MainLib. LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Deceived ^pp 12 1 893 . 189 Accessions No. 5"O.Q.Lfe measured as follows. PRACTICAL ELECTRICITY. [Chap. I. lla. Measuring the Distribution of Magnetism in a Permanent Magnet. This may be done with the apparatus shown in Fig. 5a, where M M is the permanent magnet placed on a board, one end of which is attached Fig. 5a. to a hinge, while the other end can be raised or lowered by turning the " micrometer screw " s.* L L is a brass bar, supported on knife edges at F, like the beam of an ordinary balance, and on the upper surface of this beam there is a series of equidistant grooves, in any one of which can be placed a knife edge made like a hook, and from which hangs a brass box, w, containing leaden shot. A soft iron ball, B, hangs by a thread, which passes * A micrometer screw is a screw of small pitch, accurately cut, and provided with a large head, the circumference of which is accu- rately subdivided. If the distance between two of the threads of the screw be, say -^th of an inch, and the circumference be subdivided into 200 eqxial parts, the screw will advance ^Vtith f an mcn when the head is turned through a space equal to one division. Chap.L] DISTRIBUTION OP MAGNETISM ALONG A BAR. 25 through a small vertical hole in the beam, from a brasa pin P, to which the thread is attached. Before the magnet is placed on the board, the quantity of shot in this box and the counterpoise c are so adjusted that when the knife edge supporting w is placed in the groove marked nought, the beam rests horizontal. Turning p winds up, or unwinds, a little of the thread, and so slightly raises or lowers the ball. The experiment is performed by first cleaning the upper surface of the magnet and the lower surface of the ball with fine emery cloth, and wiping off the emery. The board is next levelled, the magnet put on it, and the pin p turned until the ball is just in contact with the magnet, when the left-hand end of the beam is resting at the bottom of the slot s s, in which position the beam is horizontal. The knife edge carrying the weight is now placed in the different grooves on the upper edge of the beam until, by trial, two are found close to one another, such that if the knife edge is put in the one of them nearer the fulcrum F the iron ball remains in contact with the magnet, when the micrometer screw s is turned without shaking, so as to lower the magnet or in other words the left-hand end of the beam rises up as the magnet is lowered, whereas if the knife edge carrying w be put in the next groove, the magnet cannot pull the ball down with it when it is lowered or turning the micrometer screw s so as to lower the magnet, fails to raise the left hand end of the beam. It may then be assumed that if the knife edges were put about half-way between these two adjacent grooves, the weight w would produce a force exactly equal to that exerted by the magnet on the ball, and which, therefore, is known. Of course the experiment should be repeated several times, hanging the knife edge first in one of the grooves and then in the other, to make quite sure that the two right grooves have been found, and that the detaching of the magnet was not produced by shaking. The magnet is now moved along the board to a new position, and the force which is exerted when the iron 26 PRACTICAL ELECTRICITY. [Chap. L ball is put in contact with another part of it ascertained in a similar way, care being taken that in all cases the thread is quite vertical If experiments be made at points equidistant from one another all along, say, the central line of the magnet, it will be found that the force exerted by the magnet on the ball is very large towards each end, rapidly diminishes as we approach the centre, and becomes practically nought at the middle of the magnet. If similar experiments be conducted along a line parallel to the long edge of the magnet, but much nearer to one edge than the other, similar results will be obtained, but the forces at the ends of the magnet will be even greater than before. If the magnet be "uniformly magnetised " the attraction of the iron ball will not indi- cate any difference between the forces at two points similarly situated relatively to the two ends of the magnet, but if we approach our bar magnet M M to a suspended compass needle we find that the north -seeking end of the compass needle is attracted by one end of the bar magnet and repelled by the other, and so for the south-seeking end of the compass needle. Hence, although the foices exerted on a piece of soft iron by points symmetrically situated relatively to the two ends of a uniformly magnetised steel bar are the same in every respect, the forces exerted by the two ends of the large magnet on one end of a compass needle are opposite in character. Further, if we slip the bar magnet M M through a stirrup of paper suspended by a filament of unspun silk, and place it so that it is balanced and turns freely, we can find which is its north-seeking and which is its south- seeking pole, by observing the position it takes up relatively to the earth. This being done we note that it was the north-seeking pole of our large magnet that attracted the south-seeking pole of the compass needle, and repelled the north-seeking pole. Hence we are led to the general rule that similar poles repel one another, dis similar poles attract one another. Chap. I.] CALIBRATING A GALVANOMETER. 27 12. Experiment for Calibrating a Galvanometer Relatively or Absolutely. Fig. 6 shows a volta,- meter v, connected up with a galvanometer G, and a " box of resistance coils " R, ready for use for a relative or for an absolute calibration experiment. The course of the current is shown by the thick and dotted lines ; the thick lines representing the wires above, and the dotted lines the wires underneath, the board on which the ap- paratus is placed, and by means of which it can be moved Fig. 6. about from place to place without disconnecting the in- strument. T T are the terminals, or binding screws, to which the wires coming from the battery, dynamo machine, accumulators, or other source of electricity, are attached. The galvanometer in this case consists of a vertical circular coil of wire G, at the centre of which is suspended a very short magnetic needle carrying a long pointer of aluminium or of brass wire, or, best of all, made of a thin thread of glass, g is a shallow circular box, with a glass lid. A scale is fixed to the bottom of the box, and from the centre of the glass lid the small magnetic needle hangs by a filament of unspun silk. The posi- tion of the pointer on the scale can easily be read off if 28 PRACTICAL ELECTRICITY. [Chap. I. the ends of the pointer are blackened, and parallax* .can be avoided by fixing the scale close under the pointer. As this, however, is liable to lead to one or other of the ends of the pointer touching the scale, if the instrument is not very well made and carefully levelled, it is better to avoid parallax by fastening the scale, which in this case takes the form of a mere circu- lar ring, to a disc of looking-glass, and by the observer always taking care, when making a reading, to hold his head so that the pointer exactly hides its reflection in the looking - glass under- neath it. Fig. 7 shows the interior of the resist- ance box R, which con- tains coils of wire w 1 , &c., wound on wooden or ebonite bobbins B, &c. The ends of these coils are soldered to stiff wires w, which again are fastened to the brass pieces c 1 , c 2 , c 3 , &c., the latter being screwed to the wooden or ebonite top, E E, of the resistance box. When a plug P 2 is inserted tightly between the contact pieces, c 2 and c 8 (which can be best done by giving to the plug a down- ward screwing motion) the current flows along the short path, c 2 P 2 c 3 , across the metal plug, and practically none through the wire wound on the bobbin w 2 . If, however, a plug P 1 be withdrawn, then all the current passes through the .coil w 1 , and none across the space * Parallax is the error arising from looking at the pointer rather sideways, instead of looking directly down on it, and so causing its end to appear to be over a part of the scale a little to the right, or a little to the left, of its true position. Fig. 7. Chap. I.I CALIBRATING A GALVANOMETER. 29 separating c 1 and c 2 . Hence, by taking out one or more plugs the path for the current may be lengthened at will,* and the strength of the current diminished. The brass pieces, c 1 , c 2 , c 3 , are undercut, as seen in the figure, so that a strip of clean washleather can be inserted between them, and the ebonite cleaned. If the ebonite between the brass pieces were left dirty there would be leakage of the electricity across the film of dirt when the plug was removed, and the resistance between two of the brass pieces would be a little less than that of the coil of wire connecting them. (See 140, page 266.) For the benefit of those who may be accustomed to use resistance coils, it may be noticed that in the particular experiment shown in Fig. 6, it is quite unnecessary to know the length or gauge of the wire that has been wound on the various bobbins, nor is it at all necessary that all the coils should be made of the same wire, since whatever resistance be inserted in the box R, the cur- rent that passes through the voltameter is the same as the current that passes through the galvanometer, so that the variation in strength of the current is known from the voltameter observations, and not from the length of wire that has been introduced into the circuit. Indeed the resistance box in this experiment may be dispensed with altogether when there is any easy mode of altering the current strength by using different num- bers of cells or a different kind of battery to produce the current, but in practice this result is generally most easily attained by the use of a box of resistance coils. The calibration is performed by observing for a num- ber of different currents the rise of the liquid in the gra- duated tube of the voltameter v (Fig. 6), in a given time, and the corresponding steady deflection of the needle, or of the pointer, of the galvanometer. More accurate obser- vations can be made if, instead of observing the different lengths of the tube through which the liquid rises in the * Further details of the construction of resistance coils will be found in 89, page 151 ; 94, page 159 ; 95, pago 163. 30 PRACTICAL ELECTRICITY. [Chap. I same time corresponding with the different currents, the times be noted during which the liquid rises through a fixed length of the tube, say the whole of it, and from these results a calculation be made of the distances through which the liquid would have risen in the same time. In this case two marks only are necessary, one at each end of the tube. If the tube t (Fig. 5) has been graduated in cubic centimetres or cubic inches, and if the apparatus be so constructed that it can be kept duiing the experiment under water, so that the temperature of the gas is the same as that of the water, and therefore can be easily measured by a thermometer dipping into the water, then the actual currents in amperes producing any particular deflection on the galvanometer will, from what is given previously on page 12, be known, or the galvanometer will have been calibrated absolutely. If, however, the tube has been divided into portions having equal volumes, but of unknown value in cubic centimetres, or in cubic inches, or if, what is approximately the same in the case of a well-drawn tube, the divisions merely mark off equal lengths of the tube, then the result of the experiment will merely give the relative calibration of the galvanometer. 13. Graphically Recording the Results of an Ex- periment. The results of this -experiment, and indeed of all experiments, are best recorded graphically by points on a sheet of squared paper,* that is, paper subdivided into a number of small squares, by a large number of straight lines drawn at right angles to one another. The * Prior to the commencement of the courses at the Finsbury Technical College, in 1879, squared paper was practically used in Englan.d only for the recording of results of original experiments. And as these results, rather than the training of the experimenter, were the most important part of the investigation, the paper was very accurately divided, and sold at a high price totally out of the reach of students. It became, therefore, necessary to have squared paper specially made, cheap, and at the same time sufficiently accu- rately divided for students' purposes ; and such paper, machine-ruled, can now be obtained at between a farthing and a halfpenny per sheet, or at about one-twentieth of the cost of the older squared paper. Cliap. I.] GRAPHICAL RECORD OF RESULTS. 31 distances of the points from o Y (Fig. 8) should be taken to represent the deflections on the galvanometer G, and the distances of the same points from o x the correspond- ing amounts of gas produced in a given time, that is, the corresponding values of the current. In Fig. 8 the two sets of lines at right angles to one another, which divide galvanometer deflection Fig. 8. the paper into squares, have been omitted to avoid con- fusion. They will, however, be seen on referring to Fig. 93, page 245. It may be asked how distances along a line can re- present the angular deflections on a galvanometer, or the amount of gas produced in a given time. What is meant is this : the line o x is subdivided into a number of equal divisions by the ruling on the squared paper ; one or any convenient number of these subdivisions is taken arbitrarily to stand for 1, then any deflection is represented by this number of divisions that we have arbitrarily taken to stand for 1, multiplied by the num- ber of degrees on the deflection. Similarly one or any convenient number of the divisions along o Y is taken arbitrarily to stand for one cubic centimetre of gas, or the volume, it may be, contained in unit length of the tube, then any number of cubic centimetres, or the volume contained in any length of the tube, will be re- presented by the number of divisions along o Y that has 32 PRACTICAL ELECTRICITY. [Chap. I. been taken to stand for one cubic centimetre, or for unit length of the tube, multiplied into the number of cubic centimetres, or into the length of the tube. In selecting the scale, that is, in determining the number of divisions along o x or along o Y, that is to be taken to represent 1 deflection, or unit volume of the tube, we must remember that it is desirable that the curve, which we are about to draw, shall be as large as possible, since the larger it is the more accurately we can draw it. The scale should, therefore, be so selected that the maxi- mum deflection of the galvanometer that has been used in the experiment should be represented by nearly the whole of o x, and the corresponding maximum quantity of gas developed in the given time by nearly the whole of o Y, since with this arrangement the curve would occupy nearly the whole of the sheet of squared paper. For ex- ample, suppose that the length o x is divided by the ruling of the paper into 170 equal divisions, and o Y into 100, and suppose that the maximum galvanometer deflection was 60, and that when that deflection was produced the liquid ascended from the zero mark at the bottom of the tube to the top mark in twenty-two seconds, then, if one minute be the fixed time decided on, the most suit- able scales for distances measured along o x and along Y would be selected as follows : 170 - = 2-8 about 60 60 22 = 2 '' " 2-7 " 2*8 divisions per 1 would be a little awkward to em- ploy when deflections of 17, 29 1, &c., had to be repre- sented ; 2J divisions per 1, or 25 divisions per 10, would therefore be better. 37 divisions along OY, to represent the whole length of the tube would just Chap. I.] GRAPHICAL RECORDS CP RESULTS. 33 enable the maximum volume, corresponding with 2'7 lengths of the tube in the minute, to be represented by the whole of o Y ; but 37 divisions for the whole length would be a little awkward to employ when other lengths of the tube had to be represented ; probably, therefore, 30 divisions along o Y, to stand for the whole of the tube, would be more convenient. Having obtained a sufficient number of points by ex- periment, a curve should be drawn connecting these points. Such a curve can be best drawn by bending an elastic piece of wood, and holding it so as to pass as nearly as pos- sible through all the points that are plotted on the squared paper to record the results, and then using the bent piece of wood as a ruler D along which to draw a line. But unless the experiment has been performed with great accuracy to attain which requires, not merely the careful at- tention of those engaged in making the experiment, but a certain amount of practice in experimenting it must not be expected that a curve so drawn will pass through all the points ; some of them, 6, are sure to be a little too low, meaning that the deflection on the galvanometer has been read too high, or that the rise of liquid in the graduated tube has been read too low, from, perhaps, an error having been made in taking the time, or from the current not having been kept on for a sufficient time before the pinch-cock c (Fig. 5) was closed for the gas to have commenced to come off regularly. Some of the points e (Fig. 8), on the other hand, are sure to be too high, meaning that the deflection on the galvanometer has been read too low, or the rise of liquid in the graduated tube too high ; or it may be that the experiments were fairly well made, and that b and e are merely plotted incorrectly, and so do not represent the results of the ex- periment. 14. Practical Value of Drawing Curves to Graphic- ally Record the Results of Experiments. It may be asked, But is it not possible that the points b and e, although not on the curve, may be quite correct? The D 34 PRACTICAL ELECTRICITY. [Chap. L answei is. No. because experience makes us quite sure, from the fact that the connection between the deflection of the galvanometer G and the current strength must be a con- tinuous one, that the points correctly representing the true connection must all lie on an elastic curve, or on such a curve as can be obtained by bending a thin piece of wood or steel, and, consequently, that if no mistake has been made in plotting the points b and e, some mis- take must have been made in taking the observations. But what is even more important, we are also sure that the points b' and e on the curve, obtained by drawing lines through b and e respectively parallel to o Y, give far more accurately the relative strengths of the currents producing respectively the two deflections in question, than the currents obtained directly from the experiment itself. Drawing the curve, then, corrects the results ob- tained by the experiment. But it does something more than that it gives, by what is called "interpolation" the results that would have been obtained from intermediate experiments correctly made, that is to say, it tells us what would be the relative strengths of the currents that would produce deflections intermediate between the de- flections that were actually observed. For example, suppose it be required to know the strength of current which will produce a deflection of 43, for which deflection no experiment has been made, compared with that which will produce a deflection of, say 27, for which deflection also no experiment has been made, then all that is neces- sary is to draw a line parallel to O Y, through the point A in ox corresponding with 43, similarly to draw a line parallel to OY, through the point B in ox, corre- sponding with 27, and observe the lengths of the lines between o x and the points P and Q, where they cut the curve, then the strength of the current which produces the deflection 43 on this particular galvanometer bears to the strength of the current that produces the deflection 27 the ratio of the length A P to the length B Q. If the curve is an absolute and not merely a relative Chap. L] GRAPHICAL RECORDS OP RESULTS. 3f> calibration curve, then the scale on which it is drawn will be known, and therefore the number of amperes cor- responding with either A p or B Q. The method of plotting the results of experiment on squared paper, and drawing a curve through them to graphically record the result, has a third important use in that it enables us to see the nature of the law connecting the current with tJie deflection, which might easily escape observation if only a few disconnected experiments had been made. For example, suppose that the results ob- tained in some particular case are : Deflection. Relative Strength of Current. 10 24. 17-3 41-5. 22-8 54-7. 29-5 70-8. 37-4 ... 89-7. then plotting the results on squared paper a straight line is obtained, and from this we see at once that this par- ticular galvanometer has, somehow or other, been so made that the angular deflection of the needle is directly proportional to the strength of the current. 36 CHAPTER II GALVANOMETERS. to. Tangent Galvanometer 16. Spale for a Tangent Galvanometer 17. Mode of Making a Tangent Scale 18. Best Deflection to use with a Tangent Galvanometer 19. When the Tangent Law is True 20. Preceding Conditions are fulfilled in the Tangent Gal- vanometer 21. Adjusting the Coil of a Tangent Galvanometer 22. Variation of the Sensibility of a Galvanometer with the number of Windings and with the Diameter of the Bobbin 23. Thomson's Galvanometer for Large Currents 24. Values in Amperes of the Deflections of a Tangent Galvanometer con- trolled only by the Earth's Magnetism 25. Galvanometers having an Invariable Absolute Calibration 26. Calibrating any Gal- vanometer by Direct Comparison with a Tangent Galvanometer 27. Pivot and Fibre Suspensions 28. Sine Law : under what Conditions it is True 29. Preceding Conditions are fulfilled in the Sine Galvanometer 30. Calibrating a Galvanometer by the Sine Method 31. Calibration by the Sine Method of the Higher Parts of the Scale 32. Calibration by the Sine Method with a Constant Current 33. Method of Making a Sine Scale 34. Portable Galvanometer with .Approximately Invariable Abso- lute Calibration 35. Construction of Galvanometers in which the Angular Deflection is Proportional to the Current 36. Shielding Galvanometers from Extraneous Magnetic Disturbance 37. Direct Reading Galvanometers 38. Advantages of the Previous Types of Galvanometers 39. Ammeter. 15. Tangent Galvanometer. Using the particular galvanometer of the shape shown as G (Fig. 6), experi- ment proves that the calibration curve has the shape shown in Fig. 9, page 37, if (1st) The controlling force be produced by the needle moving in a "uniform magnetic field," like that produced by the earth's magnetism, and in which the force acting on a given magnetic pole is uniform in magnitude and direction ; (2nd) The diameter of the bobbin round which the wire is wound be large compared with the length of the suspended magnetic needle ; Chap. II.] TANGENT GALVANOMETER. 37 (3rd) The centre of this needle be at the centre or the bobbin ; (4th) The plane of the bobbin be so placed that it contains the " magnetic axis " of the needle, that is, the Fig. 9. line joining its magnetic poles, when no current is passing round the coil. And it is easy to ascertain by measurement that if any three points, P, Q, R, be taken on this curve, the lengths A P, B Q, c R, parallel to o Y, bear to one another the ratios of the tangents* of the angles * To find the tangent of any angle A o B (Fig. 10). In either line o A or p B take any point P, and drop a perpendicular P Q on the other. Then in the triangle P o Q we have two perpendiculars one, P Q, 38 PRACTICAL ELECTRICITY. [Chap. II. represented oy o A, o B, and o c respectively. Such a gal- vanometer is, therefore, called a " tangent galvanometer" Fig. 11. and it may be henceforth used without reference to any voltameter for the comparison of current strengths, as they will be simply proportional to the tangents opposite to the given angle ; the other, O Q, adjacent to it ; and a third side, opposite the right angle, called the hypotenuse. The ratio of the opposite side to the adjacent side is called the tangent of the angle A o B, or 3LS tan. A OB. OQ The ratio of the opposite side to the hypotenuse is called the sine of that angle, Fig. 10. Chap. II.] MAKING A TANGEXT SCALE. 39 of the angles through which the magnetic needle is deflected. 16. Scale for a Tangent Galvanometer. The scales of tangent galvanometers are frequently simply divided into degrees, and a reference has constantly to be made to a table of tangents to enable the galvanometer to be used. A better plan is to divide the scale, not into equal divisions, but into divisions, the lengths of which become smaller and smaller as we depart from the zero or un- Fig. 12. deflected position of the needle, in such a way that the number of divisions in any arc is proportional, but not necessarily equal, to the tangent of the angle corre- sponding with that arc. Or the scale may, as shown in Fig. 11, be divided into degrees on one side, and on the tangent principle on the other. 17. Mode of Making a Tangent Scale. Fig. 12 shows the method of constructing such a tangent scale. The lengths A B, B c, CD, &c., along the line A F, which is a tangent to the circle at the point A, are all made equal to one another ; hence if from the centre, o, of the circle straight lines, o A, o B, o c, &c., be drawn, cutting the cir- cumference of the circle in the points A, 1, 2, 3, &c., the 40 PRACTICAL ELECTRICITY. [Chap. II. numbers 1, 2, 3, 4, &c., will be respectively proportional to the tangents of the angles AOl, A02, A03, &c. A H For tan. AO 1 = ~~ o A tan. A02 = o A 2 AB OA tan. A03 = A OA and so on. Beginners are apt to think that, because the divisions on such a tangent scale are very much crowded together in the higher part of the scale, the value of a current can be more accurately ascertained by taking a reading on the degree side, and then finding the value of the tangent in a table of tangents, than by reading it off on the tangent scale. But this seeming greater accuracy is quite delusive, since what has to be ascertained in either case is the tangent of the angle, not merely the angle, and although on the degree side of the scale the angle can be read much more accurately than can be its tangent, or a number pro- portional to its tangent, on the other side, this only indi- cates that the error of a tenth of a degree in a large angle, although a much smaller proportional error than a tenth of a degree in a smaller angle, produces a far greater pro- portional error in the tangent. For example, if 20'l be read instead of 20, the error is ^o> whereas if 85*1 be read instead of 85, the error is only ^^, or less than a quarter of the preceding error. But the tangents are in the first case 0-3659, and 0-3640, the error in the tangent, therefore, is sifo> or about T92> whereas the tangents in the second case are 11-66 and 11 -43, so that Chap. H.] WHEN THE TANGENT LAW IS TRUE. 41 the proportional error is Tftif> or about ^, which is nearly four times as great as before. Hence in this case, when the proportional angular error is diminished to one- quart 3r, the corresponding proportional error in the tan- gents is increased four times. The crowding together of the divisions on the tangent scale at the higher readings is, therefore, a correct indication of the inaccuracy likely to occur in taking readings in that part of the scale. 18. Best Deflection to use with a Tangent Gal- vanometer. It can be shown that if one current strength has to be measured by a tangent galvanometer, the result, other things being the same, will be most accurate when the deflection produced is 45 ; or if two currents are to be measured, the measurements will be most accurate when the deflections are as nearly as possible at equal distances on the two sides of 45. 19. When the Tangent Law is True. Any galvano- meter may now be calibrated either relatively or abso- lutely, by comparison with a tangent galvanometer ; and if the galvanometer to be calibrated be a very sensitive one, a tangent galvanometer with a bobbin wound with fine wire should be selected. Before, however, entering into the calibration of other galvanometers in this way, it may be well to consider under what circumstances a gal- vanometer will be a tangent galvanometer, especially as beginners are too apt to think that if the law of some galvanometer is unknown to them, then it must be the tangent law. The apparatus shown in Fig. 13 enables us to decide under what conditions a force acting on a body turning on a pivot is proportional to the tangent of the angle through which the body is deflected from the position it had before the force acted on it. A short piece of wood, N N', turning on a pivot, o, is acted on by a weight, w, which produces a force constant both in magnitude and direction. Variable weights, w', are put into the scale-pan hanging at the end of a long cord, which passes over a distant pulley, p, and which is attached at its other end to the piece of wood PRACTICAL ELECTIUCITY. [Chap. II. at N. The height of the pulley, p, is such that the long portion of the cord is horizontal when N N' is vertical, chat is, when there is no weight in the scale-pan, which in the figure is shown holding a weight, w'. And owing to the pulley being distant from N N', the long portion of the cord remains nearly horizontal, even when the piece Fig. 13. of wood N N' is deflected through an angle. Under these circumstances experiment shows that the weights w' put successively into the scale-pan are proportional to the distance s P, intercepted between the position s on the scale where the cord supporting w cuts the scale when N N' is vertical, and the point P where the pointer P N cuts the scale when N N' is deflected by the weight put into the scale-pan. Now this length s P divided by e o is the tangent of the angle through which N N' is deflected, and, Chap. II.] WHEN THE TANGENT LAW IS TRUE. 43 therefore, since s o is a constant length, 8 P is proportional to the tangent of the angle through which N N' is deflected. Hence with the apparatus the tangent law holds. What are the conditions of the apparatus? They are : 1st. The controlling force is unaltered in magnitude and direction by the motion of N N'. 2nd. The deflecting force always acts in the same direction, and at right angles to the controlling force. Hence, whenever these two conditions are fulfilled the deflecting force will be measured by the tangent of the angle of deflection. 20. Preceding Conditions are Fulfilled in the Tan- gent Galvanometer. The first condition, constancy in magnitude and direction of the controlling force, is prac- tically fulfilled in all galvanometers where the controlling force is produced by a distant magnet, since such a mag- net produces a practically uniform magnetic field through- out the space in which the galvanometer needle can move, for, as the length of the needle is small compared with its distance from the poles of the controlling magnet, the controlling force exerted on the needle cannot be materially altered in magnitude and direction when it is deflected. In all galvanometers, therefore, in which the controlling force is due to the attraction produced by the earth's magnetism, condition (1) is absolutely fulfilled. Next with reference to condition (2) with all flat coils the magnetic force due to a current passing round them is perpendicular to the plane of the coil for all points in the plane of the coil. But the direction of this force rapidly alters as we proceed outside the coil, unless we are near the axis, in which case the direction of the force remains practically perpendicular to the plane of the coil. And, indeed, for all points on the axis itself the magnetic force is strictly perpendicular to the plane of the coil, that is, acts along the axis. In Fig. 14 are seen a number of lines, called " lines offeree." These lines tell us the paths along which a magnetic pole would be pulled, or pushed, by the action of a current passing round a circular 44 PRACTICAL ELECTRICITY. [Chap. II. wire or coil* perpendicular to the paper, and cutting it in the two small circles c c. It will be seen that at any point p on the axis A A of the coil the direction is everywhere perpendicular to the plane of the coil, also that near the axis the direction is nearly perpendicular to this plane for Fig. 14. a considerable distance, while near the coil itself the direction of the force changes rapidly. Hence, if we sus- pend at the centre of a coil a very short magnetic needle, m m, having a length not greater than one-tenth or one- * This wire or coil, the plane of which is in reality perpendicular to that of the paper, is represented in the figure in a kind of oblique perspective by a double line. Cliap. IL] COIL OF A TANGENT GALVANOMETER. 45 twelfth the diameter of the coil, the deflecting force due to a current passing round the coil will be perpendi- cular to the plane of the coil, even after the needle is deflected, and will be also perpendicular to the controlling force, if the controlling force acts in the plane of the coil, that is, if the coil is so placed that its plane contains the magnetic axis of the suspended needle when no cur- rent is passing through the coil. In fact, if the coil occupies the position of the semi- circular wire seen in Fig. 13, and if this wire is in the " plane of the magnetic meridian"* the conditions neces- sary for the deflecting force being proportional to the tangent of the deflection will be fulfilled. We have seen, from the experiment described in 15, page 36, that the tangent of the deflection of the needle of a tangent galvanometer is directly proportional to the current strength, or simply to the current ; hence, we may conclude that the force acting on a magnetic pole at a fixed point on, or near, the axis of a circular coil is directly proportional to the current flowing round that coil. Later on we shall see that this law is true for a fixed magnetic pole in any position relatively to the coil acted on by a current flowing round a coil of any shape. It is not necessary that the coil of a tangent galva- nometer should be circular, but m order to obtain the straightness of the lines of force in the neighbourhood of the axis, as seen in Fig. 14, and not merely for points actually on the axis, of which we could only avail our- selves by using an infinitely short magnet, the diameter of all parts of the coil must be large. Hence, if an elliptic, or other non-circular coil, were used, its smallest Jiameter would have to be large, and consequently its largest diameter unnecessarily so. From what has been said, and from an examination of Fig. 14, it will be seen that for very small. deflections of the needle any galvanometer, no matter what be th * The "plane of the magnetic meridian" at any place is that vertical piano in which lies the axis of a compass needle. 46 PRACTICAL ELECTRICITY. fChap. H. size of the needle and of the coil, or how near be the con- trolling magnet, will be a tangent galvanometer, And further, since the tangents of very small angles are simply proportional to the angles, the deflections of the needle, as long as they are very small, in any galvanometer are directly proportional to the strengths of the currents pro- ducing them. 21. Adjusting the Coil of a Tangent Galvanometer. Returning now to ordinary tangent galvanometers to be used for large deflections, how can we adjust the coil so as to be sure that its plane contains the axis of the needle 1 ? Owing to the coil having a certain breadth, it is impossible to see the needle when looking down on to the coil ; indeed, it is for this reason that the long light pointer attached to the needle is placed at right angles to the needle. It would not be right to assume that be- cause the instrument has been so turned that the pointer points to the zero on the scale, therefore the plane of the coil contains the magnetic axis of the needle, for even if the scale has been attached to the instrument so that the line of zeros is at right angles to the plane of the coil, it does not follow that the pointer itself is at right angles to the needle. The two may even have been placed at right angles to one another by the maker, and yet the pointer may have been bent subsequently, so that they are not at right angles at present ; or no experiment may have been made by the maker to test this, as he is aware that the user will probably make a test and adjust the pointer for himself. This test may most simply be made as follows : Turn the instrument until the pointer points to 0, send any convenient current through it, and observe the deflection, then reverse the direction of the current without altering its strength, and observe the deflection on the other side. If these deflections are exactly equal, then the plane of the coil contains the axis of the needle when the pointer points to 0, and the instrument is properly adjusted. But if, on the other hand, one deflection is, say, 47 to the left, and the other, say, 44 to the right, the Chap. II. j ADJUSTING A TANGENT GALVANOMETER COIL. 47 pointer is not at right angles to the magnetic axis of the needle, supposing, of course, that the scale hss been so fixed that the line of zeros is exactly at right angles to the plane of the coil. Next, turn the instrument a little about its centre in the direction opposite to that in which the needle moved when the greater deflection was obtained. The pointer will now, of course, not point to zero ; let it stand at 1 to the left. Again send a current, first in one direction, obtaining a deflection, say, 46 to the left, and in another direction, when it gives a deflec- tion of, say, 45 to the right. Now remembering that the pointer started from 1 to the left, the true deflections of the needle are respectively, 46 -1, or 45 to the left, and 45 + 1, or 46 to the right. Hence, the fault is now on the other side, or the left deflection is smaller than the right, and we have, consequently, turned the instru- ment too much. Turn, therefore, the coil round a very little in the opposite direction, so that when no current is passing through the instrument the pointer stands at, say, | to the left, and send as before reverse currents of equal strength, obtaining apparent deflections, 45^ to the left and 44J to the right, which, corrected for the initial zero error, correspond with equal deflections of 45 to either side. The instrument will now be correct when it is so placed that for no current the pointer stands at J left, and it can be so used, but not, however, with the tan- gent scale. To enable us to employ the side of the dial graduated in tangents, as well as to avoid having to remember the J left error, do not alter the position of the instrument, but bend the pointer until it points to for the same position of the instrument in which it previously pointed to J left. The instrument will now behave as a correct tangent galvanometer when the pointer stands at for no current. We have spoken of reversing the direction of the cur- rent without altering its value. Th ; s may be done by causing the current to pass through any galvanoscope, 48 PRACTICAL FLECTRICITY. [Chap. II, the law of which may be quite unknown ; and taking care that the deflection of the needle after the current has been reversed is the same in amount as it was before the current was reversed ; indeed, if we reverse the connections of the galvanoscope at the same time that we reverse the connections of the battery or other cur- rent generator employed in the experiment, it will not be even necessary to know that the coil and needle of this auxiliary galvanoscope are symmetrical, or that the strength of a current producing a deflection to the right is the same as that of a current producing a de- flection to the left. 22. Variation of the Sensibility of a Galvanometer, with the number of Windings and with the Dia- meter of the Bobbin. A tangent galvanometer, on the bobbin of which a short thick wire has been coiled, can be calibrated absolutely by direct comparison with a volta- meter. To obtain a more delicate tangent galvanometer, we must replace this thick wire with many turns of fine wire, and the numbers of amperes or fractions of an ampere producing any particular deflection on this deli- cate galvanometer will also be known if we know the exact change in the sensibility produced by replacing the thick wire with many turns of tine. The apparatus shown in Fig. 15 is for the purpose of enabling this to be ex- perimentally tested, as well as for testing the variation in sensibility produced by altering the diameter of the coil. g g is a flat cylindrical box, containing, as in Fig. 6, a scale fastened to its bottom, and a short needle carrying a long light pointer, suspended by a short piece of unspun silk, fastened to the centre of a circular piece of glass, forming the cover, c c is a bobbin of large diameter, and such that its centre is exactly the same height above the base-board B B as is the centre of the suspended magnetic needle, c c is a smaller bobbin, of which the diameter is exactly half that of the larger bobbin, but still large com- pared with the length of the suspended magnet. The centre of the smaller bobbin is also on the same level Chap. II.] SENSIBILITY OP A GALVANOMETER. 49 as the suspended magnet when the base-board b b of the smaller bobbin is placed on that of the larger. On the larger bobbin c c are wound two distinct coils of insulated wire, one consisting of twelve convolutions, and having its ends attached to two of the binding screws, 1, 2, the other Fig. 15. of four convolutions, and having its ends attached to the other two binding screws, 3, 4. If the binding screw 2 at the end of the first coil be joined by a piece of wire, as shown in the figure, to the binding screw 3 attached to the beginning of the second, the current will go 12 + 4, or sixteen times round the bobbin ; whereas if the wire connect the end of the first coil, 2, with the end of the 50 PRACTICAL ELECTRICITY. [Chap. IL second. 4. and the current enter and finally leave the bobbin by the two binding screws 1, 3, attached respec- tively to the beginnings of the two coils, then the current will go twelve times round the bobbin in one direction and four times in the other, or practically 12 4, or eight times round the bobbin. Now, experiment shows that if the controlling magnet be untouched, and a cur- rent of constant strength be passed successively first four, then eight, then twelve, then sixteen times round the bobbin, which is kept fixed in position during the expe- riment, the tangents of the corresponding deflections pro- duced will be as four to eight, to twelve to sixteen, that is, simply proportional to the number of times the current passes round the bobbin. The constancy of the current can be tested by the deflection on the auxiliary galvano- scope G, and if the insertion in the circuit of the greater or less number of coils on the bobbin G c, or any other cause, tends to make it vary in strength, its constancy can be maintained by sliding the screw clip s along the stretched wires w w,* by means of which the length of the wire in the circuit can be increased or diminished, and the current strength diminished or increased. If we next experiment with the bobbin c c of half the diameter, and. on which a coil of four convolutions is wound, we find that if the two bobbins be placed so as to be in one plane, and if their centres coincide with that of the suspended magnet, the tangent of the deflection produced by a certain current flowing round the smaller one is twice as great as the tangent of the deflection produced by the same current flowing four times round the larger bobbin ; and also if the same current pass four times round the smaller in one direction, and eight times round the larger in the opposite direction, that no deflection is produced. * To prevent these wires being accidentally damaged, it is better to put them in a groove formed in the base-board instead of above the board as shown in Fig. 1 5. In that case it is convenient to shape the clip s so that it can slide in the groove in the base-board, the ends o/ the clip being guided by the sides of the groove. Chap, n.] SENSIBILITY OP A GALVANOMETER. 51 From this we learn that the tangent of the deflection produced by a current, that is, the sensibility of the instrument is directly proportional to the number of convolutions of wire, and inversely proportional to their diameter. On the bobbin c c the sixteen convolutions of wire all occupy practically the same position relatively to the suspended magnet. If, however, many turns are to be wound on a bobbin, the bobbin will have a certain depth in the direction of the diameter of the coil, and a certain width at right angles to the plane of the coil. The error introduced by the depth of the coil is that of making the convolutions of wire have different diameters, and the effect of this we have just seen. The error intro- duced by the width of the coil can be seen by observing how the deflection produced by a constant current varies as the bobbin cc is moved parallel to itself along its axis. The additional error introduced by the non- centring of the coil and the needle may also be experi- mentally investigated by examining how the deflection produced by a constant current alters as the bobbin is slid in its own plane. It is not necessary in this book to consider exactly how to correct these errors, nor the error arising from the diameter of the bobbin in all .actual tangent galva- nometers not being infinitely large compared with the length of the needle ; and it will be sufficient to state that with a tangent galvanometer made with a single bobbin having a rectangular channel, within which the coils of insulated wire are to be wound, Prof. Silvanus Thompson has shown that the tangent law is most ac- curately fulfilled when the depth of the channel in the radial direction bears to the breadth in the axial direction the ratio of v/3 to \/2", or about eleven to nine. When an experiment is made to determine the altera- tion in sensibility produced by moving the coil parallel to 52 PRACTICAL ELECTRICITY. [Chap. II. itself along its axis, it is found that the tangent of the de- flection produced by the same current when a coil of radius r is made to occupy different positions parallel to itself at distances ce, measured along the axis from the centre of the needle, is proportional to that is, the sensibility of the galvanometer is proportional to this expression. Example 9. A tangent galvanometer is made with two coils of equal diameter, the first consisting of 500 convolutions of wire, the second of one convolution. If a current of 0'25 ampere sent through the first cause a deflection of 45, what current sent through the second in the opposite direction, while the same current was still flowing through the first, would cause the deflection to become one of 10 1 Let x be the unknown number of amperes : Then ' 25 ~ C tan - 500 x 0-25 tan. 45 Answer. 103 amperes. Example 10. A galvanometer is about to be con- structed of two coils : the first, six inches in diameter, consists of 350 convolutions of wire ; the second has two convolutions only. A current of 0*4 ampere sent through the first causes a deflection of 30. What must be the diameter of the second coil, in order that a cur- rent of 80 amperes, in the opposite direction, sent through it, while 0'4 amperes is still flowing through the first, may cause the deflection to become 5 ? Let x be the diameter of the second coil. Since the effect of the current is directly proportional to the number of convolutions, and inversely proportional to the diameter chap. ii.i THOMSON'S LARGE CURRENT GALVANOMETER. 53 0-4 x 350 80 x 2 6 x tan. 5 0-4 x 350 tan. 30 6 Answer. 8 inches nearly. Example 11. A galvanometer is about to be con- structed of two t.oils : the first, seven inches in diameter, consists of 600 convolutions of wire ; the second is to be 5-5 inches in diameter. A current of 0'1656 ampere sent through the first causes a deflection of 40. Of how many convolutions of wire must the second coil consist, in order that while 0'1656 ampere is still flowing through the first, a current of 65 amperes flowing through the second may cause the deflection to become 8 1 Answer. One convolution. 23. Thomson's Galvanometer for Large Currents. A tangent galvanometer, with a scale graduated in tan- gents, and controlled by a permanent magnet rigidly fixed to the instrument, has been arranged by Sir William Thomson, and is shown in Fig. 16. It has the peculiarity that the needle, scale, and permanent magnet M can be slid along a board p, and so withdrawn parallel to itself farther and farther from the action of the coil c ; hence a wide range of sensibility can be given to the instrument, in accordance with the last formulas. To prevent the current which flows in the long wires connecting the galvano- meter with the rest of the circuit acting directly on the suspended magnetic needle, these coming and going wires are twisted together into a form of cable, which is shown in the figure, and which is supplied with the instrument. The advantage of this galvanometer is that, first, owing to its being a tangent galvanometer the ratio of two current strengths can be very accurately compared ; secondly, from the method of sliding the needle away from the coil, two currents, widely differing in strength, can be compared. The disadvantage is that, PRACTICAL ELECTRICITY. [Chap. II. small action that the coil, even with a very strong cur- rent flowing round it, can exert on the needle, when they are at opposite ends of the base- board, the controlling force of the perma- nent magnet has to be kept small ; hence the instrument, as we shall see afterwards, cannot be made very " dead beat " (see 38, page 78), and fur- ther, the indications are much disturbed by any external mag- net. In fact,the in- strument is rather for use in a laboratory, where the magnetic field is constant in strength, and known, than in a dynamo room or workshop, where large pieces of iron and powerful magnets are being moved about. 24. Values in Amperes of the De- flections of a Tan- gent Galvanometer controlled only by the Earth's Mag- netism. The sensi- bility of a tangent galvanometer depends not merely on the bobbin, but also on the strength of the controlling field. If, however, the Chap. H.] TANGENT GALVANOMETER WITH EARTH CONTROL. 55 "horizontal component of the earth's magnetic force"* in London be alone employed as the controlling force, and if the instrument be used with the centre of the coil and the centre of the needle coinciding, then the connection between the current A in amperes, the deflection d in degrees, the radius r of the coil in inches, and the number of convolutions N of wire on the bobbin, is given by the following equation for 1886 : 73735 x r x tan. d A. -- J N the coefficient 073735 for 1886 becoming 073844 for 1887, 073953 for 1888, and 074062 for 1889. From this 'it follows that in the year 1887 a deflection of 45 will be given by one ampere when there are five convolutions of wire on a bobbin 6772 inches in radius. Example 12. How many amperes would deflect the needle of a tangent galvanometer 60 in the year 1886, the controlling force being the horizontal component of the earth's magnetism, and the galvanometer having a bobbin five inches in radius, wound with six con- volutions of wire] The number of amperes is ' 73735 X 5 X ^ 3 . Answer. 1-064 amperes. Example 13. Through what angle would 0'598 ampere deflect the needle of a galvanometer with a bobbin seven inches in radius, wound with five con- volutions of wire, in the year 1888, the controlling force being the horizontal component of .the earth's magnetism 1 * The horizontal component of the earth's magnetic force is that portion of the earth's force which acts on a compass needle. 56 PRACTICAL ELECTRICITY. [Chap. H. 0-598 - 0-73953 x 7 x tan, d 5 , 5 x 0-598 . . tan. d = 0-73953 x 7 = 0-5775 d = 30. Answer. 30. Having tan. d, d may be found either by looking in a table of tangents or in the following way : Take a sheet of squared paper, and on it select two axes, or lines of reference, ox, o Y, at right angles to one another. Choose any number of the divisions on your paper to represent unity, taking care that there are more than 100 of these larger divisions along ox, and at least 58 along OY. These numbers are chosen because the tangent of the angle required is approximately gi\ 7 en by 57*7 the ratio T^/. Along ox mark off o A, equal to 100 of the divisions, then on the line through A, parallel to o Y, mark off A B as nearly as possible equal to 57 '7 of the divisions. Join o B. Then B o A is the angle d. T> A For tan. BOA = - o A 57-7 100 = tan. d. The angle d may now be found by means of a pro- tractor. Example 14. If the horizontal component of the earth's magnetism in 1887 be the controlling force in a tangent galvanometer, the bobbin of which is 11 inches in diameter, how many convolutions of wire must be wound on the bobbin in order that a current of 1-015 amperes may give a deflection of 45 ? Answer. 4 convolutions. Chap. II.] INVARIABLE ABSOLUTE CALIBRATION. 57 Example 15. If the horizontal component of the earth's magnetism in 1885 be the controlling force in a tangent galvanometer, the bobbin of which is wound with eight convolutions of wire, what must be the radius of the bobbin in order that a current of 0'384 ampere may give a deflection of 50? Answer. 3J inches. Tan. 50 may be found either in a table of tangents or in the following way : Take a sheet of squared paper ; on it take axes o x, o Y ; with a protractor make the angle BOX, equal to 50, and produce o B as far as the paper will allow. Let A B be the farthest line from o, parallel to o Y, which cuts A TC B o. Then tan. 50 = . o A Count the number of divisions and fractions oi a division in A B and o A, and divide the one by the othei. If the angle be large, great care must be taken to lay it down accurately with the protractor, since a small error in a large angle will introduce a large error in the tangent. Example 1 6. About how many times the horizontal component of the earth's magnetism must the controlling force be in a tangent galvanometer, having a bobbin five inches in radius wound with six convolutions of wire, in order that a current of 20 amperes may make a deflection of 45 ? Answer. Nearly 32 times. 25. Galvanometers having an Invariable Absolute Calibration. In order that the absolute calibration of any galvanometer may remain invariable, the magnetic field in which the suspended magnet moves must remain constant in strength ; and if the galvanometer is to be moved about near masses of iron, or near the large power- ful electromagnets of dynamo machines, probably the most satisfactory of all the methods that have been tried for securing approximate constancy of the controlling field is either to attach a powerful permanent magnet to the instrument, or still better to substitute the force of 58 PRACTICAL ELECTRICITY. [Chap. II. a spring for a magnetic controlling force.* In either case this controlling force must, of course, be large compared with any magnetic forces that are likely to be exerted by outside magnets on the suspended needle, and must be very many times as large as that due to the earth's magnetism. But, in that case, un- less the instrument is only to be employed to measure the most powerful currents, the coil must be near the needle, so that the condition (No. 1, page 36) for obtain- ing the tangent law cannot be complied with. And gene- rally the necessity of having a coil of very large diameter compared with the length of the needle makes a tangent galvanometer unsuitable for a portable galvanometer, or else necessitates the employment of so short a needle that its oscillations are much impeded by the mass of even an extremely light pointer attached to it. Hence with all portable galvanometers, and especially in the case of those which may be used near masses of iron or dynamos without serious error, it is better to abandon any attempt to obtain the tangent law, and calibrate the galvano- meter by direct comparison with a tangent galvanometer. 26. Calibrating any Galvanometer by Direct Com- parison with a Tangent Galvanometer. Fig. 17 shows the simplest way of doing this. G is the standard tangent galvanometer, D the galvanometer, which, if rough and portable, is sometimes called a " detector," requiring to be calibrated, v is a vessel containing two zinc plates dipping into a small quantity of a solu- tion of zinc sulphate, which is used for varying the strength of the currents passing through G and D by altering the distance between the bottoms of the plates. The wires coining from the generator of electricity are attached to the terminals, one only of which, T, is seen in the figure, and a key placed between G and D enables the current to be made or broken. As the same current passes through G and D, it is quite unneces- * For further information on shielding galvanometers from extra- neous magnetic disturbance, see 36, p. 73 ; $ 63, p. 103 j and 202, p. 390. Chap. II.] CALIBRATING, USING TANGENT GALVANOMETER. 59 sary to know the value of the resistance introduced by v ; all that has to be done is to observe a number of cor- responding deflections of the needles of G and of D, then, since the true value of the current is proportional to the tangent of the deflection in G, a calibration curve can be drawn for D, in which horizontal distances represent the observed angular deflection of the needle of D, and verti- cal distances the relative strengths of the currents pro- ducing these deflections. If the number of amperes Fig. 17. producing any parcicular deflection in G is also known, then D will be calibrated absolutely. It frequently happens that, on account of the great increase in sensitiveness produced by putting the wires conveying the current close to the needle, a rough galva- nometer with a few turns of wire is even more sensitive than a tangent galvanometer with many turns. Under such circumstances it would be difficult to compare them, as a large deflection on D would only correspond with a small one on G, and a smaller deflection on D would not produce deflections on G large enough to be read at all accurately. This difficulty may, however, be overcome by putting a piece of wire s (Fig. 17), a "shunt " as it is called, 60 PRACTICAL ELECTRICITY. [Chap. II. between the terminals of D, and which allows a portion of the current to pass through it instead of through D. As, however, for the same shunt the same fraction of the total current is, as we shall see later on (page 178), always shunted past D, the sensibility alone of D, and not the law connecting current strength with de- flection, is altered by using such a shunt. The use of a shunt, therefore, alters the absolute but not the rela- tive calibration of a galvanometer ; consequently, if D is absolutely calibrated, the same shunt must always be employed when it is desired to use the absolute calibra- tion curve of that galvanometer. 27. Pivot and Fibre Suspensions. The galvano- meters G and D differ also in another particular, namely, in the way in which the magnetic needle is supported. In D the little magnet has a jewel in its centre, and rests on a sharp pivot, as in an ordinary pocket compass ; whereas in G the needle is supported by a fine fibre of unspun silk, the upper end of which is rolled round a brass pin hj by turning which the needle can be lowered on to the card s s, 011 which the scale is engraved, when the instru- ment is being carried about, or raised again so as to be in the centre of the coil when the instrument is in use. The fibre suspension introduces far less friction to the motion of the needle than the best jewel and pivot, and, in addition, costs far less ; but with a fibre suspension it is generally necessary that the instrument should have levelling screws, such as are seen attached to G, Fig. 17, and that it should be levelled before being used. There is one form of fibre suspension, however, which is used by Sir Wm. Thomson in his " marine galvano- meter," and which, although not employed in other in- struments, has advantages that make it worthy of more general adoption in portable galvanometers. To a silk fibre stretched between a fixed support and one end of a spring, there is attached the magnetic needle and pointer, or other indicating arrangement, and when these are well balanced, the whole instrument may be tilted through Chap. II.] WHEN THE SINE LAW IS TRUE. 61 several degrees without any practical alteration of the deflection. (See 53, page 103.) 28. Sine Law : Under what Conditions it is True. When the controlling force acting on the needle of a galvanometer remains constant in magnitude and direc- tion on the needle being deflected (a result that will always practically happen when the control- ling force is produced by the attraction of a distant magnet), there is a very simple plan, suggested to the author by Prof. Carey Foster, for calibrating the galvanometer relatively by employing what is known as the " sine prin- ciple" in a particular way, and which does not require the use of any other gal- vanometer at all. We have already seen under what conditions a force acting on a body is pro- portional to the tangent of the angle through which the body is deflected, and in a similar way the ap- Fig. 18. paratus shown in Fig. 18 will enable us to decide under what circumstances a force acting on a body is directly proportional to the " sine " of the angle of deflection. N o is a piece of wood, in this case not necessarily short, turning on a pivot at o, and having suspended from its lower end a weight w, which produces a force constant both in magnitude and direc- tion. The same end of the piece of wood N o is also acted upon by a force produced by a cord carrying the 62 PRACTICAL ELECTRICITY. [Chap. IL scale-pan in which is placed the weight w', the magnitude of which can be varied. Now experiment shows that, if different weights be successively put into the scale-pan, and if in each case the framework AB carrying the pulley c be turned about the centre o, so that the piece of wood N o always occupies the same position relatively to A B, the weights are proportional to the horizontal dis- tance (ss, Fig. 19), measured along the scale between the point where the cord carrying w cuts now, and where it cut it when w was nought. But s s, or PN, which is equal to it, divided by N o, the half-length of the deflected lever, is equal to the sine of the angle PON, through which N o has been de- flected. It is also obvious that turning A B, so that it always takes up the same position relatively to N o, is only a means of causing the angle between the cord carrying w' and NO to be constant, in order that the only change in the force exerted by the string carrying w' may be that caused by the change of weight, not by any change in the direction of the pull. From this we conclude that in order that a force acting on a body turning on an axis may be directly proportional to the sine of the angle through which the body is deflected : 1. The controlling force must be constant in magnitude and direction. 2. The deflecting force, although variable in its direc- tion in space, must be fixed in direction relatively to the deflected body. 29. Preceding Conditions are Fulfilled in the Sine Galvanometer. In any galvanometer in which the con- Cbup. II.) SINE GALVANOMETER. 63 trolling force is produced by the earth's magnetism, or by any distant fixed magnet, this force will be constant in magnitude and direction, and independent of the needle changing its position ; also the deflecting force produced by the current passing round the bobbin, can be made to have an invariable direction relatively to the needle, if the bobbin, or the framework of the instrument to which the bobbin is attached, be turned round after the deflected needle ; for it will be found that, although on turning the bobbin the needle turns away from the bobbin, it does not turn as fast as the bobbin. Under these circum- stances, the sine of the angle through which the needle has been deflected from the position of rest which it had when no current was passing through the bobbin, will be directly proportional to the current strength. Now, if the coil be placed so as to have a fixed position relatively to the needle, both when no current passes through the coil and when a given current passes through the coil, then the angle through which the coil has to be turned from the drst position to the second, is the same as the angle through which the needle has been deflected ; and hence, in the so-called sine galvanometers, there is, in addition to the scale moving with the bobbin, an independent fixed scale, to show through what angle the coil has been turned. This, however, is not absolutely necessary, since, if, after the coil has been turned until it has the fixed position relatively to the needle, the current be inter- rupted, without the position of the instrument being disturbed, then the needle will swing back, and, after a few oscillations, will take up its original undeflected posi- tion, the angle between which and its deflected position will be the angle of which the sine has to be taken. As a current passing through a coil has usually the greatest effect on a magnetic needle suspended inside it when the axis of the needle is perpendicular to the axis of the coil, this is the fixed position of the coil relatively to the needle usually adopted, and the one in which the pointer stands at on the movable scale. But this particular 64 PRACTICAL ELECTRICITY. fChap. H, position is not at all necessary for the fulfilment of the sine law, and therefore special precautions need not be adopted, as in the case of the tangent galvanometer (see ante, page 45), to insure the axes of the needle and of the coil being at right angles when the pointer stands at zero on the scale, Any galvanometer which is controlled by a distant magnet, and which can be turned round a point that is approximately the centre of the needle, can be used as a sine galvanometer, and, therefore, can be calibrated by the employment of the sine principle. All that is neces- sary to be done to make a measurement is as follows : Place the instrument so that the pointer points to some fixed mark on the scale ; is a convenient mark, but not a necessary one; then send any convenient current through the galvanometer, obtaining a deflection of, say, d. Turn the instrument until the pointer again points to the fixed mark on the scale. Stop the current, and observe through what angle D^ the needle comes back. D! will, of course, be larger than d. Now turn tfrft in- strument round, so that the pointer points to its original mark on the scale, for example, and repeat with a second current, obtaining in the same way deflections c? 2 , D 2 . Then the currents producing the deflections d and d z respectively with the galvanometer, are pro- portional to the sines of D^ and D 2 . 30. Calibrating a Galvanometer by the Sine Method. Fig. 20 shows an apparatus arranged for calibrating the galvanometer in this way. Three little blocks of wood, two only of which, c c, can be seen in the figure, are temporarily fixed so as to allow the galvanometer to be turned round without shifting its position, a precaution of practically no consequence if the controlling force be due to the earth's magnetism alone, but desirable if the whole or part of the controlling force is produced by a not very distant magnet. Of course the magnet must be so far away that neither the magnitude nor direction of its attraction on the suspended needle is altered by the Chap. II.] CALIBRATING BY THE SINE METHOD. 65 turning of the needle ; but this need not be very far, unless the needle employed is long, v is a vessel containing two zinc plates for adjusting the strength of the current in the manner described in a previous experiment, w is one of the wires leading to the current generator, and T is the terminal to which the other is attached. To calibrate a galvanometer by the employment of the sine principle, requires the current in each case to remain constant long enough for the instrument to be Fig. 20. turned round after the needle, until the two are in a fixed position relatively to one another. But when once the calibration curve has been drawn, a galvanometer so calibrated can, of course, be used to measure currents as transient as a galvanometer calibrated in any other way. "31. Calibration by the Sine Method of the Higher Parts of the Scale. If the first deflection is more than about 45 it is found impossible to use the sine principle in the ordinary way, because, on attempting to turn the coil after the deflected needle, so as to bring the fixed mark on the scale under the pointer, the needle moves so far round in advance of the coil that at last the 66 PRACTICAL ELECTRICITY. [Chap. II. attraction of the earth or other controlling magnet begins to assist the current instead of opposing it. The equilibrium then becomes unstable, and the needle swings right round. The cali- bration of the higher parts of the scale, however, may be effected by the sine method, by using currents which produce a first deflection of less than 4.5, in the following way : Select some other starting- point, say 40 on the scale, for the zero, that is, let the galvano- meter be turned, so that the pointer points to +40, when no current is flowing ; now send a current through the galvanometer, deflecting the pointer to, say, -|- 60 (Fig. 21). Next, turn the galvanometer round until the division, or whatever fixed mark was previously used in 29 and 30, comes under the pointer. Lastly, stop the current and let the pointer now take up a position 30 say; then, when the galvanometer is Fig. 21. placed in the ordi- nary position, so that the pointer points, say, to 0, when no current is passing, the current that will deflect the pointer to 60 will be sin.3p_x sin. 60 sin. (60 40] ' or, generally, the current that will deflect the pointer to any angle d will be sin. D Q xsin. d sin. (d 40) ' where D is the angle through which the pointer comes back on stopping the current After experiments have been made in the way described in 29 and 30, and a curve drawn with the values of d as ab- scissae, and of D as ordinates for values of d up to about 45, experiments may be made in the way just described, and the curve extended by using for the ordinates the values of sin. D x sin. d 40 ~ ' The reasoning of this extended method of calibration is as follows : From Fig. 19 we see that when a needle is controlled by Chap. IL] CALIBRATING BY THE SINK METHOD. 67 a uniform magnetic field, the moment of the controlling force * is pro- portional to P N, that is, to the sine of the angle through which the needle is deflected. If, then, a galvanometer is so placed that -the pointer points to when no current is passing, it follows that, in order that a current shall produce a deflection of rf, it must pro- duce a force whose moment is proportional to sin. d. When, however, the instrument is turned, as shown in Fig. 21, the cur- rent which is deflecting the needle to d produces a force whose moment is proportional to sin. (d 40). Now, what is the rela- tive strength of this current measured by the method described in 29 and 30 ? It is proportional to the sin. D. Hence, a current proportional to sin. D deflects the needle to d when the con- trolling force has a moment proportional to sin. (d 40). Con- sequently, a current proportional to sin. D x sin. d Q will deflect the pointer to d when the controlling force has a moment proportional to sin. d y that is, when the pointer points to when no current is passing. 32. Calibration by the Sine Method with a Con- stant Current. The following, due to Mr. Mather, is perhaps the neatest of the methods of calibrating a galvanometer on the sine principle, since, by means of it, the calibration can be effected throughout the whole range of the scale, and no other apparatus than the galvanometer to be calibrated, and a current generator, such as a " Darnell's cell," which will give fairly con- stant currents, is required. Send a current through the galvano- meter, such as will produce a deflection of about 30 when the galvanometer is so.placed that the pointer points to when no current is passing. \ ifext, without varying the current, turn the galvanometer until] t&e pointer points to about 35. Stop the current and observe the position taken up by the pointer when it comes to rest. Turn the galvanometer round farther and farther, and repeat, observing in each case the position of the pointer when the current is flowing, and the position the pointer takes up when the current has been broken. Also make a series of obser- vations with the galvanometer placed in such positions that the first deflection is less than 30. In some one position of the galvanometer let d be the angular deflection from when the current is flowing, and z when the current has been interrupted ; then it follows, from what was stated in 31, that this current, M hich we may call our unit current, passing round the galvano- * The "moment of a force about a point" is the product of the magnitude of the force into the length of the perpendicular let falJ from the point on the line representing the direction of the force. 68 PRACTICAL ELECTRICITY. [Chap. 1L meter coils, is able to produce a deflecting force whose moment is proportional to sin. (d -z} when the needle is deflected to d. Hence it follows that the current which would be necessary to produce a force whose moment should be proportional to sin. d for the same position of the needle must be - times our sin. (d z) unit current, that is, must be proportional to sin. d sin. (d z) ' but such a current would deflect the pointer to d when the galva- nometer was so placed that the pointer pointed to Q for no current passing. Hence, to obtain the calibration curve, we have simply to plot values of d Q for the abscissae, and the corresponding values of sin. d. sin. (d z) for the ordinates. 33. Method of Making a Sine Scale. Instead of find- ing in a table of sines the sines of the various angles through Fig. 22. which the needle swings back, we may construct a sine scale in the following way : On A p, Fig. 22, any tangent of the circle Chap. II.] MAKING A SINE SCALE. 69 on which the scale is to be made, mark off equal parts A B, B c, c D, &c. From B, c, D, &c., draw perpendiculars to A r, 1, c 2, D 3, &c., meeting the circle in 1, 2, 3, &c. Then the sines of the angles A o 1, A o 2, A o 3, i) or Vi t>g = If fi and/2 be measured in grammes, d in centimetres, and a in square centimetres, then reasoning in the same way, we obtain v/4-508 X 10-w X a Of course ^/f z ^/f-^ will be no larger than would have been the square root of the force of attraction if p and Q had been respectively connected simply, one with the fixed plate A, and the other with the movable plate and guard ring, and if the high potential of K had not been used ; but/, and / 2 , the two forces, will be each large, and can be accurately measured, and what is especially important, d will be large, and the error arising from want of perfect parallelism of the plates entirely eliminated. Another and simpler method of using the preceding apparatus consists in keeping the attractive force constant, and in varying, by means of a micrometer screw, the distance between the fixed and movable plates, so that this constant force (which must of course be known in grains or grammes) is exerted between the plates when the lower surface of the movable one is in the same plane as the lower surface of the guard ring. If then di and d? be the distances in centimetres respectively when the same force / in grains is produced when B is connected respectively with p and Q, A being connected with n, = 6-955 X 10-9 a 6-955 X 1\ which it. can lie eh-ct.ricji.lly Mlhiche.l to ;in\ oilier point of |. he stretched platinum wire \>\ nieMiisof the hindiiii^ screw H'. Ivx |>eriiiient, shown, lluil if I he scnsiltililv of the laji^Mif galvanometer is Kept uiicii.in-c,l ly the fuljiiNtin^ magnet, M not. beintf moved, of (lie l'lle,-|i,,u is dire.lly | m >p.n I IOII.M I I o I lie disi aiire \\ .. No\\, Ilic n i IMIUC of Ilir \MIT loiiimi", Llie coil of III.' l.'in^eiil ^silvniuniu-lcr is very ; M-(-M| compared \\illi lli.il of the In I. In . I pl.il ilium wire \\ \\ , lienee il follous (806 71, pftgO 127) thftt tho |>ol< nii.d diHcr< ( nc(> lcl \vccn (he points \\ :ind N' of Hie :;tr-t-ln'd wire is nnMlleel ed l>v I lie PICM-MCC of I lie ;;.'ll\ Milometer. ( 'oMHeijin'Mt l\ we in:i\ con. In. le lli.'il (he t.'in.-'Tiil of the delleet ion meaHures tlie polcnlinl diUciencc lh;i( would exist )>el \\cen the points W nnd .s if the ;;;il\:iiioineter were not present, lleiHM', \vlien :. eoiisl.int. current, is Mowing through M part icnl.'ir Chap, IV.] CONSTRUCTION OF RESISTANCE COILS. 145 wir<>, the potential dill'erence between two points is cliroctly proportional to tlin length of wire between lli<>:.<- two points, so tli;i.t potentia.l diU'erence divided by cur rent which we have defined :i,s the measure of resistance, is directly proportion.-).! to (lie length of wire. This experiment e;i,n he performed lor greater IriigiliH of wire by replacing the .stretched wire .shown in the l;i .1 li'-ure liy leir|hs; <>| the s.'i.HM' wire, wound lor con venienee round in a. screw ^roov<; turned on a wooden cylinder. l''i<^. 50 H!IOWK HU<;!I an arranj^enienl , consisting of six <-oils of iron wire of lengths, ; ;iy . r >, 10, L'O, IJO, 40, and - r )0 feet re:;peelively, all the win- hein^' drawn to have exactly the siinie dialiK'ter, say 0-()0!). r i incli. Krom uli;il li;i pree<'de<| it follows t!u,t, if distances A, o , etc. ^Fitf. r>7) ineaHunMl liori/ou tally from a point o, represent The resistance of a circuit from some fixed point, up to various points of the circuit, and if vrrti.-al distances op, A rinj in amper-es if tli<- -u- sistances a,re measurcrd in ohms, and the potentials in volt.s. 84. Construction of Coils; Multiples of the Ohm. We a,re now in a position, if we have a single wire having ono ohm rosiHtunco to Htart with, to construct, in the following way, by the Himple KiiliHiitiition metliod, coils having a resiHtanc<; of any numlier of ohms we ple.-i.se. Kirnt, make a Mscond coil having onoohrn roHistance, then 146 PRACTICAL ELECTRICITY. fCtap. IV. put these two ohm coils in series as in Fig. 54, page 140, when the resistance of the two will be, as we have seen, two ohms. Now make a single coil, having two ohms' resistance by comparison, then using this in series with one of the one-ohm coils, we shall have a resistance equal to three ohms, compared with which we can then make a single coil having three ohms' resistance, and so on. 85. Variation of Resistance with Sectional Area. For the purpose of testing experimentally how the resistance of a wire depends on its sectional area, which may be done by the simple substitution method, a board somewhat like that shown in Fig. 56 is employed, but having wires of exactly the same length (say twenty-one feet) and the same material (iron) wound round each of the cylinders. The sectional areas of these wires are how- ever different, being proportional to the squares of the diameters, which may be 0-0195, 0-0158, 0-0136, 0-0106, 0-009, 0-0078 of an inch. 86. Variation of Resistance with the Material. On the cylinders of a third board are wound wires of exactly the same length (say twenty-one feet), and drawn to have exactly the same diameter (say 0-012 of an inch), but made of the following materials : copper, platinum, brass, iron, lead, and German silver, from which the effect of difference of material can be ascertained. As in selecting a piece of wire there are three distinct things that have to be considered its length, its thickness, and the material of which it is made it is important that the change in the resistance pro- duced by a change in each of these three things should be separately measured ; and generally, in experi- menting, when it is possible to change several of the con- ditions under which tJie experiment is made, it is of the utmost importance that only one of the conditions should be varied at one time. The effect produced by the varia- tion of one condition should be fully inquired into before any one of the other conditions is in any way altered, otherwise it will be generally quite impossible after- Chap. IV.] TEMPERATURE VARIATION OF RESISTANCE. 147 wards to gather from the results what portion of the variation in the effect is produced by any particular change in the conditions. 87. Variation of Resistance with Temperature. We have already said that the resistance of a wire Fig. 58 depends on its temperature, and the apparatus shown in Fig. 58 is arranged especially for testing this. A coil of silk-covered iron wire is wound on a long, thin, hollow wooden bobbin, the top of which is seen at A. This bobbin is placed in a long thin glass tube, which itself is placed in water contained in the vessel v, the temperature of which can be raised by the Bunsen gas-burner B. s is the top of a piece of stout brass wire attached to a flat 148 PRACTICAL ELECTRICITY. [Chap. IV. piece of wood in the vessel v, and by means of which the water can be stirred up and its temperature made fairly uniform throughout. The temperature of the coil of wire is shown by the thermometer T, the bulb of which is inside the thin hollow wooden bobbin ; but as even with this arrangement there may be a difference of tem- perature between the wire and the thermometer b'llb, if the heating of the water is performed rapidly, it is better, before making a measurement of the resistance in the manner about to be described, to withdraw the Bunsen lamp, and wait a few minutes for the interior of the water-bath all to settle clown to a uniform tempera- ture, which is indicated by the two thermometers T inside the wooden bobbin, and T' in the water-bath out- side the bobbin indicating the same temperature. The double screen D D is for the purpose of preventing the heat radiated from the lamp warming the apparatus used for measuring the resistance, the action of which is based on the mode of measuring resistance shown in Fig. 52, page 137. From what was there said, it follows that if the currents flowing through A and B are equal, then the resistances of A and B are also equal. This equality of the currents might be ascertained from the deflections of two galvanometers placed in the circuits A and B, these deflections not being necessarily equal, but having values which the absolute calibration curves of the galvano- meters show to correspond with equal currents. This test could, however, more easily be made if, instead of using two separate galvanometers, a galvanometer were employed containing two distinct coils c, c' (Fig. 59), one placed in the circuit A, and the other in the circuit B, and if the positions of these coils relatively to a sus- }>endsd magnetic needle were so adjusted, that on equal currents passing through them their effects on this needle exactly balanced one another, so that the resultant deflection of the needle was nought. With such an ar- rangement a deflection nought of the needle would indicate that the resistances of the complete circuit A, including Chap. IV.] DIFFERENTIAL GALVANOMETER. 149 that of the coil c, was equal to the resistance of B, in- cluding that of the coil c'. Further, if these coils not only had equal and opposite effects on the needle when equal currents were passing through them, but had also equal resistances, then a deflection nought of the needle would indicate not merely that the resistances of the cir- cuits A and B, but also that the resistances of the re- mainders of the two circuits A and B, after excluding the resistances of the two coils c and c', were also equal. Hence, with the conditions of eqval magnetic effect and equal resistance of the two coils c and c', it follows that when there is no deflec- Fig. sr. tion of the galvanometer needle, the two wires, A and B, short or long, used to join the point P with the ends of the coils, have equal resistances. The instrument for measuring resistance, constructed on this principle, is called a " differential galvanometer" and such a galvanometer is seen to the left of Fig. 58. In the apparatus shown in Fig. 58, these two wires, A and B of Fig. 59, are our experimental coil of iron wire in the water-bath, and the wire in the resistance box R, hence, as the resistance of the wire in the water-bath varies by being warmed, we can, by varying the resistance in R so as to always obtain no deflection of the needle of the differential galvanometer, measure the change of re- sistance produced by the variation of temperature. 88. Construction of a Differential Galvanometer. The actual way in which the two conditions, equality of magnetic effects, and equality of resistance of the wires of the two coils of the differential galvanometer are fulfilled, is as follows : Two reels of silk-covered copper wire are chosen, so that the diameter of the 150 PRACTICAL ELECTRICITY. [Chap. IV wire on each is as nearly as possible the same, and the two wires are wound side by side on the galva- nometer bobbin until it is nearly full; the wires are then tested and cut, so that the resistance, but not of course necessarily the length, of each wire is the same. A current is now sent in opposite directions through the two coils in series, when it will be found that, although the wires have been wound on side by side, one of them will have a greater magnetic effect than the other, partly perhaps because, being a trifle thicker, it has to be longer than the other, so as to have the same resistance, or partly because it is, on the whole, nearer the suspended needle than the other. To remedy this, a small portion of the wire having the greater magnetic effect is un- wound, and without being cut, which would of course destroy the equality of the resistances of the two coils, the portion so unwound is coiled up out of the way in the base of the instrument. In this way, by unwinding more or less from the coil that was magnetically the more powerful, a very good balance can be obtained. In the use of differential galvanometers in which the needle is suspended by a silk fibre (as, for example, it is in Fig. 58, where the silk fibre is inside the tube t), a final and most delicate adjustment can be obtained by raising or lowering one of the levelling screws s s slightly, so as to tilt the needle nearer to or farther from one of the coils. And the spirit-level L should then be permanently adjusted so that the bubble is in the centre of the glass cover of the level, after the instrument has been tilted in the manner just described. The plugs p 3 , P 4 , seen in the figure, are for the purpose of enabling the two coils of this differential galvanometer, which is known as Latimer Clark's differential galvanometer, to be joined so as to oppose one another's effect, or to assist one another when it is desired to use the instrument as an ordinary galvanometer instead of a differential one, and the plugs p 1 , p 2 are for the purpose of shunting either coil of the differential galvanometer (see 107, page 185). Chiip. IV.] PLUG RESISTANCE BOXES. 151 89. Construction of Plug Resistance Boxes. The general construction of a resistance box was explained in 12, page 28 ; but in the one shown in Fig. 58, the coils used to connect the various pieces of brass on the top of the box are not equal, but may conveniently have the following values going round them consecutively, starting from one of the binding screws : 0-1, 0-2, 0-2, 0-5, 1, 2, 4, 10, 20 ohms. There is also an " infinity plug " that is, two of the pieces of brass are not connected by a coil at all. Hence, if wo take out the first and second plugs, the rest being left in, the resistance in the box will be O'l -|- 0*2 or 0*3 ohms ; if we take out the first and fourth, replacing the second, it will be 0-1 + 0-5 or 0'6 ohms, 35 0-02620 Gold, hard drawn . . 0-5884 12-60 0-4104 0-02668 Iron, annealed . 1-085 58-45 0-7570 0-1237 Tin, pressed .... 1-380 79-47 0-9632 0-1682 Gold-silver alloy (2 oz. gold, 1 oz. silver), hard, or annealed . 2-364 65-37 1 -650 0-1384 German silver, hard, or annealed . . . 2-622 125-91 1 -830 0-2666 Platinum, annealed . 2-779 54-49 1-938 0-1153 Lead, pressed . . . 3-200 2-232 0-2498 Antimony, pressed 3-418 213-6 2-384 4521 Platinum-silver (1 oz. platinum, 2 oz. sil- ver), hard, or an- nealed 4-197 146-70 2-924 0-3106 Bismuth, pressed . . 18-44 789-3 12-88 1-670 JMercury 18-51 572-3 12-91 1-211 From this we see that of the metals aluminium, has the least resistance for a given length and weight, and mercury the greatest ; whereas we saw from Table No. I, page 154, that for a given length and sectional area it was annealed silver that had the least resistance, and bismuth the greatest. 158 PRACTICAL ELECTRICITY. [Chap. IV. Example 30 What will be the weight of an iron wire 100 yards long, having a resistance of 1 ohm at 0C. ? An iron wire 1 ft. long weighing 1 grain has 1*085 ohms at C., therefore an iron wire x ft. long weighing x grs. has & X 1 -085 ohms at 0. Hence an iron wire iC 2 x ft. long weighing y grs. has x 1 '085 ohms at C. In the question as is 300, and the resistance is 1 ohm. Therefore .-. y 3002 x 1-085 grs. Answer. 13 Ibs. 15 oz. Example 31. What will be the length of a platinum wire weighing 2*8 grains, and having a resistance of 0-7891 ohms at 250 C. ? Answer. 7J inches. Example 32. Which has the greater resistance, a copper wire 20 feet long 0-015 inch in diameter, or a platinum-silver wire 10 feet long 0;037 inch in diameter, at C. 1 The resistance of the copper wire will be to that of 20 x 9-612 . 10 x 146-7 the platinum as - - is to - - , and as this ratio is 0'7973, it follows that the former has rather more than three-quarters of the resistance of the latter. Example 33. What will be the resistance, at 95C., of a copper wire 20 metres long weighing 12 grammes, and having 92 per cent, of the conductivity of pure copper? Answer. 7'092 ohms. 93. Comparison of Electric and Heat Conductivi- ties. The reciprocals of the numbers given in column 4 of Table No. I. will express the relative electric con- ductivities of the metals for the same length and sec- tional area. These numbers are given in column 2 of Chap. IV.] ELECTRIC AND HEAT CONDUCTIVITIES. 159 Table No. III. On comparing these with the conductivi- ties of the metals for heat for the same length and sec- tional area as given in column 3 of Table No. III., and which are the numbers obtained by Wiedemann and Franz, we observe that the metals arrange themselves approxi- mately, but not absolutely, in the same order for the two conductivities. TABLE No. III. Relative Conductivities per Cubic Unit. Name of Metal. Electric. Heat. 100 100 94-1 74-8 Gold 73 54-8 16-6 9-4 15-5 10-1 Tin, pressed 11-4 15-4 Lead 7'6 7-9 Bismuth 1-1 1-8 As we experiment with worse and worse conductors, we find that the electric conductivity diminishes much more rapidly than the heat conductivity. For example, the electric conductivity of copper is about 10 20 times the conductivity of vulcanised indiarubber, whereas the heat conductivity of copper is only about 10 1 times that of vulcanised indiarubber. Hence, while we can obtain in- sulators for electricity, or bodies which relatively to the metals do not practically conduct electricity at all, insula- tors for heat are unknown. 94. Material Used in Resistance Coils. We see then that it is not merely sufficient to know the length and diameter of a wire as well as the material of which it is made, but we must know also the temperature of the wire if we wish to be sure about its resistance. Fixity of length, diameter, and material, are easy enough to obtain, but constancy of temperature it is much more difficult to secure, partly on account of changes of temperature of the room, and partly on account of the slight heating of 160 PRACTICAL ELECTRICITY. [Chap. IV. a coil of wire produced by a current passing through it Consequently, in the construction of resistance coils it is important to use a metal of which the resistance changes as little as possible with temperature, and which is not too costly. To ascertain what that metal was, Dr. Matthies- sen, in 1862 and 1863 that is, in the early days of re- sistance coils made, on behalf of the Electrical Standards Committee of the British Association, a large number of very accurate experiments on the change of resist- ance with temperature, and a few of his results are contained in the following table. TABLE No. IV. APPROXIMATE PERCENTAGE VARIATION IN RESISTANCE PER 1 0. AT ABOUT 20 C. Platinum-silver alloy (I oz. platinum, 2 oz. silver), hard, or annealed . . . 0-031 German silver, hard, or annealed . . . 0-044 Gold-silver alloy (2 oz. gold, 1 oz. silver), hard, or annealed 0-065 Mercury 0-072 Bismuth, pressed ...... 0-354 Gold, annealed ) Zinc, pressed . . . . . . 0*365 Tin, pressed ) Silver, annealed 0'377 Lead, pressed ...... 0-387 Copper, annealed 0-388 Antimony 0-389 Iron about 0'5 From this we see that, whereas (of the substances ex- perimented on by Dr. Matthiessen) an alloy of platinum- silver , hard or annealed, is the one of which the re- sistance changes least by temperature, German silver, which is a very much cheaper alloy, is nearly as good in this respect. Hence, nearly all resistance coils are made of German silver, except when greater lightness and port- ability are required, in which case the alloy of one part of platinum and two of silver by weight is employed. A new alloy, called "platinoid" consisting of German Chap. IV.] MATERIAL FOR RESISTANCE COILS. 161 silver, with one or two per cent, of metallic tungsten added, has been recently found by Mr. J. Bottomley to have a resistance per cubic centimetre of about 34 mi- crohms, or about 60 per cent, higher than that possessed Fig. 60. by German silver ; and, what is still more important, its percentage variation of resistance per 1 C. is only about 0-021, or less than half that of German silver. We may, therefore, expect that platinoid will supersede both Ger- man silver and platinum- silver for resistance coils, if 1 62 PRACTICAL ELECTRICITY. fChap. IV. its resistance be found to be equally unchanged by lapse of time. Iron, we ses, is the worst of the substances shown in the table to be used in the construction of resistance coils, as far as the temperature error is concerned ; but it is not umrequeiitly used when cheap resistance coils are required for large currents, and when, as sometimes is the case, great constancy of resistance is not necessary. The resistance coil, when used as an accurate standard, is wound inside a brass box B, shown in Fig. 60, so that it may be inserted in a vessel of water v v, and its temperature accurately noted by means of the thermo- meter t. The brass box B for holding the coil is made cylindrical inside and outside, with a large diameter and small thickness, so as to expose as much surface as possible to the water, in order that the coil inside may acquire the temperature of the water as quickly as pos- sible ; and the vessel v v containing the water may with advantage have double sides, with an air-space between them, as seen in the figure, to prevent transference of heat between the water and outside space. The tubes TT are to prevent the coils being short circuited by water getting through the holes, by which the rods w w attached to the ends of the resistance coil are brought out. These tubes are made of brass, but they are lined with tubes of ebonite to prevent electric contact between these brass tubes and the rods w w. Electric connection with these rods is made by dipping their ends E E into little wooden cups containing mercury. Example 34. At what temperature, approximately, would a German silver coil, which had one British Asso- ciation unit of resistance at 16C., have the resistance of one legal ohm ? 1 legal ohm = 1*0112 B. A. units, therefore the temperature must be raised sufficiently to increase the resistance of the coil by 1-12 per cent. Therefore, since the resistance of German silver increases Chap. IV.] MODE OF WINDING RESISTANCE COILS. 163 0*044 per cent per degree, as stated in the last table, if t be the temperature above 16 to which the coil must be raised, 0-044 x t= 1-12, or t = 25 0< 5 approximately. Answer. The B.A. coil will have a resistance of one legal ohm at 41-5 C. Example 35. A set of resistance coils made of plati- num-silver are correct at 14C. Between what limits of temperature approximately may they be used without correcting the results, if the temperature error is not to exceed | per cent. 1 The resistance of platinum-silver increases about 0-031 per cent, per 1 0., as stated in the last table; therefore, if t be the number of degrees above or below 140., within which the coils may be used without the error exceeding per cent., 0-031 x t = 0-25, . . t = 8. Answer. The limits of temperature are approxi- mately 6 and 22 C. 1'xample 36. If the greatest change of temperature at some particular place between summer and winter is from 8 to 25 C. in the shade, what is the greatest per- centage variation in the resistance of a set of German silver coils ? Answer. 1*45 per cent, approximately. Example 37. At what temperature would a metre of mercury one square millimetre in section have one ohm resistance 1 Answer. 83-3 C. 95. Mode of Winding Resistance Coils. Not only must a special metal be employed in making resistance coils, but the wire must not be wound on the bobbin in the ordinary way. If it were wound on the bobbin as cotton is on a reel, then each bobbin in a resistance box would act as a magnet when a current passed through 164 PRACTICAL ELECTRICITY. fChap. IV. it. and a box full of electro-magnets would be a most inconvenient thing to have near a delicate galvanometer used in testing resistances, since one would be constantly in doubt as to whether the deflection observed on putting on the current was due to want of adjustment in the resistance, or to the temporary magnetisation of the adjacent resistance box. Hence, the wire of a resistance coil is wound back on itself as shown in Fig. 7, page 28, so that the current, in passing through the wire, first goes several times round the bobbin in one direction, and then an equal number of times in the opposite direction, and the two magnetic effects neutralise one another. The disturbing magnetic effect that might otherwise have arisen when using resistance coils, is overcome by this double mode of winding ; but the magnetic action of a current passing round an ordinary reel of wire, or a coil wound for a galvanometer or for an electromagnet, &c., must be carefully taken into consideration when anything of this form has to be tested for resistance. As such coils are frequently wound before being tested, they must, when it is desired to test them, be placed so far away from the galvanometer that the mere passage of the current round the coil produces by itself no deflection of the galvanometer needle, when no current is allowed to pass through the galvanometer. 96. Calibrating a Galvanometer by Using Known Resistances. From Ohm's law ( 74, page 130), it follows that the current passing through any circuit is inversely proportional to its resistance if a constant potential difference be maintained at the ends of the circuit. Con- sequently if a constant potential difference be maintained at the terminals T T (one only of which is seen in Fig. 61) of the circuit, consisting of the key K, the detector D, and the resistance box R, the current passing through the detector will be inversely proportional to the sum of the resistances of the key, detector, and resistance box. Such a constant potential difference can be maintained, as will be seen in 139, page 261, by attaching to the terminals TT Chap. IV.] CALIBRATING BY USING KNOWN RESISTANCES. 165 an accumulator or any galvanic cell, the resistance of which is small compared with the rest of the resistance in the circuit. To perform the calibration, it is, perhaps, best to first employ such a resistance in the box R that the deflection on the detector is about 10 ; let this be r lt and let the Fig. 61. galvanometer resistance be g, and let the deflection be d ^ Next employ a resistance r. 2 , such that r. 2 + 9 = i (n 4- g), or r^ \r^-\g, then the current will be doubled since the resistance of the key K is practically nought, if the platinum contact points be cleaned by inserting a piece of paper between them, tJien pressing them together, and pulling out the paper with the points pressed together. (Emery paper should not be used as it rubs away the platinum, and 166 PRACTICAL ELECTRICITY. [Chap. IV. less should the contacts be scraped with a knife or a file.) Let the deflection, with this value of r 2 , be d f Next employ a resistance r 3 , such that or r 3 =r 1 -fy, then the current will be trebled. Let this produce a deflection of d s , &c. In this way a series of deflections will be obtained, corresponding with currents propor- tional to 1, 2, 3, 4, &c., and a relative calibration curve can be drawn in the way already described. THE WHEATSTONE BRIDGE. 97. Wheatstone's Bridge. The differential galvano- meter, in its simple form, is a very convenient apparatus 16 Fig. 62. for testing the equality of two resistances, but there is a still better method for accurately and rapidly comparing any two resistances, which was originally devised by Mr. Christie, and brought into public notice by the late Sir Charles Wheatstone, and hence has been called a "Wheatstone's bridge," or a " Wheatstone's balance" The principle of the Wheatstone's bridge is seen from Fig. 62, and is as follows : In passing from p to Q, either along the wire P s Q, or along P T Q, there are points having all potentials between the potential of P and that of Q, therefore it follows that for every point in the circuit p s Q, there must be a point on the circuit P T Q, having the same potential. Let s and T be two such points ; then, if they were joined with a galvanometer, no current char- iv.] WHEATS-TONE'S BRIDGE. 167 would flow through it, or if joined to the opposite quarter cylinders of the electrometer described in 75, page 130, there would be no deflection. Let A be the current flowing along p s, and which also must be the current flowing along s Q, since no current passes through the galvanometer, and B the current flowing along P T Q, and let a, 6, c, d be the resistances respectively of P s, s Q, p T, T Q ; then, since the potential difference between P and s is the same as the potential difference between P and T, A a = B c. Similarly, since the potential difference between s and q is the same as the potential difference between T and Q, Therefore, combining these two equations, we have a _ c l~T which is the law of the Wheatstone's bridge. The last equation may be written in the form a _ b_ c ~~ d ' and this is the equation that we should have obtained for no current through the galvanometer, had its terminals joined P and Q, and the current generator been placed between s and T. Hence when balance is obtained with a Wheatstone's bridge, the balance will not be disturbed by interchanging the galvanometer and battery. In order, then, to tell the value of one of the resist- ances, say a, by the Wheatstone's bridge method, we must know the value of either of the adjacent ones, say 6, in ohms, and the ratio only of the other two, say c and d. Hence one mode of using the bridge to measure the resist- ance of a is to keep the ratio of c to c? constant, and simply vary the resistance of b until no current passes through the galvanometer. Another method consists in keeping b 168 PRACTICAL ELECTRICITY. [Chap. IV. constant, and varying the ratio of c to d. For example, the resistances c and d may be the resistances of different lengths of the same kind of wire, in which case we know that c will be to d simply as the ratio of these lengths, whatever be the absolute resistance in ohms of the two parts. A form of Wheatstone's bridge, in which P T Q, of Fig. 62, was one piece of stretched wire, and the ratio of c to d varied by moving the connection of the wire lead- ing to one terminal of the galvanometer, was originally employed by the Electrical Committee of the British Association, and is, for this reason, sometimes called the British Association bridge ; at other times, the " metre bridge," from the stretched wire being a metre long. The wire may be made of platinum, or bettor still, of platinum- iridium, which, being very hard, prevents the wire being worn at any part. A convenient form of metre bridge is shown in Fig. 63. It has three stretched wires w w, each a metre in length, and so arranged that either one of them alone, or two of them in series, or all three in series, can be made use of to form the two sides c and d of the Wheatstone's bridge (Fig. 62). When the plug E is, as in the figure, placed in the hole H, the current simply passes through the stretched wire which is nearest to the observer. If on the other hand the plug E be put in the hole h, then, since the brass plate P is permanently connected with the plate p by a thick copper strip under the base of the instrument, the middle stretched wire is short-circuited, and the wire nearest to the observer is in series with the one farthest from him. Lastly, if the plug be removed altogether the three wires are in series. The object of thus lengthening the wire is to increase the sensibility of the test when desired, and a still further increase in the sensibility can be effected by removing the short-circuit pieces s, S 2 , and inserting coils of known re- sistance in place of them. For example, suppose that the ratio of the unknown to the known resistance be f , then the slide K must be placed so as to divide the stretched Chap. IV,] METRE BRIDGE. 169 wire into two parts having this ratio. Hence, if one of the three wires only be used, the lengths of the two parts which will give exact balance will be 60 and 40 centi- metres, and an error of 1 centimetre in the position of 170 PRACTICAL ELECTRICITY. (Chap. IT- the slider will correspond with an error in the determine tion of the ratio of Jli. - 39 40 X 100 per cent., or 4 per cent 1-5 If, on the other hand, the three wires in series be em- ployed, then the lengths into which the three metres of wire must be divided to obtain exact balance will be 1 80 and 120 centimetres, and an error of one centimetre in the position of the slider will correspond with an error in the determination of the ratio of 181 180 100 percent., or 1-4 per cent 1-5 If now two coils, each having a resistance equal to, say, 1,000 centimetres of the stretched wire be inserted in place of the short circuit pieces s } and s 2 , an error of a centimetre in the position of the slider will only corre- spond with an error of 1381 1380 1 *5 x 100 per cent, or 0-18 per cent Contact between the platinum -tipped knife-edge k and one or other of the stretched wires, is produced by depressing the knob K, which causes the lever to which this knife-edge is attached to turn on an axis A A. On removing the pressure, the lever is pressed up by a spring underneath it , and the slider should never be moved with the knife-edge k depressed, as this would scrape the stretched wire and alter its diameter. In order to enable k to make contact with either the first, second, or third wire, the knob K is not fastened rigidly to the lever, but can slide along it in a slot, and can be so placed that the near end of the spring S rests in either of the three Chap. IV.] SENSIBILITY OF THE WIIEATSTONE'S BRIDGE. 171 grooves on the top of the lever corresponding with the three positions of k when it is in contact with the three stretched wires respectively. 98. Superiority of the Wheatstone's Bridge over the Differential Galvanometer, and Conditions affecting the Sensibility of the Bridge. The Wlieatstone's bridge is superior to the differential galvanometer, in that not merely can two resistances be ascertained to be equal to one another, but the value of any resistance in terms of another can be exactly measured, so that if we possess one single resistance the value of which is known exactly in ohms, we can, without knowing the resistance of any other wire, measure, by means of the metre bridge, the value in ohms and fractions of an ohm of any unknown resistance. Practically, however, the sensibility of the bridge is limited by the galvanometer not being sensitive enough to indicate the small current that passes through it when the ratio of a to b is not quite equal to that of c to d (Fig. 62, page 166), and when both ratios are far from unity. In fact it can be shown that the bridge is most sensitive when all the four resistances, a, b, c, d, are equal to one another. If, however, it is impossible to make them equal, then it is desirable to consider whether the galvanometer or the battery (see 129, page 226) have the higher resistance, because greater sensibility will be obtained by using the one that has the higher resist- ance to connect the junction of the two greater of a, b, c, d, with the junction of the two less, than if the galvanometer and battery be joined up in the opposite way. For example, if a = 1 ohm b = 100 ohms c = 4 ohms d = 400 ohms, and the resistances of the galvanometer and battery be 37 ohms and 5 ohms respectively, one terminal of the galvanometer ought to be connected with the junction of a and c, and the other with the junction of b and d. (See also 238, page 467.) Further, it is important to consider whether we should select a galvanometer wound with fine wire or one wound with thick wire, in order to obtain the most accurate measurements with a Wheat- stone's bridge. Calculation and experiment show that if nothing but the gauge of wire used in winding the bobbins of the galvano- meter be varied, that is to say, if the bobbins and the space on them occupied by the covered wire remain the same, as well as 172 PRACTICAL ELECTRICITY. [Chap. TV. the strength and direction of the controlling field and the suspen- sion of the galvanometer, then with a given testing battery, and with given values of the four " arms " of the bridge, a, b, c, d y the greatest deflection will be produced on a galvanometer on making a definite change in one of the four arms, say a, if the wire wound on the galvanometer bobbin be such that the resistance of the galvanometer equals the product of the sum of the resistances of the two arms on one side of it into the sum of the resistances of the two arms on the other side of it, divided by the sum of the resistances of the four arms. For example, if the galvanometer connect the junction of a and c with the junction of b and d, the wire used in winding the galvanometer bobbins ought to be selected of such a thickness that the galvanometer when wound has a resistance of (a + b} (c + d) a + b + c + d ' Of course this does not mean that a roughly-made pivot galva- nometer having this resistance will give better results than a delicate fibre-suspended reflecting galvanometer with a much greater or a much less resistance. The formula can only be used on the assumption that nothing but the gauge of wire employed in winding the galvanometer can be varied. (See 237, page 466.) 99. Commercial Form of Wheatstone's Bridge. In the Wheatstone bridges, as commonly constructed, the resistances of all three branches are made up of coils, the values of which are known in ohms, and the apparatus is frequently made of the form shown in Fig. 64, where the c and d of Fig. 62 are each replaced by three coils of 10, 100, and 1,000 ohms, called the "pro- portional coils" and the b of Fig. 62 is made up of the following coils, 1, 2, 2, 5, 10, 10, 20, 50, 100, 100, 200, 500, 1,000, 1,000, 2,000, 5,000. With these latter six- teen coils, any integral resistance between 1 and 10,000 may be formed, and this special arrangement, although not requiring the least number of coils to enable any resistance between 1 and 10,000 to be obtained, is found in practice to be the most convenient. With this bridge, then, we can measure any resistance between 1 ^g X 1, or yyyth of an ohm, and ^yj^ X 10,000, or one million one hundred and ten thousand ohms. In Fig. 64, the battery seen at the left-hand side is indicated symbolically by three thin lines, which stand Chap. IV-] COMMERCIAL FORM OF WHEATSTOXE'S BRIDGE. 173 for the copper plates, and by three shorter and thicker lines, which stand for the zinc plates or rods. The cells are understood to be coupled by the zinc plate, or rod, of the upper cell being joined to the copper plate of the second, and the zinc plate of the second to the copper plate of the third ; so that the six lines in Fig. 64 are a symbolical representation of the battery shown in the next figure (Fig. 65). This symbolical representation, Fig. 64. which is commonly used to stand for a battery, will be employed in the rest of this book, and will be found still further explained in 135, page 240. The resistance coils sold in boxes are always made so that the resistance of each is an exact number of ohms or certain special fraction of an ohm at the same temperature, which is specified on the box, and the trouble of adjusting a number of coils to fulfil this con- dition causes resistance boxes to be rather costly. It is undoubtedly more convenient that the resistance of each coil should be an exact number of ohms or a certain 174 PRACTICAL ELECTRICITY. [Chap. IV. special fraction, but it would >>e far cheaper if the coils were made approximately to have the resistance 1, 2, 5 ohms, &c., and their actual resistances in ohms and frac- tions of an ohm, when tested at some one temperature, were marked on the box. 100. Bridge Key. In using a Wheatstone's bridge it is desirable to send the current through the four arms of tho bridge a, b, c, d (Fig. 62), before it is allowed to pass through the galvanometer, and this is especially impor- tant when testing the resistance of the copper con- ductor of a long submarine cable, since the current in sitch a case takes an appreciable time to reach its maximum value and become steady, due to the cable acting as a "condenser" (see 162, page 301). Hence, if the galva- nometer circuit were completed when the battery was attached to the bridge, an instantaneous swing of the galvanometer would be produced, even if a bore to b the ratio of c to d. And although, since the ratio of re- sistances having been effected, the deflection of the galva- nometer would become nought as soon as the current in the four branches of tlie bridge became steady, great delay in the testing would be caused by this first swing of the needle. A similar difficulty would occur in measuring the resistance of an electromagnet or even of any coil without an iron core, if it were not wound doubly as are the coils in resistance boxes (see Fig. 7, page 28) ; because whenever a coil is so wound that a current pass- ing through it produces magnetic action, a short interval of time has to elapse, after putting on the battery, before the current reaches its maximum, or steady, value, arising from what is called the " self-induction " of the coil. A key for sending the current through the four arms of the bridge before it is . allowed to pass through the galvanometer, is shown at K (Fig. 65), and is a modification of the one originally employed by the Elec- trical Committee of the British Association. On press- ing down the button, contact is first made between the flexible piece of brass A and the flexible piece of brass B. Chap. IV.] BRIDGE KEY. 175 This completes the battery circuit, and causes the cur- rent to flow through the four arms of the bridge shown symbolically in Fig. 65 by the spiral lines. On the button being still further pressed down, B is brought into contact with a little knob of ebonite E on the top of the flexible piece of brass c. This does not complete Fig. bo. any other electric circuit ; but on the button being still further depressed, c is brought into contact with D, and the galvanometer circuit is completed. This form of key is to be preferred to the ordinary bridge key, because all the connections are above the base of the key and in sight, whereas when the connec- tions are made under the base, it frequently happens that the pieces of guttapercha-covered wire used to make the connections are either badly insulated, or are loosely connected at their ends with the terminals of the key, and so introduce unnecessary resistance. 176 PRACTICAL ELECTRICITY. [Chap. IV. 101. Use of a Shunt with the Bridge. It is desirable to employ also another key k (Fig. 65), which may be quite simply made of a twisted bit of hard brass wire, bent so as to press up against a sort of bridge of hard brass wire, since the resistance at the contact is in this case of no consequence. When the key is not depressed, a portion of the current is shunted past the galvanometer through any convenient shunt s, the resistance of which need not be known, as it does not enter into the calcula- tions. The object of this shunt is merely to diminish the sensibility of the galvanometer when the first approxi- mation is being made to the value of the unknown re- sistance. As soon as this has been done the key k should be depressed, and all the current in the galvanometer circuit arising from want of perfect balance allowed to pass through the galvanometer itself, and the resistances adjusted until perfect balance is obtained. Another de- vice to expedite the testing, and also to prevent power- ful currents being sent through the galvanometer, consists in not holding the key K down when the first rough approximation is being made, but merely giving it a tap, which has the effect, when the balance is far from perfect, of giving the needle of the galvanometer a slight impulse to one side or the other, according as the ratio of a to b is larger or smaller than that of c to d, instead of causing the needle to violently swing against the stops on one side or the other as it would do if the key K were held down before balance was arrived at. 102. Meaning of the Deflection on a Bridge Galva- nometer. A considerable amount of time will be saved in testing if the meaning of a. deflection of the galvano- meter needle, say to the right, be once for all definitely ascertained, and a note be made whether it means that the ratio of a to b is too large or too small. The simplest way of recording this, if we assume, for example, a to be the unknown resistance, is to put the words " in- crease b " and " diminish b " one on each side of the gal- vanometer, these being the directions to he followed Chap. IV.] SHUNTS. 177 according as the needle deflects towards one or other of them. The position of these two directions must, of course, be reversed if the terminals of the testing battery be reversed. SHUNTS. 103. Shunts. We have already seen, for example, in the apparatus shown in Fig. 17, page 59, and again when using a Wheatstone's bridge ( 101, page 176), that it is sometimes convenient to use a wire as a by-path or shunt to convey a portion of the current, the remainder only passing through the galvanometer. We will now consider what must be the relative resistances of the shunt and galvanometer to allow any particular fraction of the whole current to pass through the galvanometer. Let s, g be the resistances in ohms of the shunt and galvanometer, and S, G the currents in amperes passing through them respectively ; then, if Y be the potential difference in volts at the terminals of the shunt and galvanometer, it fol- lows from Ohm's law ( 74, page 130) that ' 0,-, or the current strengths in the galvanometer and shunt are inversely as their resistances. Also, by a well-known rule in proportion, it follows that G s S + G ~~ s + g and S but S -)- G is the sum of the currents flowing through the M 178 PRACTICAL ELECTRICITY. [Chap. IV. shunt and the galvanometer respectively, and therefore is equal to the whole current in the circuit, A amperes say, hence G_ __ s_ A ~ s + 9 and S g A = s + g 104. Multiplying Power of a Shunt. Since s the fraction -- is frequently called the " multiplying power of the shunt," that is, the quantity that the cur- rent flowing through the galvanometer must be multiplied by to obtain the total current. As an example of the last equation, let us suppose that we desire that G shall be one-tenth of A, then s 1 * + 9 10' or *=-!<,; or, again, if we wish that G shall be one-thousandth of A, then s 1 105. Combined Resistance. It would be, of course, possible to substitute for the two resistances s and V the current flowing through s . . = * V the current flowing through g . . = + y> or if two wires be in parallel,, them tke pvodkiet of their resistances divided by their sum represents tlae resistance of a single wire through which a current will pass, equal to the sum of the currents passing through the two wires, for the same potential difference. Such a single resistance is called the "combined resistance," or the "parallel resistance" of the two. From what has preceded we see that when G is a tenth of A, --- - *+g~ 10 s " or the combined resistance of the shunt and galvanometer is one-tenth of the resistance of the galvanometer. In the same way, if there be any number of resistances a, >, c, d, 44-25 A* r. In fact, 44-25 A 2 r foot-pounds per minute represents the portion of the energy that is turned into heat, and the difference represents the amount of electric energy, measured in foot-pounds per minute, that is transformed into some form of energy other than heat. ELECTROMOTIVE FORCE. 115. Work done by a Current Generator. Electro- motive Force. In order that a given amount of work may be done on the external circuit, a greater amount of work must be done by the generator itself, on account of Chap. IV. | ELECTROMOTIVE FORCE. 203 the resistance of the generator against which the current has to be sent, just as a pump has to do more work than the energy stored up in the water. Consequently, if b be the resistance of the generator in ohms, 44-25 A^ 6 foot-pounds per minute must be expended in sending the current through the generator itself, and, consequently, the total work done by the generator in foot-pounds pel minute equals 44-25 A* (r + b). Now if v be the potential difference, that would send che current A amperes through b ohms, or A 2 b = A v. Hence the total work done by the generator equals 44-25 A (V -f v) foot-pounds per minute. Further, we know that when a current passes through a voltameter, the amount of chemical action that is pro- duced in a given time is proportional to the current ; indeed, it was the amount of chemical action per minute that gave us our original definition of current strength. And a galvanic battery is but a form of voltameter, hence we may conclude that the amount of each of the various chemical actions that take place in a battery in a given time is proportional to the current, if no action takes place when no current is passing, a condition that is approximately fulfilled in a good galvanic battery. Also we know that the amount of chemical action that takes place in a given time in a battery represents the amount of fuel burnt in that time, and therefore is proportional to the total amount of work done by the battery in the same time. The total work, therefore, done by the battery per minute is proportional to A ; but we have seen that it is also proportional to A (V+v), consequently, V+v must be a constant for a 204 PRACTICAL ELECTRICITY. [Chap. IV. particular battery. This constant is called tlie " electro- motive force" and is shortly represented by the letters " E. M. F." If the current passing through the battery is very large its chemical constitution changes somewhat, so that the same current passing througli it for the same time does not produce the same chemical decomposition as before ; hence the work now done, compared with the work previously done, ceases to be in the ratio of the present value of the current to the former value, or, in other words, V-f- v or the E. M. F. is no longer constant. However, excluding such extreme cases, we can say that the current E or A = Hence V = -^-, E, if E stands for the electromotive force of the battery. 116. Variation of External Resistance, Current, and Potential Difference at the Battery Terminals. When r, the external resistance, is extremely great compared with 6, and the current, as seen from the third equation above, is very small, V, the " terminal potential difference" is, as seen from the last equation, a maximum, and becomes equal to E. And as long as r is fairly large in comparison with 6, the current remains small, and V remains nearly equal to E. When r diminishes so as to become small compared with 6, A increases rapidly, until when r is nought A becomes a maximum, and equals . V, then, is nought. Ohap. IV.J TERMINAL POTENTIAL DIFFERENCE. 205 The preceding is all given concisely in the following table : r y A Infinity. E Great compared with b. Very little less than E. Small. p, say -.2. .. E E Small compared with b. Small. Great. 0. 0. Maximum, and E equal to b The apparatus shown in Fig. 74, consisting of battery B, a delicate ammeter A, a voltmeter Y, and a variable re- sistance R, enables all the preced- ing to be tried experimentally. First, make R equal to "in- finity, then the reading on the voltmeter gives E. Secondly, make R have any suitable value, so that the cur- rent can be easily read accurately 011 the ammeter; let it be A. amperes, and the corresponding potential difference at the terminals of the battery Y volts ; then, Y = E - A b, where b is the battery resistance ; , E-Y b = ohms. Fig. 74. 206 PRACTICAL ELECTRICITY. [Chap IV The resistance of the battery can in this way be determined without knowing r the value of R, that is, without employing resistance coils of known value, and this is the best method of measuring the resistance of a current generator when the resistance is very small, as in the case of an " accumulator." Thirdly, take various values of r, and see whether the E current always equals amperes, and the terminal r -f- 6 potential difference E A b volts. As a rough analogy, the terminal potential difference of a battery may be likened to the force exerted by a locomotive engine in dragging the carriages, which is, of course, equal to the pull on the coupling connecting the engine with the first carriage, while the current strength may be likened to the speed of the tram, and the external resistance to the mass of the carriages composing the train. If the train be long and heavy, corresponding with a great external resistance, the pull exerted by the engine is great, but the speed of the train is slow. Whereas if there be only a few carriages the pull is less but the speed is greater, and in the extreme case, when the engine is running alone the pull exerted on the coupling, which is now hanging loose, is nought, and the speed of the train is the greatest. Also the pull exerted by the engine on the first carriage is always less than the total force exerted by the engine, unless the engine is attempting to pull so heavy a train that it does not move, corresponding with infinite external resistance and cur- rent nought, because if the engine is moving at all, some of its pulling power is employed in moving itself. And so with a battery, if any current at all is flowing, the terminal potential difference must always be slightly less than the electromotive force. Example 45. A Daniell's cell has an E. M. F. of 1 -07 volts, and an internal resistance of 2A ohms; what Chap. IV.] EXAMPLES. 207 current will it send through an external resistance of 32 ohms'? Answer. 0'031 ampere nearly. Example 46. A battery having an E. M. F. of 15 volts, and an internal resistance of 25 ohms, is sending a current through an external resistance of 5 ohms ; what is the potential difference at the battery terminals 1 Answer. 2J volts. Example 47. What current must the battery in the last question send so that its terminal potential difference may be 7 "5 volts'? Answer. 0'3 ampere. Example 48. If a battery, having an E. M. F. of 8 volts, have its terminal potential difference reduced to 2 volts on sending a current of 2 amperes, what is its internal resistance 1 Answer. 3 ohms. Example 49. A battery has a terminal potential difference of 15 volts when sending a current of 2 amperes, and 12 volts when sending a current of 3 amperes ; what is its internal resistance 1 If E be the unknown E. M. F. of the battery, and b its resistance, we have 15 = E"- 26, also 12 = E - 36, or 6 = 3 ohms. Answer. 3 ohms. 208 CHAPTER V, CURRENT GENERATORS. 117. Current Generators 118. Batteries 119. Darnell's Cell 120. Minotto's Cell 121. Gravity Daniell 122. Chemical Action in the Daniell's Cell 123. Local Action 124. Grove's Cell 125. Bunsen's Cell 126. Leclanche Cell 127, Potash Bichromate Cell 128. Measuring the Electromotive Force of a Current Generator 129. Measuring the Resistances of Batteries 130. P. D. 131. Comparing the Electromotive Forces of Bat- teries 132. Poggendorff's Method of comparing Electromotive Forces 133. Electromotive Force of a Cell is Independent of its Size and Shape 134. Calibrating a Galvanometer by Em- ploying Known Resistances and a Cell of Constant E. M. F. 135. Arrangements of Cells 136. Arrangement of a given Number of Cells to produce the Maximum Current through a given External Resistance 137. Variation produced in the Total Current by Shunting a Portion of the Circuit 138. Constant Total Current Shunts 139. Independence of the Currents in Various Circuits in Parallel. 117. Current Generators. The current generators in practical use may be divided into 1. "Batteries." 2. " Accumulators " or " Secondary batteries." 3. " Magneto machines." 4. "Dynamos." 5. "Thermopiles." All of these are simply contrivances for converting various forms of energy into electric energy. In thermo- piles heat energy is directly transformed into electric energy, just as in a steam-engine heat energy is directly transformed into mechanical energy, or energy of visible motion. In dynamos and magneto machines there is a direct transformation of mechanical energy into electric energy, whereas in accumulators and batteries it is stored up, or potential, chemical energy that is converted into electric energy. Chap. V.] BATTERIES. 209 118. Batteries. A " battery " is the name given to a collection of "galvanic cells." arranged so as to pro- duce a larger current than could be obtained with a single cell under the particular circum- stances. Fig. 75 shows a battery composed of five cells of the very simplest form, each cell consisting of a plate of zinc z and a plate of copper c, dipping into dilute sulphuric acid. Such a cell is frequently called a " simple Voltaic element.'' The copper plate of one cell is joined by means of a copper wire to the zinc plate of the next, so that the cells are in series (see Arrangements of Cells, 135, page 239), and on joining the two terminal copper wires marked + and in the figure, directly together, or to the terminals of a gal- vanometer, voltameter, or other indicator of the direction of the current, the current is found to flow in the direction of the arrows (see Definition of the Direction of the Current, 7, page 1 4). A great number of cells have been devised from time to time, but the most important are the o 210 PRACTICAL ELECTRICITY. fChap. V Daniell's" cell. : Grove's" cell. Bunsen's" cell. Leclanche'" cell. Potash bichromate cell. Other cells, such as the " Lalande Chaperon,'" the "Ross* the " Upward" the " Regent? &c., may be used for the Fig. 76. comparatively cheap production of large currents, when a dynamo is not available, but such cells cannot, as far as the author is aware, compare with the dynamo in economy. 119. Daniell's Cell. The "Daniell's" cell consists of a copper plate c, Fig. 76, dipping into a solution of copper sulphate contained in a glass, or glazed, highly vitrified stoneware jar, j, and a zinc plate, or rod, z, to which a copper wire, or strip, w, is soldered, dipping into either dilute sulphuric acid or a solution of zinc sulphate, the two solutions being separated by a porous partition P, v.) DANIELL'S CELL. 211 made of unglazed earthenware, and called a pot" The E. M. F. of a Daniell's cell, and of all its modifications, is roughly !! volts, but it varies from about 1O7 volts to 1'14 volts, depending on the densities of the solutions of copper and zinc sulphate. With equi- dense solutions, and with^plates of pure zinc and copper, the E. M. F. is 1-104 volts. This value is increased by increasing the density of the copper sulphate solution, and diminished by increasing the density of the zine sulphate solution, and is scarcely at ail affected by the ordinary atmospheric changes of temperature. (See 215, page 411.) The resistance of the cell varies with the area of the copper and zinc plates immersed in the liquids, the dis- tance between the plates, and the thickness and constitu- tion of the walls of the porous cell. With a cell about 7 inches high, of the relative dimensions shown in the above figure, the resistance may be as low as J of an ohm when the solution in which the zinc plate is im- mersed is dilute sulphuric acid of a specific gravity of about 1-15 at 15 C. Occasionally, however, porous pot Daniell's cells, with smaller plates, are used, having a resistance of as much as 10 ohms. The E. M. F. of the Daniell, or of any other form of cell, is quite independent of the size of the various parts of the cell, or of the cell as a whole, and depends solely on the materials employed in its construction. (See 133, page 236.) 120. Minotto's Cell. In the "Minotto's"* cell the porous pot is replaced by a layer of sand or sawdust, and it is constructed as shown in Fig. 77. At the bot- tom of a glass, or glazed and highly vitrified stoneware jar j, there is placed a disc of sheet copper c, to which is attached one end of an insulated copper wire, which. passes up through the cell. Above this plate are placed some crystals of copper sulphate c s, and on the top a piece of thin canvas c, separating the copper sulphate from the layer of sand or sawdust s } and on the top of the saw- * Often wrongly spelt " MenottVt." 212 PRACTICAL ELECTRICITY. [Chap. V. dust rests the zinc plate z, separated from the sand or saw- dust by a piece of thin canvas c. The cell is completed by pouring in some solution of zinc sulphate, so as to cover the zinc disc, but not so much as to reach up to the brass binding screw B, cast into the top of a little column of zinc, forming part of the zinc disc. Before putting in the sand or sawdust, it should be soaked in a solution of zinc sulphate, and squeezed partially dry, because, if put into the cell quite dry, a long time must elapse before the liquid will soak through the sand or saw- dust, and until this hap- pens the cell will not come into action. It is better to employ sand in stationary Min- otto's cells, as it sinks down as the copper sulphate is consumed, but if the cells have to be moved about, then it is better to use sawdust. 121. Gravity Daniell. In some types of Darnell's cells, no form of porous partition is employed, and the copper sulphate and zinc sulphate are kept separated solely by the action of gravity, the zinc sulphate solution being put at the top, as it is the lighter of the two. Such cells are called " gravity DanieWs" and examples of them are shown in Figs. 78, 79, and SO. Fig. 78 shows two forms of the " Meidinger " cell, in each of which the copper plate is put inside a small inner glass tumbler d d i so that the particles of zinc sulphate, which may become detached from the zinc plate, may fall clear of the copper plate, and be prevented from coming into contact with it. In the type of Meidinger shown on the left, the crystals . 77. Chap. V.] GRAVITY DANIELL. 213 of copper sulphate are in a glass tube A, with only a small hole at the bottom, while in the type to the right the crystals are contained in an inverted flask open at the neck. In both, the zinc plate z z, which is in the form of a cylinder, is supported on a shoulder bb, formed by a contraction of the lower part of the outer glass vessel. The Ccdlaud cell, Fig. 79, is a simplifica- tion of the Meidiuger, being without the reservoir for Fig. 78. the copper sulphate crystals, and the small glass tumbler to hold the copper plate. In the " Lockwood " cell, Fig. 80, the zinc plate is made like a kind of wheel with spokes, so as to expose a large surface to the liquid, and is supported by three lugs resting on the edge of the glass vessel. The copper plate is made of thick copper wire, bent into the form of a double spiral, with the crystals of copper sulphate placed between the spirals, the upper spiral 214 PRACTICAL ELECTRICITY. [Chap. V, being found to retard the travelling up of the copper sulphate solution to the zinc plate if the cell be kept sending even only a weak current. For the lower spiral, . a copper disc, similar to that used with the Minotto's . cell ( 120, page 211), may be substituted, and for the upper one, a perforated copper disc, without interfering with the action of the Lock wood cell. All gravity cells have the disadvantage that they cannot be moved about^ Pig. 79. Fig. 80. otherwise the liquids mix, and the sulphate of coppet solution coming into contact with the zinc plate, deposits copper on it This impairs the action of the cell by causing the zinc plate to act electrically like a copper one. Indeed, without any shaking, the liquids mix by diffu- sion, even when a porous pot is employed, and hence a Daniell's cell is found to keep in better order if it be always allowed to send a weak current when not in use, since the current uses up the copper sulphate solu- tion instead of allowing it to diffuse. Chap. V.] CHEMICAL ACTION IN THE DANIELI/S CELL. 215 122. Chemical Action in the DanielPs Cell. The DanielVs cell, and all its modifications, produce a cur- rent by the formation of zinc sulphate, and the using up of copper sulphate, the zinc plate being eaten up to form the zinc sulphate, and the copper plate growing by the deposit of metallic copper on it. Chemically, the action may be represented as follows the " water of crystalli- sation " of the copper and zinc sulphate crystals, as well as the water employed to form the solutions, being omitted for the sake of simplicity : Before sending a current (Cu) + /(CuS0 4 ) | w(ZnS04)+w(Zn), m after sending a current g (+l)(Cu)-HM)(CuSO 4 ) 2 (w+l)(ZnS0 4 ) + (w-l)(Zn); PH k and n being any arbitrary quantities of copper and zinc used in the copper and zinc plate, and I and m any arbitrary quantities of the copper sulphate and zinc sul- phate employed. Substituting the " atomic weights " for the various substances employed, we find that for every 26 ounces of zinc that are dissolved off the zinc plate, about 100 ounces of copper sulphate crystals are decomposed, and about 25 ounces of copper added to the copper plate. If dilute sulphuric acid be employed in place of a solution of zinc sulphate, the resistance of the cell is lower, and the E. M. F. higher, but the latter is not so constant as when zinc sulphate alone is used, because, if we start with dilute sulphuric acid, zinc sulphate will be gradually formed by the action of the cell, and the increase of the amount of zinc sulphate we have already seen lowers the E. M. F. The chemical action in that case will be as follows : Before sending the current : *(Cu)+/(CuSO 4 ) | w(H 2 S0 4 )-M(Zn), nfter sending the current (k+ l)Cu+(M)(CuS0 4 ) E m(H 2 S0 4 )-f(ZnS0 4 )-}-(w-l)(Zn) 216 PRACTICAL ELECTRICITY. [Chap. V If/ten, therefore, constancy of E. M. F. is desired, a solution of zinc sulphate should be used, and not dilute sulphuric acid. If the copper sulphate solution becomes too weak, the water is decomposed instead of the copper sulphate, and hydrogen is deposited on the copper plate. This deposition of hydrogen lowers the E. M. F., and care should therefore be taken to keep up a sufficient supply of crystals of copper sulphate. Indeed, it was for the purpose of preventing the deposition of hydrogen on the copper plate which occurs with a simple voltaic element, that Prof. Daniell was led to use copper sulphate as a " depolariser" and thus invent the "two-fluid cell" This polarisation is easily seen by dipping two pieces of clean copper, GJ and C 2 , and a piece of zinc, into dilute sulphuric acid, a part of each of the three pieces being inside the liquid and a part outside, but the three pieces not touching one another, either inside or outside the liquid. If the two pieces of copper, Cj and C 2 , be first joined by wires with a delicate galvanometer, no current will be observed ; but if one of them, Cj, be connected for a time with the zinc by a wire, so that a current flows from C x to the zinc through this wire, and from the zinc to Cj through the liquid, it will be found on stopping this current and con- necting Cj and Co again with the galvanometer, that a current now flows round it from C 2 to Cj, that is, from Cj to C 2 through the liquid. Using O lf therefore, as the copper plate in a simple voltaic element, causes it to act subsequently as a zinc plate to a clean copper plate. And the longer C x is used as the copper plate of the simple voltaic cell, which is sending a current through a piece of wire to the zinc plate, the more like a zinc plate does G l become, and the weaker grows the cur- rent that G! with the zinc plate can send through a given external resistance, while the stronger becomes the current that C a and a clean piece of copper will send through a given resistance. This change in the behaviour of C x is due to a deposition of hydrogen on Chap. V.] LOCAL ACTION. 217 it, which deposition gradually disappears when C T and C., are left connected. Both then when the "primary current" flows from the zinc to Cj through the liquid, and subsequently when the " secondary current " flows from Cj to C 2 also through the liquid, the hydrogen moves in the direction of the current, the result obtained with a sulphuric acid voltameter (see 7, page 15). If the solution of zinc sulphate in a Daniell's cell (Figs. 77, 80) becomes too strong by the evaporation of the water, the zinc sulphate crystallises on the sides of the cell, and the liquid passes up by capillary attraction between the film of crystals and the side of the vessel, crystallising again above. At last the film passes over the edge of the jar and forms on the outside, thus making a kind of syphon, which draws off' the liquid. This action may, to a great extent, be prevented by warming the edges of the glass or stoneware jars, and of the porous pots, before the cells are made up, and dipping them while warm into some paraffin wax melted in warm oil. It is desirable also with those Daniell's cells in which the zinc is inside the porous pot, as in Fig. 76, to dip the bottom of the porous pot into the melted paraffin wax, otherwise particles of metallic copper will be gradually deposited in the pores at the bottom of the porous pot on which the zinc rests, and the cell will become "short-circuited," that is, a strong current will be sent through this copper, and the mate- rial in the cell will be used up rapidly, exactly as would be the case if the zinc and copper plates were perma- rently connected by a short piece of thick copper wire outside the cell. 123. Local Action. Another cause of "local action" or the production of useless currents, is impurities, such as bits of coke, in the zinc. If a piece of coke and a piece of pure zinc be put into dilute sulphuric acid, then, as long as the coke and zinc do not touch one another, either in the liquid, or outside, no appreciable chemical action will take place ; but if now the parts of '218 PRACTICAL ELECTRICITY. [Chap. \. the coke and zinc that are in the liquid, or the parts that are outside, be touched together, a rapid evolution of hydrogen gas will take place, together with the forma- tion of zinc sulphate. And exactly the same effect is produced when a piece of zinc containing impurities is dipped into dilute acid. This local action, however, can be prevented by coating the surface of the zinc with an " amalgam " of zinc and mercury, or " amalga- mating " the zinc, as it is shortly called, this amalgam covering up the impurities. To amalgamate a piece of zinc, it should be dipped into dilute sulphuric acid, to clean the surface, when a little mercury should be rubbed over the zinc with a piece of rag tied to a stick. A plate of commercial zinc amalgamated, although much cheaper than a plate of pure zinc, does not give an E. M. F. as constant as is ob- tained with a pure zinc plate. 124. Grove's Cell. In the p "Grove's" cell the copper plate intheDaniell's cell is replaced by a sheet of platinum, p, Fig. 81, and the solution of copper sul- phate by strong nitric acid. Dilute sulphuric acid, in the proportion of about one pint of acid to ten pints of water, is used in place of zinc sulphate solution, since, with the Grove's cell, we wish to obtain the highest E. M. F., and the lowest resistance rather than very great con- stancy. The E. M. F. is about 1-93 volts, and with good porous cells the resistance is very low, being only about Tig. 81. 3-6 x d ohms, where d is the distance, in inches, between the platinum Chap. V.I GROVE'S CELL. 219 and the zinc plates, and A the area, in square inches, of the platinum plate immersed in the nitric acid. If, as is frequently the case, the zinc plate z z is cast in the shape shown in Fig. 81, A must be reckoned on both sides of the platinum plate P. When the cell has the dimen- sions indicated in the figure, the resistance is about 0*15 ohms when the nitric acid is strong, and the dilute sul- phuric acid has but little zinc sulphate in it. After a Grove's cell has been sending a current for some time, the nitric acid becomes weakened, as water is formed by the action of the cell, and a considerable quantity of zinc sulphate is also dissolved in the dilute sulphuric acid, both of which have the effect of diminishing the E. M. F., and increasing the resistance of the cell. The chemical action is as follows : Before sending a current 3 *(Pt)+J(HN0 8 ) | *w(H 2 S0 4 )-M(Zn), after sending a current PH *(Pt) + (I- 2) (HN0 3 ) a (m - 1) (H 2 S0 4 ) + (ZnS0 4 ) (H 2 0) +( the water originally in the cell being omitted for simpli- fication. Peroxide of nitrogen, N 2 O 4 , comes off as a dark brown gas, extremely unpleasant and unhealthy when breathed for any time ; a Grove's battery should, therefore, always be placed either in the open air or under a chimney when in use. The large E. M. F., combined with the small resist- ance, makes Grove's cells very valuable when a very strong current has to be produced ; hence, before the perfection of the dynamo and of secondary batteries, they were largely used for the production of the electric light. 125. Bunsen's Cell. The "fiunsen's" cell differs from the Grove's only in having a cylinder, or block, of carbon in place of the sheet of platinum, as seen in Fig. 82, which shows a common form of circular Bunsen's cell, C being the carbon, and Zn the zinc. A Bunsen's cell is 220 PRACTICAL ELECTRICITY. [Chap. V. cheaper to construct than a Grove's cell, as carbon is so much less expensive than platinum ; it is, however, more cumbersome, and more nitric acid is required to fill it, as the nitric acid soaks into the pores of the carbon. The E. M. F. of a Bunsen's cell is also somewhat lower than that of a Grove's, although the chemical action in the two cells is nearly the same. The carbons for the Bunsen's cells are either cut out Pig. 82. of retort carbon, or are made by baking in a furnace fine coke-dust and caking coal in an iron mould ; then, in accordance with a process invented by Bunsen, the baked mass is soaked repeatedly in thick syrup or gas-tar, and re-baked to impart solidity and conducting power to it. 126. Leclanch6 Cell. The " Leclanche" cell consists, as seen in Fig. 83, of a zinc rod to the left of the figure, immersed in a solution of ordinary sal ammoniac, and a plate of carbon put inside a porous pot, and packed tightly with a mixture of the needle form of manganese peroxide arid broken gas-carbon. Both the manganese Chap. V.j LECLANCHE CELL. 221 peroxide and the gas-carbon must be sifted to remove the dust, in order that as much surface as possible may be exposed to the action of the liquid. The porous pot is merely for the purpose of holding the mixture in posi- tion, and not for keeping two liquids separated, as in the cells previously described ; for, in fact, there is only one liquid on both sides of the porous pot the solution of sal ammoniac. The upper part of the porous pot is closed with pitch, in which a small hole is left, so that a little water or a' little solution of sal ammoniac may be poured in to start the action. The chemical action is as follows : Before sending a current after sending a current K)+ (*-4)(MnOJ + (w-2) (NH 4 C1) + (Mn 2 3 ) + 2(NH 3 ) + (H/)) + (ZnCl 2 )-K*-l)(Zn). Ammonia, NH 3 , therefore, comes off from the cell, and Fig. 83. substituting the atomic weight we see that for every 50 grains of zinc used up about 82 grains of sal ammoniac are consumed, and about 134 grains of manganese peroxide, MnO 2 , are reduced to the lower, or sesqui-oxide, Mn 2 O 3 . If too little sal ammoniac be pre- sent, zinc oxide is formed instead of zinc chloride, and the solution becomes milky. When this happens, more sal ammoniac should be added. Connection with the carbon rod is made by means of a lead cap cast on it ; and to prevent a salt of lead being formed between the cap and the carbon, which would introduce a high resist- ance, the end of the carbon rod is heated for an hour in paraffin wax, at a temperature of 110C., before the cap 222 PRACTICAL ELECTRICITY. [Chap. V is cast on, then two quarter-inch holes are drilled side- ways through the carbon, and the cap cast on, the lead which runs into these holes serving as rivets. The E. M. R of a Leclanche cell is 1-47 volts, but it falls rapidly when the cell is used to send a strong current. It will, however, regain its value if the cell be left for some time unused, and it does not sensibly diminish when the cell is put on one side, even for some months. Hence, while tJie LeclancJie cell is much in- ferior to the DanieWs for t/te purpose of sending a steady current for an hour or two, it is much superior to the Daniell for the sending of intermittent currents at any time during tJie course of many months -for example, such currents as are employed for the ringing of electric bells. 127. Potash Bichromate Cell. These cells are some- times made without a porous cell, as seen in Fig. 84, and sometimes with, as seen in Fig. 85. The plates employed are of carbon and zinc, and in Fig. 84 the two outer plates are of carbon, and dip continuously into the liquid, while the middle plate is of zinc, and is only pushed down, by means of the handle a, into the liquid when it is desired that the cell shall send a current, and with- drawn as soon as the current is interrupted. The follow- ing is the best composition to give to the liquid : Potash bichromate ... lib. Strong sulphuric acid 21bs. Water 121bs. or, as it is inconvenient to weigh the sulphuric acid and the water, ten pints of the same composition may be made as follows : Add with constant stirring to 0*832 pints of sulphuric acid, having a specific gravity of about 1*836, 0-955 Ibs. of pulverised commercial potash bichro- mate, K 2 Cr 2 O 7 ; and when the formation of the chromic acid, CrO 3 , and potash sulphate, K 2 SO 4 , produced by the mixture, is completed, pour in slowly 9*2 pints of cold water. The liquid will become gradually warm, and the crystalline precipitate be entirely dissolved. Chat). V.J POTASH BICHROMATE CELL. 223 The chemical action produced by this mixing may be represented as follows : K 2 2 7 + 7H 2 SO, = 2CrO s + K 2 SO 4 + H 2 O " + 6H 2 S0 4 , and the chemical action that takes place in the cell dur- ing the passage of the current consists in the formation Fig. 84. Fig. 85. of chromium sulphate, O 2 3(S0 4 ) ; zinc sulphate, ZnS0 4 \ and water, H 2 O, and ma/ be represented thus : 2Cr0 3 + 6H S0 4 + 3Zn = O 2 3(SO 4 ) + 3ZnSO 4 + 6H 2 0. This cell gives rise to no disagreeable fumes, has a high E. M. F. of something like two volts, and a low in- ternal resistance. The E. M. F., however, rapidly falls when the cell is employed to send a strong current con- tinuously, but recovers its original value when the cell has remained out of action for some time. With the type of potash bichromate cell, having a porous pot, the zinc z (Fig. 85) Ls frequently cast, in the 224 PRACTICAL ELECTRICITY. [Chap. V. form of a block, on to a stout copper wire, carrying the binding screw, and both the block and the wire are well amalgamated. In the porous pot containing the zinc, there is put a small quantity of mercury to maintain the amalgamation, and either dilute sulphuric acid, in which case the chemical action is the same as in the cell with- out the porous pot, or, instead, a solution of common salt, NaCl, when zinc chloride, ZnCl 3 , is formed instead of zinc sulphate, and sodium sulphate, NagSO^ in addi- tion to the chromium sulphate. The complete chemical action is in this latter case : Before sending the current -g C+;CrO 3 +3/H 2 S0 4 * mNaCl+Zn, After sending the current kC + (-2)CrO 3 + (m-6) NaCl + 3Na 2 S0 4 + 3(-2)H 2 SO 4 +Cr 2 3(S0 4 ) 3ZnCl 2 +6H 2 O+(w-3).Zn. When the supply of potash bichromate becomes ex- hausted, the orange colour of the solution turns blue, and when this change of colour is observed, more potash bichromate should be added. If, however, the cell be- gins to fail when the orange colour still remains, then more sulphuric acid is needed. As no other form of current generator than galvanic cells need be employed for any of the experiments that precede this, or, indeed, for many that follow, the descrip- tion of dynamos, thermopiles, &c., will be deferred. 128. Measuring the Electromotive Force of a Current Generator. An electrometer, or voltmeter, measures the potential difference at its terminals, and, as shown in 116, page 204, the potential difference at the terminals of a generator of constant E. M. F. is equal to its E. M. F. when no current is flowing, and practically differs but very little from its E. M. F. when but an extremely small current is flowing. Hence, to measure the E. M. F. of a generator of constant E. M. F., we must arrange that either it shall send no current at all, or, at any rate, but a very small one. The first condition can be fuelled when an electrometer is employed, and Chap. V.] MEASURING THE RESISTANCES OP BATTERIES. 225 the second even with a voltmeter if it has a very large resistance. In order to ascertain how large this resist- ance may be, we must consider the equation r + 6 and from that we see that in order that V may be practically equal to E it is necessary that r and b should be practically equal to r; that is, r must be large compared with 6, and hence the battery must be sending a very small current through the voltmeter, compared with what it could produce if its terminals were joined with a short bit of thick wire. (See 131, page 231, and following sec-, tions, for further details about measurement of E.M.Fs.) 129. Measuring the Resistances of Batteries.^, We have already seen, in 116, page 205, one way of determining the resistance of a battery without the aid of a resistance box, by making simultaneous measure- ments with an ammeter and voltmeter. This method is particularly suitable to be employed with current gene- rators of very low resistance, such as accumulators, since such generators would send a very powerful current through any coil having a resistance comparable with their own, and this current would tend to heat such a coil, and alter its resistance, unless it were made of very thick wire. Hence, it would be very difficult to employ, with such a generator, resistance coils having perfectly constant and known resistances, unless their value, coin- pared with the resistance of the generator, was so high that the slightest proportional error in the value of the coils would make a serious error in the determina- tion of the resistance of the generator, just as a large eiTor would probably be introduced if an attempt were made to weigh a few grains of some powder in a weigh- ing machine suitable for weighing a hundredweight. Beginners are apt too frequently to forget that, although a coil of 10,000 ohms, and another of Tooth of an ohm, may be put in boxes of about the same size, there is the p 226 PRACTICAL ELECTRICITY. ("Chap. V. same sort of difference between these resistances as be- tween twelve pounds and one grain, or between thirty tons and one ounce, and hence that apparatus which is arranged to measure the one is totally unsuited to measure the other. With current generators of constant E. M. F., and having higher resistances, the following methods, with which resistance coils of known value are employed, may be used. 1st. Let C and C', as determined from the deflections on a galvanometer and reference to the relative calibra- tion curve, be the relative strengths of the currents pro- duced by the generator when resistances r and r' in ohms are introduced in the circuit ; then, if b be the resistance in ohms of the generator, g that of the galva- nometer, and E the E. M. F. in volts which latter need not, however, be known E ^ _ E_ = C_ ft + r + b + r'+g C'' or + r + g (f C-C' If r and r' be so chosen that C is twice C', then b = r' 2r-g. 2nd. Let C and C' be the relative strengths of the currents produced : first, when the galvanometer is un- shunted, and a resistance r ohms introduced in the main circuit ; secondly, when the galvanometer of resistance g ohms is shunted with a shunt of s ohms, and when a re- sistance r' ohms is in the main circuit, then E 8 __ E C 0" Chap. V.] MEASURING THE RESISTANCES OF BATTERIES. 227 If and r' be so selected by trial that C' equals 0, then we have g The objection to both these methods is that on ac- count of the variation in the current strength, and on account of the time that each of the two currents C and C' has to be allowed to flow until the deflection of the galvanometer needle becomes steady in each case, the E. M. F. and resistance in some tyj>es of cells is liable to undergo a change from polarisation. On this account the " condenser method of measuring the resistance of current generators" described in 184, page 342, is to be preferred. Example 50. A Daniell's battery produces a deflec- tion of 38 on a tangent galvanometer when a resistance of 27 ohms is inserted in the circuit, and a deflection of 46 when this resistance is reduced to 12 ohms. What is the resistance of the battery if that of the galvanometer be 2| ohms 1 Inserting these values in the equation, we have b _tan. 38 x (27 + 21) -tan. 46x(12 + 2|) tan. 46 -tan. 38. Answer. 31J ohms about. Example 51. With a galvanometer having a resist- ance of half an ohm, and constructed so that the angular deflection is directly proportional to the current, a bat- tery of 20 Grove's cells in series produces a deflection of 28 divisions when a resistance of two ohms is inserted, and 14 divisions when a resistance of eight ohms is in- serted. What is the resistance of the battery ? 228 PRACTICAL ELECTRICITY. [Chap. V. If b be the resistance of the entire battery, 6 = 8-2x2-i Answer. 3J ohms. Example 52. When four ohms are introduced into the circuit of a sine galvanometer, having 6 ohms' re- sistance, and a Leclanche cell, a deflection is produced corresponding with a necessary rotation of the sine gal- vanometer through 22. When, however, the sine galva- nometer is shunted with two ohms, the rotation required is only 8. What is the resistance of the Leclanche cell ? Substituting the values in the equation, we have ^ __ sin. 22 x (4 + 6) x 2 -sin. 8x {(2 + 6) x 4 + 2 x 6} sin. 8 x (2 + 6) -sin. 22 x 2 Answer. 4 ohms about. Example 53. The same deflection is produced on a galvanometer of 2 J ohms' resistance, when 8 ohms are in circuit, as when only 2 ohms are in circuit, and the gal- vanometer is shunted with 2 ohms. What is the resist- ance of the current generator ] . 2x(8-2)-2Jx2 ~w~ Answer. 2 A of an ohm. In making measurements of the resistance of bat- teries by any of the foregoing methods, care must be taken not to introduce into the circuit resistances that are very large compared with the resistance of the battery which we desire to find, since any error in such a high resistance will probably introduce a large error into the answer. For example, suppose it be desired to use a galvanometer which happens to be so delicate that on attaching the battery directly to its terminals, so large a deflection is produced that it requires a considerable resistance to be introduced into the circuit to reduce this deflection to readable limits, then it would be better to reduce the prac- tical sensibility in some other way than by adding resistance Cliap. V.] MEASURING THE RESISTANCES OP BATTERIES. 229 in the main circuit. This may be done either by putting a magnet near the galvanometer or by shunting it. In the latter case the shunted galvanometer would take the place of the simple galvanometer in the first method given above for determining the resistance of a battery, and of the unshunted galvanometer in the second method ; the second experiments referred to in the second method being performed with the galvanometer shunted with a different shunt. For example, suppose we desire to determine the re- sistance of a battery that we know to be about one ohm, and the only galvanometer available is a very delicate one, having 1,000 ohms' resistance, how should we proceed? The deflection can be reduced to readable limits either by inserting a large resistance into the circuit, or by putting a magnet near the galvanometer, or by shunting it. As the resistance of the galvanometer is 1,000 ohms, which is large compared with that of the battery, introducing another large resistance into the circuit for the purpose of diminishing the deflection would only increase the probable error due to the large resistance in the circuit. Putting a magnet near the galvanometer would be better than this, but a still better method would be to shunt the galvanometer, because, if it be very sensitive, a suit- able deflection may be obtained with a shunt perhaps of one or two ohms, and with one or two ohms in the main circuit Suppose with a shunt of two ohms, and a re- sistance of three ohms in the main circuit, a deflection extending over about half the scale is obtained, then this arrangement can be well used, either for the first or for the second method of measuring the battery resistance. For carrying out the first method, we may make two tests, the first with the three ohms, and the second with, say, one-and-a-half ohms in the main circuit, the galvano- meter being shunted in each case with the two ohms, and having, therefore, a combined resistance with the shunt of ohms. For carrying out the second method we 2 -f- 1000 230 PRACTICAL ELECTRICITY. FChap. V might make the same first test as before, but the second might be made with an interposed resistance of perhaps one-and-a-half ohms in the main circuit, and with the galvanometer shunted with, say, one ohm instead of the two ohms previously employed. To ascertain what is the formula to be employed in this case, let r and r' be, as before, the resistances put into the main circuit in the two tests, and s and s the two shunts employed, then s E s E s+g s + g *' (* + ff)(b+r) + 8g ~~ C f If the battery be one that does not polarise quickly, that is, be one in which the E. M. F. does not fall rapidly when the battery sends strong currents, then the best way of carrying out the first method of measuring the resistance of the current generator with a delicate galvanometer, is to put no resistance r in the main circuit, but to shunt the galvanometer with a shunt that has a very small resist- ance compared with the battery, and yet is not so small but that a suitable deflection may be obtained. Now intro- duce such a resistance r' into the circuit that the current through the galvanometer becomes halved, then this re- sistance is necessarily equal to b, since b was practically the whole of the resistance in the circuit before the intro- duction of r'. 130. P. D. Throughout the remainder of this book the letters "P. D." will be used to stand for potential difference, in the same way as the letters E. M. F. are universally now employed to stand for electromotive Chap. V.J COMPARING ELECTROMOTIVE FORCES. 231 force. As these letters P. D. are here proposed as a new abbreviation, the ordinary cumbersome expression, "difference of potentials," has been used up to this point in the book, in order to familiarise the reader with the mean- ing of an expression that he will frequently meet with. 131. Comparing the Electromotive Forces of Batteries. The relative electromotive forces E and E' of the batteries, or other current generators of constant E. M. F., can be compared by observing the resistance through which they will send equal currents. Let b and 6' be the resistances of the batteries themselves, and r and r' the resistances, including in each case that of the galvanometer, which, added to the resistances b and b' respectively, cause the currents in the two cases to be equal, then E E' b + r ~ b' + r' ' E _ b + r ' E' ~ b' + r' ' If the galvanometer is sensitive, so that r and r, which each include the resistance of the galvanometer, are large compared with b and b' respectively, then E r = approximately. E r The preceding method of comparing E. M. Fs. has the advantage that the law of the galvanometer need not be known. If the currents be not the same, let C and C' be the relative current strengths obtained from the deflection of the galvanometer and reference to the calibration curve, then E E' _0_ b + r * b' + r' ~~ C' ' E b + r (^ Cr E /=: &'+r' ' 0'* 232 PRACTICAL ELECTRICITY. [Chap. V. And, as before, when r and r' are large compared with 5 and b' respectively, = . approximately. E' r' C' Another method for determining the ratio of E to E' consists in first joining the batteries up together so that they assist one another in sending a current, and secondly in joining them up so as to oppose one another's action. Let C and C' be the relative strength of the currents in the two cases ascertained from the deflection of the galvanometer and the relative calibration curve, then if p be the total resistance in circuit in the two cases, we have, sinoe p remains constant, E + E' E - E' cr E _ C + 0' E' ~ C - 0'* This method has the advantage that the resistances of neither of the batteries nor of the galvanometer need be known but it has the disadvantage that the sending of currents in opposite directions through the battery which has the smaller electromotive force is very likely to alter this electromotive force during the experiment. Example 54. Two batteries having internal resist- ances of 10 and 15 ohms produce the same deflection on a galvanometer of 40 ohms, when 250 and 305 ohms are respectively introduced into the circuit. What is the ratio of their E. M. Fs. ? Substituting the values in the equation, we have E__ 10 + 40 + 350 E'~ 15 + 40 + 305* .-. E'= 1-2 E. Chap.V.] EXAMPLES. 233 Example 55. The same two batteries produce the same deflection on a much more delicate galvanometer, having 120 ohms' resistance, when 5,000 and 6,031 ohms are re- spectively introduced into the circuit. What is the ratio of their E. M. Fs. ? Using the complete formula, we have E _ 10 + 120 + 5000 E'~15 + 320 + 6031* or E' = 1 -2 E as before. Using the approximate formula, J3 _5000 '""6031* or E' = 1-206 E, from which we see the error made by omitting the re- sistances of the batteries and of the galvanometer in the calculation. Example 56. A magneto-electric machine running at a certain speed, and having a resistance of two ohms, produces on a tangent galvanometer a deflection of 30 when a resistance of 2,100 ohms is introduced in circuit with it and the galvanometer, which has three ohms' re- sistance. A Daniell's cell, on the other hand, having an E. M. F. of 1 -07 volts, and one-and-a-half ohms' resistance, produces a deflection of 45 when 84 ohms is introduced in the circuit. What is the E. M. F. of the magneto machine ? If E be the E. M. F. of the machine, J_ ^ _ i n~ 210 ^ 3 34^5847 X T~ S a PP roximatelv - Answer. 14'7 volts approximately. Example 57. What about is the E. M. F. of a Grove's cell, if, when joined so as to assist a Daniell's 234 PRACTICAL ELECTRICITY. [Chnp. V. cell having an E. M. F. of 1-1 volts, a rotation of 38 of a sine galvanometer is necessary to be made to bring the needle to the fixed mark, whereas, when the Grove's cell is reversed, a rotation of about 8J in the opposite direction is necessary 1 ? Answer. 1'83 volts, 132. Poggendorff" s Method of Comparing Electro- motive Forces. With many types of cells the electro- motive force is fairly constant, even for wide Variations in the current passing through the cells, and in such a case any of the previous methods can be employed for com- paring their electromotive forces. But with other types, a very small current passing through the cell is sufficient to diminish the electromotive force. In such a case the following method, due originally to Poggendorff, may be employed. From what has preceded we know that if a current of A amperes flow along a wire, J K, the potential difference, or, shortly, the P. D., in volts between any two points, L M, is equal to the product of A into the resistance r of the wire, in ohms, between the points L and M. Hence if L and M (Fig. 86) be joined by another circuit containing a cell or battery of E. M. F. equal to E and a galvanoscope, G, and if one or both of the ends of this second circuit be moved along the wire J K composing the first circuit until no current passes through the gal- vanoscope G, then we know that E is equal and opposite to the P. D. between L and M, or E = Ar. If, now, a second battery of E. M. F. equal to E', and a second galvanoscope, G', be attached to two other points, Chap, v.] POGGENDORFF'S METHOD. 235 u v, of the wire J K (Fig. 87), the points u and v being so selected by trial that no current passes through this galvanoscope ; and if r be the resistance of the wire u v, then E' - A r', E r and hence the two E. M. Fs. can be compared without our knowing the value of the current flowing through the wire J K. If the generator is of such a nature as to produce a constant current through the wire J K, then Fig. 87. there is no occasion to use two galvanoscopes, as the points L and M can be first ascertained with the first cell, and then the points u v with the second, such that in each case no current passes through the galvanoscope. If, however, the current in J K is liable to fluctuate, then, since the essence of the test depends on the same currents flowing from L to M as from u to v, it is better to use two galvanoscopes, and make the two tests of no currents through the galvanoscopes simultaneously. Of course, care must be taken to attach the cells or batteries whose E. M. F. we desire to compare, in such a way that their E. M. Fs. tend to oppose the potential differences between L and M and between u and v respec- tively, since, if either of the cells or batteries be attached in the opposite way, no two points, L and M or u and v, can, of course, be found such that the current passing through the galvanoscope attached to them is nought. If the wire J K is everywhere uniform in material, 236 PRACTICAL ELECTRICITY. [Chap. V. section, and temperature, the resistances r and r' are simply proportioned to the lengths L M and u v, so that the E. M. Fs. of the batteries are simply proportioned to the lengths of L M and u v. TJie great advantage of Poggendorp's method of com- paring E. M. Fs. is that the comparison is made when neither of the batteries is sending a current ; hence the same result is obtained as if the comparison had been made with an electrometer, and the resistances of the cells under comparison need not be known. And, further, the sen- sibility of the test may be far greater than could be ob- tained with any electrometer, since the method is a " null " method, that is, we aim at obtaining a deflection nought, instead of measuring the deflections corresponding with the currents produced by the batteries ; conse- quently the galvanoscope may be made as sensitive as we please. If the galvanometers G and G' be both sensitive, the accuracy of the method will be the greater the longer are the wires L M and u v, because any given small error in the position of one of the sliders corresponding with say a millimetre in the length of the wire, will represent a less proportional error in the length, and so r and r' can the more accurately be compared. Hence it is desirable to make the wire J K as long as possible, and to send through it a steady current, so weak that the P. D., at its extreme ends, is just equal to the larger of the two E. M. Fs. to be compared. (See 215, page 413.) 133. Electromotive Force of a Cell is Independent of its Size and Shape. The Daniell's cell (Fig. 88) is so arranged that the copper plate c, which dips into a solution of copper sulphate, may be made to approach, or recede from, the zinc plate z, which dips into a solution of zinc sulphate contained in a porous cell. By turning the screw p, the slider, carrying the wire supporting c, can be clamped in any position, and electric connection can be made with the binding screws B R Experiments made with this cell show that, although the resistance of Chap. V.J E. M. F. INDEPENDENT OF SIZE OF CELL. 237 the cell is varied by moving the copper plate, the E. M. F. remains exactly the same. Further, if the screws s s be loosened, and the copper and zinc plates be raised up as shown in the lower figure, so that only the little projec- tions at tJie bottom of these plates are in contact with tlie 238 PRACTICAL ELECTRICITY. [CLap. V. liquids, the E. M. F. is still unaltered. This experiment may be quickly made by using Poggendorft's method to compare the E. M. F. of the cell with movable plates with that of a DanielPs cell with fixed plates, since, as already explained, Poggendorft's method is indepen- dent of the resistance of the cells compared. The con- denser method of comparing E. M. Fs., described in 183, page 341, may conveniently be used in place of Poggen- dorffs method. 134. Calibrating a Galvanometer by Employing Known Resistances and a Cell of Constant E. M. F. We have seen, in 26, page 58, that a galvano- meter can be calibrated by direct comparison with a tangent galvanometer; also in 30, page (54, that when the controlling force is that produced by a uniform magnetic field, and when also the galvanometer can be easily turned backwards and forwards round its centre, the employment of the sine principle enables us to cali- brate it without the use of any other galvanometer. We have also seen, in 96, page 164, that when we have no other galvanometer at hand that has been already cali- brated, and when the galvanometer cannot be moved without interfering with its adjustment, which is generally the case when we are employing a galvanometer with fibre suspension and levelling screws, we may calibrate the gal- vanometer by employing known resistances, when a con- stant P. D. is maintained at the terminals of the circuit. The same thing may be done without having a con- stant P. D. between the terminals (Fig. 61, 96, page 165), if we have a coll of constant E. M. F. of E volts instead. Let b ohms be the resistance of the cell, then, if ^i5 ^2' c ^3 & c '> ke ^ ne deflections on the galvanometer, when r 1? r 2 , r s , &c., ohms are the resistances respectively in R, we know that the currents producing these deflec- tions are respectively - , ? , 5 , + 9 + r s) equals (b + g + V,), &c., since in that case the second current is double the first, the third thrice the first, &c. Of course r l should be chosen so that the deflection corresponding with this resistance is a conveniently small one, for example, about 10 in an ordinary galvanometer having a scale reading up to 90. 135. Arrangements of Cells. A battery may be formed of galvanic cells, or elements, as they are some- Jfig. 90. Fig. 91. times called, in a variety of ways. All the cells may be "in series" as in Fig. 89, or they may be joined up all "in parallel," as in Fig. 90, or "partly in series and partly in parallel" as in Fig. 91. These three arrangements are symbolically shown in A, B, c (Fig. 92), where the long thin lines stand for the plates in the 240 PRACTICAL ELECTRICITY. [Chap. V. battery from which the positive electricity flows ; or, with the definition of direction of current we have already adopted, the current flows in the circuit out- side the battery from the plate represented by the long thin line to that represented by the short thick line, while in the battery itself the current flows from the short thick line to the long thin one. For example, in the Daniell's cell, which consists, as previously described in 119, page 210, of a plate of copper in a solution of copper sulphate, separated by a Fig. 92. porous diaphragm of nnglazed earthenware from a plate of zinc in a solution of zinc sulphate, the long thin line represents the copper plate, and the short thick one the zinc plate ; the wavy line in each -case stands for the copper wires attached to the copper and zinc plates respectively. In the Grove's cell, consisting, as we have seen in 124, page 218, of a platinum plate in strong nitric acid, separated by a porous cell from a plate of zinc in dilute sulphuric acid, the long thin line represents the platinum plate, and the short thick line the zinc plate. In a Bunseris cell, which, as ex- plained in 125, page 219, differs only from a Grove's in that the platinum plate is replaced by a carbon one, the long thin line stands for the carbon plate. When all the cells are in series, the total current produced by the battery passes through each cell ; there- Chap. V.I E. M. P. AND RESISTANCE OF BATTERIES. 241 fore it follows, from what has preceded ( 115, page 203), that the E. M. F. of the battery is equal to the sum of the E. M. Fs. of each of the cells. If, on the other hand, the cells are joined up all in parallel, the current divides itself between the cells ; and if the cells are all made with the same materials, but not necessarily of the same size nor of the same internal resistance, the total chemical action, and therefore the total amount of fuel burnt per second, is exactly the same as if the entire current went through one of the cells. Hence the E. M. F. of the battery is simply that of any one of the component cells. The resistance, however, of the battery will be less than that of one cell, as the road for the current through the battery is made wider by putting cells in parallel ; and if the cells have each the same resistance of b ohms, and if there be p of them in parallel, the resistance of the battery is ohms. If the cells be partly in series and partly in parallel, we must combine the last two sets of conclusions, so that if the E. M. F. of each cell be e volts, and if there be 8 cells in series, and p in parallel, the total E. M. F. of the battery E, and the total resistance B, will be given by E = s e volts, B = ohms ; P so that if A be the current in amperes which the battery sends through an external resistance r, A= " . P In order to experimentally test the accuracy of these results, a number of cells, freshly put together, and having their corresponding plates of the same size, the plates in the different cells at the same distance apart, and the amount of liquid in each cell the same, should be joined Q 242 PRACTICAL ELECTRICITY. |Chap T, up in a variety of ways, and the resistances of the com- binations measured, as well as the E. M. Fs. of the bat teries compared with the E. M. F. of a single cell, selected at random from the battery, by one or other of the methods of testing previously given. The cells should be of such a type that the E. M. F. of each cell is a constant, a con- dition very satisfactorily fulfilled with Daniell's cells, and to avoid the cell used as the standard having a higher or a lower E. M. F. than the average E. M. F. of the cells employed, different cells may be selected from the com- bination as the standard cell in the different experi- ments. Example 58. To find the current that twelve Daniell's cells, each having a resistance of 0'6 ohm and an E. M. F. of I'l volt, can send through an external resistance of 5 ohms if the cells be formed four in series and three parallel : A= * = Answer. 0*76 ampere. Example 59. How many such Daniell's cells must be used in series to send a current of 1 ampere through an external resistance of 8 ohms, if one line of cells in series only be employed 1 Let x be the required number of cells, then x X 1-1 ~ 8 + x x 0-6' .-. x= 16. Example 60. If in the last question the current be 2 amperes instead of 1, then how many cells will be required 1 xx M 8 + x x 0-6 .-.*= -160. Chap. V.] EXAMPLES. 243 Therefore no number of such cells put in one line in series could send this current. In fact, if one cell be short-circuited with a piece of thick wire, the current it will send will be, or 1-83 amperes, and this is the 0*6 maximum current one, or any number of cells, arranged simply in series, can send. For if there be n of them arranged in series, and the whole be short-circuited, the current will be , or 1 -83 amperes, or, simply, the n x 0'6 current sent by one cell when short-circuited. Hence, if there be any external resistance, the current sent by one row of these cells in series, no matter how many there may be in the row, will be less than 1 -83 amperes. Example 61. Forty exactly similar cells, each having an internal resistance of f ohm, when joined in series send a current of 0-5 amperes through an incandescent lamp of 80 ohms' resistance : how many cells in series would be required to produce the same current through each of two such lamps arranged in parallel ? Let e be the E. M. F. of one cell in volts, then 40 x e ^ 80 + 40 x 0-75 = ? .-. e= 1-375 volts; therefore^ if x be the required number of cells, x x 1-375 _ 80 ~~ ' + x x 0-75 since the resistance of the two lamps in parallel will be 80 -- ohms, and they will require together 1 ampere, .-. x= 64. 136. Arrangement of a Given Number of Cells to produce the Maximum Current through a given Ex- 244 PRACTICAL ELECTRICITY. [Chap. V ternal Resistance. If N be the total number of cells employed in a battery, p being arranged in parallel, and s in series, K=ps, and the formulae on page 241 may be written A- 8e ~r + N If, therefore, we desire to ascertain what arrangement of a definite number of cells, each having a fixed E. M. F. of e volts, and internal resistance 6 ohms, will give the greatest current through a fixed external resistance of r ohms, we must ascertain what value of s will make the last expression a maximum. But to do this by trial by calculating the value of A corresponding with each of a very large number of values of s would be extremely laborious, and a far better plan for those who are not acquainted with the differential calculus is as follows : Give numerical values. to e, r, and , let them for example be 2, 3, and 4, then the expression becomes 2s 3 + 4"' next draw a curve having the values of s for the abscissae, and the corresponding value of the expression for the ordinates, and ascertain, from the shape of the curve, for what value of s the expression has its maximum value, then that value of s is the value required. In selecting values for s, a certain amount of practice is, of course, necessary, in order to select the best values, but one may be guided by remembering that if on taking two or three values of s we obtain practically the same value for the expression for A, it can be no use taking intermediate values of s. The curve obtained for A has the general shape shown Chap. V.] MAXIMUM CURRENT, FIXED EXTL. RESISTANCE. 245 in Fig. 93, the values of A being calculated on the sup- position that e, r, and , have the valups 2, 3, and 4 re- Fig. 93. spectively, and we find that the value of s that makes A a maximum is about 0'85, and this is the value of 3 which makes 2A 246 PRACTICAL ELECTRICITY. [Chap. V. or, in other words, the proper arrangement of a given number of cells to send the maximum current through a given external resistance is that which makes the re- sistance of the battery equal to the external resistance. The curve falls more slowly for values of s greater than that which makes A a maximum than for values less than this, and this tells us that the current will be not so much lessened by making s too large as it will be by making it too small ; hence if the number of cells and the resistance of each are such that it is impossible to arrange the battery so that its internal resistance is equal to the fixed external resistance, it is better, when the ex- ternal resistance is midway between the resistances the battery has when arranged in these two ways, to select the arrangement that puts rather too many cells in series than the one that puts rather too many in parallel. For example, suppose we have twelve cells, each having a re- sistance of 3 ohms, and we desire to arrange them so that they send a maximum current through an external resistance of 3| ohms, if we arrange them three in series and four in parallel, the resistance of the battery will be 3x3 - or 2 J ohms, on the other hand, if we put them four in series and three in parallel, the resistance will be 4 x 3 - or 4 ohms ; o and the given external resistance of 3^ ohms is exactly half-way between 2J and 4. Let us consider the cur- rents produced by these two arrangements of the cells. With the first, if e be the E. M. F. of each cell in volts. "With the second arrangement, Chap. V.J EXAMPLES. 247 24 32 The first reduces to e and the second to e ampere, 43 #7 o and of these the second is the greater by 77777 6 of an J451 ampere. Example 62. What is the least number of Grove's cells, each having an E. M. F. of 1'8 volts, and an inter- nal resistance of 0-09 ohm, that must be arranged in series to send half an ampere through a 50 volt incan- descent lamp 1 This question may be solved in two ways we may either first find the resistance of the lamp and then the number of such Grove's cells that it is necessary to put in series to send half an ampere through this external resistance or we may consider what is the P. D. at the terminals of such a Grove's cell, when half an ampere is passing through, and hence deduce how many such cells must be put in series so that when half an ampere is passing through them, the P. D. at the terminals of the battery is 50 volts. 1. The resistance of the lamp = ohms, I = 100 ohms, . . if n be the required number of cells, \__ n x 1-8 2 ~~ n x 0-09 + 100' . . n =28-5. Hence, 28 cells would produce rather too small a current, and 29 rather too much. We should have, therefore, to choose between using 28 cells and having the lamp not quite bright enough, or using 29 cells and having it a 248 PRACTICAL ELECTRICITY. [Chap. V. little too bright, or using 29 cells and interposing a small resistance by means of a piece of wire or in any other convenient way. 2. If n be the number of cells in series, then from 116, page 206, the P. D. maintained at the terminals of the battery equals n x l-8-n x 0-09. And this is to equal 50. Hence, n x l'S-^n x 0-09 = 50, which is the same equation as was used before, and there- fore must lead to the same value of n. Example 63. If 29 cells were used in series in the last question, what must be the value of the added re- sistance, so that the current through the lamp may be exactly half an ampere 1 Let x be the required resistance in ohms, then 1__ 29 x 1-8 _ 2 29 x 0-09 + 100 + x . . x = 0-895 ohm. Example 64. If four incandescent lamps, each re- quiring half an ampere, and 50 volts P. D. maintained at the terminals, are to be fed with Grove's cells, each having an E. M. F. of 1 *8 volts, and an internal resist- ance of 0*1 ohms, what arrangement of cells and of lamps will require the least number of cells to be used 1 First, let the four lamps be put in series, and let all the cells, n in number, be in series, then the P. D. at the terminals of the battery must be 4 x 50, and n x 1-8 - X 0-1 = 4 x 50, .-. = 114-3. Next, let all the lamps be put in parallel, and all the Chap. V.] EXAMPLES. 249 cells in series, then the total current required will be 4 x % or 2 amperes, therefore n x 1-8-2 n x O'l = 50, . . n = 31-2; hence, 32 cells, with a small resistance interposed, would give the required current, and this arrangement of all the lamps in parallel would only require about one- quarter of the number of cells necessary if all the lamps were in series. Various other cases might be tried ; for example, the lamps two in series, and two in parallel, or the cells two in parallel and half in series ; but it would be found that all the cells in series, and all the lamps in parallel, is the best arrangement. Example 65. If 40 such lamps as are referred to in the last few questions instead of 4 had to be fed with Grove's cells, what would be the best arrangement of the cells and of the lamps 1 First, let us try all the lamps in parallel, and all the cells in series, which arrangement we found was the best in the previous case, then, as the total current required will be 40 x \ or 20 amperes, and the P. D. at the ter- minals of the battery 50 volts, n x 1-8 - 20n x O'l = 50, or n = 250, a negative answer. This means that no number, no matter how great, of such Grove's cells, if the cells were arranged in series, could feed 20 such lamps if arranged in parallel \ and the reason of this is clear, because, if one Grove's cell were simply short-circuited, the current that it would produce would be 1*8 - or 18 amperes, hence, no number of such Grove's cells arranged in series can produce more than 18 amperes, even if short-cir- 250 PRACTICAL ELECTRICITY. [Chap. V. cuited, and hence they can only produce less than 18 amperes if there be any external resistance, whereas we want them to produce 20 amperes. Secondly, let us try half the lamps in parallel and two in series. In that case the total current must be 10 amperes, and the P. D. 100 volts. Hence we have n x 1-8 -10 n x 0-1 = 100, or n= 125. We may now try all the lamps in parallel and half the cells in series, and two in parallel. Let n be the number in series, that is, half the total number, then nx 1-8-20 nx Q' 1 = 50, 2 . . n = 62-5. Consequently the total number of cells required is 125. Hence, whether we put the 40 lamps two in series and 20 in parallel, and use all the cells in series, or put half the cells in series and two in parallel, and use all the lamps in parallel, exactly the same number, 125, of cells is required. There is one other arrangement that might be tried, viz., all the lamps and all the cells in series, but from what we saw in the first part of example No. 64, we may anticipate that this will be a very bad arrangement. With this arrangement the current required will be half an ampere, the P. D. 40 X 50 volts, .-. n x 1-8-iw x 0-1 = 2,000, or n = 1,142-9. Hence 1,1 43 cells would be required with this arrangement. Example 66. How many Daniell's cells, each having an E. M. F. of 1 -1 volts, and an internal resistance of 0'8 ohms, would be required to feed two Edison incan- descent lamps, each requiring 0*75 of an ampere, and 110 volts at its terminals 1 Chap. V.I EXAMPLES. 251 One such Daniell's cell, short-circuited, would produce or 1-375 amperes, 0-8 hence, if we put the lamps in series, one row of Daniell's cells in series will produce sufficient current. If, how- ever, we put the two lamps in parallel, then, since the total current must be 1'5 amperes, we must have two rows of cells. First, let the lamps and cells be in series, then n x 1-1-075W x 0-8 = 220, or n = 440. Second, let the cells be half in series and two in parallel, and let n be the number in series, the lamps being still in series, then nx 1-1 -0-75 !L?'* = 220, 2 or n = 275. Hence, the total number of cells necessary will be 550, or this arrangement is worse than the preceding. Third, let the cells be half in series and two in parallel, but let the lamps be also in parallel, then x 1-1-1-5 " x ' 8 = 110, 2 or n = 220. Hence, the total number of cells required is 440, or the same as in the first case. Fourth, let the cells be three in parallel and n in series, and let the two lamps be still in parallel, then n x Mr- 1-5 n X ' 8 = 110, .-. n = 157-1, and the total number of cells required would be 472. 252 PRACTICAL ELECTRICITY [Chap. V. Therefore, arrangements Nos. 1 and 3 require the least number of cells, but with any arrangement the number of Darnell's cells required is very large in con- sequence of the high resistance of the cells, and of the fact that the greater part of the energy is expended in send- ing the current through the cells themselves. Example 67. How many lamps in parallel, each re- quiring SO volts, and 0*6 of an ampere, can be fed with 42 accumulators in series, each having 1*95 volts E.M.F. on discharging, and 0'005 ohms' internal resistance 1 Let I be the number of lamps, then, since the total current will be I x 0*6, we have 42 x 1-95 -I x 0-6 x 42 x 0-005 = 80. Answer. 15. Example 68. If the number of accumulators in the last question be increased by one, by how many may the number of lamps be increased 1 Answer. The number of lamps may now be 29'8, that is, may be 30 all a trifle too dull, or 29 a trifle too bright, unless a small resistance be introduced. The ad- dition, therefore, of one accumulator practically doubles the number of lamps that can be fed by them. Example 69. If there be 44 accumulators in series, and if 46 lamps be fed by them, each lamp requiring, as before, 80 volts at its terminals, and 0-6 of an ampere passing through it when properly glowing, how much per cent, will the current passing through the lamps be too great or too small ? 80 The resistance of each lamp is- or 133 '3 ohms, hence 0*6 i oq.o the resistance of all the lamps will be - or 2-899 46 ohms, consequently the current passing through them will be Chap. V.] VARIATION IN TOTAL CURRENT BY SHUNTING. 253 41x1-95 44 x 0-005 + 2-899 or 27-51 amperes, The current that ought to pass through the lamps is 46 x 0-6, or 27*6 amperes. Hence the current is about 0*3 per cent, too small. 137. Variation produced in the Total Current by Shunting a Portion of the Circuit. We can now cal- culate the entire effect produced on the current passing through a galvanometer of resistance g, by shunting the galvanometer with a shunt of resistance s. Let E be the E. M. F. in volts, and b the resistance in ohms, of a battery, r the resistance in ohms of the rest of the cir- cuit, excluding the galvanometer, and g the resistance of the galvanometer ; then, before shunting, the current G M in amperes, that passes through the galvanometer, is simply the whole current A 1? that passes through the bat- tery, and this equals E . - amperes. b + r + ff After shunting, the current A 2 , now flowing through the battery, becomes _g - amperes, s + g and the fraction - of this passes through the galva- s + g nometer ; therefore, if G 2 be the current now passing through the galvanometer, s _ E G 2 = - -- -I- g)(b + r) 254 PRACTICAL ELECTRICITY. [Chap. V. If 6 + r be very large compared with g> then, approximately, s E \JTn - - - . *+g b + S and A* = - . * + r also A! = - , b + r that is to say, the current passing through the battery and through r is practically unchanged by shunting the galvanometer, and, therefore, after the galvanometer has been shunted, it is not merely the fraction -- of A 2 , * + 9 but -- of A 1? that passes through the galvanometer. On the other hand, if b + r be small compared with g, then, approximately, 89 E i andG 1 = A 1 = ~, 9 . . G 2 = G! approximately. Hence, as long as - is large compared with b + r, s + g that is, as long as the shunted galvanometer is the major part of the whole resistance in the circuit, shunting the galvanometer produces no diminution in the current flowing through it. And it is not until the resistance Thai). V.I EXAMPLES. 255 of the shunted galvanometer is reduced to a value com- parable with b + *% that the galvanometer deflection is seriously diminished. Example 70. If the resistance of a galvanometer be 1,000 ohms, what must be the resistance of a shunt to diminish the current passing through the galvanometer to one-half, first, when the resistance of the rest of the circuit is 100,000 ohms; secondly, when it is only 100 ohms 1 In the first case we have *E __1 E (s + g)(b + r) + sg ~~ 2 b + r + g or substituting (s + 1,000) x 100,000 + * x 1,000 " 2 ' 101,000* . . * = 990-1 ohms; that is, 8 is only a little less than 1,000 ohms, which is the resistance of the galvanometer. In the second case (*+ 1,000) x 100 + s x 1,000 2 1,100 . . s = 90-9 ohms, or not as much as one-tenth of the galvanometer re- sistance. Example 71. What must be the resistance of a galvanometer relatively to that of the rest of the circuit, so that shunting the galvanometer with a quarter of its own resistance may halve the current passing through it ? From what has preceded, we have s 1 1 = - x , r) + sy 2 256 PRACTICAL ELECTRICITY. and since s = i. t 4 .-. g = 3 (6+r). Example 72. In example No. 38, given 011 page 180, what resistance must be added to the main circuit, so that the insertion of the shunt shall not alter the total current ] To solve this question we must consider by how much the resistance of the circuit has been diminished by the insertion of the shunt, this diminution being, of course, equal to the difference between the resistances of the galvanometer shunted and unshunted. The shunted galvanometer has a resistance of 1,808 x 452 1,808 + 452' or 361 '6 ohms, therefore the resistance of the circuit has been diminished by 452 361-6, or 904 ohms, and this resistance must be added if we wish that the total current shall be kept constant. Example 73. What resistances must be added to the main circuit to keep the total current constant when a galvanometer, having 1,000 ohms' resistance, is shunted with the three shunts which respectively allow r^th, T^oth, and ToSoth of the current to flow through the galvanometer 1 If s be the resistance of the shunt, and g the resist- ance of the galvanometer, the diminution of the resistance produced by shunting the galvanometer is Chap. V.J CONSTANT TOTAL CURRENT SHUNTS. 257 , - , or 8 + g s + g From what has been given in 104, page 178, the resist- 1000 1000 ances of the three shunts must be > ~^~ and ohms respectively. Therefore, the resistances that y t/ */ must be added are 10002 or 900 ohms. + 1000 9 10002 or 990 1000 99 1QOQ2 125? + 1000 999 or 999 138. Constant Total Current Shunts. There are two ways, differing somewhat from one another, by means of which a box of shunts can be so arranged that the insertion of the shunt coil, parallel to the galvanometer, also introduces a compensating resistance in the main circuit, and so keeps the main current un- altered in strength. The first of these is due to Mr. Kempe, and the second to Mr. Rymer Jones. Fig. 94 shows symbolically Mr. Kempe's arrangement, and it will be seen that the insertion of a plug into one of the holes A, B, C, for the purpose of introducing a shunt parallel to the galvanometer Gr, also adds one or more of the resistances r lt r 2 , r a , to the main circuit, whereas, if the plug be inserted in the hole which is not lettered, the galvanometer is unshunted, and all the three coils r 1? r 2 , r s , are cut out of the circuit. A plan of the actual shunt box is seen in Fig. 95. To determine what should be the values of these resistances, we have to remember that, if n lt 2 , 3 be the three multiplying B 258 PRACTICAL ELECTRICITY. LChap. V. powers of the shunts, so that the three currents GI, G 2 , G 3 , passing o f 1 o through the galvanometer are respectively equal to , , , n\ n flowing along the first line, is Chap. V.] EXAMPLES. 263 IT- 200 E - x : amperes. + + 20 + 200 250 300 J_ , 1 , 1 200 250 300 Therefore, G l = amperes, 2 = 236 * and C 3 = 2494 Hence, C^ is diminished by about 6-8 per cent, by allow- ing a current to flow along the second line, and by about 11-7 per cent, by allowing a current to flow along both the second and the third lines. Example 77. If two telegraph lines each have a resistance of 500 ohms, including the resistances of the receiving instruments, what may be the greatest resist- ance of the battery employed to send the current along both, so that the current flowing along either shall not be diminished by more than 1 per cent, by sending a current also along the other 1 Let E be the E. M. F. in volts, and b the resistance of the battery in ohms, then the current flowing along either line, when no current is being sent along the other, is and the current flowing along either line, when a cur- rent is also being sent along the other, is 1 x E 2 6T250 am P eres - 264 PRACTICAL ELECTRICITY. (Chap. V Now we want b to be of such a value that E I E ig not greater 1 x _ 6 + 500 2 6+250 than 100 6 + 500' Consequently, the largest permissible value of 6 will be found by making * _*-- = -J-x E , b + 250 100 6 + 500 or ,_ x l 6+500 2 6 + 250 Answer. 5'1 ohms. Example 78. There are two telegraph lines , one having a resistance of 400 ohms, and the other of 500 ohms, including the resistance of the receiving instru- ments. The receiving instrument on the first line is so arranged that it will work without adjustment, with cur- rents varying between 5 and 5*2 thousandths of an am- pere. What must be the E. M. F. of, and resistance of, the common battery, for the two lines, so that the cur- rent flowing along the first line may be always between these limits, whether or not a current is being sent along the second line 1 If E be the E. M. F. in volts, and 6 the resistance in ohms of the battery, the maximum current flowing along the first line will be amperes> and the minimum current 500 E 400 + 500 400 x 500 h 400 + 500 500 E amperes, or 900 b + 200,000 Chap. V.] EXAMPLES. 265 The first current must not exceed 5 '2 thousandths of an ampere, and the second must not be less than 5 thousandths of an ampere. Taking, therefore, the limit- ing values, we may say that E 52 md 6 + 400 " 10,000 5E 5 96 + 2,000 1,000 Solving these two equations for E and 6, we find that E = 2-19 volts about, and b = 21 ohms In practice, larger E. M. Fs. than this must be used to allow for leakage along the line, in consequence of which only a portion of thp current that leaves the send- ing or signalling end arrives at the receiving end. Example 79. If 10 of the 30 lamps in example 68, page 252, be turned out, what will be the P. D. at the terminals of the remaining 20 ? Answer. 81-27 volts. Example 80. If 50 or more incandescent lamps in parallel, each requiring 0'8 amperes and 100 volts to glow properly, be fed with 55 accumulators in series, each having an E. M. F. of 1'98 volts when discharging, what must be the resistance of each accumulator, and what is the maximum number of lamps that can be lighted, so that the P. D. at their terminals never ex- ceeds 101, and is never less than 99 volts? 1 r\f\ The resistance of each lamp may be taken as - or 125 ohms. Hence, considering the case of the least number of lamps, 50, which will correspond with the highest number of volts, 101, we have, if b be the resist- ance of one accumulator, 266 PRACTICAL ELECTRICITY. [Chap. VL 55 x 1-98 101 50 50 from which it follows that b = 0-003555 ohms. Next, considering the case of the largest number of lamps n, which will correspond with the lowest number of volts allowed, viz. 99, we have 55 x 1-9 99 Substituting in this the value previously found for 6, and solving for n, we n'nd that n = 63-92. Hence, 64 lights would be practically the largest number. CHAPTER VI. INSULATION. 140. Surface Leakage, and Leakage through the Mass 141. Coating Insulating Stems with Paraffin Wax, or Shell-lac Varnish -142. Sealing up One End of a Cable when under Test 143. Construc- tion of an Insulating Stand 144. Laws of Surface Leakage, and of Leakage through the Mass 145. Corrugating the Sides of Ebonite Pillars 146. Common Fault made in Constructing Ebonite Pillars 147. Telegraph Insulators 148. Testing Insu- lators during Manufacture 149. Measuring High Resistances 150. Subdividing a P.D. into Known Fractions 151. Constant of a Galvanometer 152. Very Delicate Galvanometers 153. Thomson's Astatic Galvanometers 154. Importance of the Gal- vanometer being "Well Insulated. 140. Surface Leakage, and Leakage through the Mass. There are two ways in which electricity may pass from one body to another ; it may either creep along Chap. VI.] LEAKAGE. 267 a layer of dirt and moisture on the surface of an insulating rod, or it may pass through the mass of the insulating material. The former may be called " surface leakage"; and the latter, "leakage through tJie mass." In the case of a charged body supported on a rod of glass or ebonite, surface leakage is the main thing to guard against ; whereas, with a long submarine cable, consisting of a copper conductor surrounded with guttapercha or with indiarubber, and immersed in the sea, the main loss of electricity is through the guttapercha or indiarubber. If, however, the piece of insulated cable be very short, then the surface leakage at the ends, arising from the electricity creeping from the ends of the copper conductor over the ends of the guttapercha covering Pig. 98. to the water or the iron sheathing which is outside the guttapercha, may be the cause of the most important part of the loss. Hence, when it is desired to test the actual passage of the electricity from the conductor through the in- sulating material, it is usual, in order to diminish the surface leakage to a minimum, to cut the end of the core like a pencil, as shown in Fig. 98, so as to expose a long freshly bared, clean, dry surface of guttapercha or indiarubber. The insulation of the end can be still further improved by coating the surface with a thin layer of clean paraffin wax, which has been first melted by heating, to a temperature not however much above that of boiling water, otherwise the wax would be par- tially decomposed, and its resistance diminished.* 141. Coating Insulating Stems with Paraffin Wax Or Shell-lac Varnish. Coating the surface of any insu- lating stem which is exposed to the air with paraffin wax * To avoid the paraffin wax being overheated, it is well to warm the vessel containing it by means of a water bath in the same way that glue is usually heated in an ordinary glue-pot. 268 PRACTICAL ELECTRICITY. [Chap. VI has not only the advantage that it renders the surface much less "hygroscopic" or attractive of moisture, but it enables the wax to be easily partially scraped off at any time, and a new clean dry surface exposed. Shell-lac varnish, made by dissolving shell-lac in alcohol, may be employed in the place of paraffin wax, but, in many cases, it is not as good, partly because shell-lac, being hard and brittle, cannot be easily scraped so as to expose a new clean surface, and partly because, at the present day, it is very difficult to buy really good shell-lac, the material of commerce being much adulterated.* If, fiowever, a (/lass rod can be kept free from dust, and artificially dried, then it is better to put neither paraffin wax nor any kind of varnish on it. 142. Sealing up One End of a Cable when under Test. The insulation of a cable may be tested by measuring with a very delicate galvanometer the current that a battery of high E. M. F. can send through the indiarubber, guttapercha, or other insu- lating material used in its construction. To do this it is only necessary to have one end of the copper conductor bare, hence it is desirable after pointing the guttapercha at the other end, as shown in the last figure, to seal it up altogether by dipping it into paraffin wax two or three times, so as to cause a lump of paraffin wax to adhere to it, which can be best done when the paraffin wax has cooled until it is approaching the temperature of solidification. 143. Construction of an Insulating Stand. In Fig. 29 the plate A, and in Fig. 40 the pot P, are supported on a special form of insulating stand, in which * Dr. A. Muirhead, who has had great experience in the use of shell-lac in the construction of condensers, recommends the following process for obtaining good insulating varnish. Obtain " button" lac, pick out the cleanest lumps, and dissolve them in absolute alcohol. Allow the solution to stand for some time, and use only the upper part of the solution. When the highest insulation is required, first dissolve the button lac hi ordinary alcohol, and precipitate it by allowing the solution to trickle into distilled water, thsn dissolve the precipitate in absolute alcohol. Chap.VI.J INSULATING STAND. 269 the glass rod is kept free from dust and artificially dried. This device for obtaining high insulation is far superior to the old-fashioned plan of using a simple rod of glass or ebonite, since such a rod, whether it was coated with varnish or not, required perpetual cleaning and drying to prevent the electricity leaking down its surface. The special arrangement shown in these figures, and which has been designed by the author for experiments on statical electricity, consists of a glass vessel made of any convenient kind of glass, and having at its bottom a tubulure of glass attached vertically at the centre. This tubulure, or collar, of glass is ground inside like the inside of the neck of a glass-stoppered bottle, and into this tubulure the ground end of a rod of highly insulating glass fits, much in the same way as a glass stopper does into a bottle. On to the top of this glass rod anything can be fixed ; for example, the plate A (Fig. 29), and the pot P (Fig. 40), are supported in position by a little collar of metal, which is soldered to the bottom of A and of P, and which slips fairly tightly over the top of the glass rod. Before the glass rod is inserted a little strong sulphuric acid is poured in, and rests on the expanded bottom of the glass vessel, exposing a large surface of acid for absorbing the moisture contained in the air in the vessel. When the instrument is not in use a split indiarubber stopper I, seen in Fig. 40 resting on the base of the instrument, is inserted to close up the neck of the glass vessel, which is contracted at the top, partly for this purpose, and partly to avoid a too rapid inter- change of air between the inside and the outside of the glass vessel when the instrument is in use. The advantages of this insulating stand are : 1. The rod can be easily taken out and cleaned. To clean such a rod hold it by the end, and wash it by means of a clean brush with soda and warm water to remove the grease ; then rub it with another brush while a stream of warm ordinary water flows over it, to remove the soda ; and, lastly, let a stream of distilled water flow 270 PRACTICAL ELECTRICITY. [Chap. VI. over it to remove the trace of salt which is dissolved in ordinary water. The rod should be dried before a fire ; or, better, by being hung up under a glass shade, or in some confined space free from dust, in which there is a vessel containing a little strong sulphuric acid. On no account dry the glass rod by rubbing it with a cloth, nor touch it with the Jingers except at the extreme end. 2. The rod may be made of dense flint glass which insulates well, while the vessel may be made of any kind of glass that can be easily, and, therefore, cheaply blown, without reference to its insulating qualities. 3. As the rod is easily taken out, the sulphuric acid can be put into the vessel without splashing the rod ; or the old acid, after it has become weak by absorbing water- vapour, may be emptied out, and fresh acid put in without fear of dirtying the rod. This it would be difficult to do, even with another opening in the vessel, if the rod were immovable. 144. Laws of Surface Leakage, and of Leakage through the Mass. The film of dirt and moisture on a rod acts like an exceedingly thin layer of conducting matter, therefore for stems equally damp and dirty (and the cleanest glass stem rapidly becomes damp and dirty when exposed to the air), the surface resistance or insu- lation where I is the length, and d the diameter of the stem, since resistance is directly proportional to the length, and inversely as the sectional area of the conducting layer. The stem also conducts through its mass, and its resist tance in ohms is where g is the resistance in ohms between the opposite faces of a cubic unit of the glass or other material, of Chap. VI.] LAWS OF LEAKAGE. 271 which the insulating stem is made, I its length, and d its diameter. If I and d be in centimetres, g must be the resistance of a cubic centimetre ; or, if I and d be in inches, g must be the resistance of a cubic inch. The approximate values of g in ohms per cubic centi- metre, for some good insulators, are given in Table No. Y. The resistance of an insulator increases up to a certain limit with the time the current is kept on, or with the time of " electrification," as it is shortly called, so that the values in the table, which have been obtained after several minutes' electrification, represent approxi- mately this maximum value. The resistance of insula- tors also varies with the temperature, but while the resistance of conductors increases with elevation of temperature, the resistance of insulators diminishes with elevation of temperature. TABLE No. V. Substance. Tempera- ture Centigrade. Approximate Re- sistance in ohms per cubic centi- metre after several minutes' Authority. electrification. Mica .... 20 84 X 10 12 Author. i Standard adopted Guttapercha . 24 450 X 10 1 - by Mr. Latimer Clark. Shell-lac. . . 28 9,000 x 10 12 Author. Hooper' sVulca- ] nised India- I 24 15,000 x 10 12 Tests of Cables. rubber . . j Ebonite . . . 46 28,000 X 10 W Author. Paraffin Wax . 46 34,000 x 10 12 The resistance of dense flint glass has not, as far as the author is aware, been measured at as low a tempera- ture as 40 C. after a long period of electrification. At 100 C., Mr. Thomas Gray found that it was about 206 x 10 12 ohms per cubic centimetre, at 60 C. about 1,020 x 10 12 , and that it increased very rapidly as the temperature diminished. Some experiments made by 272 PRACTICAL ELECTRICITY. [Chap. VI. the author showed that, after several hours' electrifica- tion, the resistance per cubic centimetre at ordinary temperatures had a far greater value than this. In the above formulae for the surface resistance and resistance of the mass of a rod, the more I is increased, that is to say, the longer the stem is made, the larger both the surface and the mass insulation become ; while, on the other hand, the larger the value of d, the smaller are both the surface and the mass insulation, the latter, however, diminishing much more rapidly than the former, as d is increased. Consequently, while for a long thin rod of fairly good insulating material the main loss of electricity will be over the surface, for a very short thick rod, for a sheet, in fact, of insulating material (for that is what a rod ultimately becomes, as it is made shorter and thicker), the main leakage will be through the material if the elec- tricity is conveyed to the different parts at each side of the sheet by means of a piece of tin-foil, stuck on both sides of the sheet of insulating material, and if sufficient of the surface of the insulating material near the edges of the sheet be left uncovered to prevent surface leakage. (See construction of condensers, 173, page 318.) 145. Corrugating the Sides of Ebonite Pillars. In order to increase the value of I in the case of an in- sulating stem without making it very tall and weak, it may be made with corrugations, as shown in Eig. 99. These rings have not only the advantage that I is in- creased, but the thin edges may be very easily wiped with a clean cloth, and the insulation thereby improved. Further, although these edges may be dirtied if the rod be touched or taken hold of, the cavities between them will probably be left clean, and hence a continuous line of dirt will not be formed from the top to the bottom of the pillar, as would probably be the case if the surface of the pillar were smooth without corrugations. 146. Common Fault made in Constructing 1 Ebonite Pillars. A common fault made in constructing insu- lating stems of ebonite, and which should be most care- Chap. VI.' j COMMON FAbLT IN EDONITE PILLARS. 273 fully guarded against, consists in drilling a hole right through the stem, and then inserting into the top of this hole the screw which holds on the terminal, and into the bottom the screw which holds the pillar to the base. This continuous hole makes it impossible by any amount of cleaning and paraffining of the outside of the stem to obtain good insulation, for even if the sides of this hole between the ends of the screws were quite clean, the length of ebonite surface separating the ends of the screws would be small compared with the length of the pillar outside, and so the leakage from 274 PRACTICAL ELECTRICITY. [Chap. VI. screw to screw inside the ebonite pillar would be greater than along the outside : but when in addition the sides of this hole are, as is frequently the case, dirty, the insulation of the pillar is immensely diminished by the hole being bored right through. The hole should, there- fore, on no account be drilled through ; and in the case of any old apparatus in which this mistake has been made, the screws should be taken out, and the sides of the hole carefully cleaned with a small brush, such as is sold for cleaning glass tubes, using first soda and warm water, then warm water without soda, and, lastly, ^ allowing a stream of distilled water to flow through the hole ; finally, when the sides of the hole are quite dry, melted paraffin wax should be poured in, so that there is a little block of paraffin wax filling up the hole between the ends of the screws. 147. Telegraph Insulators. In the case of the earthenware, or porcelain, insulators used to sup- port telegraph wires, length of sur- face, combined with small periphery of a transverse section, is obtained by means of the " double cup insu- lator" (Fig. 100). This form of insulator, which was originally pro- posed by Mr. Latimer Clark, has also the advantage that the inner surface 2, 2 of the outer cup, as well as the inner 4, 4, and outer surface 3, 3 of the inner cup, are kept tolerably clean and dry. Before the electricity escaping from the wire, which is bound in the groove at the upper part of the insulator, can reach the iron stalk, by means of which the insulator is attached to the wooden or iron bracket on the telegraph post, it must leak down tho outside of the outer cup 1,1, then up the inside of the Fig. 100. Chap. VL] TELEGRAPH INSULATORS. 275 outer cup 2, 2, then down the outside of the inner cup 3, 3, and, lastly, up the inside of the inner cup 4, 4. The porcelain, or earthenware, cups should, as origi- nally suggested by the late Mr. Cromwell Vaiiey, be moulded separately, and cemented together after they are baked, in order that a possible flaw in the one may not be accompanied by a flaw in the other, which would probably be the case if they were moulded in one and then baked. The lips of the cups should be shaped as shown in the figure, for, with this shape, Mr. Varley found that the drops of water hanging on the lip during, or after, rain, were simply blown a little way up inside the cups, instead of being broken and the moisture scattered all over the inside of the insulator, moistening all parts. 148. Testing Insulators during Manufacture. In order to test the quality of insulators, a hundred of them are placed, inverted, so that they can hold water, in a shallow metal-lined trough, containing sufficient water to come to within half an inch of their lips, and water having been poured into both the cups so as to reach to about the same height, the insulators are left in the water for at least forty-eight hours, to give time for the water to soak into any cracks in the earthenware or porcelain. The metal stalks of all the insulators are fastened together with copper wire, and the resistance between this copper wire and the water in the trough, or, what is electrically the same thing, the metallic lining of the trough, will measure the parallel resistance to leakage through the earthenware or porcelain of which the cups are made, and over the surface of the lips of the cups. To diminish the surface leakage as much as possible, the lips are dried, just before the test is made, by large red-hot rollers being rapidly rolled backwards and forwards over the troughs along iron rails fastened on the tops of the sides of the troughs, this operation being performed so quickly that the lips of the insulators are dried before any appre- ciable quantity of the water in the trough or in the 276 PRACTICAL ELECTRICITY. &hap. YI, insulator cups is evaporated, and the air in the neigh- bourhood of the cups thus rendered steamy. Then, before the lips have had time to cool, and, therefore, before any fresh moisture can settle on them, the parallel resistance is measured. The resistance of one double cup insulator made of porcelain, and tested in this manner, varies from five hundred thousand million to four million million ohms, depending on the size of the cups, and the quality of the clay of which the cups are made. Taking two million "meg- ohms" that is two million million ohms, as the average resistance of each of a batch of 100, the 100 should have a parallel resistance of twenty thousand megohms. If a set of 100 are found to have a parallel resistance much below the other sets of 100 of the same type, it is either due to faulty drying of the lips, or to the presence of one or more cracked porcelain cups in the batch, or to one or more of the porcelain cups having been badly baked. Under these circumstances a red-hot iron roller should be again rolled backwards and forwards over the trough, when, if the same low resistance is again obtained, the wire should be unwound from the iron stalks, and each insulator should be tested roughly and quickly, by touch- ing the stalk with one of the copper wires connected with the measuring apparatus, the other wire coming from the measuring apparatus being still attached to the metallic lining of the trough. In touching the stalk with the wire, care must be taken to hold the india- rubber or guttapercha covering at some little distance from the end, and the insulating coating must be cut like a pencil, as shown in Fig. 98, page 267 ; otherwise the leakage to earth along the outer surface of the in- sulated wire will be mistaken for leakage through the porcelain of an insulator. In this way the defective in- sulator or insulators may be detected and removed from the batch. This rough method of picking out defective insulators may with advantage be employed before the stalks of the Cttap. VI.] TESTING TELEGRAPH INSULATORS. 277 insulators are wired together, and the parallel resistance of the batch of 100 tested accurately. For supposing one million megohms were taken as the " specified " or con- tract minimum resistance of each insulator, then, if ninety- nine of them happened to be each of them better than the specified standard, having, say, each three million megohms, whereas one of them was much below the standard, and had only, say, twenty thousand megohms, the parallel resistance of the 100 would be 12,048 megohms. But as this would be more than the specified resistance of a good hundred, which would be ten thousand megohms, it follows that, although the batch contained an insulator having only the y^o*h ^ * ne resistance of each of the remaining ninety-nine, the batch would be allowed to pass if the insulators were only tested in hundreds, and were not subjected individually to any test. But such -an insulator, which had only the r |~oth of the resistance of each of the rest, should certainly be rejected, since, although the defect at present is only a small one, it is extremely probable that this defect will go on increasing, so that if it be put up with others on a telegraph line, more electricity will eventually leak through this insulator to the ground than will escape over the surface of all the insulators which support several miles of the telegraph wire. 149. Measuring High Resistances. With an or- dinary Wheatstone's bridge we can test resistances up to 1*11 million ohms, but not above that, consequently resist- ances of thousands of megohms are usually tested in quite a different way, by measuring the current that a known P. D. will send through them. As, however, the gal- vanometer must be extremely sensitive to enable such small currents to be measured by means of it, and as the absolute value of the deflection of such a very delicate or sensitive galvanometer is liable to vary from day to day, we do not attempt to calibrate the galvanometer absolutely in amperes, or rather in millionths of an am- pere. Further, it is not necessary to know the value in 278 PRACTICAL ELECTRICITY. [Ciap. VT. volts of the P. D. employed, since, if we compare the current seut by this P. D. through the unknown resist- ance with that sent by the same P. D. T or by a known portion of it, through a known resistance, the value of the unknown resistance can be ascertained. 150. Subdividing a P. D, into Known Fractions. The simplest arrangement for obtaining a known fraction of a P. D. is to cause a steady current, by means of a battery B (Fig, 101), to flow through a very high resist- ance L M ; then the P. D. between any two points s T, bears to the P. D. be- tween any other two points L M, the ratio that the resistance q of the part s T bears to the resistance p of the whole L M. The P. D. between the points L M 101. may be employed to send a current through the unknown resistance a?, and the P. D. between the points s T, through a known resistance r. It is hot, of course, necessary that both the points s and T should be distinct from L and M ; one of them, for example, s, may be the same as L. 151. Constant of a Galvanometer. If the unknown resistance x be very large, the galvanometer must be very sensitive ; hence either the known resistance r must be also very large, or q must be very small compared with p, or, lastly, the galvanometer must be shunted in taking what is called "the constant of the galvanometer " If the resistance L M be very accurately subdivided, then there is no objection to taking q as small as we like ; indeed, taking q very small has in such a case an advantage over shunting the galvanometer, arising from the fact that the smaller q is, and the higher the resistance of the galvanometer circuit (the coils of which are attached to the two points s and T), the more accurately is the parallel resistance between Cbap. VI.] MEASURING HIGH RESISTANCES. 279 s and T equal simply to q. If, on the other hand, the resistance L M be not very accurately divided, then it is not advisable to take the points s and T too near together, since a very small absolute error in the value of q will make a very large error in the ratio of q to p when q is very small. In that case, shunting the galvanometer is a better method of diminishing the galvanometer deflection. Let C and C' be the relative strengths of the currents passing through the galvanometer when, first, the P. D. between L and M is employed in sending a current through x with the galvanometer unshunted (Fig. 1 02), Fig. 102. Fig. 103. and when, second, the P. D. between s and T is sending a current through r, the galvanometer of resistance g, being shunted with aVesiiitance s (Fig. 103), then *? s q _C! P x = - x - x - ---' f (r + -^f-)-9. (J S \ S _)_ g/ Generally ' may be neglected in comparison with r, and g in comparison with x. In which case very approximately we have p C' X X r. s 280 PRACTICAL ELECTRICITY. [Cbap. Vt If we have, not a large subdivided resistance, L M (Figs. 102, 103), then we must employ a battery of many cells in series when sending the current through the high resistance x, and a small battery, one cell perhaps, when sending the current through the known resistance r. In such a case the ratio of the electromotive forces of the large number of cells to that of the small number will be approximately proportional to the numbers of cells employed, but it may be more accurately ascertained by one of the methods already described ( 131, 132, pages 231, 234) for comparing electromotive forces. Let N be the ratio of the electromotive forces, and let b and b' be the resistances, in ohms, of the two batteries, then if and C' be the relative strengths of the current, as before, _ _ x+b+g's+g r+ 5' + S 9 9+9 Os Or, as usually b' -f is small compared with r, and as b + g is also small compared with #, we have approximately x = x x x r , s Example 81. Using a galvanometer, the deflection of which is directly proportional to the current passing through it, and having a resistance of 7,500 ohms, a deflection of 220 divisions on the scale is produced when p is 10,000 ohms, and the current is sent through the unknown resistance. On the other hand, when q is 100 ohms, and the current is sent through a known resistance of 10,000 ohms, a deflection of 300 scale divisions is obtained with the galvanometer shunted with 7*508 ohms. What is the value of the unknown resistance 1 Using the complete formula we find that the un- Chap. VI. j VERY DELICATE GALVANOMETERS. 281 known resistance is 1,364,561,591, while the approximate formula gives as the result 1,363,636,364. For all practical purposes it would be sufficient to know that the resistance was 1,364 megohms, which result would be ob- tained quite as accurately from the second answer as from the first. Example 82. With 100 cells and the unknown re- sistance a deflection of 192 scale divisions is obtained, whereas with one cell and a known resistance of 25,000 ohms in circuit a deflection of 243 scale divisions is pro- duced when the galvanometer is shunted with the one- hundredth shunt. What is the value of the unknown resistance 1 ? Answer. 316 megohms approximately. Example 83. If one cell give a deflection of 100 scale divisions when 10,000 ohms are in circuit, and the galvanometer is shunted with the one-thousandth shunt, how many .cells must be used to test a resistance of 10,000 megohms if a deflection of not less than 50 scale divisions is to be obtained 1 Answer. 500 cells approximately. Example 84. If one cell give a deflection of 127 scale divisions when 12,000 ohms are in circuit, and the galvanometer is shunted with the one-thousandth shunt, through what resistance would one cell give a deflection of one scale division if the galvanometer were unshunted] Answer. 1,524 megohms approximately. 152. Very Delicate Galvanometers. For measuring accurately the current that 100 Daniell's cells will send through, say, 20,000 megohms, which is only the one two- hundred-millionth part of an ampere, we must employ a galvanometer which is far more sensitive than anything that has hitherto been described in this book. To obtain this high degree of delicacy three conditions must be fulfilled : 1. The number of turns of wire on the galvanometer bobbin must be very large. (See 217, page 418.) 282 PRACTICAL ELECTRICITY. [Chap. VI. 2. The suspended magnetic needle must be strongly magnetised. 3. The controlling force must be very weak. In order to fulfil condition No. 1, and, at the same time, to keep all the turns of wire close to the suspended magnet, very fine wire must be used in winding the bobbin. No. 2 is fulfilled by making the needle of hard steel; a piece of watch spring heated to redness and cooled suddenly by being dipped in water answers well. By the proper adjustment of an auxiliary magnet the controlling force due to the earth or other controlling magnet may be rendered very weak for any one position of the suspended needle of the galvanometer, but unless the controlling magnet be very large and far away it is difficult to obtain a sufficiently uniform field for the controlling jo*. force acting on the sus- pended magnet to be weak throughout the whole range of motion of the suspended magnet. A better plan is to make the suspended ar- rangement of two magnets N S, N' S' rigidly fastened, with their poles reversed, to a stiff vertical wire (Fig. 104). If these two magnets N S, N' S' be of exactly the same length and strength, and if their poles be in exactly the same vertical plane, the earth's magnetism will have no effect on the arrangement, hence it will rest indifferently in any position about a vertical axis as far as the earth's attraction is concerned.* But if one of these magnets be * As it is extremely difficult to fix the magnetic needles to the vertical wire so that their magnetic axes are in the same vertical plane, the practical test for the needles being equally strong is not that the arrangement will rest indifferently in any position when it is acted on by the earth's magnetism alone, but that the needles place themselves east and west, since this is the only position in which the Chap, vi.] THOMSON'S ASTATIC GALVANOMETERS. 283 inside one coil of wire, and if the other be inside another, and if the current flow in opposite directions round these coils, " the moment of the deflecting couple"* acting on the combination will be the sum of the moments of the couples acting on the two needles separately, and hence may be made as large as we please. Such an arrangement is called an " astatic combination " of magnets, and with it a galvanometer of great delicacy, called an " astatic gal- vanometer," may be made. In practice a small directive force is produced partly by one of the needles being a slightly stronger magnet than the other, and partly by a controlling magnet M (Tig. 108) being placed nearer one of the needles than the other, and so acting more strongly on that one. 153. Thomson's Astatic Galvanometers. Usually in Sir William Thomson's astatic galvanometers the forces acting on the arrangement due to the earth's magnetism balance one another. Actually the needles place themselves so that their axes are equally inclined to the east and west line, but the inclination is so slight that they appear to lie east and west. In Fig. 105 the equilibrium 105. JPig. 108. position is shown, the needles being seen in plan, and their axes, for the purpose of clearness, being drawn more inclined to one another than they would be in practice. Fi-r. 1(K> shows the arrangement slightly turned round, when it is seen that equilibrium cannot exist. * When two equal forces opposite in direction and parallel to one another, but not in the s;imo line, act on a body, they constitute a "couple" whose "moment" is the product of either force into the perpendicular distance between them. 284 PRACTICAL ELECTRICITY. [Chap. VL mirror is fastened to one of the magnets, and an aluminium vane to the other, to produce "damping" or resistance to quick vibrations of the needle, in con- sequence of which it is rapidly brought to rest when deflected ; and the mirror and the vane are attached to a vertical wire made, like the vane, of aluminium for the sake of lightness suspended by a fibre of nnspun silk. This arrangement, however, has two disadvantages : the one that, as the mirror and the vane are much larger than the magnet, the inner windings of the wire in the coils cannot be brought close to the little magnets ; the other that, in order to allow the reflected ray (see Fig. 38, page 107) to emerge from the coil when the mirror is deflected, the hole in the coil must be enlarged at the front, that is, made trumpet-shaped, which causes the wire to be still farther removed from the suspended magnet. A better plan is to dispense with the aluminium vane and attach the mirror and the magnets to a vertical strip of mica ss (Fig. 107), as such a strip produces suffi- cient damping to render the galvanometer dead beat. Fur- ther, by attaching the mirror o to the part of the vertical strip that is between the coils, as shown in the figure, the space inside the coils which is not wound with wire need only be large enough to allow sufficient clearance for the free motion of the magnets when they are deflected, so that the convolutions of wire can be brought close to the magnet and the instrument made very delicate. Also the arrangement enables a larger mirror to be employed and a brighter image obtained on the scale. The astatic combination shown in Fig. 107 consists of four small magnets m, in the centre of one pair of coils, with their marked poles, say, all turned to the right, and four similar small magnets m in the centre of the other coil, with their marked poles all turned to the left. The strip of mica s s, to which these two sets di magnets are fastened, hangs by a fibre of unspun silk from a small hook at the end of a screw, which can be raised or lowered by turning the nut n. To prevent the Chap. VI. ] MODIFIED THOMSON'S GALVANOMETER. 285 screw also turning and twisting the fibre when the nut n is turned, there is a small vertical groove cut in the side of the screw, in which runs a small pin attached to the framework of the galvanometer. In order to insert the astatic combination of magnetic needles in the instrument, two of the coils must be re- moved. This is much facilitated if the coils be mounted in hollow boxes B B, attached by hinges to the frame- work of the galvanometer, as seen in Fig. 107, which shows two of these boxes containing the coils turned back so that the interior of the galvanometer may be seen. To prevent the coils touching the suspension when the boxes are closed, strips of paraffin wax or guttapercha, F, are inserted. All reflecting galvanometers which have not an ad- justment for centring the fibre should be provided with two adjustable spirit-levels L L, attached, at right angles 286 PRACTICAL ELECTRICITY. [Chap. VI to one another, to the base of the galvanometer. When the instrument is made, the levelling screws, on which the galvanometer rests, should be adjusted until the sus- pended needles hang quite freely inside the coils, then the levels should be adjusted until the bubble of air is in the middle of each tube. On all future occasions when the instrument is used, the levelling screws should be turned round until the bubbles are in the centres of the tubes, and then we may be sure that the needles are hanging freely inside the coils. If the whole apparatus could be made perfectly true, the mere levelling of the base with an ordinary carpenter's level when the galvano- meter was about to be used would be sufficient to insure perfect freedom of the needles ; but if the aluminium wire be not perfectly straight, or if the coils be not perfectly symmetrical, from the wire perhaps having bulged, the mere levelling of the base would not suffice. 154. Importance of the Galvanometer being Well Insulated. In many cases when a high resistance has to be measured it is the resistance between some insulated body and the earth ; for example, the resistance of the layer of guttapercha between the copper conductor of a cable and the water. It is impossible, of course, to insert the galvanometer between the guttapercha and the water, hence it must be placed between the battery and the insulated body. The currents, therefore, that will pass through the galvanometer will be the sum of the current that passes through the resistance that we desire to measure, and the current that will leak to earth from the terminal of the galvanometer that is attached to the insulated body, if this terminal be not well insulated. The value of this leakage current can be ascertained by disconnecting the galvanometer from the body whose insulation we desire to test, and testing the insulation of the galvanometer alone ; but a better plan is to endeavour to render these leakage currents prac- tically nought by having all parts of the galvanometer well insulated, as well as the wire connecting the Chap. VI.] MODIFIED. THOMSON'S GALVANOMETER. 287 88 PRACTICAL ELECTRICITY. ("Chap. VI. galvanometer with the insulated body. To insulate the coils of the galvanometer from the earth the hollow boxes B B (Fig. 107) in which the coils are held, as well as "the pillars P P, are, in the best galvanometers, made of ebonite. The ends of the coils should be fastened to ebonite pillars p p, inside the outer brass case of the instrument, and the wires employed to connect the galvanometer with other apparatus can be attached to the terminals at the top of these pillars either by passing the wires through openings in the brass case, which openings may be closed by little doors when the galvano- meter is not in use, or, better still, the flexible wires may be attashed to terminals T T, at the ends of horizontal stiff brags wires w w, the other ends of which are screwed into the terminals t t, at the tops of the ebonite pillars p p, as iseen in Fig. 107. These stiff brass wires pass through holes H H, in the brass cover Q, which is shown removed from the galvanometer in Fig. 108, without touching it, and by pushing in the ebonite collars E E, which slide on the wires w w, the holes H H can be closed up, either when the galvanometer is not in use, or when it is employed for experiments not requiring the highest insulation of the terminals. When it is desired to remove the cover, the wires w w are first unscrewed from the terminals t I and withdrawn, then the small screws at the bottom of the cover (Fig. 108), which screw into the brass lugs at the base of the galvanometer (Fig. 107), are loosened. G (Fig. 108) is a window let into the cover for the light to pass through on its passage to and from the mirror ; 8 is a screw held against the worm-wheel w by a spring r, and by turning the handle the controlling magnet M can be turned round, and the spot of light brought to the centre -of the scale. By raising or lower- ing M the sensibility of the galvanometer is increased or diminished. In some cases the unknown resistance is so large when it is, for example, the insulation resistance of a Chap. VII. | THE COULOMB. 289 short bit of good cable that even the method of testing described in 151, page 279, is not sensitive enough to give its value ; in such a case the " leakage method of measuring resistance " described in 185, page 344, must be resorted to. CHAPTER VII. QUANTITY AND CAPACITY. 155. Coulomb 156. Ballistic Galvanometer 157. Correction for Damping 158. Logarithmic Decrement 159. Determining the Logarithmic Decrement when the Damping is very Slight 160. Comparing Quantities of Electricity 161. Capacity 162. Condenser 163. Capacity of a Condenser is Constant 164. Variation of the Capacity of a Condenser with the Area of its Coatings 165. Variation of the Capacity of a Condenser with the Distance between the Coatings 166. Farad 167. Charge in Terms of Capacity 168. Capacity of a Cylindrical Condenser 169. Specific Inductive Capacity 170. Condensers for Large P. Ds. 171. Leyden Jar 172. Battery of Ley den Jars 173. Con- structing Condensers of very Large Capacity 174. Comparing Capacities 175. Condensers are Stores of Electric Energy, not of Electricity 176. Charge and Discharge Key 177. Absolute Measurement of a Capacity 178. Statical Method of Comparing Capacities 179. Measuring Specific Inductive Capacity 180. Standard Air Condenser 181. Every Charged Body is One Coat- ing of a Condenser 182. Capacity of a Spherical Condenser 183. Condenser Method of Comparing the E. M. Fs. of Current Gene- rators 184. Condenser Method of Measuring the Resistance of a Current Generator 185. Measuring a Resistance by the Rate of Loss of Charge 186. Rate of Loss of Charge from Leakage through the Mass depends on the Nature of the Dielectric, and not on the Shape or Size of the Condenser 187. Galvanometric Method of Measuring Resistance by Loss of Charge 188. Multi- plying Power of a Shunt used in Measuring a Discharge 189. Production of Large Potential Differences 190. Condensing Electroscope 191. Calibrating a Gold-Leaf Electroscope 192. Electrophorus 193. Ebonite Electrophorus arranged to give Negative Charges 194. Accumulating Influence Machines 195. Thomson's Replenisher 196. Wimshurst Influence Machine 197. Dry Piles. 155. Coulomb. A " coulomb " is the unit of electric quantity, and it is denned as tlie quantity of electricity that flows per second past a cross section of a conductor conveying an ampere. In the case of a stream of water T 290 PRACTICAL ELECTRICITY. [Chap. VII through A pipe we can measure the current by putting a bucket under the end of the pipe, and actually measuring the number of cubic feet or gallons of water that flow out per minute, but in the case of an electric current there is no end to the pipe or conductor, since the electric circuit is necessarily a closed one, and if we attempted to cut the wire for the purpose of inserting some apparatus in order to catch, so to say, the electricity, we should stop the current. What we have, therefore, to do in order to measure a quantity of electricity is to discharge the body containing it through the coil of a galvanometer, and observe the current produced during the discharge. This discharge of electricity, and the current produced by it, last a very short time, and, further, the current changes in value rapidly during the discharge. For example, suppose that an insulated con- ductor containing K coulombs of electricity, and charged to a potential of V volts, be discharged by being con- nected with the ground through the coil of a galvano- meter ; then, as the electricity flows out, the potential of the conductor will fall, hence the P. D. between it and the ground, and consequently the current, will rapidly grow less, until, when the discharge is nearly completed, and the potential is nearly reduced to that of the earth, the current will be extremely small. The effect, therefore, of sending such a discharge of electricity through a galvanometer coil is to cause the needle of the galvano- meter to be suddenly deflected, after which it returns through the zero position, at which it finally stays at rest after a few swings. Although the current during the discharge is rapidly growing less and less, and although, therefore, the impulses given to the needle during successive equal short intervals of time during the discharge become feebler and feebler, it is possible, when the whole discharge is completed before the needle begins to move, to sum up the effects of all these impulses, and so to estimate the number of coulombs of electricity that pass during the discharge from the instantaneous Chap. VII.] MEASURING QUANTITIES OF ELECTRICITY. 291 deflection or " elongation," or " throw " of the needle, as it is sometimes called. The magnitude of this first angular deflection of the needle k depends 1. On K the number of coulombs that pass. 2. On the moment of inertia of the needle and pointer, or other indicating arrangement. 3. On the moment of the controlling forces, that is, the forces which resist the needle moving away from the zero position, and which tend to pull it back to that position. 4. On the moment of the forces that " damp " the vibrations, that is, the forces, due to air or "magnetic friction," that simply resist the motion of the needle (see 156, page 294). 5. On the moment of the deflecting forces exerted on the needle by a given constant current flowing through the coil. Increasing either 1 or 5 will increase the magnitude of the first swing, which, on the other hand, will be diminished by increasing either 2, 3, or 4. If the needle be set swinging when no current is flowing, the quickness of the vibration will depend on the largeness of 3, and on the smallness of 2 and 4, so that if P be the " periodic time of vibration " of the needle in seconds, that is, the number of seconds that intervene between the moment when the needle ^Kisses any position and the moment when it next passes the same position swinging in the same direction, P will be increased by diminishing 3, or by increasing 2 or 4. On the other hand, if a be the angular deflection produced when a steady current of A amperes flows through the coil, a will be increased by increasing 5, or by diminishing 3, but will be unaffected by altering 2 or 4. Taking all these effects into consideration, it can be shown that, when both k and a are small, and when the damping is very small, p . k K=" x Ax 8m '2 292 PRACTICAL ELECTRICITY [Chap. V1L If a reflecting galvanometer be employed, k and a will necessarily be both small, because, with a scale say two feet long, put four feet away from the mirror, the spot of light will be deflected from the centre to the end of the scale by the mirror tux-ning through an angle of only 7. Indeed, with a reflecting galvanometer, as explained in 56, page 108, we may, with considerable accuracy, replace the angular deflections by the number of divisions on the scale through which the spot of light is deflected. Let these be k and a respectively, then K = x -9 x very approximately. In order that we may employ this formula without error to measure a quantity of electricity directly in coulombs, it is necessary to employ a "ballistic galvanometer" 156. Ballistic Galvanometer. In order to employ an ordinary reflecting galvanometer as & ballistic galvano- meter, the " air vane " should be removed to diminish the damping as much as possible, or if the support for the mirror and the magnets be the air vane as in s s (Fig. 107), it should be replaced by a vertical aluminium wire ; and, in addition, the needle should be weighted, as this not only still further diminishes the damping action, but makes the vibrations much slower, and so enables the periodic time P to be accurately determined. Also this increase in the periodic time tends to prevent the needle starting before the discharge has been completed, which is the fundamental condition that must be fulfilled in order that this formula may be true. A very suitable form of galvanometer to be used as a ballistic galvano- meter is shown in Fig. 109, in which R, R are the coils, and inside which is suspended a bell-shaped magnet, devised by Messrs. Siemens and Halske, seen in elevation in M, and in plan in n s, to the left of Fig. 109. By means of an alumi- nium wire the magnet is attached to a mirror s, and the whole suspended by a long fibre of unspun silk, hanging inside a glass tube r. The fibre can be raised or lowered Chap. VII.] BALLISTIC GALVANOMETERS. 293 by means of the vertical pin at the top of the tube, and it can be centred by means of the three horizontal screws (two only of which are seen in the figure)which hold- in posi- t i o 11 the outer brass collar cover- ing the ver- tical pin. In the case of a gal- vanometer provided with a cen- tring ar- rangement, such as is shown in Fig. 109, it is not neces- sary to have adjustable levels, as seen, in Fig. 107,because, when the in- strument is constructed, the base can be levelled with an ordi- nary level, and the nee- die then centred by means of the three adjusting screws at the top of the tube. On all future occasions when it 294 PRACTICAL ELECTRICITY. [Chap VII is desired to use the galvanometer, all that need be done is to level the base, since when this is done we are sure that the needle is properly centred. This galvanometer, as usually constructed, contains a large copper ball inside the coils, which is shown in section in K, at the upper right hand of the figure ; but this ball, which is introduced for the purpose of damping the vibrations, must, of course, be removed when it is desired to use the instrument as a ballistic galvanometer. The copper ball damps by the magnetic friction produced by the attraction between the moving magnet and the electric currents induced in the copper by the motion. When making experiments with a ballistic galvano- meter, great care must be taken that the needle is absolutely at rest when the discliarge test is made, otherwise the ap- preciable momentum, which is possessed by the needle of large moment of inertia, even when moving slowly, will be added to, or subtracted from, that given to it by the current, and will introduce an error. This necessity of waiting for the undamped needle to come absolutely to rest makes observations with a ballistic galvanometer most tedious, and it is well to place, at some convenient spot outside the galvanometer, a small independent coil of wire, in circuit with a cell and a reversing key, by means of which small impulses may be given to the needle to stop it when it is swinging. Example 85. "With a galvanometer, the needle of which executes 11 complete swings in 6J seconds 1 Daniell's cell, having an E. M. E. of 1'07 volts, and an internal resistance of 3 ohms, produces a deflection of 127 scale divisions when there is a resistance of 10,000 ohins in the circuit, excluding the galvanometer which has a resistance of 7,560, and which is shunted with the one - thousandth shunt. What number of coulombs is discharged through the galvanometer when an instantaneous deflection of 230 scale divisions is produced 1 Chap. VII.] EXAMPLES. 295 The current producing the steady deflection of 127 scale divisions, is 1 1-07 - amperes. 3 + 10,000 1,000 or - amperes approximately, 10,000,000 . . K = _ 6 ^- X _ ^ _ x -^coulombs 11 x IT 2 x 10,000,000 127 approximately. Answer. 0'01822 microcoulombs approximately. Example 86. What alteration could be made in the galvanometer referred to in the last example other than altering the coils, so that one-tenth of a microcoulomb should produce an instantaneous deflection of 100 scale divisions 1 Answer. Either the sensibility of the galvanometer must, by slightly approaching the controlling magnet, be diminished in the ratio of "01 8 22 x 100 to 0-1 x 230, or the needle must be weighted so that the periodic time is increased in the ratio of O'l x 230 to 0'01822 x 100. Example 87. Which galvanometer would be the more sensitive for the measurement of quantity, one whose needle made 9 complete vibrations in 3 seconds, and with which a deflection of 200 scale divisions was produced by 1 Daniell's cell when 10,000 ohms were in circuit, and the galvanometer WHS shunted with the one- hundredth shunt, or one whose needle made 11 vibra- tions in 7 seconds, and with which a deflection of 85 scale divisions was produced by the same Daniell's cell when 6,000 ohms were in circuit, and the galvanometer was shunted with the one- thousandth shunt? In order to produce an instantaneous deflection of 100 scale divisions, there will be required with the two galvanometers respectively, 296 PRACTICAL ELECTRICITY. [Chap. VIL 3_ 1 E 100 9*- X 2 x 100 X 10,000 X 200* and -1 x \ x x coulombs, 11 T 2 x 1,000 6,000 85 if E be the E. M. F. in volts of the Daniell's cell, 0-08333 E . 0-06238 E or and microcoulombs. 7T 7T Consequently the sensibility of the second galvanometer for measuring quantity bears to that of the first the ratio of 0*08333 to 0-06238, or 1-336 to 1, hence the second is rather more than one-third more sensitive than the first. 157. Correction for Damping. If it is not to remove the vane of a galvanometer so as to diminish the damp- ing to a very small value, or if it is desired to make very accurate experiments, in which case the damping, however small, ought to be allowed for, the following formula should be employed : where I is what is known as the " Napierian logarithmic decrement" This formula is correct when the damping is too great to be en- tirely neglected, but still not exceedingly large, in which case the formula is much more complicated. 158. Logarithmic Decrement. When there is damping, the amplitude of the oscillations of the needle will grow gradually less and less, and the "decrement " is the name given to the ratio of the amplitude of one oscillation to the amplitude of the succeeding one, and this ratio experiment shows is the same for any two successive vibrations. The Napierian logarithmic decrement is the logarithm of this ratio to the base e, or 2'71828, and this again equals the log- arithm of this ratio to the base 10, divided by the logarithm of c to the base 10, that is, log. e ratio = log- __ log. 10 ratio ^ 0-4343 If not merely the value of log. 10 ratio be found in a table of logarithms, but if the value of the fraction be also calculated by Chap. VII.] LOGARITHMIC DECREMENT. 297 using logarithms, care must be taken to employ log. 10 log. 10 ratio, that is, to extract the logarithm twice over, because log. 10 log.e ratio = log. ]0 log. 10 ratio log. 10 0-4343. 159. Determining the Logarithmic Decrement when the Damping is Very Slight. If the damping is very slight, it will be very difficult to detect any difference between the amplitudes of two succeeding vibrations, so that the ratio or decrement will appear to be unity, and its logarithm nought. The decrement can, however, be determined as follows : Since the ratio of the amplitude of the first oscillation to the amplitude of the second equals the ratio of the amplitude of the second to the amplitude of the third, &c., each ratio being equal to the decre- ment, it follows that the ratio of the amplitude of the first oscilla- tion to the amplitude of the wth oscillation after it, that is the (n + l)th oscillation, equals the nth power of the decrement, or generally the ratio of the amplitude of any oscillation to the amplitude of the nth oscillation after it equals the nth power of the decrement. Consequently, , amplitude of any oscillation 7 1O^. ^^ fl X vj the nth after it , 1 , amplitude of any oscillation n the nth after it Now, although it may be difficult to distinguish the decre- ment from unity, it is comparatively easy to measure the ratio of the amplitude of an oscillation to the amplitude of the nth after it, since n may be taken so large that the ratio differs considerably from unity. Example 88. If, on causing the needle of a galvanometer to vibrate, the readings on the scale, at which the spot of light stops, be + 130, - 120, -f 105, - 97, + 85, &c., the -f and - indicating deflections to the opposite side of the zero, what is the value of the factor 1 -f- -, the correction for damping ? Answer. The amplitude of the first oscillation is 130 + 120, of the second 120 + 105, of the third 105 + 97, &c. Hence, the decrement equals ? 5 .P- or, &c., or about Mil. 225 202 298 PRACTICAL ELECTRICITY, [Chap. VII. __ 0-0457 ~ 0-4343* = 0-1052. Hence, 1 +L = 1-0526. Example 89. What amount of damping is allowable so that the omission of the factor employed to correct for damping shall not make an error of more than ^ per cent. ? Answer. I must equal 0-01, consequently if d be the decre- ment log. e d = 0-01, log. 10 d = 0-01 x 0-4343, .-. d = 1-010, or the ratio of the amplitude of one vibration to the amplitude of the next must not exceed 1-01, or the amplitude of one vibration must not exceed that of the next by more than 1 per cent. Example 90. With the value of the decrement given in the last answer, what will be the ratio of the amplitudes of the 1st and the 15th vibrations ? amplitude of 1st vibration Answer. 0-01 = ^ log. e " "" amplitude of 1st vibration _ Q . u _;-:,, 15th or more simply, thus : amplitude of 1st vibration _ 15th = 1-150. Example 91. If the ratio of the amplitude of the 1st vibration to that of the 21st is 1-2, what is the value of the decrement ? Answer. I = ^ log., 1'2, .-. 1= 0-00912, and d = 1-009; or we may say at once. i d = i-r* . ; d = 1-009. From this and the previous examples we see that the error in neglecting the damping will be about per cent, when the ampli- tude of any vibration exceeds the amplitude of the wth vibration after it by n per cent, of the latter. Chap. VII.] COMPARING QUANTITIES OF ELECTRICITY. 299 160. Comparing Quantities of Electricity. If two quantities of electricity K and K' coulombs are to be compared with one another, it is not necessary to deter- mine P nor a since, if k and k' be the number of divisions on the scale over which the spot of light swings in the two cases, we have from the complete formula in 157, page 296. K_ = k_ K' " k'' The correction for damping has also disappeared, hence when simply comparing two quantities of elec- tricity our galvano- meter may conveni- ently, and without in the least complicating the calculation, have a certain small amount of damping. A simple, conveni- ent, and cheap reflect- ing galvanometer, to be used for the simple comparison of quanti- ties of electricity, has been arranged by Mr. Mather, and is shown in Fig. 110. It con- sists of two coils, cc', supported in position by fitting into channels formed on the base, and a vertical narrow strip of mica, s s, suspended by a fibre of unspun silk, F, carrying the mir- ror M, and three sets of magnets, ra T , m 2 , and m 3 ,the first and third of which form an astatic combination wjth the middle set, m 2 , which is inside the coils : m^ and m s , although not surrounded with wire, are nevertheless deflected by the current passing round the adjacent convolutions of the coil Fig. 110. 300 PRACTICAL ELECTRICITY. [Chap. VII. in the same direction as m. 2 , which is inside the coil, so that the magnetic forces acting on all three sets of magnets conjoin in their effects. The damping arising from the resistance of the air to the motion of the mirror will be sufficient for very accurate capacity experi- ments, and the strip s s may be replaced by an aluminium wire. If, however, rather greater damping be desired it can easily be produced by using the narrow ,trip of mica to support the needles and mirror, as in the galvanometer shown in Fig. 110. The magnets maybe raised or lowered by the pin p, and to avoid torsion Fig. 111. being given to the fibre by the head of the pin being turned round in an unknown way, there is a vertical line drawn on the pin, and a mark made 011 the collar in which this pin slides, and by keeping the line on the pin always opposite the mark on the collar when the pin is raised or lowered, all turning of the pin can be avoided. This contrivance is, of course, cheaper than the simplest mechanical arrangement for preventing rotation of the pin when it is raised or lowered. 161. Capacity. When one conductor is completely surrounded by another, the " capacity " of the inner one is the number of coulombs required to be given to the inner to produce 1 volt P. D. between the two. For example, the capacity of A (Fig. Ill), is the number of coulombs on A when there is 1 volt P. D. between A and B. The capacity of a conductor, therefore, depends on its external shape, and on its position relatively to the Chap. VII. 1 CAPACITY. 301 conductor surrounding it, since, as seen in <$ 66, 67, page 119, the potential of a conductor relatively to another can be varied without altering the quantity of electricity on the former, by varying either its external shape or its position relatively to the latter. If a metallic plate A (Fig. 112) be surrounded with a flat metallic box B, the top and bottom of the box being- parallel to A, and very near A, then the capacity of A will be very large, since it will require a very large charge of Fig. 112. electricity to be given to A in order to raise the P. D. between A and B to 1 volt. 162. Condenser. An arrangement of conductors such as is shown in the last figure is called a " condenser" so that a condenser may be denned as two conductors separated by an insulator, and so placed relatively to one another that the capacity of the arrangement is large compared with the size of the conductors. A condenser having a large capacity does not, of course, mean that it would hold a large charge without its insulation breaking down, but that it would hold a large charge for the P. D. between its coatings. As far as power to hold a charge from the non breaking down of the insulation is concerned, a condenser of small capacity may be able to hold a larger charge than a condenser of much larger capacity. If A (Fig. 112) be charged with positive electricity, there will be a charge of negative electricity on the inside of B, whereas if A'S charge be negative, then the charge on the inside of B will be positive. We have further seen ( 60, page 113) that the quantity of elec- tricity on A is exactly equal in amount to the charge of the opposite kind of electricity on the inside of B. We 302 PRACTICAL ELECTRICITY. [Chap. VII. may, therefore, define the capacity of the condenser either as the number of coulombs necessary to be given to A, or tlie number of coulombs on the inner surface of B when t/te P. D. between them is 1 volt. If we desire to make a condenser with a very large capacity, we may either make the plates very large, or the distance between them very small. There are Fig. 113. obviously practical difficulties in making the distance separating the plates very small, as the insulation is liable to be insufficient, either from particles of dust passing rapidly backwards and forwards between the charged plates, and so discharging them, or from actual sparks passing when the P. D. between the plates is high. On the other hand, if the plate A and the box B Fig. 114. (Fig. 112) be very large in area the apparatus becomes cumbersome. This difficulty, however, may be overcome by making both A and B consist of a series of plates (shown in section in Fig. 1 1 3), and a condenser is usually symbolically represented in this way, or, still more simply, by two lines drawn parallel to one another, as in Fig. 114, and the sets of plates, A and B, are called the " coatings " of the condenser. 163. Capacity of a Condenser is Constant. By charging a condenser with different P. Ds. , and measuring with a galvanometer the quantity of electricity that Chap. VII.] CONDENSERS. 303 enters one of the coatings, or the quantity that leaves this coating when the condenser is discharged, it can be experimentally proved that this quantity is directly pro- portional to the P. D. The capacity of a condenser may, therefore, be denned as tJie ratio of the number of coulombs in one coating to the P. D. in volts between the coatings, this ratio being a constant for a given condenser. Unless the galvanometer employed be very sensitive, it is better when making the experiment just referred to, for testing the constancy of the capacity of a condenser, to use a condenser of large capacity of the type described in 173, page 317. 164. Variation of the Capacity of a Condenser with the Area of its Coatings. That the capacity of a con- denser is directly proportional to the effective area of either of tlie coatings hardly needs proof, because a condenser with coatings of large area may be regarded as being made up of two or more smaller condensers, such that the sum of the areas of one set of coatings of the smaller condensers is equal to the area of one of the coatings of the larger, the distance between the coatings in the large condenser and in each of the smaller ones being the same, and it is clear that the capacity of the set of smaller condensers is the sum of their capacities. 165. Variation of the Capacity of a Condenser with the Distance between the Coatings. If we had a con- denser of large capacity, and the distance between the coatings of which could be varied at will, an examination of the variation of the capacity, with the distance between the coatings, might be made by fixing the coatings at various distances from one another, and measuring the number of coulombs, or the fraction of a coulomb, required to charge the condenser in the different cases with the same P. D. But practically it is found that any condenser, the size of whose coatings is not so large but that the distance between them can be conveniently adjusted, has KO small a capacity that when charged with even a large battery of galvanic cells in series, its charge cannot be 304 PRACTICAL ELECTRICITY. [Chap. VII. measured with even a very delicate galvanometer. Hence we are compelled to use some statical method for in- vestigating the variation of the capacity of a condenser with the distance between its coatings. One plan would be to give the condenser a charge, and then, on varying the distance between the coatings without discharging it, to measure the variation of P. D. between the coatings by means of a suitable electrometer. From this the variation of the capacity could be at once determined, since, with a constant charge in the condenser, the capacity must be inversely proportional to the P. D. between the coatings. The following method, devised by the author, however, enables us to ascertain the law of variation of the capacity with the distance between the coatings, without making measurements either of the various distances between the coatings, or of the various P. Ds. corresponding with these distances. BB, B'B', Fig. 115, are wooden boards (one of which B' B' in the figure is shown removed from the apparatus, in order that the interior may be seen) with their surfaces opposed to one another, carefully planed so as to be parallel, and coated with tinfoil, so as to make them conducting. These surfaces together form the outer coating of a condenser corresponding with B (Fig. 1 1 2). The inner coating consists of the two sheets of tinfoil, T T, T' T', which are parallel to the surfaces of B B and B' B'. This tinfoil is stuck on thin cloth to give it strength, as it has to roll over the small rollers R R', when the rod n, to which one of the edges of each of the sheets of tinfoil is attached, is pulled down by the thin silk cord c c, or when, on this cord being slackened, the weight w w, to which the opposite edges of the two sheets of tinfoil are attached, pulls T T and T' T' down, and the rod n up. The rollers R R', which are made of steel, are only about one-tenth of an inch thick, and are placed close together, so that the surface of the tinfoil wrapped round them may be as small as possible, and so that there may be no inductive action between the tinfoil on Chap. VII. J CAPACITY OF A CONDENSER. 305 the vertical wooden boards and the inner surfaces Of the sheets T T and T' T'. The rollers are pointed at their ends, where they are supported by the brass pieces b b , which are firmly cemented to the tops of the glass rods G G'. The two sheets of tinfoil are, therefore, insulated u 306 PRACTICAL ELECTRICITY. fChap. VII. from the ground. To keep the glass rods dry they are each surrounded with a tube F F, inside which is placed dry flannel which absorbs moisture. The tubes are hinged down their sides, so that they can easily be opened and removed, and in the figure the one belonging to the rod G' has been removed. Swaying of the weight w w side- ways, as well as side attraction of the suspended sheets of tinfoil T T, T' T', are prevented by the weight being guided by the cord c c passing through it. The boards B B and B' B', which are, as seen in the figure, strongly stayed at the back to prevent warping, can be made to recede from one another by pushing in the wedge w w, by means of the screw s, or to approach one another by turning the screw in the opposite direction, when the wedge is withdrawn, and a spring pressing against each plate pushes them together. In addition to the horizontal boards H n', carrying B B and B' B', being always pressed by these springs against the side of the wedge w w, a pin on the underside of each board slides in a groove, the groove g' g' seen in the figure being that in which the pin attached to H' slides. B B and B' B', there- fore, move parallel to themselves, so that in all positions the opposed surfaces are parallel. The cord c c first, passes under a little pulley P attached to the base of the instrument, then under a second pulley p, moving with the wedge, and its end is attached to the pin q (the wedge in the figure being cut away to show the pulleys). Hence on turning the scre\v s, so as to push in the wedge and separate B B and B' B', the cord c c is slackened, and consequently the rod n rises, and the weight w w descends, causing the area of the surface of the tinfoil T T and T' T' opposed to B B and B' B' to increase, and by selecting a proper angle for the wedge w w, and a proper pitch for the screw, the area of the two surfaces of the tinfoil T T and T'T' can be made to increase, so as to be exactly pro- portional to the distance separating them from the surfaces of B B and B' B'. Under these conditions, if the inner coating of the Chap. VII.] THE FARAD. 307 condenser be connected with the gold-leaves of an electro- scope, and the outer coating of the condenser be connected with the outside of the electroscope, and if a potential difference be set up between the coatings, it will be found that no alteration of the divergence of the gold-leaves will be produced by approaching or separating B B and B' B'. Now the quantity of electricity on the outer sur- faces of T T and T'T' is a constant, since there is no electricity inside a conductor ( 64, page 118). Conse- quently this experiment tells us that if the ratio of the area of the inner coating to the distance between the coatings is kept constant, the capacity of the condenser is constant. But we have seen ( 164, page 303) that the capacity of a condenser is directly proportional to the effective area of either of the coatings, hence it fol- lows that the capacity of a condenser with plane parallel plates is inversely proportional to the distance between the coatings. 166. Farad. A "farad" is the unit of capacity, and a condenser has a capacity of one farad when a P. D. of 1 volt between its two sets of plates charges each of them with 1 coulomb. If A be the area in square centimetres of the entire surface of either of the two sets of opposed parallel plates of an air condenser, and t be the distance in centi- metres separating them, and if F be the capacity of the condenser in farads, 1-131 x 1013 x t If A be reckoned in square inches, and t in inches, A "4-452 x 1012 x |" A farad is rather a large unit of capacity for ordinary purposes, hence, one-millionth of a farad, or a "micro- farad," is more commonly employed. If M be the 308 PRACTICAL ELECTRICITY. [Chap. VII. capacity in microfarads of the air condenser, and A and t be in square centimetres and centimetres respectively, M= A 1-131 x 107 x t' whereas, if A and t be in square inches and inches re- spectively, M= A 4-452 x 10 6 x t In order that the preceding formulae may be strictly correct, the linear dimensions of the plates must be largo compared with the distance between them. It can, however, be made rigorously true even when this is not the case if a guard-ring, described in 44, page 89, be employed with one of the plates, and be at the same potential as this plate. In that case A is the area of the smaller plate, not including the area of the guard -ring, and F, or M, is the capacity of this plate, not including the capacity of the guard-ring itself. 167. Charge in Terms of Capacity. If K be the charge in coulombs in an air condenser, having a capacity of F farads, when there is a P. D. between the coatings of V volts, it follows from the definition of capacity, that K = F x V, also if M be the capacity in microfarads that M x V 10 6 168. Capacity of a Cylindrical Condenser. If the two coatings of an air condenser consist of two concentric cylinders A B, c D (Fig. 116), of length / centimetres, and of radii or diameters, H and r respectively, the capacity F in farads 2-413 I X 10 13 log. 10 R log. 10 r p As log. 10 R log. 10 r equals log. 10 it is obvious that it Chap. VII.] CAPACITY OF A CYLINDRICAL CONDENSER. 309 is quite immaterial what units of length are employed in measur- ing K and r, provided that the same unit is employed in each If M be the capacity in microfarads, 10 7 log. 10 R log. 10 r A common example of a condenser having its coatings con- centric cylinders is a submarine cable (see Fig. 98, 140, page 267), the outer coating being the water or the iron sheathing in contact with the insulating core, and the inner coating, the sur- face of the copper conductor. Consequently, if R be the radius Fig. 116. of the core, and r the radius of the conductor, and if n be the length of the cable in knots, the capacity in microfarads M _ 2-413 x 2029 X 91-44 n 10? log. 10 R log. 10 r' 4-476 n 10 2 log. 10 R log. 10 r 169. Specific Inductive Capacity. The capacity of a condenser can be still further increased by using, in- stead of air for the insulator, glass, guttapercha, india- rubber, paraffin oil, or some other solid or liquid insulator. If K be the number of coulombs of positive electricity required to be given to A, and of negative electricity to B, so as to produce 1 volt P. D. between them when they are separated by air, then if the air be replaced by some other substance, and no other change be made in the condenser, the number of coulombs now required to pro- duce 1 volt P. D. between A and B, will be K x " tJie specific inductive capacity." Hence the specific inductive capacity of a substance is the ratio of the capacity of a condenser when its plates are separated by this substance to the capacity of the same condenser ivhen its plates are separated by air. The following table gives a list of the specific inductive 310 PRACTICAL ELECTRICI1T. [Chap. VII. capacities of some important substances as determined by various experimenters, whose names are given in the third column : TABLE No. VI. Specific Inductive Capacity. Subst mce. Specific Inductive Capacity. Authority. Vacuum, air at about 0-001 millimetre pressure . . 0-94 about. Author. Vacuum, air at about 5 milli- 0-9985 Author. metres' pressure . . . i 0-99941 Boltzmann. Hydrogen at about 760 milli- 0-9997 Boltzmann. metres' pressure . . . 0-9998 Author. Air at about 7 60 millimetres' Taken as the pressure . .... . standard. Carbonic Dioxide at about 1-000356 Boltzmann. 760 millimetres' pressure . Olefiant Gas at about 760 millimetres' pressure . . 1-0008 1-000722 Author. Boltzmann. Sulphur Dioxide at about 760 millimetres' pressure . | 1-0037 Author. fl-92 Schiller. 1-96 Wiillner. Paraffin Wax, Clear . . . j 1-977 Gibson and Bar- clay. U-32 Boltzmann. Paraffin Wax, Milky . . . 2-47 Schiller. [ndiarubber, Pure .... 2-34 Schiller. Vulcanised. . 2-94 Schiller. 2-55 Boltzmann. (2-56 Wiillner. Ebonite ! 2-76 Schiller. \ ** t v ( 3-15 Boltzmann. ( 2-88 to 3-21 Wiillner. \ 3-84 Boltzmann. Shell-lac 2-95 to 3*73 Wullner. Guttapercha 4-2 Mica 5 Flint Glass, Very light . . 6-57 1 Light . . . 6-85 Dense . . . 7'4 > J. Hopkinson. Double extra 1 dense > 10-1 J Chap.VII.J SPECIFIC INDUCTIVE CAPACITY. 311 Not merely is the capacity of a condenser increased by using, say glass instead of air, as the " dielectric " or insulating material through which the induction takes place, but the resistance to loss of charge by sparking is immensely increased ; hence, with a glass condenser far greater P. Ds. can be used than with an air condenser of the same size. The resistance to sparking does not de- pend on the insulating quality of the substance, but on its rigidity and the resistance it in consequence op- poses to rupture. If, instead of air, a substance having a specific induc- tive capacity i be employed, in a condenser made of parallel plates, F = tx , 1-131 x 1013 x t A and M = i x 1-131 x 107 x t if A and t are reckoned in square centimetres and centi- metres respectively ; and 4-452 x 10*2 x t and M = t x 4-452 x 106 x t if A and t are reckoned in square inches and inches re- spectively. Similarly the logarithmic formulae given in 168, page 308, for the capacity of a cylindrical condenser, must be multiplied by i, the specific inductive capacity of the dielectric when this is paraffin wax, glass, &c., or when, as in the case of a submarine cable, guttapercha or indiarubber fills up the space between the two con- ductors. Example 92. If the distance between the plates in an air condenser be 1 millimetre, what must be the area 312 PRACTICAL ELECTRICITY. [Chap. VLL of each set of plates in order that the capacity may be 1 microfarad 1 A nswer. About 1,131,000 sq. cent . Example 93. How many plates about 1 foot square would be necessary to produce the area required in the last answer, and what would be the exact size of each plate? If we assume that the plates were each 1 square foot, then, since the area on both sides of each plate is utilised, it follows that the number of plates required would be ~^r or 608-7. We could, therefore, either use 608 1,858'02 plates, each a little larger than 1 square foot, or 609 plates, each a little smaller. The latter will be hearer in size to the square foot, and using this number, it is easy to calculate that each plate must be 0'9994 square feet, or 11 '99 inches square. For the other coating B (Fig. 113, page 302), there must be, of course, 610 plates, since one surface of each of the outer plates of B will have no action as a condenser. Example 94. If the insulating material in a condenser be paraffined paper, and if we assume that the specific inductive capacity of the paraffined paper is the same as that of paraffin wax, 1'977, what must be the thickness of the paper in order that the condenser may have one-third of a microfarad capacity when the area of each set of plates is 205 square feet? Answer. 0*03933 of an inch. Example 95. A cylindrical glass jar one-tenth of an inch thick, and 3 inches in diameter, is coated inside and outside with tinfoil on the bottom, and on the sides for a height of 3 inches. If the glass be extra dense flint, what must be the P. D. between the tinfoil coat- ings so that the charge may be one-millionth of a coulomb ? The glass being very thin, the formulae for a condenser formed of plane parallel plates may be used. The area _ vy O2 of tinfoil at the bottom is - sq. inches, that on the Chap. VH.J CONDENSERS FOR LARGE P.Ds. 313 sides TT x 3 x 3 sq. inches. If, therefore, V be the un- known P. D. in volts, ^A 2 + TT x 3 x 3 _ _ in.i x - _ y 1Q6 " 4452 x 1012 x -i- .'. V = 1247 Answer. 1247 volts. Example 96. What is the capacity of the glass con- denser referred to in the last question ] If F be the capacity in farads, F = _ 106 x 1,247 hence the capacity is '0008021 microfarads. Example 97. The diameter of the copper conductor of the Direct United States cable being 0'16 of an inch, the diameter of the guttapercha core 0'446 of an inch, and its length 2,443 knots, what is its capacity ? From the formulae in 168, page 309, we have lo 160 = 1031. Answer. 1031 microfarads. The actual capacity determined by experiment is 1000*4 micro- farads. 170. Condensers for Large P. Ds. The charge in a condenser, K coulombs, equals, as we have already seen, Fx V, hence this charge can be made great by making one or other, or both of the factors, F and V large. For experi- ments with the old form of "frictional electrical machines" or with the more modern form of " influence machines " (see 196, page 371), it is V that is always made large, whereas when galvanic batteries are used as the source of the P. D., it is F that is usually made large. In the recent experiments, however, made by Drs. De La Hue 314 PRACTICAL ELECTRICITY. [Chap. VII. and Hugo Miiller, with their large silver chloride battery, consisting of some 20,000 cells, the condensers have been made to stand the high P. D. produced by this battery as well as to have a large capacity. When thousands of volts are to be employed, a large resistance to sparking is therefore quite as important as high specific inductive capacity, and, as already stated, requires that the dielectric should be rigid. (See the note to 192, page 358.) 171. Leyden Jar. Some kind of glass is usually employed in. the construction of condensers that are to be charged with a very large P. D., and the condenser takes the form of a "Leyden jar," a type of which is seen in Fig. 117. The name is derived from the town of Leyden, at which the property of electric capacity was accident- ally discovered in 1746, by Musschen- broek, and his pupil Cuneus. Desiring to collect the supposed electric fluid, they used a bottle partly filled with water, into which dipped a nail, passing through the cork, to carry the fluid from the electric machine to the water, and on Cuneus touching the nail with one hand, the bottle being held in the other, he received a shock. In the ordinary Leyden jar, such as is seen in Fig. 117, the tin coatings are sheets of tinfoil, one pasted inside the jar, and the other outside. Electric connec- tion is made with the inside coating either by a metal rod or rods resting on the bottom, or more commonly, by a chain or a flexible bit of wire hanging from a brass rod, which, in this case, is supported by a wooden Pig. 117. Chap. VII"! LEYDEN JAR. 315 cover to the jar to which the rod is fixed. But such a Ley den jar, even when the surface of the glass, which is not covered with tinfoil, is coated with shell-lac or other varnish, has but a poor insulation in damp weather, and requires the glass to be constantly held in front of the fire to be dried . For with the wooden cover in contact with both the metal rod and with the edge of the jar, in accordance with the unscientific form of construction usually adopted, the interior of the glass helps but little towaids holding the charge, seeing that if the outside of the wooden cover and of the jar be dirty and moist, there is a direct road for the electricity to leak from the rod to the tinfoil outside, without passing at all over the glass on the interior. Hence, that portion of the glass which it is most easy to keep dry and clean, is rendered useless by the presence of the wooden cover in contact with the rod. On this account the form of Ley den jar shown in Fig. 118, and originally employed by Sir William Thomson, is much to be preferred. The outer coating consists of tinfoil T T, as in the ordinary Ley den jar, but the inte- rior is formed of strong sulphuric acid ss, into which dips a leaden rod L, expanded at the lower part into a sort of foot so as to stand firmly on the bottom of the glass jar. Both rod and foot are made of lead so as not to be acted upon by the acid, but the upper part I of the rod, which does not dip into the acid, may be conve- niently made of iron, being less liable to bend than lead. The mouth of the jar is partially closed with a wooden cover w, to keep out dust, and retard a too rapid inter- change of the air between the inside and outside, which would prevent the sulphuric acid being able to keep the interior surface of the glass dry. A cork c, sliding on the rod i, is pressed down when the jar is not in use, but is raised up to prevent electric contact between the rod and the cover w w, when the jar is to be charged. In Fig. 118 there is seen carried by the iron rod a metallic cone. This may be used for making experiments 316 PRACTICAL ELECTRICITY. I'Chap. VII. in density with the proof plane (see 63, page 118), and the advantage of attaching the charged cone, or other conductor (the distribution of density over whose surface we desire to measure), to another conduc- tor of large capacity, is that the amount of electricity removed by the proof plane, each time we touch the surface of the cone, does not sensibly diminish the poten- tial or the total charge pos- sessed by the cone. Without the use of the Leyden jar, the effect of touching any point A on the cone with the proof plane, and removing the proof plane, is not merely to remove the amount of electricity that was on the surface of the cone touched by the proof plane, but to slightly diminish the density of every other part of the surface of the cone, since electricity has to flow from the rest of the body to re- charge the part touched by the proof plane. Hence, if the cone be first charged to a given potential, and then the relative densities at any points A and B be determined by touching them succes- sively with the proof plane, slightly different results will be obtained, according to the order in which these two points are touched. The use of a well-insulated Leyden jar removes the difficulty, which may also, to a certain extent, be overcome by first touching A, and measuring the charge q lt taken away by the proof plane, then touching B, and measuring the charge q z , removed, and thirdly, touching A again, and measuring the charge and still further charge the condenser, and so n on, what will be the total waste of energy 1 The number of coulombs put into the condenser in the first charge equals FE - > n and the work done by the first battery equals 44-25 FE2 __ x __ footlbs . The number of coulombs put into the condenser in the second charge equals FE and the work done by the battery equals, 44-25 FE 2E , - x - x - - foot Ibs., 60 n n 326 PRACTICAL ELECTRICITY. [Cl.ap. VII. or 4 -||^ 2 F o foot Ibs., &c. 60 n 2 So that the total work done in charging the condenser equals 44-25 FE 2 . ..+ GO 445 FE. \ n] _ 60 nS ' 2 60 \2n 2 The store of energy in the condenser equals, as before, quite independently of the way in which the condenser has been charged. Hence, the waste equals which becomes the same as before if n is unity, but on the other hand becomes as small as we please if n be made larger and larger. In fact, the more nearly we make the rate of increase of the E. M. F. in charging equal to the rate of the decrease of the P. D. between the coatings of the condenser in discharging, the less will be the waste in charging. Example 101. If an air condenser be formed of two parallel metallic plates, each two square feet in area, placed gfeth of an inch apart, and charged with a P. D. of 250 volts, what amount of work must be done in separating the plates, so that the distance between them is increased to -^th of an inch, if the wires used in charging the condenser be removed before the plates are Chap. VIL1 MEASURING CAPACITY ABSOLUTELY. 327 separated, so that the charge in the condenser remains unaltered during the separation 1 The capacity before separation equals from 166, page 307, 288 4-452 x 10" x & '' or 1-940 x 10~ 9 and after separation, 288 4-452 x 1012 x T V or 6-467 x 10- therefore if K be the charge in coulombs in the con- denser, and V the P. D. after separation in volts, K = 1-940 x lO- 9 x 250 = 6-467 x 10 -w x V, .-. V = 750 volts. The store of energy, in the condenser before separation equals 1-940 x lO- 9 x 2502 -j&sr " fo s - or 4-471 x 10-* and the store of energy after separation equals 6-467 x 10-io x 75Q2 -j - foot lb,, or 1-341 x 10-* hence the work done in the separation equals 8-939 x 10-5 f 00 t ibs. 177. Absolute Measurement of a Capacity. The absolute capacity of a condenser can be determined in 328 PRACTICAL ELECTRICITY. [Chap. VII. farads by using a battery, whose E. M. F. we know ' in volts, to charge it, when there is in the circuit a galvanometer which has been calibrated so that the number of coulombs or fraction of a coulomb that causes any particular instantaneous swing is known. Bat this absolute measurement of a capacity can more easily be effected as follows, the only thing that is required to be previously known being the value of a resistance in ohms. Let B (right hand, Fig. 125) be a battery of un- known E. M. F. and resistance, but of such a large Fig. 125. number of cells, that when it is used to charge the condenser c, F farads in capacity, a suitable instan- taneous deflection is obtained on a reflecting galvano- meter G. In order that we may use two P. Ds., whose ratio is known, shunt the battery with a large resist- ance r, then if a portion r' (right hand, Fig. 125) of this resistance bears to the whole r, a ratio equal to R, it follows, without our knowing either r or r' in ohms, that V, the P. D. between L and N, the terminals of r', bears to V, the P. D. between L and M, the terminals of r, the same ratio R. Charge the condenser with the battery thus shunted, by depressing the key K (left hand, Fig. 125), and let the instantaneous deflection be d^ Next using V Chnp. VIL] MEASURING CAPACITY ABSOLUTELY. 329 (right hand, Fig. 125), send a steady current through the galvanometer in series with a large resistance coil, and let the value of the resistance of these two be o ohms. Let d^ be the steady deflection so obtained, then P R d, F= x x-j 1 - 2 v o a 2 For if K be the unknown number of coulombs re- quired to charge the condenser to the unknown P. D. of V volts, K = F x Y, also from 155, page 292, we know that TT P A d\ K = - x -- x -\ TT 2 a where a is the steady deflection that is produced by A amperes. But since the deflection is proportional to the current, and since the deflection do is produced by a * V current of amperes, o A x o P R x V d, . ' . K = X - - X S T 2x0 d 9 P R d, .-. F = x x 1. 2 7T 0? 2 If the vibrations of the needle be damped, then the above must be multiplied by 1 + , where I is the Napierian logarithmic decrement (see 157, page 296), in order to obtain the correct value of F. 330 PRACTICAL ELECTRICITY. [Chap. VII. This method was employed by the late Professor Fleeming Jenkin, in 1867, in making the first absolute measurements of the capacity of a condenser. 178. Statical Method of Comparing Capacities. Let F and F' be the capacities of the two condensers that are to be compared. By means of the arrangement shown to the left (Fig. 126), charge the two condensers with the P. Ds. between the points L and c, and c and M respectively. Let these P. Ds. be called V and V volts, the numerical value of which it is not necessary to know. Now, without discharging the condensers, separate the coating A of the one and the coating B' of the other from the resistance coil, and join these coatings together as shown to the right (Fig. 126), the other coatings B and A' being joined together as before. Let V l be the resultant P. D. in volts between A B' and B A', the numerical value of which also need not be known, let K and K' be respectively the numbers of coulombs on the plates A and B' before discharge, then K:= FV and K'=:-F'V', also we know that K K' is the charge in the compound plate A B' of the joint condenser to the right (Fig. 126), of capacity F -f F, .-. K-K'=(F-fF / )V 1 . Substituting, we have F V - F V = (F + F') Vj, F 7 V - V In order to compare V, V, and Vi, observe the deflection pro- duced by Vx on a suitable electrometer, and, without altering the arrangement of the battery and resistance coil shown to the right (Fig. 126), let two points, separated by a resistance r^ be found, by trial, such that the P. D. between them produces the same deflection on the electrometer, then ViV'iV,-:: r-.^'.n. Consequently, F_ / + r^ F r ; r t If / and r be so selected by shifting the connection c (Fig. 126), in one direction or other, that K equals K', or V, is nought, then F / F'~~7* This method of discharging one condenser into another, and measuring the resultant P. D., may be employed not only when the condensers are small, but when one or both of them are long Chap. VII.] COMPARING CAPACITIES STATICALLY. 331 lengths of submarine cable, in which case, owing to the " retarda- tion" or time taken in charging or discharging the cable, the sim- ple galvanometer method would give erroneous results unless the period of the needle were made most inconveniently long so as to insure the charge or discharge being completed before the needle began to move. If, however, the method just described of discharging one condenser into the other, and measuring the resultant effect be employed, not on account of the smallness of the capacities of the condensers under comparison, but because one or both of them have considerable retardation, then a galvanometer can be used to measure approximately the resultant P. D., the test giving perfectly accurate results when the point c is so selected, by trial, that the discharge of the compound condenser through the galvanometer is nought. Fig. 126. If the resultant charge be not absolutely nought, we can, in- stead of making a great number of tests to find the point c, for which it would be absolutely nought, and which may occupy more time than is at our disposal, correct approximately for a small re- sultant discharge as follows : Let d be the resultant deflection, and let d' be the deflection obtained on charging the compound condenser with the P. D. be- tween two points in the resistance coil, separated by a small re- sistance r. 2 ; then, if, as before, TI be the resistance between two points in the coil having a P. D. between them equal to Vj, but which we cannot now find directly, as we are not using an electro- meter, it follows, disregarding the retardation, that d r Hence, = 332 PRACTICAL ELECTRICITY. [Clm?. VIL F F d'r - dr* 179. Measuring Specific Inductive Capacity. If we know the area A of each of the coatings of a con- denser in square centimetres, and t the thickness of the dielectric in centimetres, then, from 169, page 311, it follows that i, its specific inductive capacity, F x 1-131 x 1013 x t where F is the capacity of the condenser in farads, which, if large enough, can be measured either absolutely by the method described in 177, page 328, or relatively by comparison with another condenser, whose capacity is known in farads, using the . method described in 174, page 319. Frequently, however, we desire to measure the specific inductive capacity of a comparatively small specimen of an insulating material, too small to be employed in making a condenser of large capacity, unless the dielectric were made so thin that it would be extremely difficult to determine its thickness accurately. In such a case we may employ the statical method described in 178, page 330, of comparing the capacity of a condenser made with the specimen of insulating material with the capacity of a condenser of somewhat similar dimensions, but having air for the dielectric. To use this method, however, we must have an electrometer of considerable sensibility, with its quarter cylinders far better insulated from one another and from the outside of the instrument than are those in the instrument illustrated in Figs. 47 and 48, 75, page 131. We also must have a charge and discharge key of high insulation, and enclosed in a metallic box, so as to be shielded from induction (see 51, page 99). This statical method, therefore, of comparing the capacities of two condensers, each of small capacity, although susceptible of giving extremely accurate Chap. VII.] MEASURING SPECIFIC INDUCTIVE CAPACITY. 333 results when carried out with the various precautions that would be adopted by a skilled experimenter, is alto- gether unsuitable to be employed by a beginner. The following method, however, based on a plan of experimenting originally suggested by Dr. Sauty, has been used by the author with good results. c and c' (Fig. 127) are the two condensers of small capacity, M and M', that we desire to compare ; a and b are two ad- justable resistances wound double in the ordinary manner employed in constructing resistance coils (see Fig. 7, 12, Fig. 1L7. page 28), K is a key, turning about its centre and making contact either at ^ or at & 2 , so that by moving the handle down and up the two condensers can be charged by the battery B or discharged, and T is an ordinary Bell telephone connecting the points P and Q, and which is an extremely delicate instrument for detecting small rapid fluctuations in the strength of a current passing through it. If the key K be alternately moved up and down there will be a succession of currents in opposite directions through the telephone, unless the potentials at p and Q always remain equal to one another, and in order that the P. D. between these two points may be 334 PRACTICAL ELECTRICITY. [Chap. VII. always nought, the rise or fall of potential at each of these points must be the same in the same time. This condition will be fulfilled when the quantities of elec- tricity that flow into, or out of, the two condensers in the same tvme, are directly proportional to their capaci- ties, and when there is no sensible retardation. Further, if the potentials at P and Q are equal to one another, the quantities of electricity that flow through the two wires, o P and o Q respectively, must be inversely proportional to their resistances a and b. Hence, combining these two conditions, no sound will be heard in the telephone if a and b are adjusted until M b The substance of which we desire to measure the specific inductive capacity, as, for example, a sheet of glass or a sheet of guttapercha, should have pasted on each side of it sheets of tinfoil of equal size, and about one inch smaller all round than the sheet of dielectric, so as to secure little surface leakage. If the sheet of dielectric be itself small, the space left uncovered with tinfoil must be less than one inch in width, but in that case the uncovered portion should be carefully cleaned and dried. It is also desirable for the purpose of diminishing this surface leakage to rest the condenser on a block B, as shown in Fig. 128, so as to keep the underneath portion of the sheet of dielectric D that is not covered with a sheet of tinfoil, corresponding with T above, from touching anything. 180. Standard Air Condenser. The standard air condenser may be conveniently constructed, as shown in Fig. 129, of thin slabs of plate glass about one-eighth of an inch thick, coated on both sides with tinfoil. These sheets of glass do not act as the dielectric, but Chap. VII.] STANDARD AIR CONDENSER. 335 merely form convenient supports, with very plane sur- faces, for the sheets of tinfoil, hence the two sheets of tinfoil on the two sides of any one of the slabs of glass must be electrically connected. With every alternate slab 1, 3, 5, &c., the sheets of tinfoil are pasted over the Fig. 129. whole surface of the glass, and may be each about one square foot in area, while in the case of the other set 2, 4, 6, &c., there is one inch left all round the glass not coated with tinfoil, as seen on the top plate P P of the condenser in the figure. This is in reality the top plate but one, the top plate T T, which is wholly covered with tinfoil, having been removed to enable the plate P P to be seen. The first set form together the outer coating, and 336 PRACTICAL ELECTRICITY. [Chap. VII. their terminal A is connected with s (Fig. 127), while all the smaller sheets of foil form the inner coating, and their terminal B, mounted on a block of ebonite, is con- nected with P. The glass slabs are piled one on the top of the other, but separated by fragments of glass FF, all of the same thickness, conveniently about one- tenth of an inch ; and there is one more of the slabs with the larger sheets of tinfoil on it than of the others, so that there is one of the former both at the bottom and at the top of the condenser when it is thus built up. The glass plates are prevented from sliding over one another when the condenser is moved, by their corners fitting into grooves in the four ebonite pillars E, E, E. The capacity of* the standard condenser, in farads, oquals A^ 4-452 "x 10" x f where A is the sum of the areas, reckoned in inches, of all the smaller sheets of tinfoil, and t is the thickness of one of the little glass fragments. The capacity of the experimental condenser equals A' t x 4-452 x 1012 x t? where A' is the area of one of the tinfoil coatings, t' the thickness of the sheet of dielectric under test, and i its specific inductive capacity. Hence, if the resistances a and b (Fig. 127) are so adjusted that no sound is heard in the telephone, a A t' * v v . ' b A' t The construction of the Bell's telephone, such as may be used in the previous experiment, is shown in Figs. 130 and 131, where m is a permanent magnet, terminated at the right-hand end (Fig. 130) by a piece of soft iron of Chap. VII.] THE BELL TELEPHONE. 337 the same thickness. Round this piece of iron is a coil of wire b 6, the ends of which d d are led to the terminals V Y. Close to the end of the piece of soft iron, but not touching it, is a thin plate of ferrotype iron c e. The Fig. 130. piece of soft iron is magnetised by the permanent magnet w, and thus attracts the centre of the thin plate of iron, and the amount of this attraction is varied by any cur- rent that passes round the coil b. Hence, if there be rapid fluctuations in the strength of the current passing round this coil, and still more, if there be rapid alterna- Fig. 131. tions in the direction of the current passing round this coil, the thin iron plate will be set in rapid vibration, and a sound will be emitted. If the telephone be well made, and if the ear be placed near the opening shown at the right hand in Fig. 130, and at the left hand in Fig. 131, the sound produced by even extremely small w 338 PRACTICAL ELECTRICITY. [Chap. VII. alterations in the current strength, can be heard, if they follow one another with sufficient rapidity. 181. Every Charged Body forms One Coating of a Condenser. In practice, as already explained, a con- denser is the name given to two sets of sheets of metal so arranged that the one set has a large capacity rela- tively to the other ; but, in reality, every charged body forms a condenser with some other body j it may be with the walls of the room, or the ceiling, or the table, or the body of the experimenter, or with all of them ; hence we see that the statement made at the foot of page 109, that when one conducting body A is entirely surrounded by another conducting body B, the quantity of electricity on A is directly proportional to the P. D. between A and B as long as the position of A, relatively to B, is abso- lutely fixed, is only another way of saying that the capacity of A relatively to B is constant as long as their relative positions are unchanged. In 67, page 120, it was explained that the poten- tial of the charged metal plate P could be diminished by bringing near it the metal plate M, connected with the earth. We now understand that this arises from the capacity of P relatively to M being increased by approaching them, in consequence of which the potential of P, cor- responding with a given charge on it, is dimin- ished (see 167, page 308). 182. Capacity of a Spherical Condenser. If a metallic sphere A (Fig. 132) of a centimetres' radius be insulated concentrically inside another hollow metallic sphere B of b centimetres' radius, Fig. 132. Chap. VIL] CAPACITY OF A SPHERICAL CONDENSER. 339 and if the dielectric separating them be air, the capacity of A, relatively to B, can be proved to be ab farads. 9 x 10 11 (b-a) This last expression can be written in the form a - 9 x 10 n (l - d from which we see that as b grows greater and greater, the capacity of A grows smaller and smaller. Con- sequently, although we have no experience of a single charged body insulated alone in space, we can see what is the limit to which the capacity of A approaches, as b becomes larger and larger. The value of this limit is obtained by making b equal to infinity, when the capacity of A becomes farads, 9 x 10 11 and this is practically the capacity of a sphere when, as in the case of A, Fig. 43, page 121, it is so far away from other bodies as to be practically beyond the range of their inductive action. But because we can calculate the capacity of a body when it is so far away from other bodies as to be practi- cally beyond the range of their inductive action, it must not be imagined that we can have a charged body exist- ing alone in space. Indeed, as seen in 60, page 115, we cannot produce only a single quantity of electricity, since equal and opposite quantities are produced simul- taneously, therefore it is impossible to have one body charged positively or negatively without some other body existing with an equal and opposite charge on it. And just as we have no experience of a single 340 PRACTICAL ELECTRICITY. [Chap. VII. charged body existing by itself, so it is equally impossible to obtain two bodies charged with the same kind of electricity without a third one oppositely charged. Al- though, therefore, we are accustomed to speak of two positively or of two negatively electrified bodies repelling one another as if this action could take place without the presence of any third body, we must not allow this very convenient form of ex- pression to cause us to forget that all our ex- perience of the action of electrified bodies is derived from experi- ments made inside a room, the walls, ceiling, and floor of which are more or less good con- ductors, and which form condensers with the electrified bodies in- side the room. For ex- ample, if A and c (Fig. 133) be two spheres electrified positively, and placed inside a conducting room B B, the distribution of the density will be roughly as in the figure, the density being greatest where the plus or minus signs are nearest to- gether. If A and c be free to move, then, as is well known, they will separate from one another, and ap- proach the sides of the room. This action is usually regarded as being caused, partly by the repulsion of the positive electricities on A and c, and partly by the at- traction of the positive electricity on each of the bodies by the negative electricity on the side of the wall ad- jacent to the two bodies respectively. But as we have no experimental evidence of what would happen if A and c Fig. 133. Chap. VII.] CONDENSER METHOD OF COMPARING E. M. Fs. 341 could exist with their positive charges apart from B B, it may be that it is the attraction of the opposite elec- tricities that causes A and c to separate, and that there is no repulsion at all between the similarly electrified bodies A and C ; and this, of course, is true whether A and C be spheres inside a conducting room with flat walls, ceiling, and floor, or whether they be conduc- tors of any shape inside another of any other shape, as shown in Fig. 134. Example 102. What is the capacity of the earth regarded as a sphere insulated in space 1 Answer. The mean radius of the earth is 6 3703 x 10 8 centimetres, hence its capacity is 0-0007078 farads, or roughly 708 microfarads, which is the capacity of about 2,000 miles of ordinary submarine telegraph cable. 183. Condenser Method of Comparing the E. M. Fs. of Current Generators. We have already seen ( 132, page 234) that with cells which polarise, as it is called, the ordinary galvanometer methods of comparing KM.Fs. cannot be employed to obtain accurate results, and that a null method like that of PoggendorfFs is much to be preferred. When, however, a condenser and a suitable reflecting galvanometer for measuring capacity are at hand, the following method may be employed instead of PoggendorfFs. Charge the condensers successively with the two current generators, and in each case measure the charge or discharge with the galvanometer, then, since the deflections are proportional to the charges or dis- charges ( 160, page 209), and since these charges are proportional to the E. M. Fs. employed, it follows that the E. M. Fs. are proportional to the deflections. If the plates of the cell have only a very small surface 342 PRACTICAL ELECTRICITY. [Chap. VII. in contact with the liquid, the polarisation arising from the flow of electricity into the condenser to charge it may be sensible if the condenser have a large capacity. Hence, in such a case, it is important to use a condenser of as small a capacity as can be employed to give a satisfactory deflection with the most delicate galvano- meter available. Such a precaution is especially neces- sary when experiments on the E. M. Fs. of cells made of simple pieces of wire dipping into various liquids are performed. 184. Condenser Method of Measuring the Resistance of a Current Generator. We have seen, 115, page 204, that if a current generator having a fixed E. M. F. equal to E volts, and a resistance of b ohms, be shunted with a resistance of r ohms, the P. D. at the terminals will be x E volts. If, then, we employ first the generator unshunted to charge the condenser, and obtain, on charging or on dis- charging through a suitable galvanometer, a first swing d l of the spot of light ; second, if the generator be shunted with a resistance r ohms, and we obtain, on charging or on discharging, a first swing d 2 , we know that r + b With cells that polarise it is very important that the battery should be shunted with the resistance r only at the 'moment of charging the condenser, and that the act of disconnecting the battery from the condenser should also disconnect the shunt. This may be conveniently effected, without the employment of any special key, by joining up the arrangement as shown in Fig. 135, the key in the Chap. VII.] CONDENSER TEST OF A BATTERY RESISTANCE. 343 figure being exactly the same in principle as that shown in Fig. 121, page 320, but not possessing such high insulation, as this is unnecessary with the present experi- ment. One pole Q of the battery B is permanently con- nected with one end of the resistance r, with one coating C, of the condenser, and with the upper screw s. 7 of the key ; the other pole P of the battery is insulated as long as the contact at s l is broken. On depressing the lever the contact at S 2 is broken and that at Si made ; this has the effect of connecting the pole P of the battery to the Fig. 135. other end of the resistance r and to the other coating C 2 of the condenser through the galvanometer g, hence the condenser is charged through the galvanometer with the cell shunted. On liberating the key, which should be done directly the first swing is completed, the contact at BI is broken and that at S 2 made ; P is therefore discon- nected from the shunt and the galvanometer, and the condenser is discharged through the galvanometer. To observe the charge with the battery unshunted, the infinity plug in r must be withdrawn, or one of the ends of the resistance r must be disconnected from the rest of the circuit. 344 PRACTICAL ELECTRICITY. [Chap. VII. 185. Measuring a Resistance by the Rate of "Loss of Charge. When a resistance of not merely thousands of megohms, but of millions of megohms has to he measured, the galvanometer method described in 151, page 278, is not sensitive enough, unless an enormously large battery be employed, and a mode of testing depending not on measuring the rate of leakage but on measuring the amount that has leaked in a given time has to be resorted to, as follows: If a charged condenser have its two coatings connected by a resistance, it will be discharged with more or less rapidity depending on the magnitude of the resistance, and the capacity of the condenser. If F farads be the capacity, r ohms the resistance, and if the P. D. between the coat- ings be V volts at a certain time, and V 7 volts t seconds afterwards, then we can prove that _ 0-4343* hence the resistance r may be ascertained if we know F, V, V', and t. To prove this formula we shall assume that the whole interval t seconds, during which the discharge is observed, is subdivided into a great number n of very small equal intervals of time T, so small that during the whole of any one of these small intervals, the P. D. between the coatings may be supposed to remain constant, so that instead of the P. D. falling gradually from V volts to V volts, we suppose it to fall by n small jumps, one jump being made at the end of each interval. The same sort of approximation to the truth is made when a curve is supposed to be formed of a very great number of very short straight lines, each two adjoining straight lines differing very slightly from one another in direction, since, instead of the gradual change of direction which occurs in going along a real curve, we have a discontinuous change in moving along the succession of short straight lines. At the commencement, the number of coulombs in one coating of the condenser is FV, and during the first interval the quantity in coulombs that flows out of the one coating into the other is so that the quantity that will remain in this coating is V-IrFV(,_JL); Chap. VII.] MEASURING RESISTANCE BY LOSS OF CHARGE. 345 hence, the P. D. between the coatings at the end of the first interval equals vA_JL During the second interval of r seconds the number of coulombs that will flow from one coating into the other equals BO that the quantity that will remain in each coating will be -- \ Fr/ coulombs. Similarly, the number of coulombs remaining on each coating at the end of the third interval equals and at the end of the , the interval that is at the time <, I ut this is equal to FV, .-. FV/i_ JH\ W = \ Fr/ or dividing both sides by F, and substituting - for T, it follows that 346 PRACTICAL ELECTRICITY. [Chap. VH. and this is more and more true the larger n be made. But it can be shown mathematically that when n is infinitely great when t stands for 2-71828. So that V~/ r = V, Consequently, converting the logarithm to the base e to a logarithm to the base 10, by the method given in 158, page 296, we have r = If an electrometer, with well-insulated quarter cylinders, be available, then the loss of potential can be easily observed by attaching the two coatings of the condenser to the opposite pairs of quarter cylinders, giving the condenser a charge, and observing the times at which the spot of light passes two definite positions on the scale, for V and V may be measured in any units, since we have merely to deal with the ratio of V to V. In this way the insulation of even a short length of well-insulated cable can be measured. For, as the cable is shorter, and r is larger, F is pro- portionately smaller, so that the time the P. D. takes to fall from one given value to another is independent of the length of the cable. 186. Rate of Loss of Charge from Leakage through the Mass depends on the Nature of the Dielectric only, and not on the Shape or Size of the Condenser. Not merely is the time the P. D. takes to fall from one given value to another independent of the area of the coatings of the condenser, but it is independent of the thickness of the dielectric. Take the case of a condenser with flat parallel plates. Then, if A be the area of one of the coatings in square inches, d the distance Chap. VII.] RATE OF LOSS DEPENDS ON DIELECTRIC ONLY. 347 between them in inches, and * the " specific resistance" or resistance per cubic inch of the dielectric. and from 169, page 311, if be the specific inductive capacity of the dielectric, 4-452 x 10 12 X d* .*. if t be the time in seconds during which the P. D. falls from V to V', d x s _ 0-4343* X 4-452 x 10 12 d A 1 V 1-934 x IP 1 * the right-hand expression depending only on the specific re- sistance, and specific inductive capacity of the dielectric, and not on its shape or size. So in the same way with a cylindrical condenser the capacity in farads, as we have seen from 168, page 308, and 169, page 311, is low log. 10 D-log. 1( / where i is the specific inductive capacity of the dielectric, I the length of the condenser in centimetres, and D and d the diameters of the coatings. It may also be shown that if *' be the resistance, in ohms, per cubic centimetre of the dielectric, r, the resistance ot length I of the cylindrical condenser is 0-8686 Ttl Consequently, V_ lo g-io v' 4-912 x 10 U 348 PRACTICAL ELECTRICITY. [Chap. VII. It has to be remembered that whereas for the condenser with flat parallel plates, * was the resistance per cubic inch of the dielec- tric, here s' is the resistance per cubic centimetre. Hence, since the resistance is proportional to the thickness, and inversely as the sectional area, 2 ' 54 that is, the resistance per cubic centimetre of any substance it 2 '54 times the resistance per cubic inch. The specific inductive capacity, t, is independent of the unit of length or area. Hence, substi- tuting the value for ', we obtain y 10g ' 10 V' 1-934 x 10" which is the same expression as that obtained with flat parallel plates. 187. Galvanometric Method of Measuring Resist- ance by Loss of Charge. In the formula given in 185, page 344, we may substitute for V and V the number of cou- lombs K and K', on one of the coatings of the condenser when the P. D. between the coatings is V and V' volts, so that 0-4343 t If the capacity of the condenser be sufficiently large, K and K' can be measured by charging the condenser through a gal- vanometer at a certain moment, and discharging it again at the end of t seconds, using the arrangement shown in Fig. 123, page 322. To enable the lever L of the key, seen more plainly in Fig. 121, page 320, to be left without completing the contact at Sj or at S 2 during the time the condenser is left insulated, the screw which makes the upper contact S 2 should be screwed out so far that it would require a slight upward pressure to be given to the lever to cause it to make this upper contact. If the resistance to leakage be very large, K and K' will be nearly equal to one another unless t be taken inconveniently long. This difficulty may be overcome by using a large battery, and charging the con- denser with the galvanometer shunted at the beginning of the Chap. VH.J POWER OF SHUNT WITH DISCHARGE. 349 time t, and then charging it again with the galvanometer un- shunted, and therefore in a much more sensitive condition at the end of the time t. In this way K and K - K' will be measured, and by properly choosing the shunt, the second test may be made as delicate as the first. Since, however, as mentioned in 174, page 319, a difficulty is introduced when comparing two quantities of electricity if the galvanometer be shunted in one case and not in the other, this method is not a perfectly accurate one unless the following correction be introduced. 188. Multiplying Power of a Shunt used in Mea- suring a Discharge. When a quantity of electricity is passed through a shunted galvanometer, the quantities that pass respectively through the galvanometer and shunt are inversely as their resistances exactly as in the case of a steady current ; but when, after the discharge has been completed, the needle begins to move, its motion induces a current in the galvanometer and shunt in such a direction as to tend to stop its motion. This in- 'duced current, therefore, damps the motion of the needle, and we have, therefore, to use the formula for damped vibrations given in Io7, page 296. It can, however, be proved mathematically that with a given galvanometer, and with a given adjustment of the con- trolling magnet, $c., the damping in this case has simply the effect of increasing the resistance of the galvanometer by a definite amount, in- dependently of the resistance of the shunt. So that if g be the actual galvanometer resistance, and * that of the particular shunt em- ployed, the multiplying power for a discharge is where of has a definite value, independent of that of , for a given galvanometer with a given adjustment of the controlling magnet, &c. Instead, therefore, of employing the formula for damped vibrations, to do which we must measure the decrement when its vibrations are damped, we may simply determine the constant of in the following way : Charge a condenser with a small P. D., say of Vj volts, through the galvano neter unshunted, obtaining a first swing d lt say. Next, having discharged the condenser, shunt the galvano- meter with any convenient shunt of resistance *, increase the P. D. to a suitably larger value V 2 volts, and charge the condensei through the shunted galvanometer, obtaining a first swing d 2 . Then, since the quantities which pass into the condenser are pro- portional to Y! and 350 PRACTICAL ELECTRICITY. [Cliap. VII. or the multiplying power of the shunt, and , + g'=s( d l. Y? -lY W V / As YI and V 2 only occur in a ratio, we do not require to know their absolute values in volts, and the simplest method of obtaining two P. Ds. having a known ratio is that given in 150, page 278. Example 103. On charging a slightly leaky condenser through a galvanometer of 1,000 ohms' resistance, shunted with the yJ-yth shunt, a deflection of 230 scale divisions is obtained. The condenser is then insulated, and at the end of half a minute it is again charged but with the galvanometer unshunted, and a deflec- tion of 112 scale divisions is obtained. What is the resistance of the condenser ? To ascertain the value of the first deflection in farads, as well as to find the increased multiplying power of the shunt for a dis- charge, let us charge a well-insulated condenser of known capacity, say ^rd of a microfarad, with the same P. D. as was used in the previous experiment ; let this give a deflection of 175 scale divi- sions with the galvanometer unshunted. Next discharge the con- denser, shunt the galvanometer with, say, the same shunt as was used before, increase the P. D. employed, and again charge the condenser, obtaining, say, a deflection of 295 scale divisions. Let these two P. Ds. be those between the points S and T, Fig. 101, ;e 278, and L and M, and let the ratio of the resistances of q .p be in the ratio of 10 to 1,736. The multiplying power of the shunt for a discharge equals = 103, therefore the capacity of our slightly leaky condenser is 103 ^x^ farads, 175 3 x 10 or 45-12 microfarads. Next, K being the number of coulombs in one coating of our Chap. VH.] PRODUCTION OF LARGE P. Ds. 351 slightly leaky condenser at the moment of charging, and K the quantity at the end of half a minute, TT- -rrt '-- = 112 -r- 230 x 103, A, .-. log. 10 | 7 =0-0021. Hence, 0-4343 x 30 ohms. x 0-0021 10 8 Answer. 137'5 megohms. LARGE POTENTIAL DIFFERENCES. 189. Production of Large Potential Differences. When any two dissimilar substances are brought into contact, there is a certain P. D. set up between them in consequence of what is known as the " contact potential difference" The two substances, therefore, become charged, like the two coatings of a condenser, with equal and opposite amounts of electricity, depending on the contact P. D., the proximity of the two bodies and their size. If either, or both, of these bodies be an in- sulator, or be held by an insulating handle, some, or all, of the charge will remain when the bodies are separated. If the bodies be separated in such a way that practically all the points of contact are broken at the same time, then all the charge will remain on each of the bodies if they be properly insulated. As the distance between the bodies increases the capacity of the condenser rapidly diminishes, hence the P. B. between the bodies rapidly increases. In this way a P. D. of many hundreds, or thousands, of volts can easily be produced by bringing a piece of dry, clean glass into close contact with a piece of silk, or a piece of dry, clean ebonite into close contact with a piece of cat's-skin, and then separating them ; and 352 PRACTICAL ELECTRICITY. [Chap. VII. just as work has to be done in separating the two plates of a charged condenser (see Example 100, page 326), work has to be done in separating the glass from the silk, or the ebonite from the cat's-skin, and the power that the glass or ebonite has to give a spark when the knuckle is brought near it, arises from the condenser possessing a store of potential energy. (See 176, page 322.) The ebonite forms one of the coatings of this condenser, and the surface of the room the other, because, as the cat's- skin is not a good insulator, the charge of positive elec- tricity induced on it when it is in contact with the ebonite, spreads itself over the walls, ceiling, and floor of the room on the separation. As explained in 61, page 115, the object of rubbing the glass with the silk is to bring all parts of the surface of the insulating glass into successive contact with the silk. The well-known cylindrical and plate-glass frictional electrical machines are merely contrivances for bringing different portions of the surface of a cylinder, or a sheet of glass, successively into close contact with a silk rubber, and separating them again. The electrical energy pro- duced by such an apparatus depends simply on the work required to perform the separation of the positively elec- trified portions of glass from the negatively electrified rubber, whereas the actual power expended in turning such a machine is mainly wasted in overcoming friction and producing heat. Hence, such frictional machines are extremely inefficient converters of mechanical energy into electrical energy, and they are, therefore, rapidly becoming obsolete, and being replaced by the much more efficient influence machines. (See 194, page 361.) 190. Condensing Electroscope. The increase of P. D. between the two coatings of a charged condenser, produced by separating the plates, may be employed to cause an ordinary gold-leaf electroscope to indicate the P. D. existing at the terminals of two or three cells in series. For, let the plate M, Fig. 42, page 120, be con- nected electrically with the tinfoil coating of the gold* Chap. VII. J CONDENSING ELECTROSCOPE. 353 leaf electroscope, and placed close to the plate P ; then let them be connected with the terminals of, say, three Daniell's cells in series, which will cause them to be charged with a P. D. of about 3 -3 volts. Now, discon- nect P from the cells, and remove M altogether, then the P. D. in volts between the gold-leaves and the tinfoil coating of the electroscope will become 3 '3 multiplied by the ratio of the capacity of P when M was close to it, to its capacity when M has been removed far away, that is, when p forms a condenser with the walls and ceiling of the room, and with the tinfoil coating of the electroscope ; since, with a given charge on the coatings of a condenser the P. D. between the coatings is inversely as the capacity (see 167, page 308). This ratio will be the greater the nearer M was brought to P during the charg- ing, and may easily be made 100 or more (so that the P. D. between the gold-leaves and the tinfoil coating is now between 300 and 400 volts) by having the surfaces of the plates carefully coated with a layer of shell-lac, and by simply resting M on p. Strictly speaking, the ratio of capacities to be considered is that of P plus that of the gold-leaves when M is close to P, to that of p plus that of the gold-leaves when M is far away ; and although the capacity of the gold-leaves is insignificant in compari- son with that of p when M is very near p, it is not so when M has been removed. The above will be practi- cally the same whether M be disconnected or not from either the tinfoil coating or the cells, before it is re- moved. In order that the distances separating all parts of M and P may be very small, their surfaces must be made quite plane, and it is difficult to do this unless the plates be fairly thick. But if they are thick they will be too heavy to rest on the stem of the electroscope, hence it is better to support p as the plate A (Fig. 29, page 88), is sup- ported, by means of an insulating stand having a fairly strong glass rod, and to connect it with w of the electro- scope by a thin piece of wire. x 354 PRACTICAL ELECTRICITY. [Chap. VIL 191. Calibrating a Gold-Leaf Electroscope. If the ratio, r, say, that the sum of the capacities of P and of the gold-leaves when M is placed in a fixed position near p bears to the sum when M is far away, be accurately known, then a gold-leaf electroscope, which will not in- dicate directly a P. D. of less than 100 or 200 volts, may be calibrated for any divergence of the leaves by the employment of some ten or twelve cells. For if P and M, when near together, be charged with one cell, and then M be removed, and the divergence of the gold-leaves c?! noted, then p and M be charged with two cells, M be removed, and the divergence d% noted, &c., these diver- gences d lt 'd%, &c., will correspond with a P. D. between the gold-leaves and the tinfoil coating of r E, 2 r E, &c., volts, where E is the E. M. F. of one cell, and which is 1*104 volts if the cells be Daniell's cells made with equidense solutions of copper and zinc sulphate, and if pure zinc and copper plates be employed (see 119, page 211). It would be practically impossible to determine this ratio, r, by calculation, owing to the difficulty of calcu- lating the capacity of P, and the gold-leaves when M was removed. To determine it experimentally would be nearly as difficult as calibrating the gold-leaf elec- troscope directly by experiment. We must, therefore, employ some condenser, the capacity of which can be made to have two very distinct values, both of which are large compared with the capacity of the gold-leaves, having a known ratio to one another of about 100 ; or we may employ the arrangement suggested by Sir William Thomson, in 1885, for increasing a P. D. in a known ratio, and which is shown symbolically in Fig. 136. A, B, c, &c., are well-insulated condensers of not necessarily equal capacities, joined up in series, the outer coating of the first a being connected with the outside of the electro- scope, and the inner coating z of the last with the gold- leaves. A well-insulated battery, ss, of a convenient number of cells, having an E. M. F. equal to E volts, has Cfoap. VII.] CALIBRATING A GOLD-LEAF ELECTROSCOPE. 355 its terminals connected, first with a and 6, then, instead, with b and c, then with c and c?, &c. On the battery ter- minals being connected with a and 6, the coatings of the first condenser will have a P. D. of E volts produced between them, and similarly on the battery terminals being connected with b and c a P. I), of E volts will be produced between b and c, therefore the P. D. between a and c will be 2 E volts. Again, on connecting the battery terminals with c and d, the P. D. between a and d will become 3 E volts, &c. Hence, if there be 100 condensers in series, and if the battery be moved along so that its terminals make successive contacts with the pairs of coatings of each of the condensers, the P. D. between a and , that is between the outer coating of the electroscope and the gold - leaves, will become 100 E, and by making E first, say 2 volts, next 3 volts, and so on, the electroscope can be calibrated with P. Ds. of 200, 300, &c., volts. In the last paragraph it is stated that the coatings of the condensers are well insulated from one another, but if the battery terminals s s be rapidly moved backwards and forwards so as to make rapid successive contacts with the coatings of the various condensers, it will only be necessary for the insulation of the condensers to be fairly good, as there will be no time for leakage to take place between the successive contacts of the coatings of each condenser with the battery terminals. The following gives the result of the approximate \ n Fig. 136. 356 PRACTICAL ELECTRICITY. [Chap. VII. calibration of a gold-leaf electroscope, the gold-leaves being about 1 J inch long : P. D. between the It aves and the tiufoil coating in volts. 26 500 42-6 750 Angle between the gold 60-2 92-7 1,000 1,500 192. Electrophorus. The oldest form of influence machine is the " electrophones," which consists of a plate of some insulating sub- stance I (Fig. 137), usually ebonite in the modern electrepho- rus, fastened into a metal backing B, and a movable metal plate p, into which screws a metal ferrule at- tached to an insu- lating rod or handle E. The electrophorus can be made to give a succession of either positive or negative charges of high po- tential by the varia- tion of capacity of the condenser formed of the ebonite and the plate P, produced by altering their distance from one another The ebonite, on being rubbed with a piece of cat's- skin, becomes negatively charged, and forms a condenser of fixed capacity with the uninsulated backing B,the upper surface of which is therefore charged positively. Further, this condenser-action causes the negative charge produced Fig. 137. Chap. VII.] THE ELECTROPHORUS. 357 on the upper surface of the ebonite to be attracted a small distance downwards into the insulating substance of the ebonite, and so prevents the charge being easily removed by the metal plate P when it is laid for a short time on the ebonite. If this plate be held by the insulating handle R, and placed on the ebonite, the potential of the ebonite will be slightly diminished numerically that is, become less negative (see 67, page 120), and the plate P will be raised to a fairly high negative potential, the density on its lower surface being positive, and on its upper negative (see 69, 8, page 124) ; P, in fact, forms a condenser with the ceiling and walls of the room. If now, by means of the insulating handle, held at the extreme end to diminish the surface leakage as much as possible, P be removed again without being touched, its negative potential will grow less and less as its distance from the ebonite grows greater and greater, and the density on its upper and lower surfaces will also be diminished, until at last when P is beyond the range of the inductive action of the ebonite it will be simply an uncharged body at a potential nought. But if, on the other hand, while P is resting on the ebonite, it be connected with the backing, B, or with the earth, by means of a wire, or more simply by touching it with one's finger, its potential will be reduced to nought, and the potential of the ebonite will be numeri- cally diminished. Hence, some of the positive charge previously induced in the backing will flow away, all the negative charge on the upper surface of P will also dis- appear, and some more positive electricity will be attracted to the lower side of P, the density on its upper surface will become, therefore, nought, and on its lower surface more positive than before. P and B together now form the earth coating, and the ebonite the insu- lated coating, of a condenser. On removing p by means of the insulating handle R, its potential rapidly rises positively, and that of the ebonite increases negatively. When p has been removed some little distance from the 358 PRACTICAL ELECTRICITY. [Chap. VII. ebonite, its potential becomes high enough to enable it to give a positive spark* to a conductor brought near it. And as the ebonite is not sensibly discharged by the action of placing p on its surface and removing it, the operation of inductively giving p a large positive charge can be repeated again and again ; and we may thus charge an insulated conductor with even a large capacity to a high positive potential. To save the trouble of having to electrically connect p with B each time p is laid on the ebonite, it is desirable (if an electrophorus is made simply for practical use and not also for the purposes of instruction, as is the case with the one shown in Fig. 137) to drill a hole through r^^^^^xJL^ *^ e Backing B (Fig. 138) and the J8 Uf ebonite I, and insert a small brass Mh '\\u \np<^t^^i^im^ screw s into it of such a length Fi 13g that, when screwed in, its point is a little below the upper surface of the ebonite, for with this arrangement a spark passes across the small air space when p is laid on the ebonite in consequence of .the high negative potential induced in P ; but no spark passes on raising p, since its posi- tive potential only becomes large when p is raised so far from the ebonite that a spark cannot pass to the screw. The presence, therefore, of this screw, with its slightly countersunk point, has precisely the same effect as connecting p with B when p is resting * When the P. D. between two conductors reaches a certain value, depending on their shapes, their distance apart, and the insulating material separating them, a crack or hole is found in the insulator, and a spark, produced by the burning of minute particles of the sur- faces of the conductors, passes along the crack or hole. The P. D. re- quired to produce a spark through air is given in 196, page 370, but for paraffined paper, guttapercha, glass, &c., it is much greater. While the air is momentarily cracked, during the passage of a spark, its resistance is comparatively small, but after the spark has passed, the crack closes up, and the resistance regains its original value ; if, however, the spark has passed through paper, a small hole may be seen, differing, however, from a hole made by a pin, in that the former is burred on both sides, as if the electric force making it had acted from the centre of the paper outwards towards each side. Chap. VII.] NEGATIVE CHARGES WITH ELECTROPHORUS. 359 on the ebonite, and removing this connection before p is raised. If it be desired to charge an insulated conductor of large capacity to a high negative potential, we might use an electrophorus with I (Fig. 137) made of glass, which becomes charged positively on being rubbed with silk ; but as glass is a much more hygroscopic body than ebonite, and therefore much more difficult to keep electrified when exposed to the air, it is better to use an ebonite electro- phorus in the following manner. 193. Ebonite Electrophorus arranged to give Nega- tive Charges. Unscrew the handle from the plate p and screw ib into the back- ing (Fig. 139). Excite the ebonite by rubbing it with cat's-skin, and suppose that the back- ing has been brought to a potential nought by connecting it for a moment with the ground when it was held at some distance from P, which is lying on the table. The ebonite is now the in- sulated coating of a condenser, the uninsu- lated one being B and the walls of the room. Next holding the back- ing and ebonite by the insulating handle R, place the ebonite on p (Fig. 140). The po- tential of the ebonite will then become less negative, the potential of B will be raised to a high positive value, the density on Fig. 139. 360 PRACTICAL ELECTRICITY. [Chap. VII. its upper side will become positive, the density on its lower side less positive than before, and the density of the upper surface of P positive. Connect B with p, the potential of B will be reduced to nought, the potential of the ebonite will be made still less negative, the density on the upper surface of p made less positive, the density on the upper .surface of B nought, and on its lower sur- face more positive than before. Raise the backing and the ebonite by the handle, the potential of the ebonite will become more negative, and that of B will become negative and will reach a high negative value when the backing and ebonite are removed some little distance from P, so that a spark of negative elec- tricity can be taken from B by a conductor brought near it. In the preceding we have considered the various electrical changes that take place on all the parts of an electrophorus when in use, but probably the simplest way of looking at the action of the electrophorus, whether it be used to give positive or negative charges to some conductor, is to remember that when P is in contact with the ebonite plate, and p and B are electrically connected together and with the earth, there are charges of positive electricity on the surfaces of P and B facing the ebonite, and these charges may in each case be regarded as being due to the excess of the inductive action of the negative charge on the ebonite over that of the positive charge on the other metal plate, the effect of the negative charge in each case preponderating. Consequently if both p and B could be separated from the ebonite by means of insu- lating handles, both would be found to have a positive Chap VII.l ACCUMULATING INFLUENCE MACHINES. 361 potential, and to be in a condition to give a positive charge to some other conductor. And if the ebonite and backing be removed without separation, P will, as before, have a positive potential ; but the action on B will now be quite different from before, for, instead of the induc- tive action of the positive electricity on P, together with the preponderating inductive action of the negative electricity on the ebonite, being removed simultaneously, only the former is removed. Hence the inductive effect on B of this negative electricity on the ebonite will pro- duce an effect greater than before, B will therefore have a negative potential, and be in a condition to give a negative charge to some other conductor. In the electrophorus shown in the figures the ebonite is held to the backing by three pins p p, instead of being cemented to it as is usual in an electrophorus, and can be removed by withdrawing these pins. Hence we can examine the electrification of the ebonite or of the backing in any stage of the experiments described above. To charge a body of large capacity with a simple electro- phorus is a slow process, and hence a " rotatory electro- phones " has been devised by Bertsch for enabling the operations described in 192 to be rapidly performed, but even this apparatus is inferior to the machines described in the following sections. 194. Accumulating Influence Machines. With the electrophorus we can, as we have seen, increase the potential of an insulated body until it is equal to that of P, when p, with its induced charge in it, has been removed far away from the ebonite, but we have no means of increasing the charge in the ebonite itself \ and so, in order to use an electrophorus, it is necessary to commence by charging the ebonite by rubbing it with a piece of cat's-skin. With an " accumulating influence machine" on the other hand, we are able to increase the charge on the inductor, and hence to start such a machine with practically little or no charge on the inductor. The action of all such machines depends on the folk wing prin- PRACTICAL ELECTRICITY. TChap. VII. ciple : If A and B (Fig. 141), be two insulated metallic pots possessing a small P. D. between them, the potential of A being the higher, and if c and D be two uncharged conductors, c being placed near the outside of A, and D Fig 141. near the outside of B, the potential of c will be a little higher than that of D ; hence if c and D be connected by a piece of wire w, or other conductor, a small quantity of positive electricity will flow from c to D, so that there will be a small charge of positive electricity on D, and of negative on c. If, now, the wire be disconnected from c and D, and by means of insulating threads c be put in- Chap. VII.] ACCUMULATING INFLUENCE MACHINES. 363 side B and be made to touch B near the bottom, while D is put inside A, and is made to touch A near the bottom (Fig. 142), the negative charge on c will be given up entirely to B, and the positive charge on p entirely to A (see 64, page 118) ; hence the P. D. between A and B Fig. 142. will be increased, c and D are now withdrawn, totally discharged from B and A, and on being put again into the position shown in Fig. 141, the operation is repeated. If this be performed a sufficient number of times, the P. D. between A and B may be made as large as we like ; and as the charges induced in c and D depend 011 the P. D. already existing between A and B, it follows 364 PRACTICAL ELECTRICITY. [Chap. VII. that the increase of P. D. goes on more and mere rapidly according to the " compound interest law." 195. Thomson's Replenisher. An accumulating in- fluence machine for rapidly performing the operations Fig. 143. described in the last section was devised by Sir William Thomson about 1867, and has been much employed. The balls C and D, in Fig. 141, are replaced by two gilt brass " carriers " c, D, seen in perspective in Figs. 143, 145, and in plan in Fig. 144. These are carried eccentrically at the ends of an ebonite rod R, fixed to an ebonite spindle E, and by turning this spindle by means of the milled head M at the top (Fig. 145), the carriers are rapidly carried round. The metal pots A and B, of Fig. 141, Chap. vii.] THOMSON'S REPLENISHED 365 become the gilt brass "inductors" AB (Figs. 143, 144, 145), and the wire w is replaced by two springs s s', con- nected by a strip of brass M fixed round the edge of the piece of ebonite P. This ebonite carries the springs and also the end of the spindle, and is itself supported as seen in Fig. 145. When the carriers c D simultaneously touch Fig. 144. the springs s s', they are practically in the same electric condition as are c and D (Fig. 141), and are acted on inductively by the charges in the inductors A B ; while, on the other hand, when they have been turned round further in the direction of the arrow (Fig. 144) until they touch the springs s' s, which are connected respectively with the two inductors, the carriers are electrically in the same condition as are c and D (Fig. 142) that is, they are under cover of the inductors, and so part with their charges to these inductors. It is found that there is always a sufficiently large 366 PRACTICAL ELECTRICITY. [Chap. VII. P. D. between the inductors AB (Fig. 143), no matter how well they may have been previously discharged, to start the action of the " Thomson's replenisher," and to enable the apparatus (if it be well constructed, and also clean and dry ) to rapidly produce sparks on the compound interest principle. To prevent the carriers c D causing the inductors A B to lose electricity by being left in contact with them, or by being electrically attracted round so as to come into contact with them, when the replenisheris not in use, the milled head M (Fig. 145) is fixed in the position seen in this figure by a pin attached to the farther side of the square head H, fitting into a hole in the head M. On turning the head H, this pin is withdrawn from the milled head M, which is then free to turn, and the spring K press- ing against the square Fig. 145. head H is for the pur- pose of holding the head in one or other of two definite positions in one of which the pin locks the milled head M, and in the other leaves it quite free. The earliest machine in which this compound interest principle of electrophone action was used, was the " re- volving doubter " invented by Nicholson more than one hundred years ago. This apparatus, however, seems to Chap. VII.] WIMSHURST INFLUENCE MACHINE. 367 have remained practically unknown, and unused. In 1860 C. F. Varley invented a somewhat similar appa- ratus, and still later a well-known machine was devised by Holtz, which, however, required an initial P. D. to be set up between the inductors by a piece of rubbed ebonite in order to start the action. So far the Holtz machine resembles the electrophorus, but while in a simple electrophorus, or even in Bertsch's rotatory elec- trophorus, there is no contrivance for even maintaining the P. D. between the inductors, the Holtz machine is so designed that the P. D. is increased by the action of the machine. This machine differs, however, from Thomson's replenisher : first, in that the carriers are practically infinite in number ; secondly, in the connect- ing wire w (Figs. HI, 142), and s s' (Figs. 143, 144), having a break in it so that it is divided into two parts, and the P. D. that is set up between these two parts when any pair of carriers are simultaneously in electrical contact with them, being the P. D. that is practically made use o The next improvement was made by Voss, who pro- duced an accumulating influence machine which com- bined the advantages of the Thomson's replenisher and of the Holtz's machine, in that it required no initial P. D. to be given to the inductors to start the action, and produced considerable quantities of positive and negative electricity for an influence machine. It is, however, un- necessary to describe either this or the Holtz machine in detail, because the latest accumulating influence machine constructed by Mr. Wimshurst is not only extremely simple in construction, but is probably the most perfect machine of this type that has yet been devised. 196. Wimshurst Influence Machine. This machine consists of two circular discs of ordinary window glass (Fig. 146), each attached to the end of a hollow boss of wood, or ebonite, upon which is turned a small pulley. These bosses are mounted on a fixed horizontal steel spindle, so that the glass discs are about one-eighth of an inch apart, and are rotated in opposite directions by the 368 PRACTICAL ELECTRICITY. [Chap. VII. cords which pass over the pulleys at the base of the in- strument, one of the driving cords being crossed for this Eurpose. The glass discs are carefully coated with shell- ic varnish, and on the outside of each of them there are cemented an equal number of radial, sector-shaped plates of Fig. 146. thin metal at equal distances apart, which act the part not only of the carriers c D (Figs. 143, 144, pages 364, 365), but also of the inductors A u, the carriers on one disc acting as the inductors for the carriers on the other. If only ten sectors be stuck on each of the glass discs, it is found that the machine will only excite itself under very favourable circumstances, whereas if there be sixteen or eighteen, it will excite itself under all atmospheric con- ditions. Two curved brass rods, terminating at their Chap. VII.] WIMSHURST INFLUENCE MACHINE. 369 ends in fine wire brushes, are placed, as seen in the figure, one at the front of the machine, and one at the back, making an angle of about 90 with one another, and about 45 with the horizontal " collecting combs" These rods act like the springs s s' (Figs. 143, 144) in con- necting a pair of carriers when they are under the induc- tive action of the inductors, which in this machine are the adjacent carriers on the other plate. The combs are four in number, two being placed at the front of the machine, as seen in the figure, and two at the back, the points of the combs being directed towards the discs. The two combs at the left hand are connected together, and form one terminal of the machine, while the two at the right hand form the other. These combs are sup- ported in position by the brass cylinders to which they are attached, and which stand on glass legs. These cylinders carry the two " discharging rods " which terminate in two balls, and in order to charge any two bodies (the inside and outside of a Ley den jar, for ex- ample) to a high P. D., they must be connected with pieces of wire to the brass cylinders, and the balls at the ends of the discharging rods separated. It does not appear that the collecting apparatus takes any important part in the inductive action of the Wims- hurst machine, for if it be removed and the glass discs made to spin round in opposite directions, their whole surface is seen to glow with a luminous discharge, and a sharp crackling sound is heard. The collection of the positive and negative charges might be effected by attach- ing springs to the horizontal rods so as to touch the car- riers as they pass instead of using the combs which collect by a " brush* discharge," but the combs introduce, of course, far less frictional resistance to the motion of the plate, and act very well, because when a carrier comes * If the P. D. between two conductors be raised, it is found that before it reaches the value that will cause a spark to pass between the conductors, a hissing sound is heard, and a "brush" or "glow discharge " takes place, rendering the space between the conductors luminous in the dark. Y 370 PRACTICAL ELECTRICITY. [Chap. VII. between a pair of combs, it is practically inside a con- ductor ; and we have seen that when a body is inside a con- ductor, no charge that the conductor may have can prevent the body discharging itself into the conductor, and as, in addition, the density is very great at a point (see 63, page 118), the charge easily passes across the small air space separating the points of the teeth of the comb from the surface of a carrier when it is passing the comb. Hence, in all modern frictional or influence machines, such combs have been used as the collectors. By attaching the inner coatings of Leyden jars to the sets of collecting brushes, the outer coatings -of the jars being connected together, the capacity of the collectors is much increased, hence the brightness of a spark and the noise that it makes in passing from one of the balls to the other is also much increased. As, however, we cannot augment the rate of work done by the machine in this way, and as the work given out by each spark equals lllfootlb,, 2-712 (see 176, page 323), where F is the capacity in farads of one of the Leyden jars that is discharged, and V the P. D. between their inner coatings, it follows that for a given influence machine and for a given rate of turning, the rapidity of producing sparks will be diminished by connecting Leyden jars with the collecting combs. The P. D. produced between the terminals ot an in- fluence machine can send a spark from one of the balls to the other when they are separated by a distance of several inches. When the surfaces of two metallic balls are separated by more than about one-tenth of an inch, the experiments made by Drs. De la Rue and Hugo Miiller, show that the P. D. required to produce a spark is nearly proportional to the distance between their surfaces, and increases at the rate of, roughly, 10,000 volts per one-tenth of an inch, so that it Chap. VII.] VARIATION OF STRIKING DISTANCE WITH P.D. 371 would require a P. D. of about 100,000 volts to start a spark between two metal balls separated by a distance of one inch. If the bodies between which the spark passes be a point and a plate, the " striking distance "* is greater for the same P. D., being at the rate of one inch for every 23,400 volts P. D. between the point and the plate. From this it will be seen that an influence machine can produce a P. D. between its terminals of some hundreds of thousands of volts ; consequently, the quantity of electricity that passes in the sparks must be very small, since the work, in foot pounds, done per minute by the machine, equals 44-25 A V, (see 114, page 201), where A is the mean value in amperes of the current passing, and Y the mean P. D. in volts between the terminals, and this product cannot ex- ceed about 5,000, the greatest work, in foot pounds per minute, that a man can do in turning the machine. Hence, although brilliant sparks and powerful shocks can be pro- duced with such a machine, we cannot expect that it will produce any visible decomposition in a voltameter used to join its terminals, or that it will cause a de- flection of the needle of even a sensitive galvanometer. A galvanic cell of small resistance can produce a cur- rent of many amperes through a small external resist- ance, and yet can only produce a maximum P. D. of a volt or two, whereas an influence machine is, to a certain extent, like a very large number of cells in series, each cell having a very high resistance, for such a bat- tery can produce a very high P. D. between its terminals * The striking distance is the distance that separates two conduc- tors when a spark is started between them. To maintain a continuous "electric arc between two conductors requires a much smaller P. D. than to start a spark between them ; for example, to maintain an arc one inch long between two carbon rods only requires a P. D. of about 118 volts if the carbons be hard, and a less P. D. if they be soft. (See " The Resistance of the Electric Arc. " Phil. Mag. , May, 1883.) Hence in all " arc lamps " there must be some mechanism for first bringing the carbons into contact, to start the arc, and then separating them. 372 PRACTICAL ELECTRICITY. [Chap. VII. if they be insulated, but only a very weak, steady current, even if its terminals be joined together with a short thick piece of wire, and the battery short-circuited. The low resistance cell is in fact analogous with a large shallow reservoir of water which is constantly kept filled with a big supply tap, while an influence machine with the balls at some distance apart is analogous with a very tall, very narrow tube, into which water slowly but steadily trickles. If a tap at the side of the former be opened and left open, there will be a large, steady stream of water, but the distance through which the stream will spurt from the side of the reservoir will be small, whereas if a tap at the side of the tall, narrow tube, near the bottom, be opened, the water will spurt out through a distance of many feet, but the stream will rapidly fall off as the tube empties, and the spurt can only be repeated by keeping the tap at the bottom of the tube closed, while the tube is refilling. The distance at which the balls of an influence machine are separated, determines the maximum P. D. that can be set up between the discharging rods, or be- tween any two- conductors connected with them ; hence, by placing the balls at a given distance apart, and then turning the machine until a spark is just going to pass between them, we know approximately the P. D. set up between two conductors connected with them. 197. Dry Pile. When it is desired to maintain a high P. D. between two conductors that are well insu- lated from one another, as. for example, the outside of an electrometer, and the needle inside (see 75, page 130), a battery consisting of a large number of cells in series, each cell having a high resistance, may be em- ployed, since, as the resistance external to the battery is infinite, the P. D. at its terminals will be simply the E. M. F. of the battery, no matter how high may be the resistance of each cell. Fig. 147 shows a section of such a battery, consisting of a large number of small, simple voltaic elements, joined up in series. The liquid part Chap. VII. 1 DRY PILE. 373 of each cell may be made smaller and smaller without affecting the P. D. at the terminals of the battery, pro- vided that it is not required to send any current, and it may be reduced to simply the moisture which exists in ordinary paper when exposed to the air. In that case the zinc and copper plates may be pieces of metallic foil stuck on to the two sides of each piece of paper, or the cell may be formed simply of a piece of paper with a little powder rubbed on each side. In Zamboni's con- Pig. 147. struction of a dry pile, sheets of paper are prepared by pasting finely laminated zinc or tin on one side, and rub- bing manganese peroxide, or what is sometimes called black oxide of manganese, on the other. Discs are punched out of this paper, and several hundred of them are piled up into a column, with their similar sides all facing the same way, inside a glass tube TT (Fig. 148), which has been carefully coated inside and out with shell-lac varnish. The discs are kept in contact with one another, and electric connection is made with the two outside ones by their being pressed between the brass plate P and the brass cap B, cemented to the bottom of the tube. The plate P is pressed down by the wire w, which is held 374 PRACTICAL ELECTRICITY. [Chap. VII. in position by a small pinching screw s (Fig. 149), which fixes it in a collar c soldered to the inside of the other- brass cap A, which latter is cemented to the tube at the top. The dry pile may be conveniently hung by one of its terminal wires from the outside of the Edelmann electro- Fig. 143. Fig. 119. meter seen in Fig. 48, page 132, and its lower wire con- nected with the wire p of the electrometer. Although the pile will bring any two insulated bodies attached to its ends to a fixed P. D., its resistance is too high to enable it to instantly supply the electricity necessary to do this if the capacity of one of the bodies be suddenly changed, therefore, to avoid the capacity of the brass end of the C^ap. VII.] ELECTROMETER CHARGED WITH PILE. 375 pile, which is electrically connected with p, being suddenly increased by some conductor in connection with the earth being brought near it, which would have the effect of momentarily lowering the potential of this end, and there- fore of the electrometer needle attached to it, it is desir- able to enclose the pile in a brass tube tt of somewhat larger diameter than the glass one, and to support the pile inside this metal " guard tube." This may be done by fixing the end of one of the terminal wires by a pinching screw s to a collar c, soldered to the outside of the end of the guard tube as seen in section in Fig. 149. The brass cap B at the bottom of the pile forms a condenser of fixed capacity with the brass tube, and must not, of course, even momentarily, touch this tube. Tlie whole apparatus may then be conveniently supported from the outside of the electrometer, by placing a lug L projecting from the metal top of the guard tube, under the clamping nut N of one of the levelling screws of the electrometer (Fig. 149). A dry pile is much more simple and compact than a battery, consisting of some hundreds of cells, but expe- rience shows that when considerable accuracy is desired, it is better to use some form of battery (such as that illustrated in Fig. 147, for example) than a dry pile to keep the electrometer needle charged. 376 CHAPTER VIII. COMMERCIAL AMMETERS AND VOLTMETERS. 198. Defect of Permanent Magnet Meters 199. Siemens' Electro- Dynamometer 200. Cunynghame's Ammeter and Voltmeter 201. Instruments with Magnifying Gearing 202. Magnifying Spring Ammeter and Voltmeter 203. Gravity Control Meters 204. Crompton and Kapp's Meters 205. Paterson and Cooper's Electro-magnetic Control Meters 206. Testing Ammeters 207. Test for Accuracy of the Graduation 208. Test for Kesidual Mag- netism 209. Test for Error on Reversing the Current 210. Test for Error Produced by External Magnetic Disturbance 211. Test for Permanent Alteration of Sensibility 212. Testing Voltmeters 213. Test for Accuracy of the Graduation 214. Latimer Clark's Cell 215. Standard DanieU's Cell 216. Test for Heating Error 217. Variation of the Sensibility of a Galvanometer with its Resistance 218. Rate of Production of Heat in Galvanometer Coils 219. Standard Voltmeter 220. Cardew's Voltmeter 221. Commutator Ammeter and Voltmeter 222. Calibrating a Com- mutator Ammeter 223. Calibrating a Commutator Voltmeter 224. Best Resistance to Give to a Galvanometer. COMMERCIAL instruments for the accurate direct measure- ments of amperes and volts are quite as important as boxes of resistance coils accurately graduated in ohms ; hut while the construction of resistance coils has engaged the attention of manufacturers for the last twenty years, it is only since about 1880 that the construction of com- mercial ammeters and voltmeters has been considered. This, combined with the fact that it is far more easy to construct a coil of wire that will have a perfectly con- stant resistance at a fixed temperature, and even a fairly constant resistance within a considerable range of tem- perature, than a measuring instrument that will be con- stant in its indications, makes it desirable to devote a chapter to commercial ammeters and voltmeters. 198. Defect of Permanent Magnet Meters. The ammeter? and voltmeters described in 36, 72, pages 73 128, have the disadvantage that, if they be placed too near a large powerful magnet, such as a dynamo machine Chap. VIII.] SPRING CONTROL METERS. 377 or an electromotor, not only is the strength of the con- trolling field, and consequently the sensibility of the in- strument, temporarily varied, but the permanent magnet of the ammeter, or voltmeter, may have its magnetism permanently altered, in which case the sensibility of the instrument will also be permanently altered without the user being in many cases aware that any such change has taken place. To avoid the possibility of this very serious error arising, the permanent magnet must be dispensed with, and the controlling force produced in some other way. Three forms of controlling force not produced by perma- nent magnets have been made use of, namely : 1. The pull of a spring ; 2. The attraction of gravity ; 3. The attraction of an electro- magnet temporarily magnetised by the whole or a portion of the current to be measured. SPRING CONTROL METERS. 199. Siemens' Electro-Dynamometer. Probably the oldest form of commercial current measurer, employing a spring to produce the controlling force, is " Siemens' electro-dynamometer" shown in perspective in Fig. 150, and symbolically in Figs. 151 and 152. It consists of a fixed coil A BCD (Fig. 151), and a movable coil E F G, which latter is frequently made of a single stiff wire. The current passes round the fixed coil and through the movable coil or wire in series, electric connections with the two ends of the latter being maintained by their dip- ping into mercury cups mm (Fig. 151). The movable coil is suspended by a thread and "by a delicate spiral spring N (Fig. 151), which latter can be twisted by turning the milled head T (Figs. 151 and 152) through an angle, which is measured by the pointer M attached to the head T, turning over a scale gradu- ated in degrees, or, instead, in 400 equal divisions, and seen in Fig. 152. The instrument having been 378 PRACTICAL ELECTRICITY. [Chap. VIII. levelled by means of the plumb-line, seen to the right of Fig. 1.50, the head T is turned until the plane of the movable coil E F G is at right angles to that of the fixed coil A B c D, which is indicated by the pointer p attached to the movable coil (Figs. 151 and 152) coming opposite rig. 1,0. the on the dial. Should the pointer M not now also point to the 0, a small pinching screw which clamps the pointer M to the head T is loosened, and M is turned to the without turning the milled head T, or twisting the spring N. If a current be sent through the instru- ment entering at the left-hand binding screw (Fig. 151), and following the path ABCDWEFG m', and leaving Chap, viii.] SIEMENS' ELECTRO-DYNAMOMETER. 379 therefore by the right-hand binding screw, the movable coil turns, tending to place its plane parallel with that of the fixed coil, until the pointer P comes up against the right-hand stop s (Fig. 152). On turning the head T, and the pointer M attached to it, through an angle, say, of 50, P can be again brought to 0. The couple exerted between the coils is balanced by the couple exerted by the twisted spring, and the moment of the Fig. 151. latter is proportional to the angle through which M has been turn yd. To compare the current now passing through the dynamometer with some other current, exactly the same adjustment is made when the other current is passing, and since the movable wire, or coil, is always brought back to the same position relatively to the fixed one, the couple exerted between the coils is proportional simply to the product of the current passing through one coil into the current passing through the other that is, to the square of the current passing through them in series. Hence, the angle through which M has to be turned from 380 PRACTICAL ELECTRICITY. [Chap. VIII. the zero position to bring the pointer P to 0, is propor- tional to the square of the current. In the actual instrument, as seen in Fig. 150, there are two fixed deflecting coils having a different number of convolutions, and either of which can be employed by using the middle and the right-hand, binding screw, or the middle and the left-hand one. The two coils have usually the one about five times as many convolutions as the other, so that the sensibility of the instrument when using the one is about five times as great as when using the other. The advantages of this instrument, in addition to the one already mentioned that it contains no permanent magnet, are : First, since the fixed and moving parts between which the electric attraction is exerted always occupy exactly the same position relatively to one another when an observation is being made that is, since the dynamometer is a "zero instrument " one experiment is all that it is necessary to make to enable the graduation of the wlwle scale to be effected with great accuracy, since the law of the instrument is known exactly, arising from the fact that as long as two wires occupy exactly the same relative positions the force exerted by each on Chap, viii.] SIEMENS' ELECTRO-DYNAMOMETER. 381 the other is directly proportional to the product of the currents passing through them respectively ; second, this dynamometer can be used with considerable accuracy to measure an alternating current that is, one the direc- tion of which Undergoes rapid reversals, since the direc- tion of the current in both the moving and stationary coils will be reversed simultaneously, and the force be- tween them will therefore remain the same as before the reversal. The disadvantages of the Siemens' dynamometer are : First, the instrument being one in which the moving coil has always to be brought to zero, cannot show at once, without adjustment, the strength of a current, and as a little time is necessary to enable this adjustment to be made, the instrument cannot be used for measuring sudden variations in the strength of a current ; second, owing to the moment of inertia of the suspended coil being rather large, the instrument is not dead-beat ; third, the readings are much affected by neighbouring magnets, or wires conveying currents ; indeed, the wires leading the current into and out of the dynamometer must be carefully twisted together, so that their mean distance from the moving coil may be the same, and the action of the current in the one leading wire balanced by the action of the equal and opposite current flowing in the other ; further, as the suspended coil when traversed by a current is acted on by the earth's magnetism, the instrument must always be placed so that the plane of the suspended coil, when p is at 0, is at right angles to the plane of the earth's magnetic meridian, since this is the position in which the coil desires to place itself as far as the action of the earth's magnetism is concerned when a current is passing through it ; fourth, as the instrument must be placed in this particular position before use, also as it must be levelled and mercury poured into the cups m and m' (Fig. 151) if it has been spilt when the instrument is carried about, it is not very portable ; fifth, the movable coil being quite uncovered, 382 PRACTICAL ELECTRICITY. [Chap. VIII. is blown about by draughts of air, and the spring is liable to be accidentally damaged by things being knocked against it ; sixth, the scale, being graduated in degrees, or arbitrary divisions, is not direct-reading ; and lastly, the instrument gives no indication of the direction of the current, which, in electroplating, electrotyping, the charging of accumulators, &c., is as important as the strength of the current. Shortly, therefore, we may say that the Siemens' dynamometer is an extremely valuable standard instru- ment when it can be kept and iised in a, fixed position in a laboratory far away from all moving magnets, or wires in which strong currents are passing, tfec., and its con- stant experimentally determined in that fixed position ; but for a portable instrument to be carried about in a workshop or room containing dynamos in motion, and used wherever required, there are other instruments more convenient. 200. Cunynghame's Ammeter and Voltmeter. These zero instruments are a modification of the Siemens' dynamometer, an electro-magnet EE (Fig. 154) being substituted for the stationary deflecting coil, and a pivoted soft iron needle N (Figs. 153 and 154) for the movable one, the magnetic axis of the needle, as seen in Fig. 153, which shows a sectional plan of the in- strument, making an angle of about 30 with the line joining the poles F p of the electro-magnet, when a pointer attached to the moving needle is at 0. The soft iron core c c of the electro-magnet, seen in sectional elevation in Fig. 154, is made massive, in order that a considerable magnetic force may be produced by it for a comparatively small magnetic action of the current, be- cause experiment shows that when the core of an electro- magnet is only slightly 'magnetised, the strength of the magnet is directly proportional to the current, the strength of the magnet being measured by the force with which it attracts or repels one end of a hard steel permanent magnet, put in a given position relatively to the electro- Chap, via.] CUNYNGHAME'S METERS. 383 magnet ; whereas if the magnetic action of the coil be great, the soft iron core becomes " saturated" and its Fig. 153. strength hardly increases with an increase in the current. The soft iron needle is magnetised inductively by the electro-magnet, and for a given relative position of the 384 PRACTICAL ELECTRICITY. [Chap. VIII. two the amount of magnetism induced in the iron needle will be directly proportional to the strength of the electro- magnet, provided the needle is so massive that it is far from being "saturated" (see page 388). Under these cir- cumstances the couple exerted by the electro-may net on the needle will be proportional to the square of the current. Fig. 154. This couple is balanced by the twist given to the spiral spring, as in the Siemens' dynamometer, and therefore is also proportional to the angle through which the pointer M, attached to the milled head T, has been turned. As long, therefore, as we are dealing with currents not strong enough to saturate the iron core and the iron needle, the angle through which the pointer attached 'to the milled head has to be turned to bring the pointer attached to the moving needle to is proportional to the square of the current. Chap, yin.] CUNYNGHAME'S METERS. 385 The scale is, therefore, graduated not in degrees, but in numbers proportional to the square roots of the number of degrees, and the adjustable pole-pieces F F enable the instruments to be made direct-reading (see 37, page 76). The wires leading the current to and from the instrument are fastened to the binding screws BB (Fig. 153). The advantages of this type of instrument are : First, the controlling force not being produced by a per- manent magnet, the sensibility cannot be permanently changed by placing the instrument near a powerful magnet ; second, its indications are but little affected by an outside magnet, as the mass of soft iron in the core and pole-pieces of the electro-magnet shields the needle to a great extent from external magnetic disturbance (see 52, page 102) ; third, it is direct-reading ; fourth, it is dead beat ; fifth, it has no mercury cups, does not require levelling, can be used in any position, is not likely to be damaged, as the pointers and spring are all boxed in ; and hence the Cunynghame instruments are very portable. The disadvantages are : First, being a zero instru- ment, an adjustment has to be made before the value of a current can be read, and therefore the magnitude of sudden changes in a current cannot be measured ; second, it can only be used to measure currents in one direction ; third, in spite of the mass of iron the current is not quite pro- portional to the square root of the angle, and therefore the reading is a little too small for large currents (see 208, page 401); fourth, in consequence of "residual magnetism"* the value of a current corresponding with a particular reading depends somewhat on whether the currents previously passing through the instrument were larger or smaller than the one being measured (see 208, page 401) ; fifth, in consequence also of residual magnetism, a reverse current sent for a short time through the * "Residual magnetism " is the name given to the magnetism that remains in a substance after the magnetising force has ceased. With very soft iron the amount of residual magnetism is small, whereas with hard steel it is very large. 7 386 PRACTICAL ELECTRICITY. [Chap. VUL instrument diminishes the subsequent indications for small direct currents (see 209, page 403). Shortly, therefore, we may say that while the instru- ment has not an exact law, and cannot, therefore, like a Siemens' dynamometer, be used as a standard instrument, it is far more convenient for general use in the workshop and in an electric lighting establishment. 201. Instruments with Magnifying Gearing. We have seen ( 20, page 46) that if all the deflections of a galvanometer are small, the deflections will be directly proportional to the current whatever be the shape of the coil and needle ; hence, attempts have been made by M. Deprez to use a form of portable current galvanometer, in which the needle could only deflect through a small angle, and to magnify this deflection by attaching the pointer to a small grooved pulley geared by a tine end- less thread to a much larger grooved wheel attached to the needle. A similar result has been attained by the author by using instead of the small and large grooved wheels a small toothed wheel, or pinion, attached to the pointer, and a larger toothed wheel to the axle or staff of the needle. Such contrivances, however, for magnifying the motion by means of pivoted gearing cannot be recom- mended, as they introduce friction as well as add to the moment of inertia of the moving parts, and so diminish the dead beat character of the apparatus. These diffi- culties, however, have been overcome in the following apparatus : 202. Magnifying Spring Ammeter and Voltmeter. In these instruments, devised by the author, a special form of spring is employed, shaped like a narrow shaving curled up into a cylinder of very small diameter (Fig. 155). Such a spring, quite unlike an ordinary spiral spring, has the peculiarity that for a small increase in length along the axis there is large rotation of one end of the spring relatively to the other, the angle of rotation being directly proportional to the axial extension. Hence, if one end of the spring be fixed and the other be slightly Chap. VIII.] MAGNIFYING SPRING METERS. 387 pulled axially, a pointer attached to this end will turn through a large angle, and so will measure in a very magnified way the axial extension of the spring, without the employment of a rack and pinion, or of levers, or of any other magnifying arrangement, and without, therefore, the cost or the friction attending the use of such magnifying arrangements. The instrument is shown in Fig. 156, where TT is a thin tube of charcoal iron, attached at its lower end to a brass cap c, terminated in a brass pin P, guided at the bottom in the way shown. To C is attached the lower end of the spring s (made of hard phosphor-bronze), the upper end of which is attached rigidly to a brass pin p, passing through a hole in the glass top of the apparatus G G, and fastened by means of a screw and nut to the brass milled head H outside the glass top. This pin p, to which the upper end of the spring is attached, also serves as a guide to the top of the iron tube. In the space w w a "solenoid" * wire or strip is wound, its ends being attached to the terminals shown. Hence, when a current is passed through this solenoid, the iron tube is sucked down into the solenoid, and its lower end c, to which the spring is attached, receives a large rotatory motion, which is communicated directly to the pointer attached to the top of the iron tube. Parallax, in taking readings of the pointer, is avoided by the horizontal scale having a piece of looking-glass let in it in the well-known way. (See 12, page 28.) By making the iron tube T T very thin, so that it ia * A coil of wire wound as cotton is on a reel, is called a " solenoid " when the length of the coil is not small compared with its diameter. Fig. 155. 388 PRACTICAL ELECTRICITY. CChap. VIII. " magnetically saturated " for a comparatively weak cur- rent that is, so that a current passing round the coils much weaker than the instrument is intended to measure Fig. 156. is able to impart to the iron as much magnetism as it is possible for any current to give to it also by fixing the iron tube so that it projects into the solenoid a definite distance, which has been carefully determined, partly by calculation and partly by experiment, arid lastly by con- structing the spring so as to produce a large rotation Chap. VIII.] MAGNIFYING SPRING METERS. 389 with the minimum pull, and with not too much axial motion of the free end of the spring, deflections up to 270 can be obtained directly proportional to the current,, excepting for the first 15, where the scale is not gra- duated. This instrument being direct-reading has to be pro- vided with an adjustment for sensibility, and this is ob- tained partly by the amount of wire or strip that is wound on the bobbin, and partly by means of a small movable bobbin, wound with a coil of fine wire of the same length as that employed in winding the main coil, joined up in parallel with the main coil. This movable coil slides up and down on the main bobbin, and by trial a position is found for it such that the readings on the dial are correct, and in that position this auxiliary coil is permanently fixed by the maker of the instrument. The pointer will deflect in the same direction, no matter which way the current passes through the in- strument, and owing to the softness of the iron used in making the tube T T, and the smallness of its mass, there is but very little residual magnetism left in it ; hence the pointer indicates the correct strength of the current, no matter which way it passes through the instrument. To ascertain the direction of the current, a smair compass needle is let into the base of the instrument, as seen in Fig. 156, which is deflected when the current passes through the instrument in such a way, that when the blue- coloured end of the compass needle points inwards, the current enters at that one of the binding screws that has an A marked on it, the nearer binding screw in this figure. As, however, experience shows that the compass needle may have its magnetism reversed by a sudden very strong current sent through the ammeter (in spite of the needle being surrounded by iron to partially shield it from the action of the current), and as, in addition, its position can- uot be very easily seen by an observer unless close to the 390 PRACTICAL ELECTRICITY. [Cliap. VIII. instrument, the direction of the currents in the latest magnifying spring instruments is indicated by a much larger magnet, suspended on a horizontal axis in. front of the instrument, which points to the binding screw at which the current enters. The advantages of this instrument are : First, owing to the controlling force not being produced by a perma- nent magnet, the sensibility of the instrument cannot be permanently affected by placing it near a powerful mag- net ; secondly, the sensibility will not be even temporarily affected, no matter how strong this outside magnet may be, provided that it is so far away that the magnetic field is uniform throughout the small space in which the little iron tube TT moves (see 15, page 36). For example, although an ordinary compass needle is turned round by a uniform magnetic field, there is no force tending to pull the compass needle bodily along, as may easily be proved by floating a compass needle on a piece of cork in a basin of water, when it will be found that while the needle will place itself at once so that its axis points north and south, it will not move towards the side of the basin as it would if it were pulled as a whole in some direction. Or the experiment may be tried thus : suspend a bar of unmag- iietised hard steel by one of its ends from the pan of a delicate balance, so that the bar hangs vertically down- wards, and weigh it, then magnetise the bar, and weigh it again, when it will be found that its weight is neither increased nor diminished in the slightest by the magnetic action of the earth. This fact is expressed by saying that a uniform magnetic field can produce a motion of rotation, but not a motion of translation of a magnet. Now, the magnet that is moved in the magni- fying spring instrument is the soft iron tube T T, which has a north-seeking pole induced on its lower end, say, and a south-seeking pole on its upper end, or vice versd, by the current passing round the coil of wire or strip, and this tube is simply pulled downwards by the attraction of the current passing round this coil. Henco. Chap. VIII.] GRAVITY CONTROL METERS. 391 this pulling action is neither increased nor diminished by the magnetic action of the earth, nor by the action of any magnet, no matter how strong it may be, if the field it produces is uniform over the space in which the iron tube moves ; second, by using the magnification introduced by the special form of spring, the distance moved through by the attracted iron tube is not large, so that the in- strument has much of the advantage of a zero instrument (see 199, page 380), that is, the force depends simply on the current, and is practically unaffected by the motion of the attracted soft iron tube. This, combined with the small mass of iron, causes the increase of force to be directly proportional to the increase of current. The scale is therefore long, and the distances corresponding with a given fraction of an ampere or of a volt are equal throughout the whole length of the scale, which not only facilitates the manufacture of the scale, but greatly increases the power of estimating by eye the decimal parts of a division. Hence, a current, or a P. D., can be read to a very small fraction of its total value. The main disadvantage of the instrument is that currents or P. Ds. less than about one-fifth of the maximum current or P. D. that the instrument is in- tended to be used for cannot be measured, since for currents under this value the iron tube is not mag- netically saturated. GRAVITY CONTROL METERS. 203. Gravity Control Meters. Instruments in which the controlling force is produced by a weight at- tached to the needle have been devised by Sir William Thomson, Messrs. Schuckert, Edelmann, Statter, and others. The advantages of such instruments are : first, as the .controlling force is absolutely constant, the sensibility oi 392 PRACTICAL ELECTRICITY. [Chap VIIL the instrument cannot vary from time to time on account of a variation in the force; second, the price is low, arising from the simplicity of construction. The disadvantages are : first, the readings usually are easily varied by extraneous magnetic disturbance ; second, there is generally a certain want of quickness of action, so that any small temporary change in the strength of the current or P. D. that is being measured is not instantly recorded. For this purpose the needle and pointer must not only be very light, but the controlling force must be great (see 38, page 78). Now, if gravity be used, the only way to obtain a large controlling force is to use a large mass to be attracted, but if a large mass be attached to the needle and pointer, the moment of inertia will be seriously increased, and slow motion will be the result ; whereas, by using a powerful controlling magnet or a comparatively strong spring, we obtain a dead-beat- ness so great that the number of times the joint in the driving-belt passes over the dynamo pulley can be easily counted, every adjustment in the carbons on an arc lamp be seen on the ammeter and voltmeter, and even the effect on. an arc lamp produced by whistling may be instantly observed on the distant ammeter. The gravity control meters of Sir William Thomson not yet being in common use, the author has had no ex- perience with them, and, therefore, cannot speak of their advantages or disadvantages. ELECTRO-MAGNETIC CONTROL METERS. 804. Crompton and Kapp's Meters. The third de- vice, which consists in using for the controlling force that produced by an electro-magnet, round which flows the whole or a portion of the current to be measured, appears at first sight to be the best ; but it is attended with very serious practical difficulties. The possibility of using a current to deflect a needle, and the very same current to Chap. VIII.] ELECTRO-MAGNETIC CONTROL METERS. 393 resist its being deflected, without obtaining the same de- flection for all currents (a result which would occur if the deflecting and controlling forces varied proportionally to one another as the current was increased), arises from the fact that whereas the magnetic force exerted on a mag- netic pole at a particular point by a current flowing round a coil of wire is directly proportional to the current, the force exerted on the same magnetic pole by the iron core of an electro-magnet round which the current is flowing increases nearly proportionately to the current when the current is small, but becomes nearly constant for all values of the current above a certain value, in conse- quence of the magnetic saturation of the iron core. Hence, by using the force due to a coil without an iron core for the deflecting force, and the force due to the iron core of the electro-magnet for the controlling force, Messrs. Crompton and Kapp have made extremely in- genious current and P. D. meters, which require the employment of neither permanent magnets, springs, nor weights. The coil of the electro-magnet has a magnetic action as well as its iron core, and as the former increases in direct proportion to the current, its action must be neu- tralised if we wish the controlling force to be constant. This can be done either by the use of a third coil of a suitable size and number of convolutions, placed in such a position that when the current flowing round the electro-magnet also flows round this coil, its action exactly neutralises that of the electro-magnet coil, or the neutralisation may be more simply effected by placing the deflecting coil in such a position that it is equivalent to two coils, one the deflecting coil, and the other a coil whose effect neutralises that of the coil round the electro- magnet. 205. Paterson and Cooper's Electro - magnetic Control Meters. These are the same in principle as those invented by Messrs. Crompton and Kapp, with the addi- tion of movable pole-pieces similar to those shown in 394 PRACTICAL ELECTRICITY. [Chap. VIII. Fig. 25, page 74, for adjusting the sensibility of the in- strument. The advantage of electro -magnetic control meters is that, as neither permanent magnets nor springs are em- ployed in their construction, their sensibility cannot be affected by variations in their strength, and hence their behaviour from year to year remains exactly the same. The disadvantage arises from the fact that as the entire controlling force, corresponding with that produced by the powerful permanent magnet in the apparatus shown in Fig. 23, page 70, for example, has to be produced by an iron core of the electro-magnet, the mass of iron must not be too small, otherwise any external piece of iron or magnet will affect the indications of the instru- ment. But it is found by experiment that unless the iron be not only very soft, but also be very small in mass, there is considerable residual magnetism, which causes the magnetic force exerted by the iron to depend not merely on the strength of the current passing round it at any par- ticular time, but also on the strength of the previous cur- rents, and this is the case even when the iron is still too small to prevent very serious variations in the reading of the instruments being produced by the presence of a neighbouring magnet (see 210, page 407). The read- ings, therefore, in the lower part of the scale, instead of corresponding with definite values of the current, or of the P. D., correspond with currents or P. Ds. differing in some of these electro-magnetic control instruments by as much as thirty per cent., depending on whether it is an increasing current or a decreasing current that is being measured, (See 208, page 402.) 206. Testing Ammeters. The faults to be looked for in an ammeter, and for which it must be carefully tested, are : 1. An error arising from the ampere-standards em- ployed by different makers differing from one another. 2. Aii error arising from a current producing a Chap. VIII.] CALIBRATING AMMETERS. 395 different deflection, depending on whether the previous currents passing through the instrument were much smaller or much larger than the current being measured. 3. An error arising from the instrument indicating a different number of amperes for the same current when it is reversed in direction. 4. An error arising from the sensibility of the instru- ment being temporarily varied by external magnetic dis- turbance. 5. An error arising from a permanent alteration of sensibility, due, for example, to the demagnetisation of a steel magnet. 207. Test for Accuracy of the Graduation. It has been explained in 6, page 11, that the standard ampere is that which deposits 0-00111815 grammes of silver per second. Makers of commercial instruments, however, do not calibrate each ammeter by comparing it with a silver voltameter, but only compare it with some standard current meter which has at some previous time been com- pared with a silver voltameter, but which may have changed its sensibility in the interval. To check the accuracy of any ammeter, therefore, it is desirable to com- pare it directly with a silver voltameter, and in Fig. 157 the apparatus is shown arranged for calibrating a magni- fying spring ammeter A, in this way. D is a platinum dish, containing a 25 per cent, solution of silver nitrate, into which is placed a thick silver disc P, wrapped in filter- ing paper, to prevent particles of oxide of silver which may become detached from the silver plate dropping on to the platinum, and making the weight appear to be too great. It is better to use a platinum dish than a silver one, be- cause the silver deposited at the bottom of the platinum dish can be removed, and re-formed into silver nitrate by pouring a little nitric acid into the dish. This could not be done with a silver dish, as the nitric acid would prob- ably burn holes in it ; hence the silver dish would gradu- ally grow thicker and heavier. The platinum dish should be made as thin and as light as possible, so that it may be 396 PRACTICAL ELECTRICITY. [Chap. VIII. accurately weighed ; with a diameter of 4 inches, and a depth of rather more than 1^ inches, it need not weigh more than 78 grammes. This silver disc is held in position by a strip s, at- tached to it, held in a clamp c, the two sides of which are pressed together by turning the nut N. The disc and the strip s are in one piece, cut out of a thick. Fig. 17. flat sheet of silver, the strip being bent up at right angles to the disc after it is cut out. Electric connection is made with the platinum dish D, by its resting on three metal pins p, connected with the wire W 2 , and connection is made with the silver disc by the wire soldered to c, the other end of which is connected with one terminal of the ammeter. The other terminal of the ammeter is connected through an adjustable carbon resistance R with the wire w t , and the circuit is closed by putting the metallic bridge-piece B into the small mercury cups H H. The current produced by a current Chap. VIII.] CALIBRATING AMMETERS. 397 generator, the terminals of which are attached, to the wires w l and W 2 , can be conveniently varied within wide limits by screwing or unscrewing the nut at the top of R, shown at n (Fig. 158), separated from the rest of the apparatus. Screwing this nut ?i, presses down more or Fig. 158. less a wooden washer e, which, in its turn, compresses more or less a pile of discs of carbonised cloth, some of which, c,c, c, c, are seen, in Fig. 158, separated from the carbon resistance. This cloth is specially prepared by Mr. Yarley, by heating ordinary cloth to an extremely high temperature in a vacuum, which carbonises the cloth without destroying its flexibility and elasticity. The carbon discs are piled up in a heap by slipping them over a thin wooden tube which surrounds the brass rod h, ter- minated at the top in a screw thread for the nut n to screw on, and contact is made with the discs by one or other of three plates of brass, p u p. 2 , p 3 , one of which, /?i, is seen separated in Fig. 158. These plates of brass 398 PRACTICAL ELECTRICITY. [Chap. VIIL are of about the same size as the carbon discs, and the hole in the centre of each is shaped like the section of the rod h that is, not quite round, so that p l and p% can slide up and down this rod without being able to turn round it. Starting with a pressure sufficiently great to keep the discs fairly well in contact, so that they cannot shake about and thus produce a varying resistance, and gra- dually increasing this pressure, but not to such an extent as to damage the discs, the resistance of the whole column can be varied from about \ to 9| ohms when the discs are about 1J inch in diameter, and when the height of the column of them is about 3 inches. A re- sistance still less can be obtained by attaching the wires to the plates p 2 andp 3 (Fig. 158), instead of to the top and bottom plates as in Fig. 157. When adjusting the carbon resistance R so as to obtain the desired current, it is desirable that no decom- position should take place in the silver voltameter, for in that case the drying and weighing of the platinum dish D would have to be carried out after the carbon re- sistance was adjusted, and it would probably be found that a fresh adjustment was required when it was desired to start the decomposition. To avoid this difficulty, the circuit through the silver voltameter should not be closed during the adjustment, but W 2 and the left-hand terminal of the ammeter should be joined instead by a piece of German silver wire, having the same resistance as the voltameter. A third mercury cup, not shown in the figure, but which we may call H', may be easily arranged so that when the bridge-piece B is put into the holes H and H', the circuit through the German silver wire is closed, whereas when one of its ends is shifted from H' to H, the other being left in the other hole H, the circuit through the voltameter is closed. At the commencement of the experiment the platinum dish D (Fig. 157) should be carefully washed with distilled water, to remove any dust or dirt, then dried over a Chap.VIII., CALIBRATING AMMETERS. 399 spirit lamp, and placed on the triangle T over the vessel v of strong sulphuric acid, and the glass cover G left over while the platinum dish is cooling. When it is cool it should be carefully weighed. The dish is now put in position on the pins p, the silver di^c placed so that its edges are equally distant from the sides and bottom of the dish, and the solution of silver nitrate poured in. Next, a current is sent through the carbon resistance R, the ammeter A, and the German silver wire above referred to, and the carbon resistance adjusted until the current, as observed on the ammeter, has the right value. The maximum value that may be given to the current so as to obtain a good adherent deposit with a particular platinum dish is (as stated in the foot-note, 6, page 11) one ampere per six square inches of surface. At a time noted on a watch the current is sent through the voltameter instead of through the German silver wire, and its strength is kept constant by slightly turning from time to time the nut n (Fig. 158) at the top of the carbon resistance so as to keep the ammeter deflection constant, and at a noted time, at the end of from ten to thirty minutes, depending on the current used, the circuit is interrupted. The silver nitrate solution having been put back into the bottle, the platinum dish, with the layer of deposited silver in it, is carefully rinsed out with distilled water ; next it is filled with distilled water, and left standing for ten or fifteen minutes to remove traces of the silver nitrate solution, then having been rinsed out again with distilled water, it is rinsed out with alcohol to remove the water, and with ether (which evaporates with great rapidity) to remove the alcohol, and finally it is dried over a spirit lamp, and left to cool under the desiccator G, when it is again carefully weighed. Then, if W be the increase in weight in grammes produced in t seconds by a current of mean strength, A amperes, A = 0-00111815 i 400 PRACTICAL ELECTRIOITY. [Chap. VIII. It is desirable to repeat this test for two or three very different currents that the ammeter is adapted to measure, as the calibration may be right in even two very different parts of the scale, and not at some inter- mediate part, arising from the law of the instrument not being exactly what the maker has supposed ; for ex- ample, he may have determined accurately the currents corresponding with two points of the scale, and have interpolated the intermediate graduations on the assump- tion that the increase of deflection was directly propor- tional to increase of current, which may not be quite true with the particular instrument. 208. Test for Residual Magnetism. In order to ascertain whether a current produces the same deflection on an ammeter, independently of whether the currents previously passing through the instrument were much smaller or much larger than the particular current in question, the instrument should be joined up in series with a Siemens' dynamometer, or other current meter containing absolutely no iron or steel, and, therefore, having no error due to residual magnetism, together with an adjustable carbon resistance, care being taken to put the dynamometer so far away from the other instrument that any magnetism produced in the latter will not affect the dynamometer. Then, starting with the carbon re- sistance unscrewed, so that its resistance is great, the circuit should be closed, and successive simultaneous readings of the two instruments taken; first, as the carbon resistance is gradually screwed down, and the current increased up to the maximum current the instrument is intended to measure ; then, as the carbon resistance is gradually unscrewed, and the current di- minished again. The following are the results of such tests made with a strongly magnetised permanent magnet ammeter, like that shown in Fig. 26 page 76 ; with a spring control meter, like that shown in Fig. 154, page 384 ; with a magnifying spring ammeter, like that shown in Fig. 156, page 388 ; and with an electro-magnetic control meter. Chap. VIII.] TEST FOR RESIDUAL MAGNETISM. 401 Amperes as measured by a Per- Amperes as measured by a manent Magnet Ammeter ; a . 1 , -p. .' reading from to 25 amperes. Siemens Dynamometer. 6-1 > 6-58 12-2 8 12-31 18-3 g, 18-32 About 24-4 1" Not read 18-3 12-3 6-4 Amperes as measured by a Spring Control Meter, with massive iron needle, and deflecting electro- Amperes asmeasurea by a magnets with massive cores; biemeus Dynamometer. reading from to 100 amperes. 20 s, 19-6 25 g 25-3 35 o 36-2 45 & 47-1 55 * 58-1 58-5 61-4 55 o 57-4 45 46-0 35 34-4 25 & 23-2 20 17-2 That it required a smaller current at the end of the experiment to produce the same deflection as was produced at the beginning, showed that the iron core of the deflecting electro-magnet retained some of the magnetism put into it when the strong current was flowing round it. Amperes as measured by the Magnifying Spring Amme- Amperes as measured by a ter ; reading from 4"5 to Siemens' Dynamometer. 25 amperes. 4-95 9-9 25 20-4 24-45 20-85 15 9-87 4-85 AA 402 PRACTICAL ELECTRICITY. [Chap. VIIL Amperes as measured by the Electro- Magnetic Con- A in peres as measured by ft trol Meter ; reading from Siemens' Dynamometer. to 100 amperes. 10 8-82 25 27-6 30 32 40 & 41-9 50 , c Fig. 160. 21 21-5 d 21 21-5 No magnet near. Chap.VIII.T TEST FOR EXTERNAL MAGNETIC DISTURBANCE. 407 Magnet moved round an Electro-magnetic Control Meter in a Horizontal Plane. Amperes as measured by the Electro-mag- netic Control Meter ; Amperes as measured by a Siemens' Dy- reading from to 100 namometer. amperes. 10 9-2 No magnet near. 10-1 9-2 Magnet in position a. 14-6 9-2 * 10-9 9-2 e - 7'9 9-2 *. 9-5 9-2 No magnet near. 82 90 No magnet near. 81-8 90 Magnet in position a. 84-6 90 b. 84-6 90 c- 81-3 90 d" 82-2 90 No magnet near. 211. Test for Permanent Alteration of Sensibility. This test is one that must necessarily extend over a long period, as permanent magnets are found to slowly de- magnetise, springs to become permanently strained, or, as it is called, get a "permanent set" &c. Frequent com- parisons should, therefore, be made between the readings of an ammeter, and the amount of silver deposited in a given time by the currents giving these readings. ERRORS IN VOLTMETERS. 212. Testing Voltmeters. In addition to the five errors given in 206, page 394, and which affect volt- meters equally with ammeters, there is a most important sixth error arising from the sensibility of a voltmeter varying with its resistance, and, therefore, with its tem- perature. This change of resistance is due partly to the variation of the temperature of the room, and partly to the coils of the instrument becoming heated by the 408 PRACTICAL ELECTRICITY. (_Cliap. VIIL passage of the current through them. Voltmeters in this respect differ entirely from ammeters ; an increase of resistance of an ammeter may diminish the current in the circuit, but the ammeter will accurately measure the current so diminished ; consequently, the sensibility of an ammeter is unchanged by a change in the resistance alone. For example, if two exactly similar ammeters be wound, the one with copper, and the other with German silver wire of the same gauge, and with the same number of convolutions, the sensibility of the one will be exactly the same as that of the other, in spite of the resistance of the latter instrument being thirteen times that of the former; whereas an increase in the resistance of a voltmeter causes a less current to pass through it for the same P. D. at its terminals, and hence the sensibility of a voltmeter varies with change in its resistance. 213. Test for Accuracy of the Graduation. From the definition of a volt (81, page 141), it follows that if we know the current in amperes passing through a resistance, the value of which is known in ohms, we know the P. D., in volts, at its terminals, since this is equal to the product of the number of amperes into the number of ohms. This leads to a very simple and accu- rate method for calibrating voltmeters, and which is shown symbolically in Fig. 161. v is the voltmeter to be calibrated, r a resistance formed of a long coil of fairly thick copper, or better of platinoid wire wound double so as not to produce any external magnetic action, and coiled up loosely so as to cool fairly quickly. A is an ammeter which has been accurately graduated, and w a Wheatstone's bridge, or differential galvanometer, with battery complete for measuring the parallel resist- ance between the points c and B, and which is made up of r l and of v. Between the terminals ^ and T 2 , there is some suitable current generator, not shown in the figure, which will send a current through the arrangement on inserting the plug P X ; r 2 is an adjustable, but not necessarily a known, resistance for varying this current Chap. VIII.] CALIBRATING VOLTMETERS. 409 and PO is a plug key for completing or interrupting the circuit through the measuring apparatus w. The experiment is performed thus : P 3 being opened and PI closed, r% is adjusted so that a convenient deflec- tion is obtained on v. This deflection is read by one observer, and simultaneously the deflection on A by another observer, when, on a signal being given at which the time is noted, P : is opened, P 2 is closed, and time mea- surements of the parallel resistance between c and B taken. These resistances being plotted as ordinates on Fig. 161. a sheet of squared paper with the times, from the moment of opening PJ, as abscissae, a curve can be drawn, and on producing it backwards it is easy to ascertain what was the exact resistance in ohms and fraction of an ohm of the circuit between c and B at the moment the simul- taneous readings on v and A were taken, then the product of this resistance into the number of amperes gives the exact number of volts corresponding with the deflection on v. r 2 is now varied so as to produce a different deflec- tion on the voltmeter v, and the number of volts corre- sponding with it ascertained as before, and so on for as many readings as it is necessary to take to determine the absolute calibration of the voltmeter. If the coil rj be made of very thin German silver wire, and the current sent through it be only a small 410 PRACTICAL ELECTRICITY. CChap. VIII. one, the resistance may not alter by the passage of the current; but if it be desired to produce a P. D. of 100 or more volts between the points c and B, and to use an ordinary ammeter A, graduated up to, say, 20 amperes, the resistance r A would have to be something like 10 ohms, and able to take a current of 10 amperes without heating at all. Such a wire would have to be very long and thick, and, therefore, expens whereas the device of taking time measurements of t resistance enables the coil to be made of even copper wire. The preceding method is based on our knowing the exact Value of a current and of a resistance, but we may calibrate a voltmeter by comparing its readings with the E. M. F. of a cell, if this E. M. F. be accurately known in volts. The cells best suited for this purpose are a "Latimer Clark's cell," or some form of gravity Daniel 1, in which the cop- per sulphate and zinc sul- phate solutions mix very slowly. 214. Latimer Clark's Cell. These cells are made in a variety of forms,* but probably what is called the H form, shown in Fig. 162, is the best. One of the legs is partially filled with an " amalgam of zinc " A, formed by putting some pure zinc into pure mer- Fi&. 162. cury, which has been previ- ously distilled in a vacuum, the other with pure mercury M, which has been similarly distilled, covered with a layer of "mercurous sulphate" M s. * Phil. Trans. Roy. Soc., vol. xvii., p. 411. Part II., 1884. Chap.VHLJ LATIMER CLARK'S CELL. 411 The whole is then filled up above the level of the cross tube with pure saturated zinc sulphate z, and a few crystals of zinc sulphate are added. Evaporation is prevented by the insertion of paraffined corks c, and electrical contact is made with the amalgam, and with the pure mercury, by platinum wires w w, sealed into the glass. Marine glue may be employed instead of paraffin wax to make the corks c air-tight, or, best of all, the upper ends of the tubes may be hermetically sealed (see note, page 20). If the zinc sulphate be saturated, but not "super-saturated"* the experiments of Lord Rayleigh t show that when this cell is not allowed to send currents, its E. M. F., after it has been set up for some weeks, is extremely constant for the same temperature, and has a very exact value for any particular temperature ; its value in legal volts being equal to 1-438 {1-0-00077 (*-15)}, where t is the temperature of the cell in degrees Centi- grade. As in the Daniell's cell (see 119, page 211), a diminution in the density of the zinc sulphate solution increases the E. M. F. of the Latimer Clark's cell. 215. Standard Daniell's Cell. In spite of the great value of the Latimer Clark's cell, it has two defects, the one that it polarises rapidly, and its E. M. F. temporarily falls off if a current be allowed to pass through the cell, the other that the variation of its E. M. F. with tempera- ture is considerable, and therefore for accurate work the temperature of the cell must be accurately known. These * When a saturated solution of a salt is cooled, some crystals are formed so as to leave the liquid simply saturated at the lower tem- perature ; but if the liquid be closed up so that the air does not get to it, and if it be cooled without shaking, crystallisation may not take place, and the liquid is then saidjto be " super-saturated," for on dropping ft crystal of the salt into it, crystallisation immediately occurs. The presence, therefore, of crystals in a liquid is a proof that it is satu- rated and not super-saturated. f Proc. Roy. Soc., voL xl., p. 79. 412 PRACTICAL ELECTRICITY. [Chap. VIII. objections are overcome by the employment of a form of gravity Daniell, in which the solutions can only mix very slowly. If the plates, or rods, be formed of clean, pure zinc, and of freshly " electrotyped " copper that is, copper on the surface of which a layer of copper has been deposited by putting the plate, or rod, into a bath of copper sulphate, and sending a current through the bath, so that it leaves by the plate or rod and if the solutions used in the Daniell's cell be formed of pure crystals of copper sulphate and zinc sulphate, then the E.M.F. will be 1-104 volts when the solutions are equally dense, and 1'074 volts if the copper sulphate solution has a specific gravity of MOO at 15 C., and the zinc sulphate solu- tion 1'400 at the same temperature. A form of gravity Daniell's cell, spe- cially designed by Dr. Fleming,* to be used as a standard, is shown in Fig. 163, and consists of a U- Fig. 163. tube | inch in diameter, and 8 inches long, provided with glass taps, &c., as shown. To use the cell, the tap A is opened, and the whole U-tube filled with the denser zinc sulphate solution ; the zinc rod which is kept in the test tube L, when the cell is not in use, is now inserted in the left-hand tube, and its indiarubber stopper p fitted * Phil. Mag., S. 5, vol. xx., p. 126. Chap.VIII.1 STANDARD DANIELL's CELL. 413 tightly into this tube. Now, on opening the tap c, the level of the liquid will begin to fall in the right-hand limb, but no liquid will flow out of the left-hand one. As the level commences to sink in the right-hand limb, copper sulphate solution can be allowed to flow in gently to replace it by opening the tap B ; and this opera- tion can be so conducted that the surface of demarcation of the two liquids remains quite sharp, and gradually sinks to the level of the tap c. When this is the case, all the taps are closed and the copper rod is removed from the test tube M, in which it is kept, and, after having been freshly electrotyped, is fitted into the right-hand tube Q. It is impossible to stop the liquids mixing together at the surface of contact, but whenever the surface of contact ceases to be sharply defined, the mixed liquid at the level of the tap c can be drawn off, and fresh solu- tions supplied from the reservoirs above. Experiment shows that the effect of oxidation of the zinc is to lower the E. M. F., while oxidation of the copper raises it. In order that the E. M. F. of a Latimer Clark's cell should be quite constant, it is absolutely necessary that the cell should not be allowed to send any appreciable current, and even with the Daniell's cell better results will be obtained if the cell be not sending a current when the test is made, since in that case the P. D. at its terminals will be equal to the E. M. F., independently of the internal resistance of the cell, which will be rather high if it be so constructed that the solutions can only mix slowly. Hence, PoggendorflTs method (see 132, page 234), or the condenser method (see 183, page 341), must be employed, care being taken to determine accu- rately the multiplying power for a discharge of the shunt employed (see 188, page 349). The complete arrangement for calibrating a voltmeter by Poggendorff's method is shown in Fig. 164, the figure being somewhat distorted so that the details of the key can be easily seen. In actual practice the 414 PRACTICAL ELECTRICITY. [Chap. VIII. board and the wires on it are much longer than they appear to be in the figure. J K is a long German silver, or platinum-silver, or platinoid wire, very care- fully drawn so as to have, as nearly as possible, the same diameter everywhere, and as it "is very difficult, if not impossible, to draw a long wire having exactly the same diameter at all points in its length, the resistance of each five or six inches of the wire should be carefully Fig. 164. measured and recorded. B is a large battery of any kind of cells that will send through r^ and the wire J K, a current that will remain constant for at any rate a few seconds. G is a sensitive high resistance galvanometer, s the standard cell, and r% is a high resistance inserted in this circuit to keep the current that would flow through the cell on closing the key quite a weak one, even if the point of contact of the key with the wire J K be far away from the position that gives no current through the galvanometer. The test is made by inserting the plug p, the handle H of the key being up, and adjusting r x until the P. D. between the points J and K, that is, between Chap. VIII. ] CALIBRATING VOLTMETERS. 415 the terminals of the voltmeter v, produces about the desired deflection ; the key is then closed for a moment, when, if there be any deflection on G, the key is slid, in the proper direction, along the wire J K, and contact again made, and so on until a point M is found such that no current passes through G ; the reading on v is taken at that moment, and we know that it corresponds with a P. D. equal to resistance of J K : x E. M. F. of the standard cell. resistance 01 J M In order to enable the contact-maker c to touch any one of the five wires composing J K, c can be slid along the slot in the lever ; and, to prevent the platinised knife- edge attached to the lower part of c being pressed too hard against the stretched wire, and damaging it, the flat spring s is made rather weak. Hence, on depressing H, the knife-edge attached to c first comes into contact with the wire, and, on still further depressing H until it comes against the stop placed underneath it, the lever turns about the knife-edge. 216. Test for Heating Error. The various errors found in ammeters occur, as already explained, also in voltmeters, and may be tested for in the same manner by using a voltmeter with no iron employed in its construc- tion, as the instrument of comparison, instead of an ammeter. As, however, the heating error (see 212, page 408) is one peculiar to voltmeters, and may exist in the voltmeter which we use as our standard when testing for the other errors, it is desirable to consider how it may be reduced to a minimum, since the existence of this heating error in the standard voltmeter might easily mask all the other errors in the voltmeters that are being tested. The first point to determine is the way in which the sensibility of a galvanometer, with coils of a given shape and size, and with a given needle and controlling force, varies with the resistance of the 416 PRACTICAL ELECTRICITY. [Chap. VIII. wire employed in winding it ; next, how the rate of pro- duction of heat, when a given deflection is produced, also varies with the resistance of the wire employed in wind- ing the galvanometer, because it may be that by winding it with some special form of wire, we may obtain con- siderable sensibility with but little heating of the coils. 217. Variation of the Sensibility of a Galvano- meter with its Resistance. When all the convolutions of wire occupy the same position relatively to the needle, we have seen ( 22, page 51) that the sensibility of a galvanometer is directly proportional to the number of convolutions that is, to the length of wire employed in winding the bobbin. This conclusion is also true, no matter what be the shape of the coil, or what the distances of the various convolutions from the needle, provided that the coil is fixed in size and shape ; for let A B c D, A' B' c' D ' (Fig. 165), be a small bit of a sec- tion of a galvanometer coil taken through the axis P Q of the coil ; A B c D being so small that all the three wires that pass through it are at practically the same distance from the needle, and therefore produce the Chap. VIII.] GALVANOMETER SENSIBILITY AND RESISTANCE. 417 same magnetic effect when the same current passes through each of them. Now, if the bobbin were wound with wire of half the diameter, there would be four wires for each of the three wires that pass through ABCD, or twelve altogether, as in Fig. 166, hence the magnetic effect due to the wires that pass through the small bit A B c D, A' B' c' D' would, for the same current, have been increased four times. And so for the wires passing through any other bit R s T u, R' s' T' u' of the section. Hence, although the magnetic effect of one convolution passing through ABCD, A' B' c' D' may, for the same current, be very different from the effect of a convolution passing through R s T u, R' s' T' u', we may say that the whole magnetic effect for the same current is directly proportional to the number of convolutions, or to the length of the wire ; and it will be observed that this result remains true even if the diameter of the wire at different parts of the coil be quite different, provided that the law of winding be maintained when the gauge is changed that is to say, the diameter of the wire used in winding the three con- volutions passing through ABCD may be quite different B B 418 PRACTICAL ELECTRICITY. [Chap. VIII. from that employed in winding the three convolu- tions passing through n s T u, and yet the whole magnetic effect for the same current will be directly proportional to the length of the wire, provided that when we halve, double, or treble the diameter of one set of wires, we do the same for every other. We may conclude, therefore, that when we have a galvanometer with coils of a given shape and size, wound according to a given law, and fitted with a given needle, or set of needles, and controlled by a given force, the sensibility of the galvanometer is directly proportional to the number of convolutions, or to the length of wire used in wind- ing it. But the resistance of the wire used in winding a given coil is, for the same material, copper, German silver, &c., proportional to the square of the number of convolutions that is, to the square of the length be- cause when we replace each convolution by four, we make the length of the wire used in winding the bit A B c D, A' B' c' D' four times as great, and the sectional area of each wire one-quarter, therefore the resistance of the wire passing through A B CD, A' B' C'D' becomes six- teen times as great, and so for the wire used in winding any other small bit R s T u, R' s' T' u', hence the sensibility of a galvanometer is directly proportional to the square root of its resistance, and the magnetic effect is directly proportional to the product of the current into the square root of the resistance. Therefore, with coils of a given shape and size, wound according to a given law, with wire of a given material, and fitted with a given needle, or set of needles, controlled by a given force, the current required to pro- duce a given deflection is inversely proportional to the square root of the galvanometer resistance. And since the current passing through a galvanometer is equal to the P. D. maintained at its terminals, divided by its resistance, it follows that the P. D. required to be maintained at the terminals of a given voltmeter, wound Chap. VIH.1 RATE CURRENT HEATS A GALVANOMETER. 419 with wire of a given material, to produce a given deflection is directly proportional to the square root of the resistance of the voltmeter. And these two last conclusions may be shown to be true whether the needle be a hard steel magnet or a piece of soft iron magnetised by the current passing round the coils of the instrument. 218. Rate of Production of Heat in Galvanometer Coils. We have seen in the last section that the cur- rent required to produce a given deflection is inversely proportional to the square root of the galvanometer re- sistance, and this is the same thing as saying that to pro- duce a given deflection the product of the current into the square root of the resistance must be constant. But the rate of production of heat in the galvanometer is, by 113, page 198, proportional to the product of the square of the current into the resistance of the galvanometer. Hence, Avith coils of a given shape and size, wound ac- cording to a given law, with wire of a given material, and fitted with a given needle, or set of needles, controlled by a given force, the rate of production of heat, when a given deflection is being produced, is a constant and is in- dependent of the gauge of wire used in winding the coils. Hence, we see that if the following things be fixed in a voltmeter : 1. The si i ape and size of the coils ; 2. The material of which the wire is made ; 3. The law of winding, i.e., the variation of the thickness of the wire with the diameter, or position, of a convolution ; 4. The needles and the controlling force ; we cannot diminish the error arising from the heat- ing of the coils when a current passes round them by winding the instrument with finer or with thicker wire. We have next to consider whether it may be diminished by varying 2, 3, or 4. As to 4, it is quite clear that the smaller the controlling force, and the more astatic the system of needles (see 152, page 282), the smaller will 4:20 PRACTICAL ELECTRICITY. [Chap. VIII. be the current required to produce a given deflection, and therefore the less the heating error. As to the material, if we are merely concerned with variations of resistance of the voltmeter arising from changes of temperature of the room, then it is better to use German silver, platinum- silver, or platinoid wire (see 94, page 160), or we may add a small piece of carbon in series with the voltmeter coils of such a length and size that its diminution of re- sistance for an increase of the temperature exactly balances the increase of resistance of the coils ; but if it is the increase of resistance due to the heating of the coil by the passage of the current that we wish to have as small as possible, then it is easy to show that it is better to wind the whole of the coils with copper wire than with German silver. For, since the resistance of German silver for the same length and thickness is about thir- teen times as great as that of copper, it follows, if two exactly similar voltmeters be wound, the one with Ger- man silver wire, and the other with copper wire of the same length and thickness, that the rate of production of heat when there is the same deflection in the two instru- ments (which will be produced by the same current) will be about thirteen times as great in the one that is wound with German silver wire, as in the one that is wound with copper wire, whereas for the same rise of temperature the increase of resistance of copper is only about 8 '8 times that of German silver (see 94, page 160). We cannot, of course, say that the rise of temperature is proportional to the rate of production of heat (see 111, page 194), but it is probable that the rise of temperature of the German silver coils will be more than 8 '8 times that of the copper ones, and, there- fore, as far as the heating due to the passage of the cur- rent is concerned, copper is to be preferred to German silver wire. The law of winding that will give a minimum heat- ing error will depend on the dimensions of the instru- ment, and for a magnifying spring voltmeter of the C*iap. VIII.] VOLTMETERS WITH SEPARATE RESISTANCE. 421 dimensions shown in Fig. 156, and where the radius of the central part not wound with wire is one-eighth of the radius of the cylinder formed by the outside of the wire, it may be shown that, if a be the sectional area of the copper wire at any distance d from the axis of the instrument, and the sectional area of the first layer of the copper wire nearest the central portion, to have a minimum heating error the following condition should be satisfied : so that the sectional area of the outside wire should be 2 '395 times the area of the inside wire. The particular sectional area given to the innermost wire must depend on the strength of the spring and the P. D. that it is desired shall produce a particular deflec- tion. A method that is frequently employed for diminish- ing the heating error, is to wind the voltmeter so that a comparatively small P. D. maintained at its terminals will produce a large deflection, and then to add a separate resistance coil joined in series with the voltmeter, when the practical terminals of the instrument become the free end of this resistance coil and the free end of the volt- meter. If V t be the P. D. in volts required to produce a deflection of, say, 100 when applied directly to the terminals of the voltmeter of resistance r lt and V 2 be the P. D. required to produce the same deflection when a coil of resistance r 2 is put in series with the voltmeter, V, r, Hence, by giving a proper value to r 2 , we can make V 2 have any value we like, but what is even more important, the temperature error arising from changes of tempera- ture of the room as well as from the heating of the coils by the passage of the current round them, will depend 422 PRACTICAL ELECTRICITY. [Chap. VIII. not merely on the variation of r u but on the variation of r i ~H r & an d this we can keep as small as we like by making r 2 large compared with r lt and by constructing the extra resistance of thick German silver wire, so that the proportional increase in the total resistance r r -f r 2 shall be small, even if the increase in r t alone be con- siderable. It might be asked, why not make the volt- meter itself large, and wind it with such thick wire that the heating would be small. The answer is that if we did so we should remove the outer layers of wire so far away from the attracted needle, that the effect of a cur- rent passing round them would be very small, and hence we should seriously diminish the sensibility of the in- strument. The separate resistance coil has to produce no magnetic action, hence the objection to using very thick German silver wire in it, and making it very large, is merely increase in cost and diminution in portability. There is, however, one objection to making r 2 large compared with r lt and that is, that the energy expended in the voltmeter itself, and which is equal to 44-25 A 2 r t footpounds per minute (see 114, page 201), is only a small fraction of the energy expended in the extra re- sistance, and which is equal to 44 -2 5 AV 2 foot pounds per minute. The former waste we cannot help, as it is a constant depending on the construction of the spring and the shape of the voltmeter (see 218, page 419), but the latter is a large waste introduced solely to diminish the heating error. Hence, a voltmeter , with a powerful con- trolling force, wound with thick wire of low resistance, and furnished with a separate coil of high resistance, can only be used in electric light, or power, installations where a small waste of energy is unimportant. 219. Standard Voltmeter. But if the controlling force be weak, then the total waste of energy will be so small as to be negligible, and hence we are led to the best form to give to a standard voltmeter : suspend the needle as delicately as possible, and use a controlling force as weak as is compatible with the instrument Chap. VIII.) CARDEW'S VOLTMETER. 423 retaining a fixed constant, wind the instrument with not very fine copper wire, and place in series with it a large resistance made of as thick platinoid wire as is obtain- able. When, as explained in 11, page 23, a galva- nometer has a single suspended magnetic needle, the alteration of its strength will not affect the sensibility of the instrument ; but if there be an astatic combination, an increase or diminution of strength of either of the needles will affect the sensibility of the instrument, hence it is better to use a single needle galvanometer when we desire great constancy in the sensibility, as in a standard voltmeter. 220. Cardew's Voltmeter. This voltmeter, designed by Captain Cardew, R.E., differs from all the instruments previously described in that the heating and not the magnetic action of a current is employed, and the eleva- tion of temperature of the conductor is measured by its expansion. The conductor consists, in the newest form of the instrument, the back of which is seen in Fig. 167, of about thirteen feet of platinum - silver wire 0-0025 inch in diameter. This wire, which is fixed at one end to a screw A, passes, at the top of the instru- ment, over a pulley p w made of bone so as to be an insulator, then down under a small bone pulley p lt then up again over a bone pulley p^ and lastly is fastened to a screw B. The pieces of brass into which the screws A and B are fastened, are connected with the terminals T, and T 2 , and on a P. D. being set up between these ter- minals a current flows through the stretched wire, the strength of which depends on the P. D. maintained be- tween the terminals of the voltmeter, and on the resist- ance of the wire. The wire becomes hot and expands, and as it is very thin, it very quickly acquires the temperature corresponding with the particular current passing through it. The support carrying the little pulley p lt is pulled down by a thread wrapped round the grooved wheel w and fastened to the spring s, ; hence when the wire lengthens, and the little pulley p descends, Fig. 167. Chap. VIII.] CARDEW'S VOLTMETER. 425 the wheel w is turned. The staff (or little shaft) carry- ing the wheel w also carries a toothed wheel L, geared into a small pinion M, hence when, by a slight lengthening of the wire, w is turned through a small angle, the pinion turns through a large one. On the farther end of the staff carrying the pinion there is fixed, in the front of the instrument, a pointer moving over a dial graduated in volts, the back of which is seen in the figure ; con- sequently the pointer is caused to move right round the scale by a comparatively small descent of the pulley p v . It will be observed that the pull of the spring Sj is balanced by twice the tension in the stretched wire, and that the descent of the pulley p l is due to the expansion of only half the total length of wire employed, that is, the expansion of only about six feet six inches of wire. The advantage, however, of using a long wire, fixed in the way shown, instead of a wire half as long, and of twice the sectional area, which would enable the same spring s t to be used and cause the same motion of the pointer for the same elevation of temperature, is that the fine wire heats and cools much more rapidly than the thicker one, and so makes the voltmeter much more dead- beat. If the P. D. to be measured is between 30 and 120 volts, the stretched wire alone may be used, but for larger P. Ds., an extra resistance (see 218, page 421) is added, and the terminals of the voltmeter are now TJ and Ty If the extra resistance be equal to that of the voltmeter itself, not merely when the wires are cold, but also when they are heated by the passage of the current, the readings on the scale will correspond with exactly twice the number of volts ; or a double scale somewhat similar to that seen in Fig. 26, page 76, can be employed, the numbers on the one being twice the corresponding ones on the other. To insure the resistance of the added wire being always exactly equal to that of the voltmeter itself, Captain Cardew uses for the extra cir- cuits a stretched wire of the same length and section, and placed under similar conditions as regards cooling as the 426 PRACTICAL ELECTRICITY. [Cliap. VIIL wire of the voltmeter itself, both sets of wires being sur- rounded with metal tubes, as will be described farther on, and the tubes, like the metal rods supporting the pulleys p,, P 2 , P S , P 4 , being lamp-blacked on the surface. This extra wire, which has one end attached to the screw c, passes over a bone pulley P 3 at the top of the instrument, then down and under the little bone pulley j) 2) then up and over the bone pulley P 4 , and lastly is attached to the spring S 2 . The support carrying the pulley p 2 is also attached to a spring S 3 , hence the stretching of the second wire which occurs when the current passes through it is taken up by the contraction of both the springs S 2 and s s , and the wire is kept tight. To prevent draughts of air cooling the stretched wires they are en- closed in metal tubes 1 t, t' t\ shown in the figure separated from the rest of the apparatus. The internal diameter of these tubes is only a little greater than that of the circular metal plates, D E, F a, carrying the bearings on which the pulleys P 1? P 2 , P 3 and P 4 turn, so that when the tubes are slipped over the plates and screwed on to J K, the top of the box, they prevent these plates having any lateral motion. To prevent the rods which support the pulleys p w P^ P s , P 4 expanding and contracting more or less than the stretched wires when the temperature of the room changes, which would cause the pointer to move, these rods may be composed partly of brass and partly of iron, so that their mean co-efficient of expansion is the same as that of platinum-silver. The mechanism contained in the wooden box in the lower part of the instrument is protected from damage by the box being closed with a wooden back (not shown in the figure) which turns on the hinges H H. The two great advantages of this instrument are : First, it has no heating error, since the elevation of the temperature produced by the passage of the current is the property of the current made use of; second, it can be used for measuring alternating P. Ds. (see 113, Chap. VIIL] CARDEW'S VOLTMETER 427 page 198). As already stated ( 100, page 174), when a current is started round an electro-magnet, it takes a certain time to reach its maximum value, so that with an alternating current, which is continually being started in opposite directions, the effecir of the self-induction of the coil is to practically increase its resistance by an amount which varies with the rapidity of the alternations ; hence, apart from the fact that the rapid reversals of magnetism, which are produced by an alternating current, prevent an ordinary galvanometer being used for measuring such a current, even a high resistance dynamometer, which can be used for measuring an alternating current (see 199, page 381), cannot be used for measuring an alternating P. D., for its self-induction would cause it to practically have a variable resistance, and we have seen ( 212, page 408) that any variation in the resist- ance of a voltmeter varies its sensibility. But as the self-induction of a straight wire bent back on itself is very small, the error in Captain Cardew's voltmeter, arising from self-induction, is negligible, and so this in- strument is much used for measuring an alternating P. D. It is also dead-beat, direct-reading, not disturbed by magnets, and fairly portable, although large. The disadvantages of the instrument, as usually made, are : First, it absorbs a good deal of energy ; second, it cannot be used for measuring a small P. D., for we can- not make it of thicker wire as we should do in the case of an ordinary voltmeter intended to measure small P. Ds., as this would render it sluggish, since a thick wire traversed by a current heats and cools slowly on starting and stopping the current; third, there is con- siderable vagueness in the readings near the zero point, and sometimes inaccuracy in the upper parts of the scale. 221. Commutator Ammeter and Voltmeter. With any of the magnetic instruments already described, the following commutating device, due to the author, may be employed, and which enables the same instrument to be used with two degrees of sensibility, the one exactly a 428 PRACTICAL ELECTRICITY. [Cbap. VIII. certain known number of times the other. This arrange- ment is very convenient when an ammeter has at one time to be used to accurately measure, say, the current passing through an arc-lamp, which may be 20 or more amperes, and at another time to measure with equal accuracy that passing through an incandescent lamp, which will most probably be less than one ampere, or when the same voltmeter is to be employed to measure Fig. 168. the P. D. at the terminals of a dynamo machine, and which may be 100 or more volts, and the P. D. at the terminals of five or six cells. Further, this power of varying the sensibility in a known ratio is of especial con- venience in enabling an ammeter which is to be employed for measuring strong currents, or a voltmeter that is used for measuring large P. Ds., to be accurately calibrated by using, in the one case, known currents, and in the other known P. Ds. only one-tenth as large as the instru- ment can be employed to measure. The device consists in winding the instrument with a strand of separate Chap. VIII.] COMMUTATOR AMMETER AND VOLTMETER. 429 wires instead of merely one wire, and employing a "commutator" by means of which the current can be made to go either through all the wires in parallel, as if through a single thick wire, or, instead, through the wires one after the other in series, as if the instrument were wound with one long fine wire. Such a commutator is seen under a cover at the back of the ammeter shown in Fig. 26, page 76, and the commutator with the cover removed is shown in Fig. 168, part of the side and some of the springs being removed to show the remainder more clearly. One end of each of the wires is permanently attached to the upright springs s 2 , s s , s 4 , &c. (Fig. 169), on one side of the ebonite barrel of the commutator cc, and the other end of each of the wires to one of the upright springs s' 2 , s' s , s' 4 , &c., on the other side of the barrel. In one of the positions of the commu- tator, all the springs on one side are electrically con- nected together by a platinised strip of brass BB, in- serted in the barrel of the commutator parallel to its axis of rotation, and all the springs on the farther side 430 PRACTICAL ELECTRICITY. [Chap. VIII. are also connected by a similar piece of metal B' B', inserted in the other side of the ebonite barrel, the tips of the springs being also platinised to insure good contact. The terminals marked P, P s, seen at the back of Fig. 26, are permanently connected, by pieces of thick wire in the base of the instrument, to the first of each of the springs s\, on the two sides of the barrel, hence the connections are now as shown symbolically Fig. 170, in Fig. 169. If, however, the barrel of the commutator be turned through a right angle, the metal bars B B, B' B' are removed from the position in which they touch the springs, and, instead, pins p lt p%, p^ &c., inserted through the barrel at right angles to its axis, now make the follow- ing connections as seen in Fig. 170 ; the broad spring s l is connected with s' 2 , the spring s. 2 with s' 3 , &c., so that the coils are connected in series, and a current entering the instrument at the terminal P s leaves it by that marked s, which is connected with s' 12 , having passed through all the wires in succession. The terminal s in the symbolical figures 169, 170 is Chap. VIII.] COMMUTATOR AMMETER AND VOLTMETER. 431 drawn inside the wires in the position that the needle would occupy in the actual instrument. This is merely to prevent the wire which connects 8 with the spring s' 12 having to cross the other wires, and so producing con- fusion in the figures. If all the coils were far away from the needle, and all occupied practically the same position relatively to it, the sensibility of the instrument ivhen all t/te wires were in series would bear to the sensibility when they were all in parallel, a ratio simply equal to the number of separate wires employed, quite independently of the way the cur- rent divided itself among the wires when they were in parallel. But if to obtain greater sensibility they be wound on the bobbin close to the needle, some of them will be, on the whole, nearer to it, and therefore have a gr?ater magnetic effect for the same current than the rest, and it will be necessary, in order that the simple ratio of the sensibilities given above shall exist, that the current shall divide itself equally among the wires when in parallel. For, since the same current passes, of course, through each of the wires when they are in series, it follows that, if matters be so arranged that equal currents also pass through them all when in parallel, any particu- lar coil will produce the same proportion of the total magnetic effect whether the commutator be turned to series or to parallel. Now, to insure that when the commutator is turned to parallel, equal currents shall pass through all the coils, it is necessary that they should be of exactly the same resistance, and this, therefore, is the con- dition fufilled in constructing commutator instruments. In the ammeter seen in Fig. 26, page 76, ten coils of equal resistance have been wound on the bobbin, and hence the ratio of the instrument in the two positions of the commutator are as 1 to 10; the scale, therefore, has two sets of graduations, the angular deflection on the one to be used when the commutator is turned to parallel, corresponding with ten times the number of am- peres indicated by the other. 432 PRACTICAL ELECTRICITY. [Chap. VIII. The binding screws P and P s are made so that a thick wire can be attached to them, while s has so small a hole in it that only a tine wire can be put in it ; hence the wires used to convey large currents, which come from a dynamo machine, for example, can only be at- tached to P and p s, and not to s, hence there is no fear of either of them being attached to the wrong binding screw ; and, further, as will be seen from Figs. 169, 170, the strong current can only pass through the instrument when the commutator is turned to parallel. Hence, even if it be accidentally turned to series while the instru- ment is connected with a dynamo, for example, or a large battery of cells, the current will be interrupted instead of being allowed to pass through all the coils in series, which would probably burn them up, or would, at an} rate, in consequence of the sensibility of the instrument being increased, say ten times, knock the pointer violently against the stops, which are inserted to limit its motion, and damage it. 222. Calibrating a Commutator Ammeter. First plan : Turn the commutator to series so that only a small current is required to produce a fairly large deflec- tion, place the ammeter in series with a silver voltameter, and calibrate by the method described in 207, page 395. Second plan : Turn the commutator to series, connect the terminals of a cell of which the E. M. F. is known accurately, with the binding screws s and p s (Fig. 26, page 76). Let it be E volts, and let a reading a l on the ammeter be obtained. Take out the plug, seen to the left-hand side of Fig. 26, which has the effect of introducing a resistance of one ohm into the circuit when the commutator, as at present, is turned to series. Let the reading on the ammeter be now a 2 . The am- meter we will suppose to be so constructed that the angular deflection is proportional to the current (see 35, page 71), and to have been originally direct-reading; but from the permanent magnet having become, say, weakened since the instrument was adjusted, the readings are now Chap. VIII. 1 CALIBRATING COMMUTATOR METERS. 433 too large, so that K times the reading gives the current in amperes where K is a constant, less than unity, the value of which we have to determine. If r be the re- sistance of the cell, together with that of the instrument (both of which may be unknown), when ai] the coils are in series, the current in the first case is E amperes, and in the second case E amperes, E and - - = r+1 Eliminating the unknown resistance r, we have The soft iron cores F (Fig. 27, page 77) should now be adjusted until, on making the preceding experiment, K is found to equal unity, when the instrument will be pro- perly adjusted for both the "series" and "parallel" scales (Fig. 26, page 76). Of these two plans of calibration the first is more ac- curate than the second. 223. Calibrating a Commutator Voltmeter. A voltmeter is more sensitive when all the coils are in parallel than when they are in series ; hence, turn the commutator to parallel, and attach to the proper binding screws the terminals of a cell of known E. M. F. ; then, if b be the resistance of the cell, and r that of the volt- c c 434 PRACTICAL ELECTRICITY. [Chap. VIII. meter when all the coils are in parallel (both of which resistances may be unknown), the P. D. maintained at the terminals of the voltmeter will be E volts (see 128, page 224). r + b Remove the plug, which, in the case of a commutator voltmeter, inserts a resistance equal to that of the in- strument when all the coils are in parallel. The P. D. maintained at the terminals of the voltmeter is now 2r - E volts, but the P. D. at the terminals of the coils of the voltx meter, which is sending the current through them, is only r , E volts. Hence, if a^ and a z be the deflections produced in the two cases on the direct-reading voltmeter, and if we suppose that they require multiplying by an unknown constant K to convert them into volts, E = Koj, 2r + 6 eliminating the unknown resistances r and 6, wo have and, as in the case of the ammeter, the soft iron cores P (Fig. 27, page 77) must be adjusted until K equals unity. Chap. VHI.1 BEST RESISTANCE FOR GALVANOMETERS. 435 224. Best Resistance to give to a Galvanometer. The considerations given in 217, page 418, enable us to solve this question, for it was shown there that the magnetic effect produced by the coils of a galvanometer of given shape and size is proportional to G */g~ where G is the current flowing through the galvanometer, and g the resistance of the coils. Our object, now, is to see what should be the value of g, or, in other words, what gauge of wire should be used in winding the galvano- meter, in order that G = x 5*089 resistance 3 '6 = 2-827 watts ; the watts employed in) = 5.^9 - 2-827 heating the battery J = 2-262 watts. Example 115. What must be the resistance of a current generator so that 95 per cent, of the power pro- duced by it shall be given to the outside circuit, consist- ing of a simple conductor having a resistance of 35 ohms? TXT , 35 95 We have = , 35 + R 100 if R be the resistance of the generator \ .-. R = 1-842. Answer. 1'842 ohms. Example 116. If a Cardew's voltmeter be used to measure the P. D. of the incandescent lamp referred to in example 110, how many watts are absorbed in the voltmeter, and what is the ratio of the watts absorbed in the voltmeter to the watts used in the lamp 1 From Table I., page 154, we see that the resistance at C. of 13 feet of platinum-silver wire 0-0025 of an inch in diameter is 9-603 x 13 x 12 x 4 mi 7T X 0-00252 or if we assume that the resistance is increased by 5 per cent, by the elevation oi temperature, the resistance will 448 PRACTICAL ELECTRICITY. [Chap. IX. be 319 ohms Therefore the number of watts absorbed in the voltmeter equals or 3 7 "9 3 watts. 319 The number of watts used in the lamp is 77, therefore about half as many watts are absorbed in the voltmeter as are used in this lamp. 229. Current that Develops the Maximum Useful Power. The power used in heating a current genera- tor is generally entirely wasted, and, in addition, if allowed to become excessive, will prevent the generator working properly, whereas all the power given to the outside circuit may be utilised with proper arrangements. The problem of ascertaining the current that will develop maximum useful power may be solved either on the assumption that the generator is fixed and the external circuit variable, or on the assumption that it is the exter- nal circuit that is fixed, and the generator is the thing to be varied. 1st. Let the generator have fixed values of E and R (which will be the case for a battery, a set of accumula- tors, or a magneto-electric machine running at a constant speed, but not usually for a dynamo machine), then the equation P 2 = A(E-AR) shows us that we must determine the value of A that makes this expression a maximum, in order to find the current that develops the maximum useful power. To do this, give numerical values to E and B, and plot a curve, having the values of A for abscissae, and of PO for ordinates. Such a curve is shown in Fig. 171, the values of P 2 being calculated on the supposition that E and R are equal to 2 and 3 respectively, and it will be seen that the value of A that makes P 2 a maximum is A A Chap. IX. J MAXIMUM USEFUL POWER. 449 thai is, a current generator having a fixed E. M. F. and resistance gives maximum power to the external circuit, when that circuit is such that the current that flows is half the current that would flow if the generator were short-circuited. We do not say that the conductor must have a resist- ance equal to that of the generator, since, although this Fig. 171. will undoubtedly reduce the current to one-half if the out- side circuit be a simple conductor, there are other ways of reducing the current to one-half, such as the insertion of an opposing E. M. F. equal to half that of the generator. When A has the value given by the last equation, -2B' B E 450 PRACTICAL ELECTRICITY. (.Chap. IX. P - E2 Pl ~ni' and P = ; therefore, with a current generator having a fixed E. M. F. and resistance, maximum power will be given to the outside circuit when the power developed by the gene- rator is expended half in the outside circuit and half in heating the generator itself. On the other hand, maximum power will be deve- loped by the generator when maximum current flows through it that is, when the generator is short-cir- cuited. 2nd. Let the external circuit consist of a simple con- ductor, and let its resistance be fixed and equal to r ohms ; also let the current generator be a battery con- sisting of a fixed number of cells N, each having an E. M. F. of e volts, and a resistance of b ohms. Then, since the power developed in the external circuit equals the square of the current into r, and since r is a constant, it follows that the arrangement of cells that will give maximum power to the external circuit, is that which will produce the maximum current. Now, this arrange- ment we have seen ( 136, page 245), is that which makes the resistance of the battery equal to the ex- ternal resistance. Hence, the arrangement of a given number of cells that gives maximum power to a simple conductor having a fixed resistance, is that which makes the resistance of the battery equal to the resistance of the conductor. With this arrangement of cells, it is easy to see that the power developed by the battery will be twice that given to the external circuit, one-half being wasted in heating the battery. But this arrangement of cells will not, as a rule, make the power developed by the battery Chap. IX.] EFFICIENCY. 451 a maximum. For, as shown in 136, page 244, the cur- rent equals se -^y amperes, r + - N and, therefore, the power developed by the battery equals 22 watts, which equals and this obviously has its least practical value when * equals unity, that is, when all the cells are in parallel, and has its largest practical value when s equals N, that is when all the cells are in series. Hence, if the resist- ance of the outside circuit be less than that of the battery, putting all the cells in series will not only give less power to the outside circuit than if the cells be so arranged that the battery resistance is equal to that of the outside circuit, but it will waste much more power, since the total power produced by the battery will be greater. 230. Efficiency. The "efficiency" of a system con- sisting of a current generator supplying power to an out- side circuit, is the ratio of the power given to the outside circuit to that developed by the generator. From the equations P = A E, P 2 = A(E-AR), we see that in all cases the efficiency equals E-AR ~E~ J 452 PRACTICAL ELECTRICITY. [Chap. IX. hence, the efficiency will be the greater the larger we make E, and the smaller we make A and K. From 229 we see that if we wish a current genera- tor having a given E. M. F. and resistance to develop as much power as possible in the outside circuit, we arrange matters so that the current is half that which would be produced if the generator were short-circuited, or, what is the same thing, so that half the power is wasted in the generator itself ; hence, when a Grove's battery is employed to produce a bright electric light, we regulate the lamp so that the P. D. at its terminals is half the E. M. F. of the battery. Whereas we have just seen that if we wish a current generator to give power econo- mically to the outside circuit, we employ a generator having a very large E. M. F., and allow it to produce only a small current ; hence, in the recent electric transmission of 50 horse-power by M. Deprez from Creil to Paris, a distance of about 37 miles, he employed an E. M. F. of between 6,000 and 7,000 volts, and a current of only 10 amperes. 231. Measuring the Efficiency of an Electric Light. The "efficiency of an electric light" is the ratio of the illuminating power of the light to the watts supplied to it. To measure the illuminating power we use a "photo- meter" the simplest, and at the same time one of the most accurate, being that designed by Rumford. A form of " Rumford' s photometer" is seen in Fig. 172, E being the electric light, an incandescent lamp, for example, held in a convenient adjustable holder H, and c a " standard candle" which is a special form of candle made so as to bum 120 grains of spermaceti wax per hour.* The lamp is placed at a convenient distance e from the screen s, which is covered with a sheet of white blotting * For rough experiments on illuminating power, No. 8 sperm candles, costing lid. per pound, may be used satisfactorily instead of standard candles costing 2s. 9d. per pound, since experiments show the No. 8 sperm candles do not differ much more from one another, or from a standard candle, in illuminating power, than standard candles are said to differ among themselves. Chap. IX.] EFFICIENCY OF ELECTRIC LIGHT. 453 paper, and the candle is moved backwards and forwards along the graduated arm G G, until, by trial, a position for it is found, at a distance, c, say, from the screen, such that the two shadows cast by a vertical rod of blackened wood R, about the thickness of an ordinary pencil, and fixed at about two inches from the screen, appear to Fig. 172. be equally dark. Under these circumstances, as the portion of the screen not in shadow is illuminated by both sources of light, whereas the two parts in shadow are each illuminated by only one, and as the screen s and the rod R are so placed that lines drawn through the rod and through each of the lights make equal angles with the screen, it follows that, when the shadows are equally dark, the quantities of light falling on a square inch of the screen, due to each of the lights, are equal to one another, hence the illuminating power of the electric light _ e* standard candle c 2 454 PRACTICAL ELECTRICITY. [Chap. EX. The correct position of the candle which produces equality in the darkness of the shadows can be best detected not by gradually moving the candle continuously towards or away from the screen, but by trying to find a position such that, if the candle be put a little nearer, one of the shadows becomes distinctly too dark, whereas if it be put a little farther away, that one of the shadows becomes distinctly too light. The current passing through the lamp is measured by an ammeter A, and the P. D. maintained at the lamp terminals by the voltmeter v, the product of the amperes and the volts giving P, the watts furnished to the lamp. Hence, the efficiency of the lamp equals e* 232. Dispersion Photometer. In the preceding sec- tion we have spoken of one type of electric lamp the incandescent one. This consists of a hermetically sealed glass bulb (see note, 10, page 20) containing usually a very fine filament of carbon, which becomes luminous when a suitable current passes through it, but does not burn away as there is a very perfect vacuum inside the glass bulb. But there is a much more powerful electric light the arc light, in which the light is produced by a current passing between two pieces of carbon slightly separated from one another, the resistance of the heated air between the carbons taking the place of that of the carbon filament in the incandescent lamp. As an arc light has often an illuminating power of several thousand candles, it would have to be put many feet away from the screen of the photometer in order that the light cast by it on a given area should be equal to that produced by the standard candle. To avoid the inconvenience of having to put an arc light so far away from the screen, the " dispersion photometer " shown in Fig. 173 was de- vised by the author. Instead of the light from the CLap. IX. J DISPERSION PHOTOMETER. 455 electric lamp being allowed to fall directly on the screen, it is allowed to pass through a double concave lens L,* which disperses the light, so that the screen is illumi- nated by only a small fraction of the light that would come to it from the powerful electric lamp if the lens L Fig. 173. were removed. Let the electric light and the lens be at distances e and I respectively from the screen, and, when the standard candle is at a distance c from the screen, let the shadows be equally dark, then the light from the electric lamp which would have illuminated an area A (Fig. 174) is now dispersed so as to illuminate a much larger area A', so that the illuminating power of the electric light _ A' e 2 ,, standard candle A c 2 To find the ratio of A' to A, let a be the area of * Dr. J. Hopkinson uses a double convex lens, and forms a real image of the electric arc between the lens and the screen. 456 PRACTICAL ELECTRICITY. [Chap. IX. the double concave lens filled by the pencil of light which would have illuminated the area A, and let the Fig. 174. light after dispersion appear to come from a distance x behind the lens, then A_ # a~(e- I)*' A' _ (/ 4. g) a ~ a* ' and - o . f+e-l where / is the "focal length " of the lens that is, the distance from the lens of the point from which light, after passing through the lens, would appear to come if the source of light were very far away, like the sun. Hence, eliminating a and x from the preceding three equations, we have the illuminating power of the electric light standard candle ( l(e c? f 'Y- Chap. IX.] DISPERSION PHOTOMETER. 457 A great difficulty in comparing an electric light with a candle arises from the difference in colour of these two sources of light, an arc light being much bluer than a candle. To partially overcome this difficulty, two dis- tinct comparisons of the electric light with the candle should be made when the screen is looked at succes- sively through green and red glass. Pieces of what are known in the trade as signal green and ruby red answer very well for this purpose, but they should be selected so that a bright light is hardly visible when looked at through the two pieces placed one over the other, as then the green glass allows practically no red, and the red glass practically no green light to pass. The two comparisons made with green and red glass will give very different results for the illuminating power of a powerful arc light in terms of that of a candle, because the ratio of green to red rays in the former is so much larger than in the latter. It is important to be able to measure the illuminating power of an arc lamp, not merely in a horizontal plane, but for rays making various angles with the horizontal. This can be conveniently done by placing the arc lamp so that its rays come in any desired direction to the mirror M (Fig. 173), and turning the mirror, with the gra- duated disc D attached to it, until the rays pass through the concave lens L, and fall properly on to the screen s. The angle that the beam of light under observation now makes with the horizontal plane at the electric light, can be read off directly by the position of the graduated disc. By causing the mirror M to turn about an axis which makes an angle of 45 with its plane, the light reflected from it always makes the same angle with its sur- face when it passes after reflection through the lens, hence the portion of the light absorbed by the mirror is con- stant, and may be determined once for all experimentally. So also the portion of the light absorbed by the lens will be constant, and may be determined experimentally, and both these fractions can easily be allowed for in any 458 PRACTICAL ELECTRICITY. [Chap. IX. measurements made of the illuminating power of an arc lamp. 233. Efficiency and Life of Incandescent Lamps. The heat produced per second in a conductor is propor- tional to the square of the current passing through it (see 113, page 198), and is therefore proportional to the product of the current into the P. D. maintained at the ends of the conductor that is, to the number of watts given to it. The temperature of the conductor will de- pend on the heat produced in it per second, and on its facility for cooling (see 111, page 1 95). But experiments show that the light emitted by a body increases very much more rapidly than the heat given to it per second ; for example, the heat given to a kettle of boiling water per second may be considerable, but is not sufficient to cause the kettle to emit any light at all, whereas if the metal of the kettle be made a good deal hotter, it will begin to glow and commence emitting light, and when it becomes white-hot, the light emitted will be considerable. So it is found that the light emitted by an electric lamp increases much more rapidly than the watts given to it that is, the efficiency increases with the power supplied to it. As far then as the cost of producing the power is con- cerned, it is more economical to cause the carbon of an electric lamp to have an intensely white-hot temperature than merely to allow it to glow at a dull red heat. But, on the other hand, the number of hours during which an incandescent lamp can be used before the carbon filament breaks, depends on the temperature of the filament. If the temperature be kept always low enough, the filament will last for several thousands of hours, the lamp emitting light all the time, whereas if the temperature be too high, the life will be reduced to a few hundred, or less number of hours. Hence it is an important question to decide how bright we should make the filament of an incandes- cent lamp when in use, or, in other words, what P. D. we should maintain at its terminals. This question is one that must be solved for each particular case, depending on Chap.ZX.] EFFICIENCY AND LIFE OF LAMPS. 459 the efficiency and life of the lamp for different P. Ds., on the cost of a new lamp, and on the cost of power at the particular place where the lamp is used.* Example 117. If power cost .15 per horse-power per annum supplied for 5 hours per night, and if a new incandescent lamp cost 3s., further, if when used so as to require only 2-J watts per candle it lasts for 500 hours, whereas when used with a lower P. D. at its ter- minals it requires 3J watts per candle, but lasts 1,500 hours, determine which is the more economical of the two modes of using the lamp r \ Eirst case : Cost for power per candle _ 15 x 20 x 2^ ,.,, . per hour ~ 746 x 5 x 3G5 S Cost for lamp renewals per 3 candle per hour = JJQQ shlllin g s ' Total cost per candle per = . OQ655 shim hour Second case : Cost for power per candle _ 15 x 20 x 3^ , .,,. per hour ~ 746 x 5 x 365 S Cost for lamp renewals per 3 candle per hour ^^ shillings, Totdcost per candle per = . OQ272 therefore using the smaller P. D., and the larger number of watts per candle, is much the more economical arrange- ment. Example 118. An arc lamp through which 8 am- peres are passing, and at the terminals of which 50 volts * See ''The Most Economical Potential Difference to employ with Incandescent Lamps." Phil. Mag. t April, 1885. 460 PRACTICAL ELECTRICITY. [Chap. IX. are maintained, produces 750 candles, while an incandes- cent lamp through which 0'6 of an ampere is passing, and at the terminals of which 70 volts are maintained, produces 17 candles. Compare the efficiency in the two cases. 750 or about 1 9 candle For the arc lamp the efficiency is per watt For the incandescent lamp the 17 or about 0*45 efficiency is Q.g x ^Q candle per watt, therefore the efficiency of the arc lamp is more than four times that of the incandescent. Example 1 1 9. A battery having a resistance of 4 ohms, and an E. M. F. of 30 volts, is sending a current through an outside circuit consisting of leading wires having a resistance of 1 ohm and 4 incandescent lamps arranged in parallel, and at the terminals of which 12 volts are maintained. If each lamp produces 3^ candles, calculate the efficiency of the arrangement. The current = 3Q ~ 12 4+ 1 = 3-6 amperes. The power produced by the battery = 3-6 x 30 = 108 watts. The power wasted in the battery = (3'6) 2 x 4 = 5 1-84 watts. The power wasted in the leading wires = (3-6) 2 X 1 = 12-96 watta Chaix IX. I THE JOULE. 461 The power given to the 4 lamps in __ v 19 i -, i -^ O O X 1 *J parallel = 43-2 watts. Therefore, of the 108 watts produced by the battery, 64'8 watts, or 60 per cent., are spent uselessly in heating the battery and leading wires; 43-2 watts, or 40 per cent of the total power, are given to the lamps ; and, as 4 X 3J or 14 candles' illumination is produced, the effi- ciency of the lamps is 0'324 candles per watt. When a power of 1 watt is being developed the work done per second is sometimes called a "joule" Hence 1 joule equals 0-7375 foot pounds. And 1 watt -second = 1 joule. 1 watt-minute = 60 joules. 1 horse-power hour = 1,980,000 foot pounds. ^ 2,685,600 joules. 462 APPENDIX TO THE SECTION ON SHUNTS. 234. Kirchhoff's First Law 235. Kirchhoffs Second Law 236. Current through the Galvanometer of a Wheatstone's Bridge 237. Best Resistance for the Galvanometer with a Wheatstone's Bridge 238. Best Arrangement of the Battery and Galvanometer with a Wheatstone's Bridge 239. Measuring a Resistance contain- ing an E. M. F. IN the case of even a somewhat complicated circuit like that shown in Fig. 175, there is no difficulty in cal- culating the current flowing in every part, if we use the principles developed in 103, page 177, and in 137, page 253, to solve the problem step by step. Let capital letters stand for the currents flowing in the several branches, and small letters for the resistances of these branches ; let x be the resistance between the points 1 and 2, and y that between 3 and 4, and let E be the E. M. F. of the battery ; then = 9 s x = CALCULATING CURRENTS IN COMPLEX CIRCUITS, 463 E B = b + p + q + T = x + r x + r + B, G = S = + g + * R, B, Hence, the currents B, T, R, G, and S are expressed in terms of E, and the various resistances b, p, q, t, r, g, and s. But if we try to do the same thing for the circuit shown in Fig. 176, and which at first sight appears Fig. 176. equally simple, it will be seen that the method previously employed is inapplicable. We may say that E B = resistance between 1 and 4 464 PRACTICAL ELECTRICITY. but how are we to express the resistance between the points 1 and 4 in terms of p, q, r, 8, and g. To do this we require to use what are known as " Kirchhoff's first and second laws" 234. Kirchhoffs First Law. This is very simple, and merely expresses the fact that if there is one current B (Fig. 176) that flows towards a point 1, and two currents P and Q that flow away from this point B = P + Q . . . . (1) Similarly, P = G + R . . . . (2) S = G+Q . . . . (3) B = R+S These equations are not, however, all independent, as any one could be obtained from the other three. KirchhofFs first law is sometimes stated thus : Tlie algebraical sum of all the currents meeting at a point is nought, the " algebraical " sum meaning that the currents that flow away from the point must be taken with a negative sign if those flowing towards it be taken with a positive sign, or vice versa. 235. Kirchhoff's Second Law. In any closed cir- cuit the algebraical sum of the products of the currents into the resistances equals the E. M. F. in the circuit. In using this law the currents are to be taken with a positive or a negative sign according as they flow in the same or in opposite directions round a circuit ; and the E. M. F. is to be taken with a positive or a negative sign according as it assists or opposes the currents that are arbitrarily taken as positive. Let Vj, V 2 , V 8 , &c., be the P. Ds. at the points 1, 2, 3, &c., then from Ohm's law (see 74, page 130) it follows that Pp = V, - V, Grg = V, - V 3 , Q 9 = V, -V,, . -. Pp + Gg - Q ? = . . . . (4) KIBCHHOFP'S LAWS. 465 Similarly, Rr = V 2 - V 4 , Gg= V 2 -V 3 , Ss = Y 3 .- V 4 , . . G^ + Ss- Rr = . . . . (5) As to the circuit containing the battery and the points 1, 3, 4, Q?= V x - V* S* = Y 3 - Y 4 , B6= E -(V^V^, (000 116, [page 205). *'. Q^ -}- Ss + B& = E . . . . (6) Three independent equations (1), (2), (3), therefore, may be obtained by using Kirchhoff 's first law, and three more (4), (5), (6), by using his second law, or six equa- tions altogether. From these the six currents B, P, Q, B, S, and G can be found in terms of E, the E. M. F. of the battery, and the six resistances 6, />, { 9 (P + <1 + r+s) + (p +q) (r + s)} + g (p +r)(q + s) + r (p + q) (q + ) - q (q r - p s) And this we see equals nought when qr = pa, * A very convenient method based on Kirchhoff 's laws, but in- volving the use of determinants for solving such questions, was sug- gested by the late Professor Clerk Maxwell, and has been recently extended by Dr. Fleming in the Proc. Phys. Soc., voL vii., part 3, page 215. E 466 PRACTICAL ELECTRICITY, i.e. when ^ = 1 q s This result for the law of the Wheatstone's bridge was much more simply obtained in 97, page 167, but the method there employed for arriving at the connection that existed between the resistances when no current was passing through the galvanometer, gave us no indication as to what the current would be if this connection between the resistances were not fulfilled. If q r equals p s there will be no current through the galvanometer, whatever be its resistance, or however it be constructed; but as our only method of insuring that qr shall be equal to ps, is by varying one or more of the resistances until no visible de- flection is observed on the galvanometer, it is important to construct the galvanometer so that the needle will deflect even when there is a very small difference between q r and p s. The proper wire to wind on the galvanometer bobbins may be calculated from the formula given in 98, page 171 ; and that formula, as will be seen in the next section, can be obtained by multiplying the >J~g (which we know from 217, page 418, is proportional to the sensibility of the galvanometer) by the value of G given above when q r p s has a fixed small value, and seeing what is the relationship between g and p, q, r t and s that makes G */g a maximum. 237. Best Resistance for the Galvanometer with a Wheatstone's Bridge. If G be the current passing through the galvanometer of a Wheatstone's bridge, and g be its resistance, the magnetic effect, which is propor- tional to GV/^~ is, from the last section, proportional to ~&(qr-ps) Jg _ + { 6 (P + q + r + s) + (p + r) (q + )} Now this expression is of the form ax BEST RESISTANCE FOR BRIDGE GALVANOMETER. 467 where a, 6, and c are constants, and x is the variable, and such an expression we saw in 136, page 245, is a maximum when Therefore it follows that G/will be a maximum when _ b (p + q) (r + s) + r (p + q) (q + s) q (qr p s) b(p + q +r + s) + (p + r)(q +s) But we want to find the best value to give to g when balance is nearly established, that is, when q r is nearly equal to p s, since that is when it is most important to have the galvanometer sensitive, hence we may assume that q r equals p s in the preceding expression for g. Under these circumstances we find that _ b q (r + s) 2 + q r (r + s) (q + s) b (r + s) (q + *) + r (q + ) _ r + s b (r + s) + r (q + g) ' q + 8 ' b (r + s) + r (q + s) ' And this when q r equals p s is the same as (p + q) (* + *)' p +.q + r + s ' which is therefore the best resistance to give to the gal- vanometer. 238. Best Arrangement of the Battery and Galvano- meter with a Wheatstone's Bridge. We have seen, in 97, page 167, that when balance is obtained the battery and galvanometer may be interchanged without disturbing the balance. But when balance has not been obtained a greater current will pass through the galvanometer when it and the battery are arranged one way than will pass when the galvanometer and the battery are interchanged. 468 PRACTICAL ELECTRICITY. In other words, one arrangement is more sensitive than the other, and the object of the following is to ascertain which is the more sensitive arrangement. As we are dealing with a definite galvanometer of fixed resistance, we are merely concerned with the current, and need not consider the magnetic effect. Let G T be the current passing through the galvanometer when it and the battery are placed as shown in Fig. 176, page 463, and let G 2 be the current when the galvanometer and battery are interchanged, then -s (pa -qr) and the value of G x is given in 236, page 465. Hence _ G ~ where D T and D 2 stand respectively for the denominators of G! and G 2 . Simplifying, we have to - 1st. Let g be greater than b. Then G l G 2 will be positive, that is, the first arrangement will be more sen- sitive than the second, when p and r are respectively both greater or both less than 8 and q. Therefore ike galvanometer sltould connect the junction of the two greater resistances with the junction of the two less. 2nd. Let b be greater than g. Then Gj G 2 will be positive, or the first arrangement will be more sensitive than the second, when p is greater than s, and r is less than q, or when p is less than s, and r is greater than q. Therefore tJie battery should connect the junction of the two greater resistances with the junction of the two less. MEASURING RESISTANCE CONTAINING E. M. P. 469 239. Measuring a Resistance containing an E. M. P. If in one of the branches 3 4 of the Wheatstone's bridge (Fig. 177) there be an opposing E. M. F. of e volts, Kirch- . 177. hoff s second law tells us that equation (5) ( 235, page 465) becomes G^ + Ss- R?= - e y and equation (6) becomes Q q + S s + B b = E - e ; the other four equations remaining as before. Using these equations we now find that E(?r -ps) - e + ff(p + r ) (q + s ) + r (p + q) (? + s ) - q ( p + Q' q - Gg = (6) R'r + S'* -f- Gff = e (7) Fig. 179. From equations (2) and (6) we have . . . 0) and from equations (3) and (7) (R- R')r = (S' - R)s . . o (9) From equations (1) and (o) it follows that P - F R - R', and from equations (1) and (4) that Q' _ p - S' - R, EXAMPLES. 473 therefore substituting these Tallies in equations (8) and (9) we have Example 121. A battery having an E. M. F. of 3J volts and a resistance of '2^ ohms, is employed in sending a current through a circuit consisting of a resistance of 1,234 ohms in series with a galvanometer of 52 ohms' Fig. 180. resistance, shunted with a shunt of 4J ohms' resistance, containing an opposing E. M. F of 1 volt. What is the current flowing through the galvanometer 1 The arrangement of the circuit is shown in Fig. 180, and if B, G, and S be the currents in amperes flowing respectively through the battery, the galvanometer, and the shunt, we have by KirchhofFs first and second laws, B = S + G, (2J + 1,234) B + 52 G = 3J, 52 G- 4J-S = 1. 474 PRACTICAL ELECTRICITY.. Eliminating B and S from these three equations, we find G = O01786. Answer. 0-01786 amperes. Example 122. What E. M. F. must be inserted in the shunt in the last question so that no current shall pass through the shunt ? Let e be this E. M. F. in volts, then we must find the value of e that makes S equal to nought in the following eqiiations : B = S + G, 1,236 J B + 52 G = 3 J, 52 G 4J S = e. Putting S equal to nought we have 1,288JG= 3J, 52 G = e, . . e = 4 * oa yolts> 1,288J Answer. 0-1413 volts. This question may be solved differently thus : If no current passes through the shunt, the E. M. F. must be equal and opposite to the P. D. that would be produced between the terminals of the galvanometer if there were no shunt circuit at all, and this we know, from 1 1 5, page 204, is equal to the E. M. F. of the battery multi- plied by the ratio of the resistance of the galvanometer to that of the whole of the circuit, or __ t-L x 3i volts, 1,2881 the same expression that is given above for &. EXAMPLES. 475 Example 123. Does the presence of the shunt in example 121 increase or diminish the current that would pass through the galvanometer if there were no shunt circuit, and by what amount is the galvanometer current varied 1 If there were no shunt the current through the galvanometer would be -* , or 0-002717 amperes. 1.288J We see, therefore, that the shunt in this particular case, in consequence of the E. M. F. in it, actually in- creases the galvanometer current by 0-01786 - 0-002717, or 15-thousandths of an ampere. 47f> Specimens of Instructions for Experiments. CITY AND GUILDS OF LONDON INSTITUTE. CENTRAL INSTITUTION. PHYSICAL DEPARTMENT. To compare the amount of CHEMICAL DECOMPOSITION produced per second by a current with the corre- sponding DEFLECTION of a TANGENT GALVANO- METER. PRELIMINARY. The current passing through the volta- meter and galvanometer can be varied by altering the resistance in circuit. The value of the resistance need not be known. When the clip is firmly fixed on the small piece of indiavubber tube, the gas evolved by passing a current through the voltameter cannot escape, and so the pressure inside becomes greater than the atmospheric pressure, and forces the liquid up the glass tube. The rate at which the liquid rises in the tube is a measure of the amount of gas evolved per second. Releasing the clip allows the gas to escape. The volume of the tube be- tween the two marks and 7 is 2-284 cubic centimetres. EXPERIMENTS. (1.) Adjust the needle of the galva- nometer to zero by slightly turning the instrument. (2.) Send a current through the apparatus by pressing the key, and open the clip so that the gas escapes. Keep the key pressed for a few minutes, until the liquid be- comes thoroughly saturated with gas. Now close the INSTRUCTIONS FOR EXPERIMENTS. 477 clip, and note the interval of time it takes for the liquid to rise from the lowest to the highest mark on the tube ; also note the steady deflection of the galvanometer.* (3.) Vary the current by altering the resistance in circuit, and repeat the observation mentioned in (2). (4.) Repeat (3) with as many different strengths of currents as possible. (5.) Tabulate your results in a convenient form. (6.) Draw a curve having for abscissae the quantity of gas evolved per second, and for ordinates the tangents of the corresponding deflections of the galvanometer. DEDUCTIONS. Write out clearly all the inferences which can be drawn from this experiment, assuming that the strengths of currents are proportional to the amount of chemical decomposition which they produce per second. Determine the constant a of the galvanometer such that A = a tan. d, where A is the current in amperes and d the deflection it produces, having given that 1 ampere liberates 0*1738 c.c. of mixed gas per second, when measured at C. and 760 rn.m. pressure. State clearly the corrections which would have to be applied in making accurate determinations of current strength by this method. * It is desirable to make two or three determinations with each particular current, and take the mean- 478 PRACTICAL ELECTRICITY. CITY AND GUILDS OF LONDON INSTITUTE. CENTRAL INSTITUTION. PHYSICAL DEPARTMENT. EXPERIMENTS on SHUNTS. PRELIMINARY.- When the current to be measured in any circuit is too large for the galvanometer available to measure it, only a known fraction of the current is passed through the galvanometer, the remainder being passed from one terminal of the galvanometer to the other through a " by-pass " or " shunt " circuit. As, however, the introduction of this shunt circuit lessens the resist- ance between the terminals of the galvanometer, and therefore the total resistance used in the experiment, the main current is increased. Thus it may happen that the effect of shunting a galvanometer is to scarcely diminish the current passing through it. The following experiments have been devised to make the student practically acquainted with the effect of shunting a galvanometer, and the manner in which the effect of a given shunt depends on the resistance in the other parts of the circuit. The resistance of the galvanometer circuit unshunted is about 200 ohms. EXPERIMENTS. (1.) Using one cell of the battery, and with no resistance in the main circuit excepting that of galvanometer, battery, and connecting wires, send a current through the unshunted galvanometer and note the deflection d produced. (2.) Place various resistances from the highest avail- able down to in the shunt circuit, and note all the corresponding deflections. (3.) Tabulate your results in some convenient form. INSTRUCTIONS FOR EXPERIMENTS. 479 (4.) Plot a curve having for abscissae the resistances in the shunt circuit, and for ordinates the corresponding currents passing through the galvanometer. (5.) Join up two cells of the battery, and introduce such a resistance into the main circuit as will give the same deflection d as was obtained in (1) when the galva- nometer was unshunted. (6.) Repeat (2), (3), (4), drawing the curve on the same sheet of paper. (7.) Repeat (5) and (6), using four and six cells re- spectively. DEDUCTIONS. Write out a clear account of the in- ferences which you can draw from these experiments. Also determine algebraically the general equation to, and charac- ter of, the curves obtained in these experiments, and show how the results obtained experimentally could be deduced from this equation. Prove that the curves have a common asymptote, and find the limits between which the other asymptotes lie. 480 PRACTICAL ELECTRICITY. CITY AND GUILDS OF LONDON INSTITUTE. CENTRAL INSTITUTION. PHYSICAL DEPARTMENT. To CALIBRATE an AMMETER by the CALORIMETRIC METHOD. PRELIMINARY. The calorimeter provided consists of a thin copper vessel supported within an air space, and screened from external radiation by a large water jacket. A coil of German silver wire is inserted in the calori- meter, and surrounds the bulb of a delicate thermometer. This thermometer serves to show the rise of temperature of the water and calorimeter caused by passing a current through the wire. Another thermometer indicates the temperature of the large water jacket in which it is im- mersed. EXPERIMENTS. (1.) Carefully dry and weigh the small copper calorimeter, the approximate weight of which is 24-8 grammes. (2.) Partly fill the calorimeter with distilled water by means of the pipette provided, and determine the weight of the water added. (3.) Replace the calorimeter within the water jacket and connect the wires to the ends of the coil. Adjust the pointer of the ammeter to zero (if necessary) by turn- ing the small milled head at the top. (4.) Complete the circuit, and adjust the carbon re- sistance till a suitable deflection is obtained on the am- meter, say 0*8, which must be maintained constant. Keep the water well agitated by means of the stirrer, and take " time readings " (about every half-minute) of the temperatures of the inner and outer vessels, until the inner thermometer has risen several degrees. Break the circuit. INSTRUCTIONS FOR EXPERIMENTS. 481 (5.) Tabulate your results in a convenient form. (6.) Plot a curve having times for abscissae and tem- peratures of the calorimeter for ordinates. (7.) Repeat (4), (5), (6), using successively currents which produce deflections of about 1*1, 1-4, 1*7, and 2-Q on the ammeter. (8.) When all the heating observations have been taken, break the circuit, and allow the calorimeter to cool to nearly its initial temperature, and take time readings of its temperature, keeping the water well stirred all the while. (9.) Plot a " cooling curve " from the observations obtained in (8). (10.) Correct the heating curves obtained in (6) and (7) by the cooling curve (9). and determine the corrected rise of temperature in a given time (say five minutes). (11.) Calculate the strength of current passing in each of the above experiments from the formula A / V 0-24 : where A stands for the current in amperes, r resistance of the coil in ohms, which is 1-0306 at 15'6 C. W weight of the water in grammes, ,, w water-equivalent of the calori- meter, thermometer, &c., which equals 2-778 grammes, T corrected rise of temperature in t seconds, t time in seconds, and compare the values so obtained with the graduations of the ammeter. DEDUCTIONS. State clearly how the heating curves are corrected from the cooling curve so as to show what would have been the true rise of temperature if no cooling had taken place during the experiment. F P 482 PRACTICAL ELECTRICITY. CITY AND GUILDS OF LONDON INSTITUTE CENTRAL INSTITUTION. PHYSICAL DEPARTMENT. To CALIBRATE an AMMETER by means of a SILVER VOLTAMETER. PRELIMINARY. The voltameter consists of a platinum dish containing a 25 per cent, solution of silver nitrate, and in which a silver plate is immersed. An adjustable carbon resistance is provided, by means of which the cur- rent passing through the voltameter can be maintained constant during each experiment, and can be varied in the different experiments. EXPERIMENTS. (1.) Carefully clean, dry, and weigh the platinum dish, the approximate weight of which is 78 grammes. (2.) Pour the solution of silver nitrate into the dish and place it on the three brass pins provided for its re- ception, and which are electrically connected with the left-hand binding screw on the board. Immerse the silver plate in the solution, and clamp it in such a posi- tion that its edges are equally distant from the sides and bottom of the dish. (3.) Turn the small milled head at the top of the ammeter so that the pointer of the ammeter comes oppo- site the zero on the scale, if not there already. Place the copper connecting wire in the mercury cups marked A and C (which cuts out the voltameter), and adjust the carbon resistance until a convenient current flows round the ammeter. Remove the connecting wire. (4.) Quickly insert the connecting wire in the mer- cury cups marked A and B, carefully noting the instant at which the circuit was completed. Allow the current INSTRUCTIONS FOR EXPERIMENTS. 483 to pass for a convenient time (10 to 30 minutes, accord- ing to the strength of current used), and keep the current constant by the adjustable resistance. Note the tem- perature of the room during the experiment, and, at the end of the interval decided on, quickly break the circuit. (5.) Empty the solution from the dish into its bottle and carefully wash the deposited silver with distilled water. Then fill the dish with distilled water and allow it to stand 10 to 15 minutes. Again wash with water, alcohol, and ether, dry over the spirit-lamp, and cool in the desiccator. (6.) Carefully determine the increase of weight due to the silver deposited on the dish. (7.) Calculate the strength of current used in the experiment, assuming thafc one ampere deposits I'll 81 5 milligrammes of silver per second. (8.) Repeat the experiment with several different strengths of current. (9.) Tabulate your results in some convenient form and write them with your name on the card, on which you will find recorded the results of previous experiments. INDEX. ABSOLUTE Calibration, Galva- " nometers with Invariable, 57 Calibration of Galvanometers, 30, 395400 Calibration of a Galvanometer Meaning of, 22 Calibration of Potential Differ- ence Galvanometers, 127, 408415 Calibration, Portable Galvano- meter with Approximate, 6971 Electrometer, 93 Measurement of Capacity, 327 Units, 141 Accumulating Influence Machines, 361 ; Holtz's, 367 ; Nichol- son's, 366 ; Thomson's, 364 ; Varley's, 367; Voss, 367; Wimshurst, 367. (Sc-e also Influence Machines.) Accumulator, Measuring Resistance of, 206 Accumulators, Small Internal Re- sistance of, 206, 261 Accuracy of Graduation, Testing Ammeters for, 395 of Graduation, Testing Volt- meters for, 408 of Readings with Tangent and Degree Scales Compared,40 Acid, Dihite Sulphuric, Effect of Electrolysis of, 15 Sulphuric, Voltameter. (See Sulphuric Acid Volta- meter.) Action, Inductive, 87 ', of the Electrophorus, 3^6361 Adjustment for Sensibility in\Mag- nifying Spring Ammeters and Voltmeters, 389 of Coil of Tangent Galvano- meter, 46 Advantage of PoggendorfFs Method of Comparing Electro- motive Forces, 236 Advantages of Cardew's Voltmeter, 426 of Cunynghame's Ammeter and Voltmeter, 385 of Electro-Magnetic Control Meters, 394 Advantages of Gravity Control Meters, 391 of Magnifying Spring Ammeter and Voltmeter, 390 ->f Permanent Magnet Meters,78 o*' Shielded, Dead -Beat, Di- rect-Reading Galvanome- ters, 78 of Siemens' Electro-Dynamo- meter, 380 of Thomson's Large Current Galvanometer, 53 Relative, of Voltameters and Galvanometers, 20 Air Condenser, Standard, 334 Specific Inductive Capacity of, at Different Pressures, 310 Alternating Currents, Definition, and Measurement of, 198, 381 Potential Difference Increases Practical Resistance of Voltmeter, 427 Potential Difference, Measur- ing, 426 Aluminium, Resistance of, for Given Length and Diameter, or for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Amalgam, Definition of, 218 Amalgamate, How to, 218 Ammeter, Advantages and Disad- vantages of Cunynghame's, 38o Advantages and Disadvantage of Permanent Magnet, 78, 376 Advantages and Disadvantage of Magnifying Spring, 390 Adjustment for Sensibility in Magnifying Spring, 389 Calibrating Commutator, 432 Commutator,Description of ,427 Commutator, Safety Arrange- ment with, 432 Cunynghame's Description of, 382 Graduation of Cunynghame's, 385 for Large Currents, Use of Commutator in Calibrating* 428-431 486 PRACTICAL ELECTRICITY. Ammeter, Indication of Direction of Current in Magnifying Spring, 389 Magnifying Spring, Description of, 386 Permanent Magnet, Descrip- tion of, 76 Permanent Magnet, Propor- tional, 71 Ratio of Sensibilities of Com- mutator in Parallel, and in Series, 431 Ammeters, 76 79, 382, 386. (See also Meters.) Calibrating, by the Silver De- posit Method, 395-400 Testing, 394 Testing, for Accuracy of Gra- duation, 395 400 Testing, for Error on Reversing Current, 402 Testing, for Error Produced by External Masrnetic Dis- turbance, 403407 Testing, for Permanent Altera- tion of Sensibility, 407 Testing, for Residual Mag- netism, 400 with Magnifying Gearing, 386. (See also Dynamometer, Galvanometer. ) Amount of a Body's Electrification, 109 of Electricity, Dependence of Potential of Conductor Partly on, 119 of Heat produced per Minute by Given Current Flowing through Given Resistance, 199 - of Heat produced per Minute, Measurement of Currents by, 197 Ampere, Definition of the, 11 Amperes, Values in, of Deflections of Tangent Galvanometer, Controlled only by Earth's Magnetism, 55 Angles, Finding, from their Tan- gents by means of Squared Paper, 56 Finding Tangents from, by means of Squared Paper, 57 Angular Deflection of a Mirror, Connection between, and Motion of Image on Plane Scale, 107 Deflection Proportional to Cur- rent, Construction of Gal- vanometers with, 71 73 Motion of Reflected Ray is Twice Angular Motion of Mirror, 106 Antimony, Change of Resistance of, with Temperature, 160 Resistance of, for Given Length and Diameter, and for given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Apparatus for Measuring Variation of Current and Potential Difference at Battery Ter- minals with Variation of External Resistance, 205 Static Electric, Necessary En- closure of, in Metallic Case, 108 Apparent Increase of Resistance in a Galvanometer Due to Damping, 349 Approximate Absolute Calibration, Portable Galvanometer with, 6971 Arc, Electric, Description of, 188, 454 Electric, Measuring Illuminat- ing Power of, in Any Plane, 457 Light, How to Overcome Differ- ence in Colour between it and Candle when Measur- ing, 457 Light, Measuring the Efficiency of, 455 Potential Difference Required to Maintain an Electric, between Two Carbons, 371 Area, Sectional, Variation of Re- sistance with, 146 Arms of Wheatstone's Bridge, Defi- nition of, 172 Arrangement for Shunting Battery while Charging Condenser only, 343 of Cells, giving Maximum Use- ful Power to Conductor of Fixed Resistance, 450 of Given Number of Cells to produce Maximum Current through Given External Resistance, 243 Arrangements of Cells, 239253 Astatic Combination of Magnets, 283 Galvanometer, Advantage of Putting Mirror Outside Coils, 284 Galvanometer, Simple Method of Damping, 284, 300 Galvanometer, Mather's, 299 INDEX. 487 Astatic Galvanometer, Mudford's, 105 Galvanometer, Thomson's, 283 Galvanometer, Thomson's Modified, 284 Attaching Leyden Jars to Collect- ing Combs of Electrical Machines, 370 Attracting Force, Potential Differ- ence and Distance between Two Parallel Plane Con- ductors, 87 Axis, Magnetic, of a Needle, Defini- tion of, 37 "DALANCE, Wheatstone's, 166 ** 177. (See also Wheatstone's Bridge.) Ballistic Galvanometer, 292 Batttries, 209 ; Bunsen's, 219 ; Cal- laud, 213; Daniell's, 211; Gravity, 212 ; Grove's, 218 ; Leclanche", 220 ; Lockwood, 213; Meidinger, 212; Min- otto's, 211 ; Potash Bichro- mate, 222 ; Secondary, 206, 261. (See also Cells.) Compaiibon of Electromotive Forces of, by Observing tbeir Joint and Opposed Currents, 232 Comparison of Electromotive Forces of, by Observing Resistance through which they send Equal Currents, 231 Comparison of Electromotive Forces of, Condenser Me- thod of, 341 Comparison of Electromotive Forces of, Poggendorff's Method of, 244 Local Action in, 217 Measuring Resistances of, 205, 225,342 Polarisation in, 216 Figures of, 239 Symbolical Representation of, 173, 240 Battery and Galvanometer in Wheat- stone's Bridge, Best Ar- rangement of, 172, 467 Arrangement for Shunting while Charging Condenser only, 343 of Leyden Jars, 317 of Simple Voltaic Elements for Charging Electrometer Needle, 373 B. A. Unit of Resistance, 141 B. A. Units and Legal Ohms, Equa- tion Connecting, 142 Bell Telephone, Description of, 336 Bertsch's Rotatory Electrophorus, 361 Best Arrangement of Battery and Galvanometer in Wheat- stone's Bridge, 172, 467 Deflection to use with Tangent Galvanometer, 41 Resistance for Coils of Wheat stone's Bridge, 170 Resistance for Differential Gal- vanometer, 436 Resistance for Galvanometer in Simple Circuit, 435 Resistance for Galvanometer in Wheatstone's Bridge, 171, 466 Resistance to Give to a Galvano- meter, 435 Bichromate of Potash Cell, Descrip- tion of, 222 of Potash Cell, Chemical Action in, 223 of Potash Cell, Composition of Liquid for, 222 of Potash Cell, Electromotive Force of, 228 Bismuth, Change of Resistance of, with Temperature, 160 Electric and Heat Conductivi- ties of, Compared, 159 Resistance of, for Given Length and Diameter, and for Given Length and Weight, Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Bobbin of Tangent Galvanometer, Proportions of Channel in, when Tangent Law is most Accurately Fulfilled, 51 Variation of Magnetic Effect of, with Current and Resist- ance, 418 Variation of the Sensibility of a Tangent Galvanometer, with Diameter of, 4851 Bridge, Wheatstone's, 166177 Wheatstone's, Best Arrange- ment of Battery and Gal- vanometer with, 172, 467 Wheatstone's, Best Resistance of Galvanometer for, 171, 466 Wheatstone's, Best Resistance of Coils for, 171 Wheatstone's, British Associa- tion Form of, 168 488 PRACTICAL ELECTRICITY. Bridge, Wheatstone's, Commercial Form of, 172 Wheatstone's, Conditions Af- fecting Sensibility of, 171 Wheatstone's, Key for, 174 Wheatstone's, Meaning of De- flection of Galvanometer of, 176 Wheatstone's, Metre Form of, 168 Wheatstone's, Superiority of, over Differential Galvano- meter, 171 Wheats- tone's, Use of Shunt with, 176 British Association Absolute Units, 141 Association Bridge, 168 Association Unit of Resistance, 141 Brush Discharge, 369 Bunsen's Cell, Description of, 219 Cell, Carbon for, 2ZO (ell, Chemical Action in, 219 Cell, Electromotive Force of, 220 Butt Joint, 79 c /""1ABLE, Capacity of a Submarine, Sealing up One End of, when Testing, 268 Calibrating Ammet* rs by the Silver Deposit Method, 395400 Ammeters for Large Currents, Use of Commutator for, 428 Commutator Ammeter, 432 Commutator Voltmeter, 433 Galvanometer by Direct Com- parison with Tangent Gal- vanometer, 58 Galvanometer by Employing Known Resistances and Cell of Constant E. M. F., 238 Galvanometer by Employing Kno wn Resistances and Fixed Potential Differ- ence, 164 Galvanometer by Sine Method, Galvanometer, by Sine Method, Higher Farts of Scale of, 65 Galvanometer by Sine Method with Constant Current, 67 Galvanometer, Relatively or Absolutely, Meaning of, 22 Galvanometer, Relatively or Absolutely, Mode of, 27 30 Gold-Leaf Electroscope, 354 Calibrating Voltmeter by Compari- son with Standard Cell, 410-415 Voltmeter by Poggendorff a Method, 413 Voltmeter with a Known Cur- rent and Resistance, 498 Calibration, Absolute, of Potential Difference Galvanometer, 127, 408415 of Galvanometer Unaffected by Change in Strength of Poles of Needle, 23 Galvanometers with Invariable Absolute, 57 . Portable Galvanometer with Approximate Absolute, 09 Callaud Cell, Description of, 213 Candle, Description of Standard, 452 Candles instead of Standard Can- dles for Rough Experi- ments, 452 Capacities, Comparison of, 319 Statical Method of Comparing, 330 Capacity, Absolute Measurement of, 327 Charge in Terms of, 303 Construction of Condensers of Very Large, 317 Definition of, 800 Measuring Specific Inductive, 332 of Condenser is Constant, 302 of Condenser, Variation of, with Area of its Coatings, 303 of Condenser, Variatioa of, with Distance betwe n its Coatings, 303 of Condenser, with Plane Parallel Plates, varies in- versely as Distance be- tween its Coatings, 307 of Cylindrical Condenser, 303 of Sphere in Space, 339 of Spherical Condenser, 338 of Submarine Cable, 309 of Collectors of Influence Ma- chines, Increasing the, 370 of Two Bodies Constant while their Relative Positions ai'e Constant, 338 Unit of, 307 Specific Inductive, 309 Carbonic Dioxide, Specific Induc- tive Capacity of, 310 Carbonised Clolh, Preparation of, for Varley's Resistances, 397 Carbons for Bunsen's Cells, Mode of Making, 220 Cardew's Voltmeter, Description of the Latest Form of, 423 INDEX 489 Cardew's Voltmeter, Advantages of, 426 Voltmeter Arranged for Measuring Large Potential Differences, 425 Voltmeter, Construction of Rods in, to Prevent Change of Length with Tempera- ture, 426 Voltmeter, Diameter of Wire used in, 423 Voltmeter, Disadvantages of 427 Voltmeter, Length of Wire used in the Latest Form of, 423 Voltmeter, No Heating Error in, 426 Voltmeter, Small Self-induc- tion in, 427 Cell, Bunsen's, 219 Callaud, 213 Daniell's, 210 Fleming's Standard Daniell's, 412 Gravity Daniell's, 212 Grove's, 218 - Leclanche\ 220 Latimer Clark's, 410 Lockwood's, 213 Meidinger's, 212 Minotto's, 211 Potash Bichromate, 222 Standard Daniell's, 411 Chemical Action in a Bunsen's, 220 Chemical Action in a Daniell's, 214 Chemical Action in a Grove's, 219 Chemical Action in a Leclanche", 221 Chemical Action in a Potash Bichromate, 223 Carbon for Bunsen's, 220 Composition of Liquid for Pot- ash Bichromate, 222 Constancy of E. M. F. of a Daniell's, 216 Constancy of E.M. F. of a Latimer Clark's, 411 E. M. F. of a Bunsen's, 220 E. M. F. of a Daniell's, 211 E. M. F. of a Standard Daniell's, 412 E. M. F. of a Grove's, 218 E. M. F. of a Latimer Clark's, 411 E. M. F. of a Lecianche", 222 E. M. F. of, Independent, of Size and Shape, 211, 236 E.M.F., Temperature Varia- tion of, in Latimer Clark's, 411 Cell, E. M. Fs. of, Comparison of, 231, 232, 234, 341 Local Action in, 217 How to prevent Local Action in a Daniell's, 217 Polarisation in a Daniell's, 216 Resistance of a Daniell's, 211 Resistance of a Grove's, 218 Resistance of, Measuring, 205, 225, 342 Cells, Arrangement of, 239 Arrangement of a Given Num- ber of, to produce Maxi- mum Current through a Given External Resistance, 243 Arrangement of for Giving Maximum Useful Power to Conductor with Fixed Resistance, 450 Galvanic, 209 in Parallel, E. M. F. of, 241 Figure of, 239 Symbolical Representation of, 240 in Series, E. M. F. of, 241 in Series, Figure of, 239 in Series, Symbolical Repre- sentation of, 240 Partly in Parallel and Partly in Series, E. M. F. of, 241 Partly in Parallel and Partly in Series, Figure of, 239 Partly in Parallel and Partly in Series, Symbolical Repre- sentation of, 240 Standard, 410 Change in Strength of Poles of Needle of Galvanometer, Calibration Unaffected by, 23 of Resistance with Tempera- ture, Results of Matthies- sen's Experiments on, 160 Charge. (See Quantity.) and Discharge Key, Descrip- tion of, 320, 343 and Discharge Key, Various Modes of attaching to Con- denser, Battery, and Gal- vanometer, 320322 Rate of Loss of, Depends on Dielectric Alone, 346 Electric, Meaning of, 109 Galvanometric Method of Mea- suring Resistance by Loss of, 348 in Condenser in Terms of Car pacity, 308 490 PRACTICAL ELECTRICITY. Charge, Measuring Resistance by Rate of Loss of, 343 Remaining on Two Bodies after Contact, 115, 351 Charged Body cannot Exist Alone, 339 Charges induced in Hollow Con- ductor by placing a Charged Body inside it, 113 on Two Conductors Enclosed by a Third, 110 on Two Bodies not Measured by the Potential Differ- ence, 85 Chemical Action in the Bunsen's Cell, 220 Action in the Daniell's Cell, 214 Action in the Grove's Cell, 219 Action in the Leclanche* CelL 221 Action in the Potash Bichro- mate Cell, 223 Property of a Current, Uses of, 4 Property of a Current, Why Used to Measure Strength of Current, 9 Circuit, Law Connecting Currents in a Closed, 464 Wires Joined in Parallel, 136 Circuits in Parallel, Independence of Currents in, 260 Clark's, Latimer, Differential Gal- vanometer, 150 Latimer, Cell, 410 Latimer, Cell, Constancy of E.M.F. of, 411 Latimer, Cell, E. M. F. of, 411 Latimer, Cell, Polarisation of, 411 Latimer, Cell, Temperature Variation of E.M.F. of, 411 Closed Circuit, Law Connecting Currents in, 464 Conductor, Density Nought on Inner Surface of, 118 Conductor, Distribution of Density in, Altered by In- sertion of Metal Rod, 119 Conductor, Potential Inside, 98 Cloth, Preparation of Carbonised, for Varley's Resistances, 397 Coating Insulating Stems with Paraffin Wax or Shell-lac Varnish, 267 of a Condenser, Every Charged Body forms One, 338 Coatings of a Condenser, Definition of. 302 Coil of Tangent Galvanometer, Ad- justment of, 46 Coils, Resistance, Construction and Use of, 28, 145 Resistance, Construction of Standard, 162 Resistance, Materials Used in Winding, 159 Resistance, German Silver, 160 Resistance, Iron, 162 Resistance, Platinoid, 160 Resistance, Platinum- Silver, 160 Resistance, Mode of Winding, 163 Resistance, Ordinary, Cannot be Used with Strong Cur- rents, 192 Resistance, of Magnifying Spring Voltmeters, Best Law of Gauge of Wire for, 421 Resistance, Temperature Va- riation of, 153 Proportional, of Wheatstone'a Bridge, 172 Rate of Production of Heat in Galvanometer, 419 Collecting Combs of Wimshurst In- fluence Machine, 369 Collectors of Influence Machines, Attaching Leyden jars to, 370 of Influence Machines, Increas- ing Capacity of, 370 Combination, Astatic, 283 Combined Resistance, 178 Commercial Form of Wheatstone's Bridge, 172 Instruments for Measuring Cur- rent, 79, 376 Commutator Ammeter and Volt- meter, 427 Ammeter, Calibrating, 432 Ammeter, Ratio of Sensibili- ties of, in Parallel and iu Series, 431 Ammeter, Safety Arrangement with, 432 Use of, in Calibrating Amme- ters for Large Currents, 428 Use of, in Calibrating Voltme- ters, for large Potential Differences, 428 Voltmeter, Calibrating a, 432 Comparing Capacities, Galvanome- tric Method of, 319 Capacities, Statical Method of, 330 Electromotive Forces of Bat- teries by Observing their Joint and Opposed Cur- rents, 232 INDEX. 491 Comparing Electromotive Forces of Batteries by Observing the Eesistances through which they send Equal Currents, 231 Electromotive Forces, Conden- ser Method of, 341 Electromotive Forces, Poggen- dorff's Method of, 234 Quantities of Electricity, Fun- damental Statical Method of, 111 Quantities of Electricity, Gal- vanometric Method of, 299 Eesistances, Equality of Cur- rent Method of, 136 Eesistances, Potential Differ- ence Method of, 140 Eesistances, Simple Substitu- tion Method of, 138 Eesistances, Use of Differen- tial Galvanometer for, 148 Eesistances, Use of Wheat- stone's Bridge for, 97 Comparison of Difference of Poten- tial with Difference of Level in Liquids, 86 of Difference of Potential with Difference of Pressure in Gases, 86 of Electric and Heat Conduc- tivities, 158 of Measurement of Potential with Measurement of Tem- perature, 85 of Resistance per Cubic Centime- tre, and per Cubic Inch, 348 of Static and Current Methods of Measuring Potential Dif- ferences, 125 of Use of Liquid and Wire Ee- sistances, 194 Component, Horizontal, of the Earth's Magnetic Force, Definition of, note, 55 Composition of Liquid for Potash Bichromate Cell, 222 Compound Interest Law of Electio- phoric Action, 366 Interest Law of Electrophone Action, when firstjUsed, 366 Interest Law of Influence Ma- chines, 364 Condenser, Arrangement for Shunt- ing Battery only while Charging, 343 Capacity of, 302 Capacity of Cylindrical, 308 Capacity of Spherical, 338 Coatings of, 302 Constancy of Capacity of, 302 Definition of, 301 Condenser, Every Charged Body forms One Coating of a, 333 Method of Ccmpiring E.M.Fs., 341 Method of Measuring Eesist- ance of a Current Genera- tor, 342 Standard Air, 334 Variation of Capacity of, with Area of Coatings, 303 Variation of Capacity of, with Distance between Coat- ings, 303 with Plane Parallel Plates, Ca- pacity of, Varies Inversely as Distance between Coat ings, 307 Condensers for Large Potential Dif- ferences, Construction of, 313 for use with Frictional and In- fluence Machines, 313 not Stores of Electricity, 322 of Very Large Capacity, Con- struction of, 317 Stores of Electric Energy, 322 Condensing Electroscope, 352 Conditions affecting Sensibility of Wheatstone's Bridge, 171 General, for Sine Law to be True 62 General, for Tangent Law to be True, 43 for Sine Law being Fulfilled in a Galvanometer, 62 for Tangent Law being Fulfilled in a Galvanometer, 43 of an Experiment, Necessity f 01 Changing only One at a Time, 146 to be Fulfilled in Making Tan- gent Galvanometer, 36 to be Fulfilled in Making Very Sensitive Galvanometer,281 Conduction and Induction, Distinc- tion between, 97 Definition of, 97 of Heat, o*, 195 Conductivities, Comparison of Ele" Given Length and Weight, 157 Resistance of, per Ctibic Centi- metre, and per Cubic Inch, 154 Voltameter, Description of, 6, 11 Voltameter, Direction of Cur- rent in, 15 Voltameter, Precautions in Using, note, 11 Voltameter, Weight of Copper deposited on Plate of, per second, by one Ampere, 11 Cores, Soft Iron, used in Galvano- meters, 73 Correcting Results of Experiments by Drawing Curves, 34 Correction, Cooling, of Observed Rise of Temperature Curve, 196 Correction for Damping, 296 Corrugating Sides of Ebonite Pil- lars, 272 Coulomb, Definition of the, 289 Couple, Definition of, note, 283 Definition of Moment of a, note, 283 Crompton and Kapp's Electro-Mag- netic Control Meters, 392 and Kapp's Electro-Magnetic Control Meters, Advant- ;es of, Cunynghame's Ammeter and Volt- meter, 382 Ammeter and Voltmeter, Ad- vantages and Disadvant- ages of, 385 Ammeter and Voltmeter, Graduation of, 385 Current, Alternating, Definition of, 198 Alternating, Measurement of, 198, 381 Amount of Heat Generated by Electric, 192 Amount of Heat produced per Minute by given, in given Resistance, 199 Arrangement of given Numbei INDEX. 493 of Cells to "produce Maxi- mum, through given Ex- ternal Resistance, 243 Current and Resistance, Variation of Magnetic Effect of Bobbin with, 418 and Static Methods of Measu- ring Potential Differences Compared, 125 Calibration by Sine Method with Constant, 67 Commercial Instruments for Measuring, 79, 376 Connection betweeu Direction of, and Poles of Magnet produced, 17 Constancy of Rate of Produc- tion of Heat in a given Coil by Constant, 197 Definition of Direction of, 14 Developing Maximum Useful Power in Generator with Fixed E.M.F. and Resist- ance, 448 Direction of, in Acid, Copper, and Zinc Voltameters, 15 Direction of, round Magnet, and Poles produced, 17 Electric, Compared with Cur- rent of Water j, 80 Electric, Heat is Evolved by, 3 Electric, Liquid is Decomposed by, 3 Electric, Magnet is Deflected by, 3 Electric, Properties of, 3 Electric, What is Meant by, 2 Electric, When said to Flow in a Conductor, 3 Flowing in Flat Coil, Direction of Magnetic Force pro- duced by, 43 Generator, Definition of Effi- ciency of, 451 Generator, Measurement of E.M. F. of, 224, 231, 23*, 341 Generator, Work done by a, 202 Generators, 208. (See also Cell and Batteries.) Increase of Total, by Shunting, 183 Indication of Direction of, in Magnifying Spring Amme- ter and Voltmeter, 389 Measuring Alternating, 198 Measuring, by Rate of Produc- tion of Heat, 197 Measuring Strength of, 4, 8 Measuring with Siemens' Dy- namometer, 379 Measuring Resistance during Passage of Strong, 187 Current of Water in Pipe Compared with Electric Current, 80 Properties of, 3 Proportional to Tangent oi Angle in Tangent Galva- nometers, 43 Ratio of, to Potential Differ- ence Constant for Given Conductor, 130 Resistance Coils Heated bj Strong, 192 Reversing, without Altering ita Value, 47 Strength, Why Measured Fun- damentally by Chemical Property, 10 Testing Ammeters for Error on Reversing the, 402 that Develops Maximum Use- ful Power, 448 through the Galvanometer oi Wheatstone's Bridge, 465 Unit of, 11 Variation of, with Variation of Potential Difference at Battery Terminals, 204 : Variation of, produced in Total, by Shunting Part of Cir- cuit, 253 What is Meant by, 2 Currents in Closed Circuit, Law Con- necting, 464 in Network, 462 in Various Circuits in Parallel, Condition of Independence of, 260 Several, Meeting at a Point, 464 Thomson's Galvanometer for Large, 53 Curve, Cooling Correction of Ob- served Rise of Tempera- ture, 196 Definition of Elastic, 34 Finding the Maximum for an Expression by means of, 244 Interpolation of Results by means of, 34 Law connecting Two Sets of Facts determined by means of, 35 Curves, Drawing.on Squared Paper, 31 Drawing, to Correct Results of Experiments, 34 on Squared Paper, Meaning of Apparent Inaccuracies in. 33 Value of, for Graphically Re- cording Results of Experi- ments, 33 Cylindrical Condenser, Capacity of, 308 494 PRACTICAL ELECTRICITY. T)AMPING, 291 "^ Apparent Increase in Re- sistance of a Galvanometer due to, 349 Correction for, 296 Definition of, 284 Daniell's Cell, Description of, 210 Cell, Chemical Action in, 214 Cell, Constancy of E. M. F. in, 216 Cell, E. M. F. of, 211 Cell, E. M. F. of Standard, 411 Cell, Gravity, 212 Cell, Fleming's Standard, 412 Cell, How to Prevent Local Action in, 217 Cell, Polarisation in, 216 Cell, Resistance of, 211 Cell, Standard, 411 Dead-Beat, Shielded, Direct-Read- ing Galvanometers, Ad- vantages of, 78 Decrement, Determination of Log- arithmic, when Damping is Very Slight, 297 Logarithmic, 296 Definition of Alternating Current, 198 of the Ampere, 11 of Brush Discharge, 369 of Capacity, 300 of Capacity of Condenser, 302 of Condenser, 301 of Conductivity, 155 of Contact Potential Difference, 351 of the Coulomb, 289 of Couple, 283 of Difference of Potentials, 80 of Damping, 284 of Dielectric, 311 of Direction of Current, 14 of Efficiency of Current Gene- rator, 451 of Efficiency of Electric Light, 452 of Elastic Curve, 34 of Electric Density, 117 of Electromotive Force, 202 of the Farad, 307 of Galvanometer, note, 21 of Galvanoscope, note, 21 of Glow Discharge, note, 369 of Hermetically Sealing, note, 20 of Horizontal Component of Earth's Magnetic Force, note, 55 of Hypotenuse, note, 38 of Inductive Action, 87 of the Joule, 461 Definition of Lines of Force, 43 of Logarithmic Decrement, 296 of Magnetic Axis of a Needle, 37 of Magnetic Saturation, 388 of Moment of Couple, note, 283 of Moment of Inertia, 78 of North-seeking End of Mag- net, 16 of the Ohm, 140 of Parallax, note, 28 of Periodic Time of Vibration, 291 of Plane of Magnetic Meridian, note, 45 of Potential Difference, 80 of Power, 441 of Quantity of Electricity, 109 of Residual Magnetism, 385 of Retardation, 331 of the Saturation of Liquid, 411 of Short-Circuited, 217 of Sine, note, 38 of Solenoid, note, 387 of Specific Inductive Capacity, 309 of Striking Distance, note, 371 of Super-saturation, note, 411 of Tanorent, note, 37 of the Volt, Legal, 141 of the Volt, Provisional, 89 of Uniform Magnetic Field, 36 of Water Equivalent, 198 of the Watt, 442 Definitions of Conduction and In- duction, 97 Deflecting Field, Magnetic, 73 Deflection, Angular, of Mirror, Con- nection between, and Mo- tion of Image on Plane Scale, 107 Best, to use with Tangent Gal- vanometer, 41 with Galvanometer of Wheat- stone's Bridge, Meaning of, 176 Proportional to Current, Con- struction of Galvanometers with, 71 Deflections of TangentGalvanometer Controlled Only by Earth's Magnetism, Values in Am- peres of, 84 Degree andTangent Scales, Accuracy of Readings Compared, 40 Delicate Galvanometers, 281. (See also Galvanometer.) Galvanometers, Importance of being Well Insulated, 286 Density, Distribution of, in Closed Conductor Altered by In- sertion of Metal Rod, lid INDEX. 495 Density Electric, Definition of, 117 Electric, Great at Pointed End of a Conical Conductor, 118 Electric, Greater Dear Edges of Flat Sheet of Metal, 118 Electric, Measuring, by means of Proof Plane, 117 Electric, Nought on Inner Sur- face of Closed Conductor, 118 Electric, Potential, and Quan- tity, Examples showing Difference between, 121 Dependence of Kate of Loss of Charge on Dielectric Only, 346 Deprez, E. M. F. used by, in Trans- mitting Power Thirty- seven Miles, 452 Detector, 58 Determination of Logarithmic De- crement when Damping is very Slight, 297 Diameter of Bobbin, Variation of Sensibility of Galvanome- ter with, 48 Dielectric, Definition of, 311 Only, Dependence of Bate of Loss of Charge on, 347 Difference between Saturation and Super-saturation, note, 411 in Colour between Candle and Arc Light, How to Over- come, in Measuring Arc Light, 457 of Potential, Adjusting Balls of Electrical Machine to produce Given Maximum, 372 of Potential, Alternating, In- creases Practical Resist- ance of Voltmeters, 427 of Potential, Alternating, Mea- suring, 426 of Potential at Battery Termi- nals, Variation of, with Change of Current, 204 of Potential between Two Conductors not Measuring Difference in their Electric Charges, 85 of Potential between Two Plane Conductors,Fprmula connecting, with Distance and Attraction between them, 87 of Potential between Two Points in a Uniform Wire Conveying Current Pro- portional to Distance be- tween them, 83 of Potential, Charges on Two Conductors Vary as, while their Relative Positions re- main Constant, 110 Difference of Potential Compared with Difference of Level in Liquids, 86 of Potential Compared with Difference of Pressure in of Potential Compared with Difference of Pressure of Water Flowing in a Pipe, 81 of Potential, Contact, 351 of Potential, Definition of, 80 of Potential Galvanometer Ab- solutely Calibrated, 127, 408, 415 of Potential Galvanometer, Long Fine Wire Used in, 127 of Potential Galvanometer, When it may be Employed, 127 of Potential, Increasing a, in Known Ratio, 354 of Potential, Large, 351 of Potential, Measuring, by Weighing, 88 of Potential Method of Com- paring Resistances, 140 of Potential, Ratio of, to Cur- rent, Constant for Given Conductor, 130 of Potential, Ratio of, to Cur- rent is Resistance, 130 of Potential Required to Main- tain Electric Arc between Two Carbons, note, 371 of Potential Required to Pro- duce Spark between Point and Plate, 371 of Potential Required to Pro. duce Spark between Two Metallic Balls, 370 of Potential, Static and Cur- rent Methods of Measur- ing, Compared, 125 of Potential, Sub-dividing into Known Fractions, 278 of Potential, Unit of, 89, 141 of Potential, Variation of, with Resistance of Given Volt- meter to Produce Given Deflection, 41? Differences between Electric Poten- tial and Pressure of Water Flowing in a Pipe, 83 Differential Galvanometer, Best Re- sistance for, 436 Galvanometer, Construction of, 149 496 PRACTICAL ELECTRICITY. Differential Galvanometer, Latimer Clark's, 150 Galvanometer, Mode of Ad- . justing, 150 Galvanometer, Principle of, 148 Galvanometer, Superiority of Wheatstone's Bridge over, 171 Galvanometer, Use of Shunts with, 183 Dilute Sulphuric Acid, Effect of Electrolysis of, 15 Diminution of Resistance of In- sulators with Increase of Temperature, 271 Direct Comparison with Tangent Galvanometer, Calibrating Galvanometer by, 58 Reading Galvanometers, 76 Reading, Shielded, Dead-Beat Galvanometers, Advant- ages of, 78 Direction of Current. Definition of, 14 of Current in Acid, Copper, and Zinc Voltameters, 15 of Current in Magnifying Spring Ammeters and Volt- meters, Indication of, 389 of Current round Magnet, Connection between, arid Poles produced, 17 of Flow of Electric Current, What is Meant by, 2 - of Magnetic Force produced by Current in Flat Coil, 43 Disadvantage of Magnifying Spring Ammeter and Voltmeter, 391 Disadvantages of Cardew's Volt- meter, 385 - of Cunynghame's Ammeter and Voltmeter, 427 of Electro - Magnetic Control Meters, 385 of Gravity Control Meters, 392 of Permanent Magnet Meters, 376 of Siemens' Electro-dynamome- ter, 381 of Thomson's Large Current Galvanometer, 54 Discharge, Brush, 369 Glow, note, 369 Multiplying Power of Shunt used in Measuring, 349 Dispersion Photometer, 454 Distance Spark can be sent between Balls of Influence Machine, 371 Distinction between Conduction and Induction, 97 between Galvanometer and Galvanoscope, note, 21 Distribution of Magnetism in Per- manent Magnet, M^asur- ing,24 of Power in a Circuit, 445 Disturbance, Magnetic, Shielding Galvanometers from Ex- traneous, 73 Drawing Curves on Squared Paper, 31 Curves to Correct Results of Experiments, 34 Dry Pile, 372 Duplex Telegraphy, Resistance Boxes used in, 186 Dynamometer, Measuring Currents with Siemens' Electro-, 379 Siemens' Electro-, 377. (See also Siemens' Electro-Dynamo- meter.) E T7ARTH, Potential of, Arbitrarily ** taken as Nousht, 84 Earth's Magnetic Force, Definition of the Horizontal Compo- nent of, note, 55 Ebonite Electrophorus for giving Negative Charges, 359 Electrophorus for giving Posi- tive Charges, 357 Pillars, Corrugating Sides of, 272 Pillars, Common Fault in Con- structing, 272 Resistance of, 271 Specific Inductive Capacity of, 310 Edelmann's Electrometer, Siig- gested Improvements in, 134 Modification of Thomson's Quadrant Electrometer, 130 Effect of Electrolysis of Dilute Sul- phuric Acid, 15 Efficiency Increases with Power in Electric Lamps, 458 of Arc Light, Measuring, 455 of Current Generator, Defini- tion of, 451 of Electric Light, Measuring, 452 of Incandescent Lamps, 458 Elastic Curve, Definition of, 34 Electric and Heat Conductivities, Comparison of, 158 Apparatus, Static, should be En- closed in Metallic Case, 108 INDEX. 497 Electric Arc, Description of, 188, 454 Arc, Measuring Illuminating Power of, in any Plane, 457 Arc, Potential Difference Re- quired to maintain, be- tween Two Carbons, note, 371 Chai ge, 109. (See Charge.) Circuit, Work done in, 199 Conductivity Diminishes more Rapidly thai Heat Con- ductivity, 159 Current. (See Current.) Density. (See Density.) Energy. (See Energy.) Lamps, Description of Arc and Incandescent, 454 Lamps, Efficiency of, Increasing with Power, 458 Light, Measuring Efficiency of, 452 Potential. (See Potential.) Quantity. (See Quantity.) Sparks. (See Sparks.) Electrical Machines, Fractional. (See Machines. ) Machines, Influence. (See Ma- chines.) Units, Ohm only one yet Legalised, 140 Electricity at Rest Resides only on Surface of Conductor, 119 Comparing Quantities of, Gal- vanpmetrically, 299 Comparing Quantities of, Stati- cally, 111 Condensers not Stores of, but of Electric Energy, 322 Measuring Quantity of, Abso- lutely, 289 Positive' an -1 Negative, 85 Potential of Conductor Depends partly on Amount of, 119 Quantity of, Defined, 109 Unit of Quantity of, 289 Quantity of, produced by Rub- bing Two Bodies together, 115 Electrification, Amount of a Body's, 109 Exterior, No Force inside Closed Hollow Conductor due to, 99 Object of Rubbing Two Bodies together to produce, 115 Electro - Dynamometer, Siemens', 377. (See also Siemens' Electro-Dynamometer. ) Electrode, Definition of, note, 131 Electrolysis, Effect of, of Dilute Sulphuric Acid, 15 Electro-Magnet, Description of, 6 Q O Electro-Magnet, Strength of, when Core is Slightly Mag- netised, 382 Maguet, Saturation of, ':88 Magnetic Control Meters, 392 Magnetic Control Meters, Ad- vantages of, 39 i Magnetic Control Meters, Crompton and fCapp's, 392 Magnetic Control Meters, Dis- advantages of, 39 i Magnetic Control Meters, Paterson and Cooper's, 393 Electrometer, Edelmaun's Modifi- cation of Thomson's, IzO Suggested Improvements in Edelmann's, 134 Use of, for proving Ohm's Law, 134 Rough, 94 Thomson's Absolute, Portable, and Quadrant, 93 Weight, Lecture-room Model of, 88 Guard Ring for Weight, 89 Weight, Increasing Sensibility of, by using Auxiliary High Potential, 91 Electromotive Force, Definition of, 204 Force, Constancy of, in Daniell's Cell, 218 Force, Measuring Resistance Containing, 4H9 Force of Cell Independent of its Size and Shape, 211, 236 Force of Bunsen's Cell, 220 Force of Daniell's Cell, 211 Force of Grove's Cell, 218 Force of Leclanche Cell, 222 Force of Latimer Clark's Cell, 411 Force of Latimer Clark's Cell, Variation of, with Tempera- ture, 411 Force of Standard Darnell's Cell, 412 Force of Cells in Parallel, 241 Force of Cells in Series, 241 Force of Cells partly in Series and partly in Parallel, Force Used by Deprez in Trans- mitting Power 37 Miles, 452 Forces of Batteries, Compari- son of, by observing Resist, ance through which thoy send Equal Currents, 231 Force of Batteries, Comparison of, by observing their Joint and Opposed Currents, 233 498 PRACTICAL ELECTRICITY. Electromotive Force of Current Generators, Condenser Method of Comparing, 341 Force, Measuring, 224 Electrophoric Action, Compound Interest Law of, 361372 Electrophorus, Action of, 360 Bertsch's Rotatory, 361 Description of, 356 Ebonite, giving Negative Charges, 359 Ebonite, giving Positive Charges, 357 Electroscope, Calibrating Gold-Leaf, 354 Condensing, 332 Gold-Leaf, Improved Form of, 94 Indicates Potential Difference, 95 Varnishing Shade of Ordinary Gold Leaf, 97 Electroscopes, Objections to Ordi- nary Gold-Leaf, 96 Element, Simple Voltaic, 209 E. M. F., Meaning of, 204. (See also Electromotive Force.) Enclosure of Static Electric Appa- ratus in Metallic Case Necessary, 108 Energy, Condensers Stores of Elec- tric, 322 Produced by Frictional Elec- trical Machine, 352 Waste of, in Voltmeters with High External Resistance, 422 Equivalent of Heat, Mechanical, 201 Error in Ammeters on Reversing the Current, Testing for, 402 in Ammeters Produced by Ex- ternal Magnetic Disturb- ance, Testing for, 403 in Ammeters Produced by Re- sidual Magnetism, Testing for, 400 in Ammeters Produced by Time, Testing for, 407 Testing Voltmeters for Heat- ing, 415 Errors in Voltmeters, Different Kinds of, 407 in Wattmeters, 445 Examples: i., 12; ii. vii., 13; viii. 14; ix.,x., 52; xi., 53 ; xii xiii.,55; xiv.,56; xv., xvi. 57; xvii., 89; xviii., xix. 90; xx., 91; xxi. xxiv. 142 ; xxv., 143 ; xxvi. xxviii., 155; xxix., 156 xxx. xxxiii., 158; xxxiv. 162; xxv?. xxxvii., 163; xxxviii. xl., 180; xli. xliii., 201; xli v., 202; xlv., 206; xlvi.-xlix., 207; 1., li., 227; Hi., liii., 228; liv., 232; lv. Ivii., 233; Iviii. lx., 242; IxL, 243; Ixii. 247; Ixiii.. Ixiv., 248; Ixv. 249; Ixvi., 250; Ixvii. Ixix., 252; Ixx., Ixxi., 255 Ixxii., Ixxiii., 256; Ixxiv. 259; Ixxv., 260; Ixx i. 262; Ixxvii., 263; Ixxviii. 264; Ixxix., Ixxx., 265 Ixxxi., 280 ; Ixxxii. Ixxxiv. 281; Ixxxv., 294; Ixxxvi. Ixxx vii., 295 ; Ixxxviii., 297 .Ixxxix. xci., 298 ; xcii. 311 ; xciii. xcv., 312 ; xcvi. xcvii., 313 ; xcviii., xcix. 323; c., 325; ci., 326; cii. 341; ciii., 350; civ., 437 cv., cvi., 438; cvii., 439 cviii., cix., 44') ; ex., cxi. 443; cxii.,cxiii.,44t; cxiv. 446 ; cxv., cxvi., 447 ; cxvii. cxviii., 459; cxix., 460 cxx., 471 ; cxxi., 473 ; cxxii. 474; cxxiii., 475 Examples showing Difference be- tween Electric Potential, Density, and Quantity, 121 Explanation of Electric Sparking, note, 358 External Resistance, Variation of, with Current and Poten- tial Difference at Battery Terminals, 204 Equality of Charges on Two Bodies obtained by Rubbing them together, 115 TJIA.RADA Y'S Experiment on Force in Closed Conductor due to Exterior Electrification, 99 Farad, Definition of the, 307 Fault, Common, in Constructing Ebonite Pillars, 272 Fibre and Pivot Suspensions, 60 Suspension used in Thomson's Marine Galvanometer, 60 Field, Uniform Magnetic, 36 Finding Angles from their Tangents by means of Squared taper, Tangents from their Angles with Squared Paper, 57 the Maximum for an Expres- sion by moans of Curve, 244 Fixed E. M. F. and Resistance, Cur- rent Developing Maximum INDEX. 499 Useful Power with Gene- rator with, 448 Fixed Resistance, Arrangement of Cells giving Maximum Useful Power to Conduc- tor with, 450 Flat Coil, Direction of Magnetic Force produced by Cur- rent flowing in, 43 Fleming's Standard Daniell's Cell, 412 Flint Glass, Eesistance of, 271 Specific Inductive Capacity of, 310 Flow, W^at is meant by Direction of, of Electric Current, 2 of Electric Current compared with that of Water, 3, 80 Focal Length of Lens, Definition of, 456 Force, Attractive, between Two Plane Conductors, For- mula Connecting, with Potential Difference and Distance between them, 87 Definition of Lines of, 43 Definition of Horizontal Com- ponent of Earth's Mag- netic, note, 55 Direction of Magnetic, pro- duced by Current flowing iu Flat Coil, 43 Electromotive. (See Electro- motive Force.) None Inside Closed Hollow Couductor due to Exterior Electrification, 99 Foster's, Prof. G. C., Simplification of Sine Galvanometer, 61 Frictional Electrical Machines, 352 Electrical Machines, Con- densers for use with, 313 Fulfilment of Conditions for Tan- gent Law in Tangent Gal- vanometer, 43 (^ALVANIC Cells, 209. (See also ^ Cells.) jralvanometer, Definition of, 21 Compared with Galvanoscope, note, 21 Constant of, 278 Absolute, 57 Astatic, Advantage of Putting Mirror Outside Coils, 284 Astatic, Definition of, 282 Astatic, '\ homson's, 283 - Astatic, Modified Thomson's, 884 Astatic, Mather's, 299 Galvanometer, Astatic, Mudford's, 105 Astatic, Damping of Vibra- tions of Needle of, 284, 300 Ballistic, 292 Ballistic, Siemens' and Halske'a Galvanometer Used as, 292 Dead-Beat, 78 Delicate, 281 Delicate, Importance of being Well Insulated, 286 Delicate, Necessity for Many Convolutions of Wire, 281 Differentia], Principle of, 148 Differential Construction of, 149 Differential,LatimerClark's,ldO Differential, Best Eesistance for, 436 Differential, Inferiority of, to Wheatstone's Bridge, 171 Differentia 1 , Mode of Adjust- ing, 150 Differential, Use of Shunts with, 183 Direct-Reading, 76 Direct-Reading, Adjustment to make, 75, 78, 385, 389 Large Current, Advantage of Low Resistance for, 136 Large Current, Deprez's, 69 Large Current, Electro-Mag- netic Control, 392 Large Current, Gravity Control, 391 Large Current, Magnifying Spring, 386 Large Current, Permanent Mg- uet Proportional, 75 Large Current, Thomson's Per- manent Magnet, 53 Large Current, Spring Con- trol, 377 Marine, 103 Marine, Fibre Suspension for, 103 Marine, Shielding, from Mag- netic Disturbance, 103 Portable, with Approximate Absolute Calibration, 69, 71 Potential Difference, 126 Potential Difference, Electro- Magnetic Control, 392 Potential Difference, Gravity Control, 391 Potential Difference, Magnify- ing Spring, 386 Potential Difference,Permanent Magnet Proportional, 75 Potential Difference, Spring Control, 382 Potential Difference, Long Fine Wire used in, 127 500 PRACTICAL ELECTRICITY. fialvanometer, Potential Difference, when it may be Employed, 127 Potential Difference, Testing, 407 Proportional, 71 Proportional, with Permanent Magnet Control, 73 Proportional, with Uniform Controlling Field, 72 Quantity, Mather's Simple Form of, 299 Reflecting, 103, 281, 293, 299 Rejecting, Deflection Propor- tional to Current with, 108 Reflecting, Mode of Using Lens with, 105 Reflecting, Lamps for, 106 Reflecting, Minor for, 105 Reflecting, Mather's Form of, 299 ' Reflecting, Mudfoid's Form of, 284 Reflecting, Spirit Level fur, 285 Sine, 62 Sine, Foster's Simplification of, 61 Shielded, 57, 73, 103, 390 Tangent, 35 Tangent, Simple Form of, 27 Tan gent, Adjustment of Coil of, 46 Tangent, Best Deflection to Use with, 41 Tangent, Conditions that a Galvanometer may be, 36 Tangent, Conditions of Tan- gent Law Fulfilled in, 43 Tangent, Controlled Only by Earth's Magnetism, Values in Amperes of Deflections of, 55 Tangent, Proportions of Chan- nel in Bobbin of, when Tangent Law is Most Ac- curately Fulfilled, 51 Tangent, Scale for, 38 Tangent, Sensibility of, Alter- ing, by Removing Needle from Plane of Coil, 52 - Tangent, Sensibility of, Al- tn-ed by Varying Number of Windings or Diameter of Bobbin, 48 Calibrating, Relatively or Abso- lutely, 22, 27, 395400 Calibrating, by Comparison with Tangent Galvano- meter, 58 Calibrating, by Sine Method. 64 Calibrating, by Sine Method in Higher Parts of Scale, 65 Galvanometer, Calibrating, by Sine Method with Constant Current, 67 Calibrating, by using Known Resistances and Cell of Constant E. M. F., 238 Calibrating, by using Known Resistances and Constant Potential Difference, 164 Calibration of, Unaffected by Change iu Strength of Poles of Single Needle, 23 Sensibility of, Increasing, by Diminishing Diameter of Wire used in Winding, 22 Sensibility of, Modes of Vary- ing. 229 Sensibility of, Variation o f , with Length of Wire Used in Winding, 418 Sensibility of, Variation of, with Resistance, 416 Sensibility of, Shunting to Diminish, 229 Sensibility of Tangent, Varia- tion of, 48 for Wheatstone's Bridge, Best Arrangement of, and Bat- tery, 171, 467 for Wheatstoue's Bridge, Best Gauge of Wire for, 172, 466 for Wheatstoue's Bridge, Cur- rent through, 4H5 for Wheatstone's Bridge, Mean- ing of Deflection of, 176 Apparent Increase of Resist- ance of, Due to Damping, 319 Best Resistance to give to, 435 Coils, Rate of Production of Heat in, 419 Method of Measuring Resist- ance by Loss of Charge, 348 Shielding, from Extraneous Magnetic Disturbance, 57, 73, 103, 390 in Simple Circuit, Best Resist- ar ~ for, 435 and Shunt, Combined Resist- ance of, 178 Soft Iron Core Used in, 73 Use of Mirror with, to Avoid Parallax, 28 and Voltameter, Relative Ad- vantiues of, 20 Galvanometer. (See also Ammeter Electro - Dynamometer Voltmeter.) Galvanos ope, Definition of, note, 21 Description of, 6 Gas-Burner, Albo-Carbon, for Gal- vanometers, note. 106 INDEX. 501 Gas- Burner, Regenerative, for Gal- vanometers, 106 Generated in Voltameter Inde- pendent of Shape, Size, aud Distance of Plates, 10 Eate of Production in Sul- phuric Acid Voltameter by One Ampere, 12 Gases, Diii'erence of Pressure Com- pared with Difference of Potential, 86, 121 Specific Inductive Capacity of, 310 Gearing, Ammeters and Voltmeters with Magnifying, 386 Generation of Heat by Electric Cur- rent, 192 Generator, Current, Definition of Efficiency of, 451 Current, Measurement of E. M. F. of, 224, 231,234, 341 Current, Measureinent of Re- sistance of, 205, 225, 342 Current, Power Wasted in Heating, 445 Current, Work done by, 202 . Current, with Fixed E. M. F. und Resistance, Current Developing Maximum Use- ful Power with, 448 Generators, Current, Forms of, 203. (See also Cell, Batteries.) German Silver, Change of Resist- ance of, with Temperature, 160 Silver, Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Silver, Resistance of, per Cubic Centimetre and per Cubic Inch, 154 Silver, Why Res'stance Coils are made of, 160 Glass, Flint, Resistance of, 271 Glow Discharge, note, 369 Gold, Change of Resistance of, with Temperature, 160 Electric and Heat Conductivi- ties of, Compared, 159 Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre and per Cubic Inch, 154 Leaf Electroscope, 94 Leaf Electroscope, Calibrating, 354 Leaf Electroscope, Objections to Ordinary, 96 Gold-Leaf Electroscope, Varnishing Shade of Ordinary, 97 Graduation of Ammeters, Test for Accuracy of, 395 of Cunynghaine's Ammeter and Voltmeter, 385 of Voltmeters, Testing for Ac- curacy of, 408. (See also Calibrating.) Graphically Recording Results of. Experiments, 30 Recording Results, Value of, 33 Gravity Control Meters, 391 Daniell's CeU, 212 Grove's Cell, 218 Cell, Chemical Action in, 219 Cell, E. M. F. of, 218 Cell, Resistance of, 218 Guard King, 89 Tube, 375 Guttapercha, Resistance of, 271 Specific Inductive Capacity of, 310 TTEAT, Amount of, per Minute Produced by Given Cur- rent flowing through Given Resistance, 199 Amount of, Produced per Second in Coil by Constant Current, Constancy of, 197 and Electric Conductivities, Comparison of, 158 Conductivity Diminishes more Rapidly than Electric, 153 Evolution of, in Conductor, by Electric Current, 3 Generated by Electric Cur- rent, Amount of, 192 Measuring Current by Rate of Production of, 197 Mechanical Equivalent of, 201 Radiation, Conduction, and Convection of, note, 195 Rate of Production of, iu Gal- vanometer Coils, 419 Heating Error in Voltmeters Di- minished by Use of Outside Resistance, 421 Error, None in Cardew's Volt- meter, 426 Error, Testing Voltmeters for, 415-422 Current Generator, Power Wasted in, 445 Property of Current, Practical Uses of, 4 Hermetically Sealing, Definition of note, 20 High Resistances, Measuring, 277 502 PRACTICAL ELECTRICITY. Higher Parts of Scale, Calibration of, by Sine Method, 65 Potential, Definition of, 85 Hoffmann's Voltameter, 15 Holtz's Influence Electrical Ma- chine, 367 Hooper's Vulcanised Indiarubber, Resistance of, 271 Horizontal Component of Earth's Magnetic Force, Defini- tion of, note, 55 Horse-Power, 201, 443 Hydrogen, Specific Inductive Ca- note, 37 pacity of, 3 Hypotenuse, Definition of, TLLUMINATING Power of Arc Lr.mp <, Measuring, 454 Power or Arc Lamps in any Plane, Measuring, 457 Power of Incandescent Lamps, Measuring, 452 Image, Connection between Motion of, on Plane Scale and Angular Deflection of Mir- ror, 107 Incandescent Lamp, Description of, Lamp, Measuring Efficiency of^ 452 Lamp, Measuring Illuminating Power of, 452 Lam]), Efficiency and Life of, 458 Indiarubber, Resistance of Hooper's Vulcanised, 271 Specific Inductive Capacity of, 310 Indication of Direction of Current in Magnifying Spring Am- meters and Voltmeters, 389 Induction, Definition of, 97 and Conduction Compared. 97 Self, 174, 427 Inductive Action, 87 Action between Conductors of Different Potentials, 87 Capacity, Specific, b'09 Inefficiency of 1'rictional Electrical Machines, 352 Inertia, Definition of Moment of, note, 78 Infinity Plug, 151 Influence Machine, Adjusting Balls of, to Produce Given Maxi- mum Potential Difference, 372 Machine, Attaching Ley den Jars to Collectors of, 370 Machine, Compound Interest Law of, 364-, 366 Influence Machine, Condensers for Use with, 313 Machine, Distance Spari can be sent between Balls of, 370 Machine, Work done by, 371 Machine, Bertsch, 361 Machine, Accumulating, 361 ; Holtz's, 367; Nicholson's, 366; Thomson's, 364; Var- ley's, 367; Voss, 367; Wimshurst, 367 In Parallel. Wires Joined, Defini- tion of, 136 In Series, Wires Joined, Definition of, 140 Instructions for Experiments, Spe- cimens of, 476 Instruments, Commercial, for Mea- suring Current, 79, 376 Insulating Stand, Construction of, 268 Stems, Coating, with Paraffin Wax or Shell-lac Varnish, 267 Varnish, How to Make, note, 268 Insulation, Importance of Good, and Mode of obtaining, in Delicate Galvanometers, 286 Insulator, Definition of, 9 Insulators, Diminution of Resist- ance of, with Increase of Temperature, 271 Obtainable for Electricity, not for Heat, 159 Table of Resistances of, 271 Telegraph, 274 Testing, during Manufacture, 275 International Electrical Congress, Unit of Resistance Adopted by, 140, 141 Interpolation of Results by Means of Curve, 31 Invariable Absolute Calibration, Galvanometers with, 57 Iron Box, Partial Magnetic Screen, 101 Change of Resistance of, with Temperature, 160 Electric and Heat Conductivi- ties of, Compared, 159 Resistance, of for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Cores, Use of, in Galvauome. ters. 73 INDEX. 503 Iron Magnetised by Electric Cur- rent, 3 Resistance Coils, 162 TAR, Leyden, 314. (See also Ley- Used for Daniell's Cell, 210 Joints, Lap and Butt, 79 Joule, Definition of the, 461 Joule's Mechanical Equivalent of Heat, 201 T7"EMPE'S Constant Total Current -*- v Shunts, 257 Key, Bridge, 174 Charge and Discharge, 320 Charge and Discharge, Simple Form of, 343 Charge and Discharge, Various Modes of Connecting, with. Condenser, Battery, and Galvanometer, 320322 Make and Break, Simple Form of, 19 Plug, Description of, 139 Kirchhoff's First Law, 4o4 Second Law, 464 T ALANDE Chaperon Cell, 210 Lamps, Description of Arc and Incandescent, 454. (See also Arc, Incandescent.) Lamps Used with Reflecting Galva- nometer, 105 Lap Joint, 79 Large Potential Differences, Pro- duction of, 351 Latimer Clark's Cell, 410 Clark's Cell, Constancy of E. M. F. of, 411 Clark's Cell, E. M. F. of, 411 Clark's Cell, Temperature Va- riation of E. M. F. of, 411 Clark's Differential Galvanome- ter, 150 Law connecting Two Sets of Facts Determined by means of Curve, 35 of Differential Galvanometer, 149, 183 Experimental Proof of Ohm's, 130 Kirchhoff's First, 464 Kirchhoff's Second, 464 Ohm's, 130 Tangent, Fulfilment of Condi- tions for, in Tangent Gal- vanometer, 43 Law, Tangent, When True, 41 Sine, When True, 61 of Wheatstone's Bridge, 167 Laws of Surface Leakage and Leak- age through the Mass, 270 Lead, Change of Resistance of, with Temperature, 160 Electric and Heat Conducti- vities of, Compared. 159 Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic enti- metre, and per Cubic Inch, 154 Leakage, Dependence of Rate of Loss of Charge from, on Dielectric Only, 348 Surface, 266 Surface, Law of, 270 through the Mass, 266 through the Mass, Law of, 270 Leclanch<* Cell, 220 Cell, Chemical Action of, 221 Cell, E. M. F. of, 222 Legal Ohms and B. A. Units, Equa- tion Connecting, 142 Unit of Resistance, 140 Length, Variation of Resistance with, 143 Lens, Definition of Focal Length of, 456 Mode of Using, with Reflecting Galvanometer, 104, 103 Levels, Spirit, for Reflecting Gal- vanometer, 285 Leyden Jar, Attaching, to Collecting Combs of Electrical Ma- chines, 370 Jar, Construction of, 314 Jars, Battery of. 317 Life of Incandescent Lamps, 458 Light, Measuring ElScieucy of Elec- tric, 452 Measuring Illuminating Power of Electric, 452 Lines of Force, Definition of, 43 Liquid and Wire Resistances, Com- parison of Use of, 194 Decomposed by Electric Cur- rent, 3 Saturation of, note, 411 Super-saturation of, note, 411 Liquids, Difference of Level in, Com- pared with Difference of Potential, 86 Local Action in Cell, 217 Action in Darnell's Cell, How to Prevent, 217 504 PRACTICAL ELECTRICITY Lockwood Cell, 213 Logarithmic Decrement, 296 Decrement, Determination of, when Damping is Very Slight, 297 Lord Rayleigh, Silver Voltameter used by, 11 M "MACHINES, Electrical, Adjust- ing Balls to Produce Given Potential Difference, 372 Electrical, Attaching Ley den Jiirs to Collectors of. 370 Electrical, Condensers for Use with, 313 Electrical, Frictional, 352 Influence, Bertsch's, 361 Influence, Accumulating, 361 ; Holtz, 367; Nicholson's, 366; Thomson's, 364; Var- ley's, 367: Voss, 3c>7; Wimshurst, 367 - Influence, Accumulating, Con- densers for Use with, 313 - Influence, Accumulating, Com- pound Interest Law of, 364, 366 Influence, Accumulating, Work done by, 371 Magnet, Connection between Poles of, and D i. action of Cur- rent round, 17 Definition of North-Seeking End of, note, 16 Deflected by Current, 3 1- lectro. (See Electro-Magnet. ) Motion of, Produced by Uni- form Magnetic Field, 390 Permanent, Measurement of Distribution of Magnetism in, 24 Permanent, Proportional Gal- vanometer Controlled by, 73 Mngnets, Position of Poles in, 23 Magnetic Axis of Needle, Definition of, 37 Disturbance, Shielding Galva- nometers from Extraneous, 57, 73, 103, 390 Effect of Bobbin, Variation of, with Current and Resist- ance, 418 Field, Motion of Magnet pro- duced by Uniform, 390 Force, Definition of Horizontal Component of Earth's, noie, 55 Force, Direction of, produced by Current in Flat Coil, <3 Magnetic Meridian, Definition ol Plane of, not", 45 Property of Current, Practical Uses of, 4 Saturation, 388 Screen, Thick Iron Box, 101 Miiguetised, Iron, by Current, 3 Magnetism, Measurement of Dis- tribution of, in Permanent Magnet, 24 Residual, Definition of, 385 Residual, Testing Ammeters for, 400 Magnifying Gearing, Ammeters and Voltmeters with, 386 Spring Ammeter and Volt-' meter, 386 Spring Ammeter and Volt- meter, Adjustment for Sen- sibility in, 389 Spring Ammeter and Volt- meter, Advantages of, 390 Spring Ammeter and Volt- meter, Disadvant age of , 391 Spring Ammeter and Volt- meter, Indication of Di- rection of Current in, 389 Spring Voltmeter, Best Law of Variation for Gauge of Wire in, 421 Making Sine Scale, Mode of, 68 Tangent Scale, Mode of, 38 Mauce's Test for Resistance Con- taining E. M. F., 470 Marine Galvanometer. 103 Galvanometer, Fibre Suspen- sion used in, 60 Galvanometer, Shielding, from Magnetic Disturbance, 103 Mass, Law of Leakage through, 270 Leakage through, 266 Material for Outside Resistance for Voltmeters, 422 for Wire for Voltmeter Coils, 420 used in Resistance Coils, 159 Variation of Resistance with, 146 Mather's Mode of Calibrating Gal- vanometer with Constant Current, 67 Proportional Galvanometer with Uniform Controlling 1 Field, 72 Reflecting Galvanometer, 299 Matthiessen's Eqm tion Connecting Resistance with Tempera- ture, 153 Experiments, Tables deduce.1 from, 154, 157 Maximum, Finding, by means of Curve, 2-J4 INDEX. 505 Maximum Potential Difference of Electrical Machine, Deter- mination of, 372 Useful Power, Current that Develops, 448 Useful Power in Generator with Fixed E. M. F. and Eesistauce, Current that Develops, 448 Measuring Arc Light, Efficiency of, 455 Arc Light, Illuminating Power of, in any Plane, 457 - Arc Light, Illuminating Power of, How to Overcome Dif- ference in Colour between it and Candle when, 457 Efficiency of Electric Light, 452 Efficiency of Incandescent Light, 452 Current, Alternating, 198 Current, Commerc al Instru- ments for, 79, 376 Current, by Eate of Production of Heat, 197 Current with Siemens' Dyna- mometer, 379 Small Currents, Disadvantage of using Voltameters for,20 Strength of Current, 4 Distribution of Magnetism in Permanent Magnet, 24 Electric Density by means of Proof Plane, 117 Electromotive Force of Cur- rent Generators, 224, 2?1, 234, 341. (See also Electro- motive Force.) Potential Difference by Weigh- ing, 88 Potential Differences, Alter- nating, 426 Potential Differences, Static and Current Methods of, Compared, 125 Power, 442 Resistance of Batteries, 205, 225 Resistance of Batteries using Known Resistances, 226 Resistance of Batteries using Known Resistances and Shunt, 226 Resistance of Current Gener- ator, Condenser Method of, 342 Resistance by Rate of Loss of Charge, 344 Resistance by Rate of Loss of Charge, Galvanometric Method of, 318 Resistance Containing E.M.F., 469 Measuring Resistance during Pcto- sage of Strong Current, 187 High Resistances, 277 Specific Inductive Capacity, Quantity of Electricity, 111, 239, 299 Measurement Absolute, of Capa- city, ,327 of Po.e.itial Compared with Measurement of Tempera- ture, 85 Mechanical Equivalent of Heat, 201 Meidinger Cell, 212 Mercury, Change of Resistance of, with Temperature,' 160 Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Meridian, Definition of Plane of Magnetic, note, 45 Metal having Least Change of Re- sistance with Tempera- ture, 160 Metals, Change of Resistance of, with Temperature, 160 Electric and Heat Conducti- vities of, Compared, 159 Resistance of, for Given Length and Diameter, or for Given Length and Weight, 156 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 153 Metallic Case, Necessary Enclosure of Electric Apparatus in, 108 Meters, Electro-Magnetic Control, 392 Electro-Magnetic Control, Crompton and Kapp's, 392 Electro-Magnetic Control, Pa- terson and Cooper's, 393 Electro-Magnetic Control, Ad- vantages of, 394 Electro - Magnetic Control, Disadvantages of, 394 Gravity Control, 391 Spring Control, 377 Spring Control, Cunynghame's, 382 ; Magnifying, 386 ; Siemens', 377 Meters. (See also Ammeter, Dyna- mometer, Galvanometer, Photometer, Voltmeter, Wattmeter.) Metre Bridge, 168 Mica, Resistance of, 271 506 PRACTICAL ELECTRICITY. Mica, Specific Inductive Capacity of, 310 Micrometer Screw, Description of, note, 24 Minotto's Cell, 211 Mirror, Angular Motion of, Half that of Reflected Ray, 106 Connection between Angular Deflection of, and Motion of Image on a Plane Scale, 107 in Galvanometer, Use of, to Avoid Parallax, 28 for Reflecting Galvanonieter,105 Moment of Couple, Definition of, note, 283 of Inertia, Definition of, note, 78 Motion, Angular, of Reflected Ray, 106 of Image on Plane Scale, Con- nection between, at>d Angu- lar Deflection of Mirror, 107 of Magnet produced by Uni- form Magnetic Field, 390 Multiples of Ohm, Construction of, 145 Multiplying Power of Shunt, 178 Power of Shunt used in Measuring a Discharge, 349 N "TNTAPIERIAN Logarithmic De- crement, 296 Negative Charges, Ebonite Electro- phorus Arranged to Give, 359 "Electricity, 85 Network, Currents in, 462 Nicholson's Revolving Doubler, 366 Nickel, Resistance of, per Cubic Centimetre, and per Cubic Inch, 154 North-seeking end of Magnet, Defi- nition of, note, 16 Nought, Poteutial of Earth Arbi- trarily taken as, 84 Null Methods, Meaning of, 236 OHM, 89, 140, 141 ^ Construction of Multiples Of, 145 Definition of Legal, 140 Only Electrical Unit yet Legal- ised, 140 Ohmmeter, Description of, 190 Ohms, Legal, and B. A. Units, Equa- tions connecting, 142 Wires having Resistance of about Ten, 143 Ohm's Law, 130 Law, Experimental Proof of, 130 Olefiant Gas, Specific Inductive Capacity of, 310 PARAFFIN WAX, Coating In- sulating Stems with, 267 Wax, How to Prevent Over- heating when Melting, not e, 267 Wax, Resistance of, 271 Wax, Specific Inductive Capa- city of, 310 Parallax, Definition of, note, 28 Mirror Used in Galvanometer to Avoid, 28 Parallel, Cells in, Figure of, 239 Cells in, Symbolical Repre- sentation of, 240 Circuit, Wires Joined in, 136 Circuit, Independence of Cur- rents in, 260 E. M. P. of Cells in, 241 Resistance, 179 Paterson and Cooper's Electro-Mag- netic Control Meters, 393 P. D., Meaning of, 230 Periodic Time of Vibration, Defini- tion of, 291 Permanent Magnet, Proportional Galvanometers Controlled by, 73 Magnet, Measurement of Dis- tribution of Magnetism in, 24 Magnet Meters, 69 Magnet Meters, Advantages of, 78 Magnet Meters, Direct-Read- ing, 76 Magnet Meters, Disadvantage of, 376 Magnet Meters, Proportional, 71 Photometer, Dispersion, 454 Rumford's, 452 Pivot and Fibre Suspensions, 60 Plane of Magnetic Meridian, Defini- tion of, 710 te, 45 Proof, 116 Platinoid, 160 Resistance of, 161 Resistance, Coils of, 161 Platinum, Electric and Heat Con- ductivities of, Compared, 159 Resistance of, for Given Length and Diameter, and for Given Length and Weight, INDEX 507 Platinum, Resistance of, per Cubic Centimetre, and per Cubic Inch, 154 Silver Alloy, Change of Resist- ance of, with Temperature, 160 Silver Alloy, Resistance of, for Given Length and Dia- meter, and for Given Length and Weight, 157 - Silver Alloy, Resistance of per Cubic Centimetre, and per Cubic Inch, 154 Plug, Infinity, 151 Key, Description of, 139 Resistance Boxes, Construction of, 151 Poggendorff's Method of Compar- ing E. M.Fs., 234 Method, Use of, for Calibrating Voltmeters, 413 Polarisation of Daniell's Cell, 216 of Latimer Clark's Cell, 411 Poles of Magnet, Connection be- tween, and Direction of Current round Magnet, 17 of Magnets, Positions of, 23 Portable Electrometer, 93 Galvanometer with Approxi- mate Absolute Calibration, 69 Positive Electricity, 85 Potential, 85 Potash Bichromate Cell, 222 Bichromate Cell, Chemical Ac- tion in, 223 Bichromate Cell, Composition of Liquid for, 222 Bichromate Cell, E. M. F. of, 223 Bichromate Cell, Form of Zinc for, 223 Potential of Conductor Compared with Pressure of Gas, l-'l of Conductor, Ways in which it can be Varied, 121 of Conductor Depends partly on Amount of Electricity on it, 119 of Conductor Depends partly on its Position, 119 of Conductor Depends partly on its Shape, 119 Density, and Quantity, Exam- ples showing Difference be- tween, 121 Difference, 80 Difference, Adjusting Balls of Electrical Machine to Pro- duce Given Jlaximum, 372 Potential Difference, Alternating, Increases Practical Resist- ance of Voltmeters, 427 Difference, Alternating, Measur- ing, 426 Difference between Two Con- ductors does not Measure Difference in their Electric Charges, 85 Difference between Two Points in Uniform Conductor Con- veying Current Propor- tional to Distance between Points, 83, 143 Difference, Charges on Two Conductors Vary as, for Constant Relative Posi- tions, 109 Difference Compared with Dif- ference of Level in Liquids, 86 Difference Compared with Dif- ference of Pressure in Gases, 86 Difference Compared with Dif- ference of Pressure of Water Flowing in Pipe, 80,81 Difference, Contact, 351 Difference, Distance and At- traction between Two Par- allel Plane Conductors, 87 Diffeience Galvanometer, Ab- solutely Calibrated, 127, 408423 Difference Galvanometers, Long Fine Wire Used in, 127 Difference Galvanometer, when it may be Employed, 127 Difference, Increasing a, in known Ratio, 354 Difference, Large, Arrangement of Cardew's Voltmeter for Measuring, 425 Difference, Large, Production of, 351 Difference.Measuringby Weigh- ing, 88 Difference Method of Com- paring Resistances, 140 Difference, Katioof, to Current Constant for Given Con- ductor, 130 Difference, Ratio of, to Current is Resistance, 130 Difference Required to Main- tain Ele'ctric Arc between Two Carbons, note, 371 Difference Required to Pro- duce Spark between Point and Plate, 371 508 PRACTICAL ELECTRICITY. Potential Difference Required to Produce Spark between Two Metallic Balls, 370 Difference, Static and Current Method of Measuring, Compared, 125 Difference, Sub-dividing into Known Fractions, 278 Difference, Variation of, at Bat- tery Terminals, with Varia- tion of Current, 204 Difference, Variation of, with Resistance of Given Volt- meter to Produce Given Deflection, 419 Higher, and Lower, Positive, and Negative, Definition of, 85 Increasing Sensibility of Weight Electrometer by Using Auxiliary High, 91 Inside Closed Conductor, 98 Measurement of, Compared with Measurement of Tem- perature, 85 of Earth Arbitrarily taken as Nought, 84 Uniform on Conductor, 86 Uniform in Conductor, 98 Power, Arrangement of Cells Giv- ing Maximum Useful, to Conductor of Fixed Resist- ance, 450 Current Developing Maximum Useful, with Generator of Fixed E. M. F. and Resist- ance, 448 DefiHti.>n of, 441 Distribution of, in Circuit, 445 E. M. F. used by Deprez in Transmitting, 37 Miles, 452 Horse, 201, 443 Measurement of, 442 Unit of, 442 Utilised in Circuit Outside Ge- nerator, 445 Wasted in Heating Generator, 446 Preparat ; on of Varley's Carbonised Cloth, 397 Pressure, Difference of, in Gases, Compared with Difference of Potential, 86 of Gas Compared with Poten- tial of Conductor, 121 of Water, Difference of, in Pipe Compared with Difference of Potentials, 81 Proof of Ohm's Law, Experimental, 130 Proof-plane, 116 Proof-plane, Measuring Electric Density by means of, 117 Properties of Electric Currf-nt, 3 of Electric Current, Practical Uses of, 4 Proportional Coils of Wheatstone's Bridge, 172 Galvanometer, 71, 75, 108, 389 Proportions of Channel in Bobbin of Tangent Galvanometer, when Tangent Law is Most Accurately Fulfilled, 51 Q QUADRANT Electrometer, Thom- son's, 93 Electrometer, Edelmann's Mo- dification of Thomson's, 130 Electrometer, Edelmann's Mo- dification of Tnomson's, Defects in, 134 Electrometer, Edelmann's Mo- dification of, Dry Pile for, 133, 372 Electrometer, Edelmann's Mo- dification of, Needle for, 132 Electrometer, Formula for, 134 Quantities of Electricity, Compari- son of, 111 299 Quantity of Electricity, Definition of, 109. (See also Charge.) of Electricity, Unit of, 289 of Electricity Produced by Rubbing Two Bodies To- gether, 113 Potential, Density, Examples showing Difference be- tween, 121 Unit of, 289 R RADIATION of Heat, Explanation of, note, 195 Rate of Loss of Charge, Measuring Resistance by, 344 of Production of Heat in Gal- vanometer Coils, 419 of Production of Heat, Mea- suring Current by, 197 Ratio of Potential Difference to Current Constant witk Given Conductor, 130 of Potential Difference to Cur- rent is the Resistance, 130 of Sensibilities of Commuta- tor Ammeter in Parallel and in Series, 431 INDEX. 509 Ratio of Sensibilities of Voltmeter in Parallel and in Series, 433 Raykigh, Lord, Silver Voltameter Used by, 11, 395 Lord, Temperature Variation of E. M. F. of Clark's Cell Determined by, 411 Recorainar Results of Experiments Graphically, 30 Results of Experiments Gra- phically, Value of Curves for, 33 Reflected Ray, Angular Motion of,106 Reflecting Galvanometer, 103, 281, 293, 299. (See also Galva- nometer, Reflecting.) Galvanometer, Different Ways of Forming Image with, 105 Galvanometer, Lamp Used with, 106 Galvanometer, Modes of Using Lens with, 105 Galvanometer, Spirit Level for, 285 Relative Calibration of Galvano- meter, Meaning of, 22 Relatively Calibrating Galvanome- ters, 27 Replenisher, Thomson's, 364 Representation of Batteries, Sym- bolical, 173, 240 Residual Magnetism, Definition of note, 388 Magnetism, Testing Ammeters for, 403 Resin, Specific Inductive Capacity of, 310 Resistance, 9, 129 Amount of Heat produced per Minute by Given Current flowing through Given, 199 and Current, Variation of Maer- uetic Effect of Bobbin with, 418 Apparent Increase of, in Gal- vanometer, Due to Damp- ing, 349 of Battery, Measuring, 205, 225, 342 Best, for Differential Galvano- meter, 436 Best, for Galvanometer in Sim- ple Circuit, 435 Best, for Galvanometer of Wheatstoue's Bridge, 172, I 466 Best, for Coils of Wheatstone's ' Bridge, 171 Best, to Give to Galvanometer, 435 Box, Description of, 28 Box, Construction of Plug, 151 I Resistance Box, Construction of Sliding, 186 Box used in Duplex Telegraphv, 187 Resistances, Calibrating Galvano- meter by Using Known, and Constant Potential Differ- ence, 164 Calibrating Galvanometer by Using Known, and Cell of Constant E. M. F., 238 Change of, with Temperature, Results of Matthiessen's Experiments on, 160 Comparing, 136 Comparing, Differential Galva- nometer Method of, 148 Comparing, Potential . Differ- ence Method of, 140 Comparing, Simple Substitu- tion Method of, 138 Comparing, Wheat-stone's Bridge Method of, 166 Comparing Use of Liquid and Wire, 194 Resistance Containing E. M. F., Measuring, 469 Coils, 28, 145; 151, 153, 159, 163 Coils, Accurate Standard, 162 Coils, Construction of, 145 Coils Heating with Strong Cur- rent, 192 Coils, German Silver, 160 Coils, Iron, 162 Coils, Platinoid, 161 Coils, Platinum-Silver Alloy,160 -Coils, Materials used in, 159 Coils, Modes of Winding, 163 Coils, Temperature Variation of, 153 Increase of, by Self-induction, 427 of Current Generator, Conden- ser Method of Measuring, 342 of Daniell's Cell, 211 of Grove's Cell, 218 of Insulators, Diminution of, with Increase of Tempera- ture, 271 of Insulators, Measuring, 275 of Insulators, Table of, '271 of Insulator to Sparking, 311, 370, note, 358 Law of Variation of, with Tem- perature, 152 Measuring, by Rate of Loss of Charge, 344, 348 Measuring, Containing E.M.F., 469 Measuring, durincr Passage of Strong Current, 187 510 PRACTICAL ELECTRICITY. Resistance, Measuring High, 277 Metal having Least Change of, with Temperature, 160 Parallel, 179 of Galvanometer and Shunt Combined, 178 of Metals for Given Length and Diameter, or for Given Length and Weight, 156 of Metals per Cubic Centimetre, and per Cubic Inch, 153 of Platinoid, 161 per Cubic Centimetre, and per Cubic Inch Compared, 348 Proportional to Ratio of Poten- tial Difference to Current, 130 should be High in Potential Difference Galvanometers, 137 should be Low in Current Gal- vanometers, 136 Unit of, British Association, 141 Unit of, Legal, 140 Unit of, Siemens', 142 - Variation of, with Length, 143 Variation of, with Material, 146 Variation of/ with Sectional Area, 146 Variation of, with Temperature, 147, 152 Variation of Sensibility of Gal- vanometer with, 416 Variation of Sensibility of Voltmeter with, 407, 418 Voltmeters with Outside, 421 Results of Experiments Corrected by Drawing Curves, 34 of Experiments, Graphically Recording, 30 of Experiments, Value of Curves in Graphically Re- cording, 33 Interpolation of, from Curve, 34 Retardation, Definition of, 331 Reversing Current without Alter- ing its Value, 47 Revolving Doubler, Nicholson's, 366 Ring, Guard, 89 Ross Cell, 210 Rotatory Electrophorus, 361 Rough Experiments, Candles to use in the place of Standard Candles for, 452 Rubbing Two Bodies together, Quantity of Electricity Produced by, 113 Two Bodies together to Pro- duce Electrification, Ob- ject of, 115 - ?wo Bodies together, Equality of Charges Obtained by, 115 Rumford's Photometer, 452 Ryiner Jones' Constant Total Cur- rent Shunts, 259 SATURATION, Magnetic, 388 3 of Liquid, Definition of, 411 Safety Arrangement with Com. mutator Ammeter, 432 Scale, Connection between Motion of Image on Plane, and Angular Deflection of Mir- ror, 107 for Tangent Galvanometer, 39 Mode of Making Tangent, 39 Scales, Accuracy of Readings with Degree and Tangent Com- pared, 40 Screen. Magnetic, Thick Iron Box, 101 Screw, Micrometer, Description of, note, 24 Sealing Hermetically, Definition of, note, 20 up One End of Cable when under Test, 268 Secondary Batteries, Small Internal Resistance of, 208, 261 Batteries, Use of, in Electric Lighting, 261 Sectional Area, Variation of Resist- ance with, 146 Self-induction, 174, 427 Induction, Small, in Cardcw'a Voltmeter, 427 Sensibilities of Commutator Am- meter, Ratio of, in Parallel and in Series, 431 of Commutator Voltmeter, Ratio of, in Parallel and in Series, 433 Sensibility, Adjustment for, in Magnifying Spring Am- meters and Voltmeters, 389 of Galvanometer, Variation of, 21, 48, 229 of Galvanometer, Variation of, with Length of Wire used in Winding, 418 of Galvanometer, Variation of, with Resistance, 416 of Tangent Galvanometer Al- tered by Removing Needle from Plane of Coil, 52 of Tangent Galvanometer Al- tered by Varying Number of Windings or Diameter of Bobbin, 48 of Voltmeters, Variation of, with Change of Resistance, 407,418 INDEX. 511 Sensibility of Wheatstone's Bridge, Conditions affecting.171,466 of Wheatstone's Bridge, Mode of Increasing, 168 of Weight Electrometer, In- creasing, by Using Auxili- ary High Potential, 91 Shunting Galvanometer to Diminish, 229 Testing Ammeters for Perma- nent Alteration of, 407 Two Degrees of, in Commutator Ammeter and Voltmeter, 427 Series, E. M. F. of Cells in, 241 Cells in, Figure of, 239 Cells in, Symbolical Repre- sentation of, 240 Wires Joined in, 140 Several Currents Meeting at a Point, Law Connecting, 464 Shell-lac, Eesistance of, 271 lac Specific Inductive Capa- city of, 310 lac Varnish, Coating Insu- lating Stems with, 267 lac Varnish, Preparation of, note, 288 Shielded, Dead-Beat, Direct- Read- ing Galvanometers, Advan- tages of, 78 Shielding Galvanometers from Ex- traneous Magnetic Disturb- auce, 57, 73, 103, 390 Short-Circuited, Definition of, 217 Shunts, 59, 177, 183, 253 Shunt Box, Construction of, 181 Shunts, Constant Total Current, 257 Shunt and Galvanometer, Combined Resistance of, 178 Increase of Total Current pro- duced by Use of, 183, 253 Measuring Resistances of Bat- teries by means of, 226 Multiplying Power of, 178 Multiplying Power of, when Used in Measuring Dis- charge, 349 Shunts, Use of, with Differential Galvanometer, 183 Shunt, Use of, with Wheatstone's Bridge, 176 Shunting Battery only while Charg- ing Condenser, Arrange- ment for, 343 Galvanometer to make it Less Sensitive, 229 Siemens' Electro-Dynamometer, 377 Electro-Dynamometer, Advan- tages of, 380 Electro-Dynamometer, Disad- vantages of, 381 Siemens' Electro - Dynamometer, Measuring Current with, 379 Electro-Dynamometer as Stan- dard Instrument, 382 Siemens' Unit of Resistance, 142 Silver, Change of Resistance of, with Temperature, 160 Electric and Heat Conductivi ties of, Compared, 159 Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Chloride Battery of De la Rue and Hugo Muller, 314 Voltameter, Description of, note, 11, 395 Voltameter, Precautions in Using, note, 11 Voltameter, Use in Calibrating Ammeters, 395400 Voltameter Used by Lord Rayleigh, 11, 395 Voltameter, Weight of Silver Deposited on Plate of, per Second, by One Ampere, 11 Similarly Charged Bodies ; Reason they Fly from One An- other, 340 Simple Substitution Method of Com paring Resistances, 138 Voltaic Element, 209 Sine, Definition of, note, 38 Galvanometer, 62 Galvanometer, Foster's Simpli- fication of, 61 Law, Conditions under which it is True, 61 Law, How Conditions of, are Fulfilled in Sine Galvano- meter, 62 Method, Calibrating Galvano- meter by, 64 Method of Calibrating Galvano- meter with Constant Cur- Method of Calibrating Higher Parts of Scale, 65 Scale, Method of Making, 68 Slidiug Resistance Boxes, 186 Small Current, Disadvantage of using Voltameter to Mea- sure, 20 Soft Iron Cores used in Galvano. meters, 73 Solenoid, Definition of, note, 387 Sparking, Resistance to, of Instu lators, 311, note, 358 512 PRACTICAL ELECTRICITY. Sparks bebween Balls of Electrical Machines, Length of, 370 Electric, 358 Potential Difference Required to Produce, between Point and Plate, 371 Potential Difference Required to Produce, between Two Metallic Balls, 370 Sphere, Capacity of, in Space, 339 Spherical Condenser, Capacity of, 338 Spirit Levels for Reflecting Galvano- meters, 285 Specific Inductive Capacity, Defini- tion of, 309 Inductive Capacity of Solids and Liquids, 310 Inductive Capacity, Measuring, 332 Specimens of Instructions for Ex- periments, 476 Sprinsr Control Meters, 377 Control Meters, Cunyng- bame's, 382 Control Meters, Magnifying, 386. (See also Magnifying Spring Ammeter and Volt- meter.) Control Meters, Siemens', 377 Squared Paper, Drawing Curves on, 31 Paper, Meaning of Inaccura- cies in Curves Drawn on, 33 Paper, Selection of Suitable Units on, 31 Paper, Use of, 30 Paper, Using, to Find Angles from their Tangents, 56 Paper, Using, to Find Tangents from their Angles, 57 Standard Air Condenser, 334 Candle, Description of, 452 Ceils, 410 Darnell's Cell, 411 Daniell's Cell. E. M. F. of, 412 Daniell's Cell, Fleming's, 412 . Voltmeter, 422 Static and Current Methods of Measuring Potential Dif- ferences Compared, 125 Electric Apparatus, Necessary Enclosure of, in Metallic Case, 108 Statical Method of Comparing Capacities, 330 Stems, Coating Insulating, with Paraffin Wax or Shell-lac Varnish, 267 Storcge Cells, Snvill Internal Re- sis Lance of, 261 Storage Cells, Measuring Resistance of, 206 Strength of Current, Measurement of, 4 of Current, Why Measured by Chemical Property, 10 of Electro -Magnet, Law of, when Core is Slightly Mag- netised, 382 of Poles of Single Needle of Galvanometer, Calibration Unaffected by, 23 Striking Distance, Definition of, note, 371 Strong Current, Measuring Resist- ance during Passage of, 187 Subdividing Potential Difference into Known Fractions, 278 Submarine Cable, Capacity of, 309 Substitution, Simple, Method of Comparing Resistances, 138 Sulphur Dioxide, Specific Inductive Capacity of, 310 SpecificInductiveCapacityof,310 Sulphuric Acid, Dilute, Ett'ect of Electrolysis of, 15 Acid Voltameter, Construction of, 18 Acid Voltameter, Description of, 6 Acid Voltameter, Objection to Ordinary Form of, 18 Acid Voltameter, Volume of Gas produced in, per Second, by one Ampere, 12 Acid Voltameter, Weight of Gaa produced in, per Second, by one Ampere, 22 Super-saturation of Liquid, Defini- tion of, note, 411 Surface Leakage, 266 Leakage, Law of, 270 of Conductor, Electricity at Rest Resides Only on, 119 Suspension, Fibre, used iu Thom- son's Marine Galvanome- ter, 6C Suspensions, Pivot and Fibre, Com- pared, 60 Symbolical Representation of Bat- teries, 173, 240 STABLE of Electric and Heat Conductivities, 159 of Resistances of Insulators, 271 of Resistances for a Given Length and Diameter, 01 for a Given Length and Weight, 157 INDEX. 5L3 Table of Resistances of Metals per Cubic Centimetre, and per Cubic Inch, 154 of Specific Inductive Capaci- ties, 310 of Temperature Variation of Resistance, 160 showing Potential, Density, and Quantity of Electricity on Conductor iu Different Conditions, 123 showing Variation of External Resistance, Current, and Potential Difference at Battery Terminals, 205 Tangent of Angle of Deflection Proportional to Current in Tangent Galvanometer, 43 Definition of, noie, 37 and Degree Scales, Accuracy of Readings Compared, 40 Galvanometer, 36 Galvanometer, Alteration of Sensibility of, by Altering Position of Needle, 51 Galvanometer, Adjustment of Coil of, 46 Galvanometer, Best Deflection to Use with, 41 Galvanometer, Calibration of Galvanometer by Direct Comparison with, 58 Galvanometer. Conditions to be Fulfilled in, 36 Galvanometer, Controlled Only by the Earth's Magnetism, Values in Amperes of De- flections of, 55 Galvanometer, Fulfilment of Conditions for Tangent Law in, 43 Galvanometer, Proportions of Cuauuel in Bobbin of,when Tangent Law is Most Ac- curately Fulfilled, 51 Galvanometer, Scale for, 39 Galvanometer, Simple Form of, 27 Law, How Conditions of, are Fulfilled in Tangent Gal- vanometers, 43 Law, When True, 41 Scale, Mode of Making, 38 Tangents, Finding Angles from, by means of Squared Paper, 56 Telegraph Insulators, 274 Insulators, Testing during Manufacture, 275 Telegraphy, Resistance Boxes used in Duplex, 187 Telephone, Description of the Bell, 336 H H Temperature, Change of Resistance with, Results of Matthies- sen's Experiments on, 160 Curve, Cooling Correction of Observed Kise of, 196 Diminution of Resistance of Insulators with Increase of, 271 Equation connecting Variation of Resistance of Metals with, 153 Law of Variation of Resistance with, 152 Measurement of, Compared with Measurement of Po- tential, 85 Variation of E. M. F. of Lati- mer Clark ; s Cell, 411 Variation of Resistance with, 147 Testing Ammeters, 394 Ammeters for Accuracy of Graduation, 395 Ammeters for Error on Re- versing the Current, 402 Ammeters for Error Produced by External Magnetic Dis- turbance, 403 Ammeters for the Permanent Alteration of Sensibility. 407 Ammeters for Residual Mag- netism, 400 Cables, Sealing up One End while, 268 Insulators during Manufac- ture, 275 Voltmeters, 407 Voltmeters for Accuracy of Graduation, 4i)S Voltmeters for Heating Error, 415 Testing. (See also Comparing, Mea- suring.) Thompson's, Prof. Silvanus T , Rule for Best Dimensi) is of Channel of Bobbin cf Tan- gent Galvanometer, 51 Thomson's, Sir William, Arrange- ment for Increasing a Potential Difference in Known Ratio, 354 Astatic Galvanometer, 283 Astatic Galvanometer, Modi- fied Form of, 284 Electrometers, 93 Electrometer, Edelmann's Form of, 130 Large Current Galvanometer. 53 Leyden Jar, 315 Marine Galvanometer, 103 514 PRACTICAL ELECTRICITY. Thomson's, Sir William, Marine Galvanometer, Fibre Sus- pension used in, 60 Marine Galvanometer, Shield- ing, from Magnetic Dis- turbance, 103 Reflecting Galvanometer, 283 Replenisher, 364 Time Rise of Temperature due to Passage of Current, 195 Tin, Change of Resistance of, with Temperature, 160 Electric and Heat Conductivi- ties of, Compared, 159 Resistance of , for Given Length and Diameter, and for Given Length audWeight, 157 Resistance of, per Cubic Cen- timetre, and per Cubic Inch, 154 U TTNIFORM Controlling Field, Proportional'Galvanonieter with, 72 Magnetic Field,Definition of, 36 Magnetic Field, Motion of Magnet Produced in, 390 Potential on Conductor, 86 Unit of Capacity, 307, of Current, 11 of Density, 117 of Potential Difference, 89, 141 of Power, 442 of Quantity, 289 of Resistance, B.A., 141 of Resistance, British Associa- tion, 141 of Resistance, Legal, 140 of Resistance, Siemens', 142 of Resistance, B. A. and Legal, Compared, 142 Units, Selection of, Suitable on Squared Paper, 32 V "VTALUES in Amperes of Deflec- tions of Tangent Galvano- meter Controlled Only by Earth's Magnetism, 55 Variable Resistance in Voltmeters caused by Self-induction with Alternating Potential Differences, 427 Variation of Capacity of Condenser with Area 01, and Distance between, its Coatings, 303 of External Resistance, Cur- rent, and Potential Dif- ference at Battery Term!- n,ils, 204 Variation of Magnetic Effect ot Bobbin with Current and Resistance, 418 of Resistance with Length, 143 of Resistance with Material, 146 of Resistance with Sectional Area, 146 of Resistance with Tempera- ture, 147 of Resistance with Tempera- ture, Law of, 152 of Sensibility of any Galvano- meter by Altering Dia- meter of Wire, 22 of Sensibility of any Galvano- meter with Length of Wire used in Windiug, 418 of Sensibility of any Galvano- meter by Shunting, 229 of Sensibility of Galvanometer with its Resistance, 416 of Sensibility of Tangent Gal- vanometer, 48 of Sensibility of Voltmeterwith Change of its Resistance, 407, 418 Produced in Total Current by Shunting Portion of Circuit, 253 with Temperature of E. M. F. of Daniell's Cell, 211 with Temperature of E. M. F. of Latimer Clark's Cell, 411 Varley's Accumulating Influence Machine, 367 Varnish, Coating Insulating Stems with Shell-lac, 267 * How to make Insulating, note, 268 Varnishing Shade of Ordinary Gold- Leaf Electroscope 97 Varying Potential Difference in Known Ratio, 278, 354 Vibration, Definition of Periodic Time of, 291 Voltaic Element, 209 Voltameter cannot Measure Alter- nating Current, 198 Copper, Description of, 6, 11. (See also Copper Volta- meter.) Hoffmann's, 15 Silver, Used by Lord Rayleigh, 11, 395 Sulphuric Acid, Construction of, 18 Sulphuric Acid, Description of, 6 Sulphuric Acid, Volume of Gaa produced in, per Second, by One Ampere, 12 INDEX. 515 Voltameter, Sulphuric Acid, Weight of Gas produced in, per Second, by One Ampere, 22 Zinc. (See Zinc Voltameter.) Voltameters, Objections to usual Mode of Constructing, 18 and Galvanometers, Relative Advantages of, 20 Direction of Current in Acid, Copper, and Zinc, 15 Disadvantage of, 20 Independence of Gas Generated and of Metal Deposited of Shape, Size, and Distance Apart of Plates, 10 Precautions in Using, note, 11 Silver, note, 11 Silver, Use of, in Calibrating Ammeters, 395 403 Weights of Metals Deposited on Plates of, per Second, by One Ampere, 11 Why Only Used in Measuring Large Currents, 20 Volt, The, 86 Practical Definition of the, 141 Provisional Definition of the, 89 Voltmeters, 128, 376 Voltmeter, Cardew's Latest Form of, 423 Cardew's, Advantages of, 426 Cardew's, Arranged for Measur- ing Large Potential Dif- ferences, 425 Cardew's, Diameter of Wire Used in, 423 Tardew's, Disadvantage of, 427 Cardew's, Length of Wire Used in Latest Form of, 423 Cardew's., No Heating Error in, 426 Cardew's, Self-induction Small in, 4J7 Commutator, 427 Commutator, Calibrating, 433 Ounynghame's, 382 Cunynghame's.Advautages and Disadvantages of, 385 Cunynghame's, Graduation of, 385 Electro-Magnetic Control, 392 Electro-Magnetic Control, Crompton and Kapp's, 392 Electro-Magnetic Control, Paterson and Cooper's, 393 Electro-Magnetic Control, Ad- vantage and Disadvantage of, 394 - Gravity Control, 391 Voltmeter, Gravity Control, Ad- vantages of, 391 Gravity Control, Disadvantages of, 394 Magnifying Spring, 386 Magnifying Spring, Adjust- ment for Sensibility in, 389 Magnifying Spring, Advantages Magnifying Spring, Best Law of Gauge of Wire for Coils of, 421 Magnifying Spring, Disadvan- tage of, 391 Magnifying Spring, Indication of Direction of Current in, 389 Permanent Magnet, 69 Permanent Magnet, Advantages of, 78 Permanent Magnet, Defect of, 376 Permanent Magnet, Direct- Reading, 76 Spring Control, 377 Standard, 422- with Magnifying Gearing, 386 Best Material for Coils of, 420 Best Material for Coils of Ex. ternal Resistance for, 422 Best Law of Gauge of Wire for, 421 Calibrating by Comparison with Standard Cell, 410 Calibrating, by PoggendorfFa Method, 413 Calibrating, with Known Cur- rent aud Resistance, 408 Errors in, 407 with External Resistance, 421 Waste of Energy in, with High External Resistance, 422 Testing, 407 Testing, for Accuracy of Gradu- ation, 408 Testing, for Heating Error, *15 Variation of Sensibility pf, with Change of its Resistance, 407, 418 Variation of Sensibility of, with External Resistance, 421 Variation of Sensibility of, with Speed of Alternation of Potential Difference, 427 Volume of Ga.s Produced per Second in Sulphuric Acid Voltameter by One Am pere, 12 Voss' Accumulating Influence Ma- chine, 367 Vulcanised Indiarubber, Hooper's, Resistance of, 271 516 PRACTICAL ELECTRICITY. w TTfASTE of Energy in Voltmeters with High External Re- sistance, 422 of Energy in Frictional Elec- trical Machines, 352 Water, Current of, in Pipe Compared with Electric Current, 3, 80 Difference between Pressure of, Flowing in a Pipe, and Electric Potential, 81 Equivalent, Definition of, 198 Jacket, Use of, 193 Watt, Definition of the, 442 Work done in One Minute and One Second, when One, is Developed, 443 Wattmeter, Construction of, 444 Errors in, 415 Wax, Coating Insulating Stems with Paraffin, 267. (See also Paraffin.) Weighing, Measuring Potential Dif- ference hy, 88 Weight Electrometer, 83 Electrometer, Increasing Sen- sibility of, hy using Aux- iliary High Potential, 91 of Gas Produced per Second, in Sulphuric Acid Volta- meter, hy One Ampere, 12 Wheatstone's Bridge or Balance, 166 Bridge, Arms of, 172 Bridge, Best Arrangement of Battery and Galvanometer with, 171, 467 Bridge, Best Resistance for Arms of, 171 Bridge, Commercial Form of, 172 Bridge, Conditions Affecting Sensibility of, 171 Bridge Galvanometer, Best Re- sistance for, 172, 466 Bridge Galvanometer, Current through, 465 Bridge Galvanometer, Meaning of Deflection of, 176 Bridge, Mode of Increasing Sensibility of, 168 Bridge, Key for, 174 Bridge, Superiority of, over Differential Galvanometer, 171 Bridge, Use of Shunt with, 176 Wiedemann and Franz's Table of Heat Conductivities of Metals, 159 Wimshurst Influence Machine, 367 Influence Machine, Attaching Leyden Jars to Collectors of, 37H Influence Machine, Collecting Combs of, 369 Influence Machine, Work done by, 371 Winding Resistance Coils, Mode of, 163 Windings, Variation of Sensibility of a Galvanometer with Number of, 48 Wire and Liquid Resistances, Com- parison of, 194 Best Gauge of, for Differential Galvanometer, 436 Best Gauge of, for Galvano- meter in Simple Circuit, 435 Best Gauge of, for Galvano- meter of Wheatstone's Bridge, 172, 466 Wires Joined in Parallel, 133 Joined in Series, 140 Work done by Current Generator, 202 done by Wimshurst Influence Machine, 371 done in Electric Circuit, 199 done per Minute, and per Second, when One Watt is Developed, 443 i/AMBONI'S Construction of Dry ** Pile, 373 Zero Instrument, Definition of, 380 Zinc Amalgam, 218 How to Amalgamate, 218 Resistance of, for Given Length and Diameter, and for Given Length and Weight, 157 Resistance of, per Cubic Centi- metre, and per Cubic Inch, 154 Temperature Variation of Re- sistance of, 160 Voltameter, Direction of Cur- rent in, 15 Voltameter, Weight of Zinc Deposited on Plate of, per Second, by one Ampere, 11 UHIVERSIT7) BELLE SAUVAGE, LONDON, B.C. 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Illus- trated. 3s. 6d. Cassell & Company's Complete Catalogue will be sent post free on application to CASSELL & COMPAN^ LIMITED, Ludgate Mill, London. "A book without which no physical library can be held to be complete." KNOWLEDGE. "All the useful applications of Electricity are described in its pages. In that respect it has no rival." ENGLISH MECHANIC. MONTHLY, price 6d. (complete in 14 Parts, or One Volume). Electricity in the Service 01 Mcill. A Popular and Practical Trea- tise on the Applications of Electricity in Modern Life. Translated and Edited, with Copious Additions, from the German of Dr. ALFRED RITTER VON URBAN- ITZKY, by R. WORMELL, D.Sc., M.A. With an Intro- duction by Prof. JOHN PERRY, F.R.S. With nearly 850 Illustrations. " This is a large work of 850 pages, profusely illustrated with 850 en- gravings, all very clear and very instructive. The work is in two parts : the first deals with Principles of Electricity, and resembles an ordinary treatise on the subject brought up to date ; the second treats of the Tech- nology of Electricity, and collects, classifies, and describes its modern applications in a popular manner, but with great completeness. This double method of proceeding solves a difficulty which presents itself in connection vrith several sciences of recent development." Educational Times. " This is a book without which no physical library can be held to be complete, containing as it does between its two covers the sum and sub- stance of numerous volumes. To the student it may be commended as an admirably full and clear introduction to the science and art of Electricity ; while to the advanced electrician it will be found of almost equal value a s a book of reference. It is furnished with that desideratum a capital index." Knowledge. 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THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. hanics bnstrator, Technical PERRY, 2J. &/. ALS. nd in Cloth. rs, Drawing rawing for. Isometrical for. Cloth. ad Shading. London. LD 21-50m-l,'3J NALDER BROS, 132, Horseferry Road, Westminb 096 / 7 UUl) JJUliUUlli Scientific Electrical Testing and Physical Instruments. Make a specialty of all the Instru- ments and Apparatus Illustrated in this Book. PRICE LISTS a Experimental Sheets, Rods, ^ M ^ IGNITE eal Purposes, THE' jBBER Co., LIMITED, ^j't. ; Manchester, 6, Charlotte St. ; ** Glasgow., 1 06, Buchanan St. [4 iirnwatcd. Price 7s. 6d. The Age of Electricity, from Amber Soul to Telephone. By PARK BENJAMIN, Ph.D. "Dr. Benjamin's work deals with the electrical appliances which have been adapted to the service of man, and it gives all readers good idea of the wonders that have already been accomplished, while in not a few it w.ll inspire an inclination to pursue some branches of the subject." English Mechanic. " Among the many books which have been recently written to bring a knowledge of the principles of electrical science and its applications home to the reading public, no one is more pleasantly instructive in general style than Park Benjamin's Age of Electricity." Scotsman, " It is full of accurate scientific information." Manchester Examiner. CASSELL & COMPANY, LIMITED, Ludrate Hill, London. Cover 3] c