, 45 BJECT-GLASS, 602 Objective, 602 Oboe, 276 Obscure radiation, 440; transmutation of, 441 Observatories, magnetic, 716 Occlusion of gases, 197 Occultation, 517 Octave, 250 Oersted’s experiment, 841 Ohm, 1000 Ohm’s law, 847 Opaque bodies, 512 Opera-glasses, 609 Ophthalmoscope, 647 Optic axis, 630; axis of biaxial crystals, 658; angle, 630; nerve, 625 Optical centre, 567; effects of magnets, 965; instruments, 597 Optics, 511 Optometer, 632 Orbit of the eye, 625 Organ, 284 ; pipes, 278; nodes and loops of, 278 Orrery, electrical, 787 Orthochromatic plates, 622 Oscillating discharges, 805 Oscillations, 553; axis of, 80; method of, 719 rays, 441 Index OSM Osmotic pressure, 141 Otto von Guericke’s air-pump, 203 Otto’s gas engine, 486 Outcrop, 112 Overshot wheels, 152 Oxyhydrogen light, 618 Ozone, 815, 863, 1037 ACINOTTITS ring, 940 Paddles of steam vessels, 152 Paint, luminous, 650 Pallet, 82 Pandzean pipe, 284 Pane, fulminating, 791 Papin’s digester, 375 Parabola, 51, 145 Parabolic mirrors, 547 5 Parachute, 201 Paradox, hydrostatic, 104 Parallel of latitude, 83; forces, 37; centre of, 37 Parallel rays, 513 Parallelogram of forces, 33 Paramagnetic bodies, 968 Partial current, 996 Pascal’s law of equality of pressures, 99 ; experiments, 165 Passage tint, 692 Passive state of iron, 874 Path, mean, of molecules, 298 Pedal, 283 Peltier’s cross, 980 ; effect, 980 Pendulum, 55; application to clocks, 82 ; ballistic, 82 ; compensation, 324 ; electrical, 746; gridiron, 324; mer- curial, 324; length of compound, 80; reversible, 80; verification of laws of, 81 Penetration of a telescope, 608 Pentane lamp, 521 Penumbra, 515 Percussion, heat due to, 489 Permanent gases, 384 ; magnetism, 905 Permeability, magnetic, 725, 905 Persistence of impression on the retina, 639 Perspective, aerial, 631 Perturbations, magnetic, 708 Phantasmagoria, 618 Phenakistoscope, 639 Phenomenon, 5 Phial of four elements, 107 Phonautograph, 291 Phonograph, Edison’s, 295 Phosphorescence, 649 Phosphorogenic rays, 585 curve:. 70/01 1135 POL Phosphoroscope, 650 Photo-electric microscope, 618 Photo-electricity, 754 Photogenic apparatus, 618 Photography, 620-624 Photometers, 521 Photophone, 966 Physical phenomena, 5; agents, 6; properties of gases, 155; shadows, 515 Physics, object of, 1 Physiological effects of the electric dis- charge, 807, of the current, 849 ; of Ruhmkorff’s coil, 951 Piano, 283 Piezo-electricity, 754 Piezometer, 98 Pigment colours, 583 Pile, voltaic, 825-838 Pincette, tourmaline, 680 Pipes, organ, 278 Pisa, tower of, 70 Pistol, electric, 815 Piston of air-pump, 203; rod, 477 Pitchiiconcerie 2s 4 wolva notes "240 5 a screw, 45 Planejs 43 smielectrical mirrors, 524 Planté’s secondary battery, $72 Plate electrical machine, 776 Plates, colours of thin, 664 ; vibrations of, 286 ; Chladni’s, 286 ; photographic dry, 622 Plumb line, 68 Pluviometer, 1021 Pneumatic syringe, 157, 489 Point, boiling, 367 Points, action of, 765; nodal, 273 Poisseuille’s apparatus, 149 Poisson’s coefficient, 89 Polar aurora, 1041 Polarisation, 871; angle of, 668; cur- reniyo7 13) of -electrodesa" S27" by double refraction, 666; by reflection, 667 ; by single refraction, 669; ellip- tical and circular, 683 ; of heat, 694 ; galvanic, 827, 871; light, 666; of the electric medium, 770 ; rotatory, 687 Polarised light, theory of, 675 ; colours produced by the interference of, 676- 682 Polariser, 670 Polarising instruments, 670 Polarity, boreal, austral, 703 Pole, glacial, 1047 Poles, 824; electric,” 754 3-of' the earth, 703 ; magnetic, 712; of a magnet, 696 ; inclined, 7073 1136 POL mutual action of, 697; austral and boreal, 703 Polygon of forces, 34 Polyorama, 618 Polyprism, 556 Ponderable matter, 6 Pores; 13 Porosity, 7, 13; application of, 15 Portative force, 740 Positive plate, 824 Postal battery, g10 Potential energy, 63; of electricity, 760 ; of a Leyden jar, 804; of a sphere, -764 Pound, 126; avoirdupois, 23, 29; foot, 61 Poundal, 27 Power ofa lever, 40; of a microscope, 606 Presbyopia, 643 Press, hydraulic, 109 Pressure, centre of, 103; on a body ina liquid, 113; atmospheric, 161 ; amount of, on human body, 166; experiment illustrating, 213; influence on melting point, 343; heat produced by, 489 ; electricity produced by, 753 Pressures, equality of, 99 ; vertical down- ward, 100; vertical upward, IOI ; in- dependent of form of vessel, 102 ; on the sides of vessels, 103 ; rate of trans- mission of, 100 Prévost’s theory of exchanges, 422 Primary coil, 921 Principle of Archimedes, 114 Prismatic compass, 711 Prisms, 555; double refracting, 673; Nicol’s, 674; with variable angle, 556 Problems on expansion of gases, 336; on mixtures of gasesand vapours, 389 ; on hygrometry, 408 Projectile, motion of, 51 Prony’s brake, 483 Proof plane, 757 Propagation of light, 514 Protoplasm, 849 Protuberances, 591 Ps¥chrometer, 405, 1012 Pulley, 41 Pump, air, 203 ; condensing, 212 ; filter, 209 Pumping engine, 477 Pumps, different kinds of, 218; suction, 219 ; suction and force, 220 Punctum czecum, 625 Pupil of the eye, 625 Pyknometer, 122 Pyroelectricity, 754 Pyroheliometer, 490 Pyrometers, 315 ; electric, 979 Index REF UADRANT electrometer, 779, 802 Quadrantal deviation, 736 — Quartz threads, 90 ADIANT heat, 418 ; detection and measurement of, 419; causes which modify the intensity of, 421 ; Melloni’s researches on, 435; relation of gases and vapours to, 446; relation to sound, 455 Radiating power, 432; identity of ab- sorbing and radiating, 433; causes which modify, &c., 434; of gases, 449 Radiation, cold produced by, 507 ; from powders, 451; of gases, 449; luminous, and obscure, 440 ; laws of, 420; solar, 490. Radiative power of vapours, 1023 Radiometer, 453 Radiomicrometer, 976 Railway, electrical, 948; friction on centrifugal, 47, 53, 480 Rain, 1021 ; clouds, 1021; bow, 1040; fall, 1012, 1021, 1022); gauge, 1021 ; drop, velocity of, 48 Ram, hydraulic, 153; powder, 489 Ramsden’s electrical machine, 776 Raoult’s researches, 347 Rarefaction in air-pump, 203; by Spren- gel’s pump, 208 Ray, incident, 548; luminous. ordinary and extraordinary, 666 Rays, actinic, or Ritteric, 441; diver- gent and convergent, 513; frigorific, 429; of heat, 418, 436 ; Herschelian, 4373; invisible, 436; obscure, 440 ; path of, in eye, 628; phosphorogenic, 585 ; polarised, 666; transmission of thermal, 442 Reaction and action, 39 Real volume, 14 ; foci, 564 ; focus, 537 ; image, 526, 540 Réaumur scale, 307 Receiver of air-pump, 203 Recomposition of white light, 579 Reed instruments, 276 Reeds, free and beating, 276 Refining of copper, electrical, 877 Reflected light, intensity of, 531 Reflecting power, 430; goniometer, 546 ; sextant, 533; stereoscope, 637 ; telescope, 610 Reflection, apparent, of cold, 429; of heat, 425 ; from concave mirrors, 426 ; irregular, 530; laws of, 424; in a 5133 lndex REF vacuum, 428 ; of light, 523 ; of sound, 239 Refracting stereoscope, 638; telescope, 610 Refraction, 548-562 ; double, 653; po- larisation by, 666, 669; explanation of single, 652 ; of sound, 241 Refractive index, 550; determination of, 5743 of gases, 562; of liquids, 561; of solids, 560; indices of media of eye, 626 Refractory substances, 342 Refrangibility of light, alteration of, 594 Regelation, 1028 Regnault’s experiments, 232; determi- nation of density of gases, 340 ; mano- meter, 189; methods of determining the expansion of gases, 337 ; of specific heat, 463; of tension of aqueous va- pour, 360; hygrometer, 403 Regulator of the electric light, 857 Regulus, 344 Reis’s telephone, 907 Relay, 910 Reluctance, magnetic, 905 Remanent magnetism, 905 Replenisher, $02 Repulsion, magnetic, laws of, 756 Reservoir, common, 748 Residual charge, 795 ; magnetism, 905 Residue, electric, 795 Resinous electricity, 750 Resistance, limiting angle of, 43; of a conductor, 847, 983; boxes, 984; of an element, 988 Resonance, 240, 258; box, 254; globe, 259 : Rest, 18 Resultant of forces, 32-34 Retardation, magnetic, 905, 933 ; Retina, 625; persistence of impression on, 625 ; Return shock, 1038 Reversible pendulum, 80, _- Reversibility of Holtz’s machine, 781 Reversion, method of, 710; spectroscope, 8 ee electric lamp, $60 Rheometer, 842 ' Rheoscopic frog, 1006 Rheostat, 982 Rhomb, Fresnel’s, 685 Rhumbs, 711 Richness, hygrometric, 398 Riess’s thermometer, 812 Right ascension, 612 electrical TPs 1137 SCH Rime, 1025 Ring inductor, 940 Rings, coloured, 680; Gravesand’s, 300; in biaxial crystals, 681 ; Newton’s, 664, - 665 ; Nobili’s, 875 Ritchie’s experiment, 433 Ritteric rays, 441 Robinson’s anemometer, 1012 Rock salt, heat transmitted through, 44 Rods, vibrations of, 285 Roget’s vibrating spiral, 882 Rolling mill,. 93 Rontgen rays, 958 Rose’s fusible metal, 344 Rotary engine, 481 Rotating mirror, 532, 816 Rotation, electrodynamic and _ electro- magnetic, of liquids, 892 ; winds, 1016 Rotation of the earth, 83; of magnets by currents, 889 ; of currents by mag- nets, 891; of induced currents by magnets, 957 Rotatory power of liquids, 691 ; polarisa- tion, 687; coloration produced by, 689 Rousseau’s densimeter, 131 Roy and Ramsden’s measurement of linear expansion, 319 Rubbers of an electrical machine, 776 Rubidium, 590 Ruhlmann’s barometric and thermome- tric observations, 182 Ruhmkorff’s coil, 949 ; effects produced by, 951 Rumford’s photometer, 521 Rutherford’s thermometers, 314 ACCHARIMETER, 692 Saccharometer, 128 Safety-catch, 851; tube, 383; valve, 100, 375 Sagitta of meniscus, 172 Salimeters, 130 Salts, decomposition of, 865 Samarium, 590 Saturation, degree of, 397; magnetic, 7373 of colours, 583 Saussure’s hygrometer, 406 Savart’s toothed wheel, 244 Scale of hardness, 94 Scales in music, 251; chromatic, 253 ; of a thermometer, 307 Scandium, 590 Scattered heat, 431; light, .530 Schehallien experiment, 68 Scheiner’s experiment, 632 Schwendler’s platinum light standard, 860 4D 11338 Index Sel SPE Scintillation of stars, 553 Size, estimation of, 631 Sciopticon, 616 Sky, 1024 Sclerotica, 625 Scott’s phonautograph, 291 Scraping sound, 285 Scratching sound, 285 Screen, magnetic, 725 pcrew, 11545 Search light, 546 Secchi’s meteorograph, 1012 pecond Of tiinmew2T 25 ! Secondary axis of a lens, 567 ; batteries, 87.2 3 currents; 627¢0col soe lm Seconds pendulum, 80 Secular magnetic variations, 706 Segments, ventral.and nodal, 273, 278 Segner’s water-wheel, 151 Selenite, 678 Selenium, 966, 992 Self-induction, 930 Semicircular deviation, 736 Semi-conductors, 747 Semipermeable membranes, 141 Semiprism, 589 Semitones, 252 Senarmont’s experiment, 413 Sensitive membrane, 232 Serein; 1023 Series, thermo-electric, 970 ; -wound ma- chine, 944 Serum, 12 Sextant, 533 Shadows, 515 Sharpness of sight, 633 Shock, electric, 805 ; return, 1038 Shooting stars, 490 Short circuit, 831 ; sight, 643 Shunt, 997 ; -wound machine, 944 Siemens’ armature, 937; dynamo-elec- trical machine, 941; unit, 983, 1000; electrical thermometer, 995 Sieve, molecular, 141 Sight, line of, 607 Silurus, 1009 Silent discharge, 815 ‘Silver voltameter, 868 Simoom, I015 Sine compass, 846 Sines, curve of, 56 Singing of liquids, 367 Sinuous currents, 884 Sinusoidal currents, 933 Siphon, 216 ; barometer, 170; recorder, 913 Sirene, 245 Sirocco, 1015 Sixe’s thermometer, 314 Sleet, 1026 Slide valve, 479 Sling, 53 Smee’s battery, 832 Snow, 1026 ; line, 1026 Soap-bubble, colours of, 664 Solar constant, 490 ; microscope, 617 ; light, thermal analysis of, 437 ; radia- tion, 4903; spectrum, 576; properties of the, 585 ; dark lines of, 586; time, 21; day, 21 Soldering, 87; autogenous, 860 Soleil’s saccharimeter, 692 Solenoidal filament, 724 Solenoids, 896 Solidification, 347; change of volume on, 350; retardation of, 349 Solidity, 4, 7 Solids, conductivity of, 411; index of refraction in, 550; diamagnetism of, 968 ; linear and cubical expansion of, 317.3 surface tension of, 92 Solids, formule of expansion, 322 Solution, 346; ideal, 141 Sondhauss’s experiments, 241 Sonometer, 270, 962 Sonorous body, 225 Sound, 224; cause of, 225; not propa- gated in vacuo, 226; propagated in all elastic bodies, 227 ; propagation of, in air, 228; causes which influence inten- sity of, 229 ; apparatus to strengthen, 230; interference of, 265 ; velocity of, in air, 2333 in gases) -23acprineliqume 237; (solids, 238 3 ‘reflection off 230. refraction of, 241 ; relation of radiant heat to, 455; transmission “of, 12371. waves, 232 Sound, Helmholtz’s analysis of, 259 Sound, Konig’s apparatus, 260; Kundt’s, Sole Sounder, 917 Sounds, intensity of, 293; limit of percep- tible, 247; synthesis of, 261; percep- tions of, 264; produced by currents, 906 Space, measure of, 22 Spar, Iceland, 673 Spark and brush discharge, 8cqg ; electri- cal, 785; duration and velocity of, 816 Speaking trumpet, 242; tubes, 231 Specific gravity, 24, 120, 125; bottle. 122; hydrometer, 121.3 of solids, 121 ¢aan gases, 339; of liquids, 124; tables of, | 125, 126 Specific heat, 457-469 lndex SPE Specific inductive capacity, 769 Spectacles, 644 Spectra, 662 Spectral analysis, 587; colours and pig- ment, 583 Spectroscope, 588 ; direct vision, 589; experiments with, 590 ; uses of the, 592 | Spectrum, 437; colours of, 578; pure, 577 ; solar, 576 Spectrum, calorific, 585 ; chemical, 585 Spectrum, dark lines of, 586 Spectrum, diffraction, 662 Spectrum, luminous properties of, 585 Spectrum of aurora borealis, 1041 Specular reflection, 530 Spherical, aberration, 545 ; mirrors, 536 ; | focus of, 537; formulze for, 542 Spheroidal form of liquids, 85; state, 391 Spherometer, 11 Spiral, 904; Roget’s vibrating, 882 Spirit-level, 111 Sprains, 17 Spray producer, 210 Sprengel’s air-pump, 208 Spring balance, 89 Springs, 1048; intermittent, 217 Stable equilibrium, 71 Standard cell, Daniell’s, 829 ; L. Clark’s, 833 Stars, declination of, 612 ; spectral analysis of, 591 Staubbach, 77 Stave, 255 | Steam, heating by, 502 Steam-engines, 475; boiler, 476; horn, 245; pipe, 210; various kinds of, 481; | work of, 483 Steeling, 880 Stereometer, 188 Stereoscopes, 636-638 Stethoscope, 243 Stills, 380 Stool, insulating, 785 Stopcock, doubly exhausting, 205 ; Gay- Lussac’s, 389 Storage batteries, 872 Storms, magnetic, 708, 716 Stoves, 501 ; Norwegian, 417 Stratification of electric light, 953 Stratus, 1019 Strength, electrical, 790 Stringed instruments, 283 Strings, 269; transverse vibration of, 269 Subdominant chords, 251 Substance, 2 Suction pump, 219; and force pump, | 220; load which piston supports, 221 | BL359 TEN Sun, 522; thermal analysis of light of, 437, 591 Sun-spots, 716 Superfusion, 349 Surface level, 68 ; tension, 92, 135, 139 Susceptibility, magnetic, 726 Suspension, axis of, 71 ; Cardan’s, 169 Suspensory ligament, 625 Swan lamps, 860 Swimming, 119; 118 Swing of a needle, 843 Switch, 962 | Symmer’s theory of electricity, 750 Synthesis of sounds, 261 Syphon, 216; barometer, 170; inter- mittent, 217 ; recorder, 913 Syringe, pneumatic, 157, 489 -bladder of fishes, ieee eee metal, 95 Tangent compass, or galvanometer, 845, 870 Tasimeter, 963 Tears of wine, 136 Telegraph, cables, Cowper’s writing, QI13 induction in, 912 ; electric, 9g08~ Qt ; electrochemical, 916 Telegraphy, duplex, 914; without. wires, 1003 Telephone, 907, 960; Edison’s, 964 ; Reis’s, 907 ; toy, 239 Telescopes, 607; astronomical, 607 ; Galileo’s, 609; Gregorian, 611 ; Her- schelian, 613; Newtonian, 612; re- Hlecting, Rosse’s, 613 Telluric lines, 586 Telpherage, 948 Temperament, musical, 253 Temperature, 301, correction for, in barometer, 1733 critical, 374; deter- mined by specific heat, 466 Temperature, absolute zero of, 508 ; in- fluence of, on specific gravity, 125 ; mean, 1042; how modified, 1043; distribution of, 1047; of lakes, seas, and springs, 1048 Temperatures, different remarkable, 316 ; influence on expansion, 321 Tempering, 91, 95 i Tenacity, 7, 92 | | Tension, 922; electric, 759; maximum of, electrical machine, 778; maxi- mum of, vapours, 357 ; of aqueous vapour at various temperatures, 360 ; of mixed liquids in two communicating vessels, 365 ; free surface, 135 I140 TER Terrestrial currents, 902, 915; heat, 491; magnetic couple, 704 ; magnetism, 703- 715; telescope, 608 Terrestrial gravitation, 68, 83 Terrestrial magnetic couple, 704 Test objects, 606 Tetanus, 849 Thallium, 590 Thaumatrope, 639 Theodolite, 10 Theory, 5; of induction, 770 Thermal analysis of sunlight, 437; unit, 456, 494; springs, 1048 Thermal effects of the current, 852 Thermal rays, transmission of, 442 ; unit, 456 Thermobarometer, 373 Thermochrose, 444 Thermo-dynamic efficiency, 484 Thermo-electric battery, 419, 972; couples, 972 ; currents, 971, 973, 977; pile, 419, 438, 973; series, 970 Thermo-electricity, 969 Thermo-element, 970 Thermometer, electric, 995 Thermometers, 302; Becquerel’s elec- trical, 979 ; correction of readings, 332 ; differential, 312; division of tubes of, 303; filling, 304; graduation of, 305 ; determination of fixed points of, 306 ; scale of, 307; displacement of zero, 308 ; limits to use of, 309; alcohol, 310 ; conditions of delicacy of, 311 ;. Kinnersley’s,- "6143 \Tesheé’s, "3712 ; Matthiessen’s, 312; Breguet’s, 313; maximum and minimum, 314; Sie- mens’ electrical, 995; weight, 328 ; air, 338 Thermometry, 301-304 Thermo-multiplier, Melloni’s, 419, 976 Thermoscope, 312 Thomson effect, 981 Thomson’s electrometers, 803; galvano- meter, 844; apparatus for atmospheric electricity, 1031 Thread of a screw, 45 Threads, fine, 90 Throw of a needle, 843 Thunder, 1036 Timbre, 249 Time, measure of, 21 ; mean solar, 21 Tint, 583 ; transition, 692 Tonation, thermal, 854 Tones, combinational, "367 Tonic, 251 Toothed wheel, 244 267; differential, Index URI Tore, 905 Torpedo, 1009 Torricelli’s experiment, 144 5 vacuum, [71 Torsion, angle of, 90; 756; force of, go Total reflection, 552 Tourmaline, 672, 7543; pincette, 680 Tourniquet, hydraulic, 151 Tower of Pisa, 70 Toy telephone, 238 Trachea, 263 Traction, elasticity of, 89 Trajectory, 25 ‘Transformation of energy, 65 Transformers, 952 Transit, 21 Transition tint, 692 Translucent bodies, 512 Transmission of heat, 410; of light, 511, 554; by the current, 866 Transmission of sound, 231 Transmitter of photophone, 966 ‘Vransparency, 7, 512 Transparent media, 554. Transpiration of gases, 195 Triad, harmonic, 251 Triangle, 285 Triangle of forces, 35 Trumpet, speaking, ear, 242 Tubes, Geissler’s, 208, 954; luminous, S11; safety, 383 ; speaking, 231 Tuning-fork, 254, 285, 294 Turbines, 152 Twaddle’s hydrometer, 128 Twilight, 530 Twinkling of stars, 553 Tympanum, 264 Tyndall’s researches, 1029 164; theorem, balance, 90, 717, 438, 455, 1024, LTRAGASEOUS state, 956 Unannealed glass, colours pro- duced by, 682 Undershot wheels, 152 Undulation, length of, 228, 651 Undulatory theory, 511, 651 Uniaxial crystals, 654 ; double refrac- tion in, 658 ; positive and negative, 657 Unit jar, Harris's, 800 ; Siemens’, 9383 ; thermal, 456 Unit of length, area and volume, 22; heat, 456 ; of work, 61 Units, fundamental, 62 Unstable equilibrium, 71 Urinometer, 130 Index VAC ACUUM, application of air-pump to formation of, 203; extent of, produced by air-pump, 204 ; Crookes’s, 454; fall of bodies in a, 77; forma- tion of vapour in, 356 ; heat radiated in, 420 ; reflection ina, 428 ; Torricellian, 171 Valency, of an element, 868 ; change of, 467 Valve, safety, 109, 375; face, 479 Van der Waals’ formula, 185 Vane, electrical, 787 Van ’t Hoff’s theory, 141, 867 Vaporisation, 354; latent heat of, 376, 472 Vapour, aqueous, tension of, at various temperatures, 359; formation of, in closed tube, 374; latent heat of, 376 Vapours, 353; absorption of heat by. 443; absorptive powers of, 448 ; density of, Gay-Lussac’s method, 392 ; Hofmann’s, 393; densities of, 395; determination of latent heat of, 376, 471; Dumas’s method, 394; elastic force of, 355; formation of, in vacuo, 356; saturated, 3573 unsaturated, 358; tension of different liquids, 363 ; of mixed liquids, 364 ; in communicat- ing vessels, 365 Variations, magnetic, annual, 707; ac- cidental, 708 ; barometric, 174 ; causes of, 175; diurnal, 707 ; relation of, to weather, 176 Velocity, 25, 62; direction of, 56; of efflux, 144; of electricity, 817; of light, 517; graphic representation of changes of, 56; Kundt’s method, 280; molecular, 298; of sound in air, 233; gases, 234, 235; formula for calcula- ting, 235; of winds, 1012 Velocities, composition of, 52; examples of, 25 Vena contracta, 147 Ventral and nodal segment, 273, 278 Verdet’s. constant, 965 Vernier, 10 Vertical line, 68 Vestibule of the ear, 264 Vibrating spiral, Roget’s, 882 Vibration, 225; arc of, 55; produced by currents, 906; of tuning-forks, 294 Vibrations, 269; formule, 279; of membranes, 287; measurement of number of, 244; number of, produc- ing each note, 254 ; of musical pipe, Hoy Bai WEL 279; of rods, 285; of plates, 286; of strings, 269 Vierordt’s quantitative spectrum analysis, 592 View, field of, 605 Vinometer, 382 Violin, 283 Virtual and real images, 526, 540 ; focus, 5373 velocity, 46 Viscosity, 97, 149; of gases, 454 Vision, distance of distinct, 633; bino- cular, 635 Visual angle, 630 Vis viva, 84, 457, 509 Vital fluid, 818 Vitreous body, 625; electricity, 750; fusion, 342 ; humour, 625 Vocal chords, 263 Volatile liquids, 353 Volt, 835, 1000 Voltas condensing electroscope, 801 ; electrophorus, 775; fundamental ex- periment, 819 Voltaic arc, 855; couple, 822; in- duction, 921 ; pile and battery, 825 Voltameter, silver, 868; Faraday’s, 868 - Voltmeter, 998 Volume, 22; unit of, 22, 24; determi- nation of, 115; change of, on solidi- fication, 350; of a liquid and that of its vapour, relation between, 396 Volumometer, 188 Voss’s electrical machine, 781 ATER barometer, 179; bellows, 210; decomposition of, 863 ; - hammer, 77; hot, heating by, 504; level, 110; maximum density of, 334; spouts, 1022 ; wheels, 152 Wave, condensed, 228; expanded, 228 ; lengths, 651; plane, 652; of a note, 256 Weather, its influence on barometric va- riations, 176; glasses, 1773; charts, 1017; forecasts, 1017 Wedge, 44 Wedgwood’s pyrometer, 315 Weighing, method of double, 76 Weight, 23, 83; relative, 43; of bodies weighed in air, correction for loss of, 409 ; of gases, 158; thermometer, 328 Weights and measures, 126 Welding, electrical, 860 Wells’s theory of dew, 1025 Wells, artesian, 112 1142 WER Werdermann’s electric lamp, 860 Wet-bulb hygrometer, 405 Wheatstone’s bridge, 986 ; photometer, 521; rheostat, 982; rotating mirror, | 816 ; and Cooke’s telegraph, 909 Wheel and axle, 42 Wheel barometer, 177 Wheels, friction, 78; escapement, 82 ; water, 152 Whirl, electrical, 787 Whispering galleries, 240 White light, decomposition of, 576; re- composition of, 579 Wiedemann and Franz’s tables of con- | ductivity, 411 Wild’s magneto-electrical machine, 938 Wimshurst’s machine, 782 Winch, 42 | Winckler’s cushions, 776 Wind chest, 276; instruments, 274, 284 Wind pipe, 263 Windhausen’s ice machine, 506 Winds, causes of, 1014; direction and | velocity of, 1012, 1013; law of rota- tion of, 1016; periodical, regular, and variable, 1615 Wine, alcoholic value of, 382 ; tears of, 136 Wire, telegraph, 908 Index ZON | Wollaston’s battery, 826; camera lucida, 615; cryophorus, 377 ; doublet, 598 Wood, conductivity of, 411 Wood’s fusible metal, 344 Work, 46, 59; measure of, 60; of an engine, 482; rate of, 483; unit of, 61; internal and external, of bodies, 299 ; of a voltaic battery, 854; required for the production of electricity, 783 Writing telegraphs, 911 ARD, British, 22, 126 Yellow spot, 625 Yoke, 905 Young and Fresnel’s experiment, 659 Young’s modulus, 89 AMBONTDS pile, 338 Zero, absolute, 508; tension of aqueous vapour below, 359 ; displace- ment of, 308 Zigzag lightning, 1035 Zinc, amalgamated, 837 ; carbon battery, 831 Zither, 283 Zoetrope, 639 Zone, isotherma], 1045 PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE LONDON i A CLASSIFIED CATALOGUE SCIENTIFIC WORKS PUBLISHED BY MESSRS, LONGMANS, GREEN, & 60. 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