flbb vD fi LO CD >- f fowmitg Division Range Shelf. ..... Received P ELECTRICAL TABLES AND FORMULAE. ELECTRICAL TABLES AND FORMULAE, FOR THE USE OF TELEGRAPH INSPECTORS AND OPERA TORS. COMPILED BY LATIMER CLARK AND ROBERT SABINR LONDON: E. F. N. SPON, 48, CHARING CROSS. 1871. LONDON : PRINTED BY WILLIAM CLOWES AND SONS, STAMFOKDSTKKET AND CHARING CROSS. PREFACE. THE Appendix to a small work on " Electrical Measure- ments,""" by one of the Authors, containing many elec- trical data and formulae, having proved useful, and met with approval amongst telegraphists, they have been induced to undertake the following more complete com- pilation, which they believe will supply an admitted want. In bringing together such a heterogeneous mass of materials it has been found difficult to follow consistently any systematic plan of arrangement ; but it is hoped that a tolerably copious index will render this unavoidable absence of system a matter of small importance. In the following pages, the " specific resistance" of any insulator has been assumed to be the resistance of a cube knot of the material, at 75 R, calculated from its measured resistance in the form of a cable. In the same way, its "specific electro-static capacity" is taken as the * "An Elementary Treatise on Electrical Measurements," &c., by Latimer Clark. E. & F. N. Spon, Charing Cross, 1868. vi Preface. capacity of a cube knot reduced from the measured capacity of a cable. The reason why the authors have adopted these definitions is because, the knot being the accepted unit of length in cable work, it saves, when thus employed, the introduction of numerical constants in some of the formulae, and at the same time affords convenient values in megohms and microfarads respec- tively. The resistance of a cube knot is the same as that of a strip of the material whose thickness (in the direction of the current) is the same as its breadth, and whose extent of surface, the other way, is one knot. The word mil has been retained as representing the thousandth part of an inch, which in electrical work is found to be a unit of measure of constant practical application. The names farad, ohm, and volt, have not been formally sanctioned by the Committee appointed to report on units by the British Association ; they have, however, come into hourly use among the members of the Committee, and among electricians at large ; and are doubtless destined to be adopted universally. It may be mentioned that, by common consent, the value at first assigned to the farad, as expressing the unit of capacity, has now been assigned to the microfarad: this was done to preserve the unity and simplicity of the system. The word veber has also been introduced to express the unit quantity of electricity, or that which Preface. vii passes through one ohm, in one second, with a difference of tension of one volt. The Authors have made free use of every source of information which was available to them, and have to acknowledge the ready assistance and co-operation they have received at all hands. Their thanks are par- ticularly due to Sir Charles Wheatstone, Mr. G. Preece, Mr. Willoughby Smith, Mr. Charles Hockin, Mr. Herbert Taylor, Mr. Bruce Warren, and Mr. H. C. Forde, for useful contributions : they are also indebted to the works and writings of Sir W. Thomson, Mr. C. W. Siemens, Messrs. Brook and Longridge, Mr. Fleeming Jenkin, and many others whom it is needless to particularize. TABLES AND FORMULAE. Formulae of the absolute system of Units. 1. Fundamental units. Length or space = L. Time = T. Mass = M. 2. Derived Mechanical Units. L 2 M Work = W = Force = F = T LM Velocity = V = . 3. Derived Magnetical Units. Strength of the pole of a magnet . . m - iJ T * M*. Moment of a magnet ml = L T~ l M*. Intensity of a magnetic field . H = L -*-T - 1 M*. 4. Electro-magnetic system of Units. Quantity of Electricity . . . Q = L* x M*. Strength of Electric Current . C = L* T - 1 M*. Electro-motive force . . . . E = iJ T -* M*. Resistance of conductor R = L T - 1 . 2 Units. 5. Electro-static system of Units. Quantity of electricity . . . q = iJ T - 1 M* = v Q. Strength of electric currents . c = IJ T - 2 M* = v C. Tji Electro-motive force . . . e = L* T - l M*= -. v TJ Resistance of conductor . . r L - l T ..=.. v 2 Note. v 310,740,000 metres, per second approximately; the ratio of the electro-static to the electro -magnetic unit of quantity. Force, Work, and Performance. The unit of force in the system of absolute measures is denned to be that force which would produce in a body weighing one gramme a velocity of one metre per second. Now gravitation, acting upon a freely falling body, accelerates it 9'8i metres per second. Therefore, calling the natural unit of force the terrestrial accele- ration of one gramme, it is evident that the absolute unit of force will be only the rr-th part of it, or - of 9-81 9-81 a gramme, acted upon by the earth's attraction, or simply the weight of 3- gramme. 9*oi The unit of work or mechanical effect is the unit of force carried up through one metre ; it is therefore equal to - gramme raised one metre high. 9*oi The unit of mechanical performance may, in the same way, be defined as the unit of work performed in the unit of time, or - gramme raised one metre, in one 9'oi second. Units. 3 Electrical Units of Measurement. The B. A. units are becoming generally adopted in England and elsewhere, and we confine our measurements to them, as being the most rational and concordant. 1. Resistance. The B. A. resistance unit is called an ohm. It is equal to the resistance of a prism of pure mercury i square millimetre section and 1*0486 metres long, at -o cent. One ohm is equal to io 7 , or 10,000,000 absolute electro-magnetic units. A megohm the unit of resistance used in expressing insulations is equal to a million ohms. A megohm is therefore equal to io 13 absolute electro-magnetic units of resistance. A microhm is the smallest resistance unit, being equal to one-millionth part of an ohm, or to io absolute electro- magnetic units. 2. Electro-motive force. The B. A. unit of tension or difference of potentials is called a volt, which is rather less than the electro-motive force of a Daniell's element. One volt equals io 5 absolute electro-magnetic units of electro-motive force, and, according to Professor Thom- son's determination, is about equivalent to 0*9268 times the electro-motive force of a Daniell's element. A megavolt = one million volts. A microvolt = one millionth of a volt, or to ^ of an absolute unit. 3. Current. The B. A. unit of current is equivalent to one veber per second; or the current in a circuit having 4 Units. an electro-motive force of one volt and a resistance of one ohm. 4. Quantity. The B. A. unit of quantity is called a veber* and represents that quantity of electricity which flows through a circuit having an electro-motive force of one volt and a resistance of one ohm, in one second. It is equal to ? or y^th of an absolute unit of quantity. A megaveber is equal to one million vebers. io 5 A microveber is one millionth of a veber or =- io 13 absolute electro-magnetic units of quantity. 5. The B. A. unit of capacity is called a farad* and is equal to io~ 7 absolute units of capacity. The capacity of any electrified body is that quantity of electricity which it contains when the inductive surfaces have a difference of potential of one volt. A megafarad is a million farads. A microfarad is the millionth part of a farad. The electro-static capacity of submarine telegraph cables, per knot length, averages \ of a microfarad. The electro-static capacity of the whole Atlantic Cable is less than 800 microfarads. 6. Heat. The unit of heat is the quantity of heat re- quired to raise one gramme of water one degree (Cent.) of temperature. According to Joule a unit of heat is equivalent to raising 423*5 grammes weight, one metre high. Therefore * See Preface. Units. 5 i unit of heat = 423-5 x 9*8 1 = 4155 absolute units of work. 7 . Electro- Chem ical equivalent. One veber of electricity decomposes 0*00142 grains of water or develops 0*0105 cubic inches of mixed gas, at a temperature of o C. and barometer pressure of 760 m / m . In a circuit through which a quantity of one veber passes, per second (or which has an electro-motive force of one volt and a resistance of one ohm), the weight of hydrogen gas developed, per second, is 0*000158 grains. Therefore the weight of any metal reduced by the unit of current, per second, is 0*000158 x its atomic weight. If a be the atomic weight of any metal in a salt sub- mitted to electrolysis ; R the resistance of the circuit in ohms; and E the electro-motive force in volts; the weight of metal reduced in / seconds will be n a E /, 0-000158 (grains). .K Various Units of Electrical Resistance. 1. WheatstonJs unit* To Professor Sir Charles Wheatstone is due the credit of having constructed (in 1840) the first instruments by which definite multiples of a resistance unit could at will be added to or subtracted from a given circuit. The standard resistance unit which he proposed and employed was that of i foot of copper wire, weighing 100 grains. 2. Jacobfs units. Professpr Jacobi of St. Petersburg * " Phil. Trans.," 1843, vol. cxxxiii., p. 303, 6 Units. has made various suggestions for units of electrical resist- ance. The unit which is commonly known as Jacobi's unit, and of which he sent copies to various physicists, was made of a length of 25 feet of a certain copper wire, weighing 345 grains. Another proposition of Professor Jacobi was to employ as unit of electrical resistance that of a copper wire i metre long and i millimetre diameter. 3. Siemens' mercury unit. This unit represents, ac- cording to the definition of Dr. Werner Siemens, the resistance of a prism of pure mercury i metre long and i square millimetre section, at o C. This unit was first produced in 1860, and resistance coils in German silver wire were adjusted from it. A reproduction of the normal resistance tubes, in 1863, was found to agree within o'i per cent, with the results originally obtained. An error, arising from the specific gravity of mercury having been taken as 13*557 instead of 1 3 -5 96, was corrected in 1866; so that all Siemens' resistance coils issued previously to that date are 0-29 per cent, too great. That is to say, the resistances which are marked as i are really 1^0029 mercury units, and the end results have to be multiplied by this constant (1-0029) m order to be expressed in mercury units according to the definition. One Siemens' unit = 0-9536 ohms. 4. French and Swiss units. In the telegraph adminis- trations of France and Switzerland the unit of the electrical resistance coils in use for some time prior to 1867 was equivalent to the resistance of a length of one kilometre of the iron wire employed for the telegraph lines, 4 Units. 7 millimetres diameter. As no very exact measurements are required to be made of overhead lines, these units were not either denned or produced very exactly, and no temperature was given to enable a reproduction of the units if it should have been deemed desirable. Conse- quently the unit coils of the Swiss ateliers, and those of Breguet and Digney, differed amongst themselves as much as 15 per cent. In 1867 both Bre'guet and Digney readjusted their units to -^ of a mercury unit, which is very nearly their original value. In all French sub- marine cable work, resistance coils adjusted to the mer- cury unit are employed. 5. Matthiesserts unit. This unit was denned as the resistance of a statute mile of pure annealed copper wire ^g- of an inch diameter, at 15*5 C. 6. Varlefs unit. This unit obtained considerable employment in cable and line work of the E. and I. Telegraph Company. Mr. Varley originally con- structed it from a statute mile of special copper wire ^ of an inch diameter; but afterwards readjusted it to 25 mercury units. 7. German-mile unit. The first unit of measurement used in the telegraph service in Berlin was that of a German mile (= 8238 yards) of copper wire, its diameter being ^ of an inch, and its temperature 20 Cent Resistances adjusted to this unit were manufac- tured as early as 1848 by Messrs. Siemens and Co., but have been long since superseded in Prussia, by coils adjusted to the mercury unit. Units. II B ? b b_ >~S M M p p b .b *r\ O O b b O* r* f w & o O) rHO ^".3 wso o O M n M O O tfl's in o p> p b M | X <| T3 1 1 5 M OT S > Units. 9 Development of Heat and Work. According to Joules law, the quantity of heat, H, developed during the time, /, by a current in a circuit in which the current is I, and resistance, R, is (i.) H = P R /. p And since I = , we have also the expressions (2.) H = IE/, and We have also the equation of the quantity, per second, Tf Q = -, therefore (4.) H = Q E /, and, if q is the whole quantity passed in the time /, (5.) H = q E, and (6.) H = Q 2 R /. Any of these expressions gives the amount of heat developed by the current in the time /. An absolute unit of work is performed, per second, by an absolute unit of electro-motive force in a circuit of one absolute unit of resistance. Therefore the amount of work performed in one second by a current of one volt in a circuit of one ohm, will be IQ 5X2 equivalent to = absolute units of work. An absolute io 7 unit of work is equal to part of a gramme raised O'ol IQ 6X2 i metre; and therefore ^ or 1000 absolute units of io Ohm's Law. work are equal to grammes raised one metre, or to 9*oi 101*92 metre-grammes. And since one unit of heat is equivalent to 423*5 (metre-gramme) units of work, a B. A. unit of electro-motive force in driving, during one second, through a resistance of one ohm performs work which is converted into 0*2405 units of heat. Therefore the heat H (in units of heat) developed in / seconds, when R and E (of the above formulae) are expressed in B. A. measures, is as follows : E 2 / H = 0*2405 And the work W (in metre-grammes) performed by the current in driving through the circuit in the time /seconds will be equivalent to . E 2 / W = 101*92 GALVANISM. Ohm's Law. 1. Let E be the electro-motive force, R the resistance, and I the current or quantity, per second, in any galvanic circuit ; then I = |. 2. The resistance R may consist of r that of the battery, and G that which is exterior to it, in which case Ohm's Law. 1 1 3. When a battery of n equal elements is connected up in series, each element having the resistance, r, nE G + nr 4. If the n equal elements are connected up all parallel to each other, 5. When the elements have different resistances, r t , r z , r 3 . . . r n , their electro-motive forces being alike, then in series, 6. When they are parallel, 7. The battery consisting of elements, whose electro- motive forces are E If E 2 , E 3 , . . . E M , and whose re- sistances are r t , r n r y . . . r n , connected in series, I = E, + E 2 + E 3 + . . . + E n G + r, + r 2 + r 3 + . . . + r w ' 8. WTien these unequal elements are connected pa- rallel 12 Kirchhoff's Laws. Kirchhoff s Laws. i. The sum of the currents in all those wires which meet in a point is equal to nothing. Let the currents which approach the point o, be I,, I 2 , I 3 , and those which leave it be / 4, *# * 4 > then I, + I 2 + I 3 - 4 - 4 - i y - i 4 = o. 2. The sum of all the products of the currents and re- sistances in all the wires which form an enclosed figure is equal to the sum of all the electro-motive forces in the same circuit. Laws of Dynamic Electric Circuits. i. The strength of a galvanic current is equal to the quantity of electricity flowing per second ; and is the same in every point of an undivided conductor. n. The strength of the current is proportional to the electro-motive force, when the resistance remains con- stant. (Ohm.) in. The current strength is inversely proportional to Galvanic Circuits. 13 the resistance of the conductor ; and therefore directly proportional to its conducting power. (Ohm.) iv. The current strength is equal to the electro-motive force divided by the resistance. v. The current strength obtained with a battery of given surface is at its maximum when the plates are so divided that the internal resistance of the battery is equal to that of the circuit without. (Jacobi.) vi. The sum of the current strengths in all those wires which converge to a point is equal to nothing. (Kirchhoff.) vn. The sum of all the products of the intensities and resistances in all the wires which form an enclosed figure is equal to the sum of all the electro-motive forces in the same circuit. (Kirchhoff.) viii. If, in any system of circuits, containing any electro- motive forces, a conductor exists in which the current- strength is equal to nothing, the currents in the remaining circuits will not be altered, in the least, if the circuit of the conductor in question be separated or removed to- gether with whatever electro-motive force it may contain. ix. If the conductor in question contain no electro- motive force, the currents will not be altered if, after its removal, the points between which it previously existed be connected directly with each other. (JBosscha.) x. If, on the other hand, it contained an ejectro- motive force, the points can only be joined again, whilst retaining the balance, by inserting between them an equivalent electro-motive force, but irrespective of the resistance which may accompany it. (Bosscha.) 14 Volta-induction. xi. In a system of linear conductors, containing electro-motive forces, the current set up in any conductor, A, by any electro-motive force contained in any other conductor, B, will be identically the same as that which would be set up in B by an equal electro-motive force in A. (JBosscha.) xii. If, in a system of electro-motive forces and con- ductors, there be two of the latter, say A and B, in which the electro-motive force in A occasions no current in B, whatever current may be circulating in B will not be affected if A be interrupted or removed ; nor will the current in A be altered if B be interrupted or removed, however the electro-motive forces in the other circuits may be arranged. (Bosscha.} xin. In any linear conductor through which a current of electricity is flowing, the difference of potential, between any two points with a given resistance between them is the same as that between any other two points having between them an equal resistance. (Ohm.} Laws of Volta-induction. i. In a secondary closed circuit, the excited induction current is proportional to the current strength in the primary circuit. ii. The induction currents arising from the action of a galvanic current upon itself are, both on breaking and making the circuit, equally great, so long as the inducing current strength remains equal. (Edlund.) in. When a metallic closed circuit and a conductor Volta-induction. 1 5 through which an electric current is circulating are either brought nearer to each other or separated, a current is induced in the metallic closed circuit This current is in the reverse direction to that which would have been necessary to effect the approach or separation of itself. (Lenz.) iv. The electro-motive force which a magnet excites in a helix of wire is, c&teris paribus, proportional to the number of convolutions of the wire. (Lenz.) v. The electro-motive force which a magnet excites in a surrounding helix is equal, whatever may be the radius of the coil. Therefore, the currents induced in the dif- ferent rings of wire are inversely proportional to their diameters. (Lenz. ) vi. The electro-motive force excited by a magnet in a helix of given number of turns is the same, whatever may be the thickness or conducting power of the wire. vii. The strengths of the induction currents in different spirals of equal number of turns are proportional to their conducting powers. vin. The longer the connecting wires are, so much more numerous should be the convolutions in order to obtain the maximum current. ix. The more turns which can be put next to each other close by the magnet or magnetised armature, the fewer turns will be necessary to give a maximum current. x. The maximum of an induction current is propor- tional to the strength of the inducing magnet. (Lenz.) xi. The retardation of the development of magnetism in soft iron cores which are wholly covered by helices, 1 6 Magnetism. depends principally upon the opposite currents induced in the helices themselves. The magnetism of the simul- taneous currents induced in the periphery of the core, and the coercive force of the iron, are of less influence. (Beetz.) xii. The retardation of the disappearance of the magnetism from soft iron cores which are wholly covered with galvanic helices, depends however principally upon the formation of currents in the periphery of the soft iron cores. (Beetz.) XIIL The retardations of development and disappear- ance of magnetism in soft iron cores which are only partially covered with helices, depends principally upon the magnetic inertia of the iron. Laws of Magnetism. i. A magnetic field is any space in the neighbourhood or under the influence of a magnet. (B. A. Report?) ii. The unit pole is that which at an unit ( = i metre) distance from a similar pole is repelled with unit force (= -|j grammes j. (Ib.) in. The intensity of a magnetic field at any point is equal to the force which the unit pole would experience at that point (Ib.) iv. The direction of the force in the field is the direction in which any pole is urged by the magnetism of the field ; this is the direction which a short, balanced, freely suspended magnet would assume. Magnetism. 1 7 v. An uniform magnetic field is one in which the in- tensity is equal throughout, and hence the lines of force parallel. ( Thomson.) vi. Opposite poles attract each other; similar poles repel each other. vn. The forces directed from any magnetic point upon equal masses are reciprocally proportional to the square of the distance. (Muschenbrock.) viii. When two magnets are very small and the distance between them very great in proportion to their length, the magnetic action between them is reciprocally pro- portional to the cube of their distance. (Gauss.) ix. The force directed from any magnetic point upon any other mass upon which it acts is reciprocally pro- portional to the square of the distance. The total action between them both is, however, reciprocally proportional to the third power of the distance, when the latter is great. (Gauss.) x. Magnetic forces between a suspended magnet and any mass upon which it acts are proportional to the square of the number of oscillations which (under their mutual action alone) the same magnet makes in a given time. ( Coulomb.) xi. Magnetic forces between a suspended magnet and any magnetic mass are inversely proportional to the square of the time which the suspended magnet takes to complete one oscillation. (Coulomb.) xii. The attraction of a magnet for an armature is pro- portional to the square of its free magnetism. xin. The magnetism excited at any given transverse c 1 8 Electro-magnetism. section of a magnet is proportional to the square root of the distance between the given section and the nearest end of the magnet. (Dub.} xiv. The free magnetism at any given transverse section of a magnet is proportional to the difference between the square root of half the length of the magnet and the square root of the distance between the given section and the nearest end. (Dub.} xv. The mean horizontal component of the earths magnetism, in England, for 1865, was = 1764 (metrical) units of force; i.e., a unit pole weighing one gramme, and free to move in a horizontal plane, would, under the action of the horizontal force of the earth's magne- tism, acquire, at the end of a second, a velocity equal to 1764 metres per second. Laws of Electro-magnetism. i. If we imagine a positive current to flow through the axis of an ordinary corkscrew, the tip of the latter, in any position, represents the direction assumed by the north end of a magnet. If a current circulate in the corkscrew-helix in the direction in which it is turned, a soft iron core in its centre will have its north end towards the tip. (L. Clark.} ii. The total effect of any infinitely long and straight conductor upon any magnetic element is inversely pro- portional to the perpendicular distance between element and the conductor. (Biot and Savart.) in. A magnetic element in the axis of a circular cur- rent is attracted or repelled from the centre with a Electro-magnetism. 1 9 force which is directly proportional to the superficial content of the circle and inversely to the third power of the distance of the element from the periphery. (Weber.} iv. A circular current flowing in the plane of the magnetic meridian deflects a magnetic needle (which is infinitely short in comparison with the radius of the current) so that the tangent of the angle of deflection is proportional to the strength of the current. (Weber.} v. The magnetic intensity of a single deflected needle is without influence upon the angle of deflection. (Weber.) vi. If the circular conductor be turned after the de- flected needle until the latter again coincides with the plane of the former, the current strength is proportional to the sine of the angle through which the conductor is turned. vn. In electro-magnets, the south pole is always found at that end where the positive current enters a right- handed helix. VHI. The free magnetism of the end faces of an electro- magnet is proportional to the current strength in its helix. (Dub.) ix. The attraction between electro-magnets is propor- tional to the square of the strength of the magnetising current. x. The material and the thickness of the helix wire of an electro-magnet are, when the current is equal, without influence upon its magnetism. (Lenz.) xi. The free magnetism of an electro-magnet, with a 2O Electro-magnetism. given current strength, is directly proportional to the number of turns of its helix. (Jacobi.) xn. Its attraction is proportional to the square of the number of convolutions. (Dub.) xm. The attraction between two electro-magnets is proportional to the sum of the products of the current strength and number of convolutions of both helices. xiv. The force with which a bar of soft iron is at- tracted by a galvanic helix is proportional to the square of the product of current strength and number of con- volutions of the helix. (Dub.) xv. The force with which a saturated steel magnet is attracted by a galvanic helix is directly proportional to the product of the current strength and number of con- volutions. xvi. The free magnetism of a solid cylindrical soft iron core of given length is, cateris paribus, proportional to the square root of its diameter. (Nickles.) xvii. The free magnetism at the poles of a horse-shoe magnet is, cateris paribiis, proportional to the square root of the length. xyin. The free magnetism of any given transverse sec- tion of an electro-magnet is proportional to the difference between the square root of half the length and the square root of the distance of the given section from the nearest end. (Dub.) xix. The poles of an electro-magnet attract most favourably when their faces have the same area as the transverse section of the magnet. xx. The attraction between an electro-magnet and Charge. 2 1 its armature increases when the mass of the armature is increased. xxi. The magnetising powers of coils of one and the same metal, with the same surface of battery plates, arranged so as to give a maximum strength of current in each case, are as the square roots of the weights of the metallic wire used. (Menzzer.)* Example. Let us select two electro-magnet coils, No. I . of which has 36 Ibs. of copper wire, giving 25 ohms resistance ; the other, No. 2, consists of 120 Ibs. of copper wire, having a resistance of 6 '3 ohms. The battery which we use in each case consists of 104 elements, each having 0*5 square feet surface, and an internal resist- ance of O'25 ohms. First, it is evident that with No. I coil, we must, in order to obtain with the given battery the greatest current, connect up the elements all in series, which will give 26 ohms. Secondly, for No. 2 coil we must connect up the battery, evidently in two parallel rows of each 52 elements, giving a resultant resistance of 6*5 ohms. Both these methods of connection are according to the rule given at page 94, and both, although not exact, are the nearest approximations to the maxima possible without cutting the plates. And when we have thus obtained for each its maximum current with the given battery, the relations of their magnetising power will be No. i : No. 2 I : <\/~$6 I q. Let ;/, for example, be 0*95 for any given condenser. then we shall have or Q - ? 10-259. WHEATSTONE'S BALANCE. The four resistances are a, Z>, c, and x, the currents being respectively / i. 2 , i z , and i' 4 . The circuit, r, contains a galvanometer ; and the circuit, R, a battery whose 24 Wheatstones Balance. electro-motive force is E. According to KirchhofFs laws : i.) 4 -4-4 = 0; 2.) 4-'4-4 = o; 3.) i iC -i tX + i.r^o; 4.) i^a -\- he i^b ix = o. When the resistances are arranged so that no current goes through the circuit r, that is to say, / 5 = o, and we eliminate the values of the currents from the above, we get a, b, and c being known, the unknown resistance x is b x - c - . a Relation of Resistances to Sensibility of Galva- nometer (Schwendler). If a, b, c, and d are the four resistance-sides of a Wheatstone's bridge, the resistance, g, of the galvano- meter, which gives the greatest sensibility with a given battery and weight of copper wire : ~ /~ i J\ IT, a-}- b + c-\- d' Wheats tones Balance. 25 This is equivalent to the resistance of the two circuits a d and b c, taken parallel between the points i and 2. Therefore, to raise the magnetic moment of a galvanometer to its maximum, its resistance must be equal to the parallel resistance of the two double bratiches which are parallel with the galvanometer. This law, which is approximately true, can only be correct when the insulating covering of the galvanometer wire, for all the different gauges, bears a constant pro- portion to the diameter of the wire itself. It is, of course, practically impossible to adjust the galvanometer re- sistance for every resistance which has to be measured ; but when a galvanometer is being constructed for any special purpose as, for instance, the measurement of knot lengths of cable core conductivity regard may be had with profit to the above law. Arrangement of Balance for reading off directly the Resistances of Copper per Knot without Calculation. For this purpose the sides of the balance are arranged as follows : A = a constant resistance of 2029 ohms. 26 Wheatstones Balance. B = a variable resistance box, which is adjusted each time to exactly as many ohms as there are yards in the length of the cable. C = the conductor of the cable. D = an adjustable resistance, expressing the resistance of the conductor in ohms per knot. The cable (whose length, L, in yards is known) is first inserted in its place ; then the box, B, arranged so as to have L ohms resistance. Equilibrium of the galva- nometer needle is obtained by adjusting the value of D as in ordinary balances. When this is done, supposing the whole resistance of the conductor to be C ohms, we have A D 2029 B C L 2 L Therefore D = C - T = the resistance of the conductor in ohms, per knot. This method is very convenient when the conductors are measured always at the same temperature, as the separate knot lengths of core are at the G. P. Works, as it saves much time in reducing the observed values. For such measurements the resistance box, D, should Wheats tone's Balance. 27 if possible, be constructed with values from croi to 50 ohms. Balance for reading off the Insulation Eesistance in Megohms per Knot without Calculation. This method is analogous to the last; but is not so exact on account of the difficulty of preventing heating of the coils. A is a variable resistance box adjusted in each ex- periment to the same number of ohms that there are knots length in the cable ; B is a constant resistance of one megohm; C is the cable resistance in megohms ; and D is a resistance which is varied until equilibrium is obtained, and which then represents the resistance of insulation in megohms per knot. In this case (supposing the length of the cable to be L knots) we have A _ D _ L I " C =: T Therefore D = C L = the total resistance of the insula- 28 Wheatstone's Balance. tion multiplied into the length in knots, or the insulation per knot, in megohms. For the periodical tests of a submerged cable, whose total insulation resistance is about i megohm, this arrangement would be found convenient ; in which case A and B would be constant values, and the insulation resistance, per knot, would be read off directly from D. Elimination of leading wires The error due to the unknown temperature of the leading wires may be eliminated by the following contrivance. The apparatus to the left hand of the dotted line a b is in the operating-room, that on the right-hand side is without. The leading wires / and /' are of the same metal (copper usually), of the same dimensions and conducting power, and are spun up close together in a suitable cable, so that, at any given point, they both have the same temperature and resistance. The junction of / and R' is to earth ; that of /' and R' is insulated ; r is made equal to r', therefore R'-f/' = R-f / R' = R. Wheatstone's Balance. 29 When the readings with positive and negative currents differ (Sckwendler). bf (a -f b) (W + W >y ) + ^ (a W + 2 W W" + aW") # and are the two branch resistances ; W the adjusted resistance with -f- ; W" that with negative current towards a and b ; and /the battery resistance. Practically we may neglect / and the required resist- ance becomes _ b fW -|- W" _(W" - W') 2 JV I """ /! a \ 2 2 (\ If W and W are not very different I W' 4- W" a 2 If E is the electro-motive force of the measuring battery and e that in one of the sides, (W' + W" Or by neglecting/, the battery resistance, + e= w'-w E ' To estimate the true resistance when balance cannot be obtained at zero : When the true resistance is between two plugged holes ; one giving a deflection a, when too small, and the other a deflection c^ , when too great, the true resistance is the smaller of the two readings from the resistance box, plus - ohms. 30 Shunts. Thus in measuring a length of wire, we plugged no ohms, and found a deflection of 2 to the right ; but with 109 ohms, which was too small, we got 3 to the left ; the true resistance was therefore 109 H ~ = 109-6 ohms. SHUNT AND DERIVED CIRCUITS. Let R,, r lt and r 2 be the resistances of the three lines E which connect the points a and b ; and I, t lt and * a , the currents in the same produced from the battery E. z = E J^^. R r, + R r, + r, r, ' f, t t = E 4= E Rr,-h Rr a r, Rrj-H Rr. + fir,' The resistance R' of the whole circuit through which the current circulates is R' = R + _!!L. The resistance of the parallel shunt circuits is / r r \ therefore ( V ) equal to the product of their resist- \n + ^/ ances divided by their sum. Insulation. 3 1 Galvanometers and Shunts. The joint resistance of a galvanometer and shunt is galv. x shunt as above, ~ c galv. -f- shunt The multiplying power of any shunt is equal to galv. -f- shunt galv. shunt shunt To prepare any given Shunt. It is sometimes necessary to prepare a shunt having some definite multi- plying power, as, for instance, 10, 100, etc. ; if we call the resistance of the galvanometer G, and of the required shunt j, and let n be the multiplying power we require, then G s = n i For example, if a galvanometer of 1089 un i ts required a looth shunt, the resistance of the latter would be 1089 1089 100 i 99 A parallel circuit (r-^ added to a line of known resistance, r ohms, giving a combined resistance, R ohms ; the resistance of the added circuit is Rr r, = - . . . ohms. INSULATION RESISTANCE. Insulation of Cable by deflection. Let the un- known insulation resistance of the Cable be x; the galvanometer resistance, G ; the battery resistance, r; the 32 Insulation. , number of elements, n; the electro-motive force of each element, E ; and the observed deflection of the needle, . CABLE The Cable is then removed, and a known resistance substituted for it of such value as to make the whole resistance of the circuit = R ohms ; the battery is re- duced to a single element; the shunt, j, is inserted across the galvanometer coils ; and the observed deflec- tion becomes \l/. The resistance of the Cable insulation is then - (G + r) (ohms). As (G -}- r) is, however, very small in comparison with x, in practice it is neglected, and x = R7(i + -] (ohms)- 9 \ $/ If the length of the cable be / yards, its resistance, per knot, is / ^ Insulation. 33 If a sine galvanometer be used sn and 2029 sm The most convenient way of employing this test is to make the shunt = ^th of the galvanometer resistance ( or s = ]. The resistance, R, is then made = 10,000 V 99/ ohms, or, more exactly, 10,000 less the resistance of the single element and the shunt. The resistance of the whole cable is then x n meghoms. And its resistance, per knot, 2029 - n (meghoms). Insulation of cable by differential method (Siemens). The galvanometer has two separate coils, a and , whose magnetic effects upon the neevlle are unequal and opposite. r = resistances of a and B. r = resistances of b and B'. E = Electro-motive force of battery B. E' = Electro-motive force of battery B' D 34 Insulation. R = adjustable resistance inserted in the circuit of b. x ~ unknown resistance of cable. The resistance, R, is adjusted until the needle remains over the zero line. The cable is then removed, and a known resistance, W, inserted in its stead ; the ends of the coils, a and b, are connected together with one pole of a single element, B 2 ; and the resistance R! readjusted until the needle points to zero. Then the resistance of the cable is If in taking the latter part of this test the operator use a shunt, s (shown in dotted lines), the value of x becomes Insulation. 3 5 The proportions W+r _ in_ R 7 ^?" m' and (R' + r') m' give the relation between the opposite magnetic effects of the coils, a and b, upon the needle when equal currents circulate in them ; m being that of coil a, and m' that of coil b. Insulation of cable, by loss of charge (Siemens). Let the instantaneous discharge from a given cable (or its full tension) be C ; the discharge after / minutes (or its reduced tension) be c; and the electro-static capacity of the cable be F microfarads. Then the insulation resistance R,, after / minutes, is Example. A knot length of French Atlantic cable had an electro- static capacity (F) = 0-3992 microfarads. The instantaneous dis- charge (C) gave 332 divisions of the scale; the discharge (<:), after I minute, gave 202 divisions. Its resistance was therefore R = 26-06 X - : - : = 300-3 megohms. 3992 (-5211 - -3054) Where the fall, is from full to half tension, or the re- C duced discharge, c = , then R, = 86-56 (megohms). The resistance (after one minute) obtained by this for- 36 Insulation. mula agrees with that measured by the direct methods, if the cable be charged 10 seconds before taking the reading, C; and again 10 seconds before insulating it preparatory to observing the throw, c. For deducing in this way the resistance of a length of cable core, it is more correct to measure its capacity, F, than to calculate it from the length of the piece and the mean capacity of the cable. With a cable of high insulation resistance, of which the loss is very small, great accuracy must be used to measure the loss ; the following plan by Dr. Esselbach is the simplest : (i). Connect up in the ordinary way for taking insula- tion. (2). Take the immediate charge through the galva- nometer with a shunt, holding the key down for at least ten seconds. Then leave the cable insulated with its charge for one minute or more. (During this time, if necessary, increase the resistance of the shunt.) (3). At end of the one or more minutes, recharge cable by pressing down the key as before, and the throw of the needle will represent the quantity required to refill the cable to its original charge, and is exactly equal to the loss during the time the cable remained insulated. To calculate the time T of falling from full to any given tension (if the electrification and resistance remain constant) lose -log/ log C - log c Insulation. 37 Where C = original charge or full tension ; c = ob- served charge (or reduced tension) remaining after / seconds ; p = quantity of charge or tension required to be in the cable at the time T. It being usually required to know the time a cable or wire will fall to half tension, the formula becomes X / (seconds). . log C - log c This formula may be written thus : _ 0-30103 / 2 'ooo log (100 nf where n = percentage of loss in interval of time t (Preece). As electrification goes on during the time the cable is insulated, / should be made as short as possible. The percentage of loss is the same for every interval, /. e. y the percentage of loss of the original charge in the first minute is the same as the percentage of the loss of the remaining charge in the next minute, and so on. At high temperatures (75 Fahr.) the loss of charge during one minute of average telegraph cores varies from 30 to 50 per cent., according to the insulation and the material. Specific Insulation Resistance. The resistance, per knot, of a cable being R megohms, its specific resistance, r, is r = R . . rr : . . . megohms. log D log d The specific resistance is assumed to be that of a cubic knot of the insulator. Insulation. An ordinary gutta-percha cable at 75 F. falls from te'nsion to half tension in about 100 seconds, irrespec- tively of its dimensions. Kesistance in Megohms of any Dielectric whose Electro-static capacity = one Microfarad. observed after i minute ~ V "7 38 27-5 186-3 63 38-7 122-8 88 46-8 95-0 14 12-3 457-9 39 28-1 182-2 64 39-0 I21-J 89 47-1 94; 2 15 13-0 429-2 40 28-6 I78-3 65 39'4 119-8 90 47'4 16 13-8 403-9 '4 1 29-1 174-6 66 39-8 118-4 91 47-7 92-7 17 *4*5 382-0 42 29-6 171-1 67 40-1 117-0 92 47'9 92-0 18 19 15-3 16-0 362-4 344-6 '43 44 30-1 30-6 167-8 164-5 68 69 40-5 40-8 115-4 114-3 93 '94 48-2 48-5 91-2 90-5 20 16-7 329-0 45 3i-o 161-4 70 41-2 113-0 '95 48-7 89-9 21 .17-4 314-1 46 3i'5 158-5 71 III-8 96 49-0 89-2 22 18-0 301-6 47 32-0 155-7 72 41-9 iro-6 '97 49-2 88-5 23 18-7 289-8 48 32-4 152-7 '73 42-2 109-4 98 49'5 87-8 2 4 19-4 279-0 49 32-9 150-5 '74 42-5 108-3 '99 49'7 8T2 25 20-O 268-9 50 33'3 148-0 '75 42-9 107-2 oo 50-0 86-6 To find the resistance, in megohms, of an insulator whose capacity, in microfarads, is known, the tension or discharge, C, being observed immediately after contact, and c after some minutes. Rule. Multiply the value given in the above table by the number of minutes (which the cable remains Insulation. 39 insulated before reading c), and divide by the capacity in microfarads. Example. A knot length of Atlantic core lost 40% of its charge in i minute. Its capacity was 0*41 microfarads. Therefore from above table, 117 X I : - = 285 megohms resistance. Loss of tension. The percentage loss of tension or charge, by an insulated core is independent of both its size and form, and is dependent only upon its material. Thus a coated plate of india-rubber of any size and thickness will lose the same percentage of charge per minute as a cable coated in the same material would, whatever might be its length or thickness of insulator. We shall see further on (p. 68) that or and (p. 35) 26-06 / p Flog^ therefore 26*06 1 ' /= --c log- and 26'o6 That is to say, the time of falling from C to c is propor- tional to the specific resistance (corresponding with its electrification and temperature at the moment), and D 40 Ratio ~j. a specific inductive capacity of the dielectric and to the log. of. D RATIO -7 FOR STRAND AND SOLID CONDUCTORS. a The approximate ratio for insertion in the insulation and induction formulas may be calculated from the weights, W Ibs. per knot of insulator, and w Ibs. per knot of copper, as follows : i. A solid wire covered with gutta-percha : 2. A strand covered with gutta-percha : D *_ / fr w d ' 5 v 97 w ' 3. A solid wire covered with Hooper's material : . W 7 3 w* 4. ^4 strand covered with Hooper's material : D* D / -= V * The value of -^ given by these formulae are the ratios between the diameter of the insulator and the mean diameter of the strand. If the extreme diameter of the strand were inserted in the formulae for calculating insulation, inductive capacity, etc., the resulting electrical conditions of the cable would be misrepresented ; therefore the measured diameter of the copper is diminished 5%, which is equivalent to increasing the measured ratio by 5%. Faults. 41 The accumulation joint test (Clark). This method is very suitable for measuring the insulation of joints, or other very short lengths of core. The battery is con- nected with the conducting wire, and the length of core to be tested is immersed in an insulated suspended trough. A condenser is connected with the water of the trough, so that all the electricity which escapes from the joint or length of wire in a given time (usually one minute) is collected in the condenser. At the end of the minute the whole of this charge is suddenly dis- charged by a key through a galvanometer, the deflection of which indicates the quantity which has leaked through the joint in the given time. Joints are now generally tested by this plan, the leakage from 12 to 20 feet of perfect cable forming the standard of comparison. If the leakage from a joint exceeds this quantity, it is considered faulty, and rejected. FAULTS IN CABLES. Murray's Loop Method. In this method the resistance of the fault is elimi- nated, that of the insulation supposed to be infinite in comparison with it. Let the two adjustable resistances, r and t*, be con- nected together with the battery-contact in the point, c- t the galvanometer be connected between a and b; and the two ends of the cable be connected with the same points. Let the distance of the fault from the ends a and b be 42 Faults. respectively y and x knots, and the total length (x -f y) be L knots. x - L Then, when electrical equilibrium is obtained, (in knots) ^ (in knots). Correction for Murray's Loop Method (Hockin). This correction is seldom available, as the resistance of the fault, as well as of the insulation, must be known. But when these are known, the position of a fault with a resistance of a megohm or upwards can be ascertained very accurately. The same figure as in the last. Let L be the length of the cable. z the distance of the fault from the centre of the cable, in knots. Faults. 43 r and r> the value of the adjustable resistance coils giving equilibrium. F, the known resistance of the fault in megohms; and I, the resistance, in megohms, of the insulation of half the cable (supposed faultless). Then L / 2 F Varley's Loop Method. The cable end c is joined to an adjustable resistance, R ; the end b of the latter and e of the cable are connected with the galvanometer, G, resistances r and p, and the battery, B, in the form of a Wheatstone's balance. x and y are the resistances in ohms of the lengths of cable from the ends to the fault, the whole conductor having / ohms. x = lp - . . . (ohms) ; 44 Faults. (ohms). If the cable be n knots long, the distance of the fault is 7 "R ** / ; r knots from the end and if the test be taken with equal branches in the bridge, 2 Another correction for loop-test (H. A. Taylor). a _ F / b Let F = apparent position of fault by loop-test. A = distance a to F obtained by loop-test in knots. B = b to F f = true position of fault. F to/" = x = distance, in knots, of true from apparent position. P = resistance, in megohms, of cable when perfect. 46 Faults. Q = resistance, in megohms, of cable when faulty. Q (A - B) _ - 2 (P - Q) The true position of the fault is of course further from the centre of the cable than the apparent position. If the true distance of fault from end of cable = d, If A and B are expressed in units, (A B) = the resistance unplugged to produce equilibrium in the loop- test; and (A-f-B) = the total copper resistance of the cable, in which case d will be in units also. Resultant fault in an insulated wire. Mr. W. Schwendler suggested a method of testing cables during their manufacture by means of Murray's loop-test, on the principle, that so long as a cable remained electrically perfect throughout, the leakage through the insulation would make the apparent resultant fault appear to be in the middle; but that if even a very small fault were developed, the apparent resultant fault would no longer be in the middle, but be shifted more or less towards one end, according to the magnitude of the injury. Unfortunately, in practice, the gutta-percha cores are sent to the machines new, and the last lengths joined on are worse insulated than those which have been made some time, so that a cable during manufacture is never homogeneous, and the resultant fault therefore does not, or should not lie in the middle, but towards the end which is being covered. If the cable-ends, during manufacture, be connected up Faults. 47 in a circuit of the loop-test, and the galvanometer needle when deflected make contact as a relay, a bell may be sounded in the event of a fault occurring, and the manu- facture stopped. FAULTS IN SUBMERGED CABLES. When the cable is submerged and only one end is to be had, its resistance R is measured when the farther end is insulated and the resistance r when it is to earth. This can, of course, only be done when the fault is not so great as to entirely prevent communication, or, when by pre-arrangement the operator of the distant station knows when to put his end to earth, and when to insu- late it. i y Let /= x-\- y the whole copper resistance of the cable, before the appearance of the fault ; the resistance of the fault bein = z. x = r - v 7 (R - r) (I - r) (ohms) y = (l-r)+ j/(R-r) (I -T7) (ohms) z = (R - r) + v/ (R - r ) (I - r) (ohms) If a knot of conductor have a resistance of n ohms, 48 Faults. Distance of fault from A = I [_ r ~ \/( R -')('-")] (knots) Distance of fault from B = - n [(/ -r) + VT^^/yi/"^?)] (knots) When, however, the fault is so great that the necessary signals cannot be transmitted to instruct the operator at the further end when to put the cable to earth, and when to insulate it, the home end is either left insulated or arrangements are made to have it insulated and "earthed" at certain agreed periods. The ship then crosses to the other end, where measurements are made, and similar ones are also made at the home end. From the two measurements with the distant ends insulated, i.) R = x + z (ohms) 2.) R' = z+y, (ohms) and we have R - R' / . . . x = 1 (ohms) R' - R , / , . y = 1 (ohms) -D T> ' i / Distance of fault from A = (knots). -nf T> i 7 Distance of fault from B = ^~- - (knots;. From the two measurements with distant ends " earthed," v z T. r - x i- . y -M Faults. 49 2 . r 1 - y -f X Z x-\-z in ohms, and in knots, Resistance of fault. When a cable having a known insulation resistance, R megohms, has a fault in it which reduces its resistance to r megohms; the resistance of the fault is Rr z = ^ . . . megohms. K. r Distance of fault by tension (Clark}. Let the line make complete earth at the fault. R is a resistance in ohms inserted between the home end of the line and one pole of a battery of galvanic elements whose other pole is to earth. T is the tension of one end, and / that of the other end of the resistance, R. Then T -/ : R : : / : x ; whence /R , x = ohms ; 5O Faults. and, if the line has n ohms per statute mile, the distance d of the fault is "p J. d = . (statute miles). n T / The tensions, T and /, are measured with an electro- meter. When f = $ T, which may easily be obtained by adjusting R, then x = R. The same where the fault makes partial earth. The battery, B, is inserted between earth and a resistance coil, R ohms, which is connected with one end of the faulty cable, whose other end, S, is insulated. The tensions of the two ends of R are T and /, and that at the further end of the cable is S. Then the cable resistance, x, between the fault and the end of R, is (/ - S) R x = T J f (ohms). During the laying of the Atlantic Cable these tensions were observed on shore every five minutes by the dis- charge of a condenser, and their value telegraphed to the ship. Method of continuous testing. This system, which is due to Mr. Willoughby Smith, was first employed in 1866, during the laying of the Atlantic line. Faults. 51 The end, a, of the cable on shore is connected with a very great resistance, R, and with the front contact of a manipulating key, K. ct The resistance, R, which may be of selenium or of gutta-percha, has a resistance of 20 to 30 million ohms ; its further end is connected (through the mirror galvanometer G) to earth. A condenser, c, is inserted between the lever of the key and earth. On the ship, the end, b, of the cable is connected per- manently with a mirror galvanometer, s, and battery of 100 cells to earth. The current of this battery causes a steady deflection of s, due principally to the leakage through the insulation, and of G (on shore), due to the passage of the current through R (which is equal to about 10 or 15 miles of cable insulation). This deflection is observed and recorded every 5 minutes. Continuity is observed on shore by the ship changing the direction of the current every 15 minutes, which causes the deflection of G to be reversed. Itmilation on board is measured by the deflection of s; the resistance of R being too great to interfere with the result. Insulation on shore is observed by measuring the 52 Faults. tension at R. This is done every 5 minutes by measuring the discharge from c. The key is pressed down for 10 seconds, putting c to line ; it is then let go, and the dis- charge measured upon the mirror galvanometer, g. The result is communicated to the ship. In the event of a fault occurring, its distance is calculated by the method given above. Speaking through the cable without interfering with the insulation test is done by making R in the form of a con- denser, and by inserting a similar condenser between the end, ^, and galvanometer, s. Then if either ship or shore charge the outside plates with -f- or electricity, a corresponding impulse will be transmitted through the cable, and be indicated upon the galvanometer, al- though no electricity really enters or leaves the cable. By making the slight sudden deflections which are thus produced to the right hand and left hand represent respectively dots and dashes, a continued and speedy correspondence may be kept up during the testing. Exposure of Copper at Fault. When the copper conductor of a cable is laid bare at a fault, if a positive current be sent through, the exposed copper will become oxydised and coated with copper salts. If a negative current be then sent through, those salts will be reduced, and afterwards hydrogen evolved at the fault. It is found useful, in measuring the copper resistance of the injured cable, to avoid the polarization currents of both the copper salts and the hydrogen, by observing the resistance in the moment between the Faults. 53 disappearance of the salts and the evolution of the hydro- gen. For this purpose the operator polarizes the fault by a copper current of some minutes' duration, and then commences his measurement with a zinc current of rather less strength. As the zinc current reduces the copper oxide and salts away from the fault, and the cause of polarization current is thus removed, the apparent resist- ance gradually increases until the first formation of hydrogen, which will cause a sudden and considerable increase. The resistance observed immediately before this sudden increase is the nearest approximation to the true copper resistance of the faulty piece of cable. FAULTS IN LINE WIRES. To find contact between two over-head wires. Let the two overland lines, a b and c d, touch each other at the point/, somewhere between the stations A and B. Let the further end, b, of one of the lines be insulated, and the further end, d, of the other be put to earth. Connect a galvanic battery, E, between earth and the home end, c, of the line c d. Then insert a galvanoscope and adjustable resistance, R, between the home end, a, of line a b, and earth, and between the junction of the galvanoscope with R and the end c of line c d insert a 54 Faults. known resistance r ohms. When the galvanoscope needle is balanced we have the proportion c_f_ r f d R ' and if the whole length, c d, is known, the distance of the fault, cf, from the end, c, is To Localise a Contact between two Wires (Schwendler). 1. Insulate the further ends, and measure the resist- ance of the two wires as a loop = R ohms. 2. Connect the further ends, and measure the resist- ance as before = r ohms. The distance, x, of the contact from the testing station is '-r) (R - r) ' . . statute miles . m -|- m in which L = the length, in statute miles, of one of the lines. m = its resistance per statute mile. L' = the length of the other line. m' = its resistance per mile. Example. Two lines (A and B), each 200 miles long, are sup- ported upon the same posts, and are somewhere in contact. (A) is of No. I wire, the resistance (m) of which is 4 ohms per mile ; the other (B) is of No. 3 wire, which has 6 '6 ohms per mile. Therefore L m 200 X 4 = 800 ; and L' m' = 200 X 6 - 6 = 1320 ohms. When measured with the further ends insulated, the combined Faults. 55 resistance was 2400 ohms ; and when connected it was only 2050 ohms. Therefore the distance (x} of the fault was _ 2050 ->/(8oo + 1320 - 2050) (2400 - 2050) 4 + 6-6 2950^156* = 1893^2 = m . les> 10-6 10-6 When the wires are of the same gauge r - A(2 L m - r) (R - r) .. x = T-^-+ - - - miles. 2 m When the two measurements (R and r) are equal to each other. i. If the wires have different gauges R x - . . miles. - , . m -j- m 2. If the wires are of the same gauge R x = - . . . miles. 2 m Contacts between Line-wires (Culley). 1. When the contact is without resistance, measure the resistance of the loop formed by the two wires. Half this loop resistance, divided by the known resist- ance per mile of the wire, will give the distance of the fault. 2. When the contact is imperfect, that is to say, has resistance, it is better to employ one of the wires between the station and the fault as a leading wire only, insulating its further end ; and using the second wire for measuring. If the two wires be A and B, insulate the further end of A, and connect its near end to the zinc pole of a battery. Connect the copper pole with the 56 Faults. middle of a differential galvanometer. Then connect one coil of the galvanometer to the near end of B ; the other coil to earth ; and the distant end of B to earth. If the needle is balanced the fault is in the middle of the line ; if not, add resistance to one side of the galvano- meter until it is balanced. Then if R ohms be the added resistance, and L ohms the original resistance of B, the length between the station and fault has L-R r = ohms, 2 and the distance, D, of the fault is D = miles, 271 r being the average resistance, in ohms per mile, of the wire. Contact between a Wire and Earth. 1. When the contact to earth is very good, the resist- ance of the section between the station and fault gives the distance of the contact. 2. When the fault has resistance, its distance may be determined with the aid of a second good wire by Murray's loop-test (see page 41). The distant ends of the two wires are joined together. Let L be the original resistance of the faulty line \ L' that of the good wire ; R and R' the proportions of the testing resistances; then the resistance, x, to the fault is L-f L' * = R RTR' 3. When no second wire is to be had, the distance of Faults. 57 the fault must be found by measuring the resistance when the distant end is to earth, and when it is insulated, the original resistance of the line being known. See page 47. Corrected Resistance of Line (Schwendler). R = the measured insulation resistance of line. r = wire resistance (without relay^at distant end) mea- sured. r 1 = wire resistance (with relay at distant end) measured. i.) The corrected line wire resistance (L) is L = 2 (R -V'MR-^) 2.) The corrected insulation resistance (R') is R' = - 3.) The relay resistance (r") at the distant station is R-r' Wires of different gauges. When a line consists of two gauges of wire of the same conducting power, the two diameters being d and d\ and the lengths of the different wires, / and /', if R is the whole measured resistance, the average resistance per mile, r, of the one gauge is r- -*L -R - d* and that of the other gauge d* Faults in short lengths of insulated wire (Clark). Minute faults in short lengths are found by connecting a 58 Faults. powerful battery to one end, and drawing wire slowly through a basin of water or wet sponge insulated by suspension on gutta-percha cords. A Peltier or Milner electrometer is connected with the basin, and renders any leakage apparent. Even the most perfect wires give a visible leakage on the electrometer, and it is some- times therefore necessary to make some imperfect con- nection with the basin by a piece of wood or a wet thread, sufficient to reduce the normal leakage of the wire to a moderate degree of deflection, and any change in this is at once apparent. If the fault be very large, a galvanometer will suffice to indicate it. A coil of a mile of wire wound on a drum, and insulated, may be treated in this way on an insulated stand, and gradually unwound ; the electrometer being connected to the drum, and also a high resistance. As long as the fault is on the drum, the electrometer will be deflected, but as soon as it is unwound the deflection will fall. Warren's Method. This is a somewhat similar, but superior arrangement. The coil of wire is wound on to two separate drums, both insulated, and an electro- meter connected to each. A powerful battery is con- nected to one end of the conductor ; the induction and leakage through the dielectric causing each of the electro- meters to become deflected. Both drums are now dis- charged by touching them with the hand, and the electrometers fall to zero. The drum which has a defect on it, soon, however, acquires its tension again, and its electrometer is deflected, the other remaining Faults. 59 unaffected. More wire is then unwound, till the fault appears on the other drum. The outside of the wire between the drums must be wiped very dry, the other parts should be moist Accumulation test (Clark, 1860). A method for locating a minute fault in an otherwise perfect cable during manufacture. The two ends of the cable are con- nected with the two poles of a large battery, B. Two condensers, C and C', are connected with the opposite poles of the battery. The fault (x) not being in the middle of the cable, the tensions of the charges of C and C' will be as the lengths between the ends of the cable and the fault, or C : C' x n x. Or if L is the whole length of the faulty wire in yards, the distance of the fault from end/ = L . from end n = L . yards ; C' ^7 yards. C-f C' The usual arrangements must be made for measuring the 60 Faults. discharges of the two condensers. If a single galvanometer be used, a commutator will be necessary to invert the coils, so as to get the two deflections on the same side of zero, as the one charge is positive and the other negative. Rupture of conductor. When the conductor of an otherwise perfect cable is severed, the distance of the fault may be found by ascertaining the electro-static capacity of the cable from the testing station to the fault by any of the methods given further on. Let the capacity of the cable be / microfarads per knot; that of the severed portion, F microfarads; the distance, D, is F D = - . . . knots. To test leading wires. When three or more leading or cable wires end near together, their several conduct- ing resistances may be measured as follows : Let the wires be A, B, and C. Connect the further ends of the wires together alternately, and measure their combined copper resistance. Let the resistance of A and B be = r ohms, A C - r ** J ^ 5? ~~ ' / JJ B C = r lt ,, The resistance of A = ' ' - ohms. 2 B = r + r " ~ r > ohms. 2 T \ r y C = "^ ' : ohms. Electro-static Capacity. 61 Determination of Capacity in Absolute Measure. The electro-static capacity of the cable may be mea- sured by means of resistances without comparison with a standard condenser. For this test it is first of all neces- sary to find by experiment what resistance, R, in meg- ohms, would be required to produce, with the same battery used to charge the cable, the unit deflection. The unit deflection with a mirror galvanometer is one division of the scale. The unit deflection of a tangent galvanometer is 90 (because tan 90 = i). The unit deflection of a sine galvanometer is 45 (be- cause sine 45 = i). When the value of R has been ascertained, it is neces- sary to know the time, / seconds, which the needle occupies in making half a complete oscillation, which is found by setting the needle oscillating and counting the number of times it passes across the meridian in a minute or other observed interval of time. Then charge the cable and observe the throw, a, of the needle. If a is read off in degrees, the electro-static capacity is a /sm - C = 2 - - . . . (microfarads) ; TT JK or, a / sin - C = "6366 . . (microfarads). ix 62 Capacity. If a is read off in divisions of the mirror galvanometer scale, '3183 at R . . (microfarads). Example. In the determination of the electro-static capacity of a condenser for the British Association Committee, it was found that with a mirror galvanometer the unit deflection was produced by a given battery power with a resistance R = 5'l6 X io 3 megohms ; the value of/ was 9^37 seconds ; and the throw, #, was 168*5 divi- sions. Therefore C = ' 3 ' 83 * ^ * 9 ' 5? = -994 8 << ferads >- The value of R for the above formula may be found by either of the methods given at pages 86 and 87. Comparison of Electro-static Capacities. i. De Sauty's Method. The resistances a and b, in ohms ; the condenser, c, of known capacity, expressed in microfarads or knots' length of cable, and the cable x, are arranged with galvanometer and battery in the form of a Wheatstone's balance, the point of junction on Capacity. 63 the right-hand side being formed by the earth to which the outsides of cable and condenser are connected. Let a and b (the two wire resistances) be adjusted until, on pressing down the contact, no deflection is observed at the galvanometer. c and x are the electro-static capacities of the con- denser and cable respectively. Then or 2. Varley's Method. The coils g' and g of a differen- tial galvanometer are connected at one end together to the key and battery ; their other ends to the standard condenser c and cable x respectively. A shunt is used across the coil g. The initial magnetic effect of the coil the needle is m, that of^-' is m'. Then 64 Capacity. If the galvanometer coils are equal (m = m 1 ) 3. Method of Swing of Needle. The cable whose capacity is x microfarads is connected with a galva- nometer, and through a contact key with battery and earth. On making contact the needle is deflected a. The cable is removed, and a standard condenser whose capacity is C microfarads is introduced instead, giving a throw of a, . Then a sm x C microfarads. . ttj sin J 2 If in each case a different shunt is used, let the resist- ance of the galvanometer be g ohms ; that of the shunt, when the deflection a with the cable is obtained, be s ohms ; and when the deflection a t with the standard con- denser be s u then x = C a sm . 2 a 1 sin . 2 (microfarads). Capacity. 65 If the shunt is used with the cable, and not with the condenser, . a g + s sm . ^ i fj g x = C . . . . (microfarads). a i sm Inductive capacity from insulation and fall of tension (Siemens)* Inductive capacity = ^ . (microfarads). R (log C - log c) ^ Where R = resistance of insulation, in megohms ; C = immediate discharge ; c - discharge after / seconds ; / = interval of time in seconds. When the cable is very long a resistance, r megohms, is inserted between galvanometer and earth. Key is depressed for T minutes, and deflection, 5 5 7 ~ -^75 words per minute ; and with Morse's apparatus d* (log D - log d) 700 - -z - words per minute, / being the length of the cable in knots, D the diameter of the core, and d that of the conductor, both in mils. Tables of Speeds with Mirror System. The following Tables are calculated from the data supplied by the Atlantic (1866) Cable, taking the working speed at 17 words per minute. The maximum speed attained experimentally with this cable was 25 words, or 50% higher than the working speed. Speed. Working Speed* with Mirror System. 77 Gutta-percha and Copper strand Equal weights. Weights of d D Speed of working in words per minute for following lengths. in in Copper strand. Gutta- percha. mils. mils. 1000 knots. 1500 knots. 2000 knots. 2500 knots. Ibs. Ibs. 100 100 84 235 I8'3 8*1 4-6 2*9 no no 88 246 2O'I 8-8 5-0 3* 2 120 120 92 257 22'0 9*7 5'5 3*5 130 130 96 268 24*O 10*6 6-0 3-8 140 140 99 278 26-0 11-4 6-5 4*2 150 150 103 288 27"5 12*2 6-9 4'4 160 160 106 297 29-3 I3-0 7'3 4'7 170 I/O 109 JX'I 13-8 7-8 5-0 180 1 80 315 33' 14 7 8'2 5*3 190 190 116 324 35' 15 5 8'7 200 200 119 332 37'o 16-4 9*2 5'9 210 210 122 340 38-4 17-0 9-6 6-1 22O 220 I2 4 348 40-3 17-9 6-4 230 230 127 356 42-1 18-7 10-5 6-7 240 240 130 364 44-0 19-5 II'O 7-0 250 250 133 371 46-0 20-4 11*2 7*4 260 260 379 48-0 2i'3 I2*O 7*7 2 7 270 138 386 49 '4 21-9 12-3 7'9 280 280 I4O 393 51-2 22* 7 I2'8 8-2 290 290 143 400 23-6 13-3 8-5 300 300 145 407 55-0 24'4 14-0 8'8 310 310 148 413 57-0 25-3 14-2 9-1 320 320 150 420 59-0 26-2 15-0 9*4 330 330 152 427 6o'4 26-8 15-1 9*7 340 340 J55 433 62-2 27-6 10-0 35 350 157 439 64' i 28-5 16-0 10-3 360 360 159 446 66-0 29*3 16-5 10*6 370 370 161 452 68-0 30-2 17-0 10-9 380 380 164 458 70-0 31-1 11*2 390 390 166 464 71-4 31-7 17-9 11-4 400 4OO 168 470 73-2 32-5 18-3 11-7 The maximum speed is 50% higher. Speed. Working Speed* with Mirror System. Gutta-percha 10% heavier than Copper strand. (7 - 2 ' 92 ) Weights of d D Speed of working in words per minute for following lengths. in in Copper Gutta- mils. mils. 1000 1500 2000 2500 strand. percha. knots. knots. knots. knots. Ibs. Ibs. IOO no 84 245 ig'O 8-4 4'8 3-0 no 121 88 257 21*0 9'3 5'3 3'4 120 132 92 268 23-0 10*2 5'8 3'7 130 143 96 279 25-0 II"! 6'3 4'P 140 154 99 290 27-0 I2'0 6-8 4'3 150 165 103 300 28-4 I2'6 7-1 4'5 160 176 106 310 30-4 !3'5 7-6 4'9 170 187 109 3 r 9 32-3 14-3 8-i 5'2 180 198 H3 329 34*2 15-2 8-6 5*5 190 209 u'6 338 36-1 16*0 9-0 5-8 200 220 119 346 38-0 i6'9 9'5 6-1 210 231 122 355 40-0 17-8 JO'O 6-4 22O 242 124 363 42-0 18*6 10-5 6'7 230 253 I2 7 37 1 44-0 19-5 II'O 7-0 240 264 J30 379 46*0 20*4 11-5 7'4 250 275 133 387 48-0 21-3 I2'0 77 260 286 135 395 49*4 21-9 12-4 7-9 270 297 138 402 5i'3 22-8 12-8 8-2 280 308 140 410 53*2 23-5 13*4 8'5 2 9 3i9 143 4U 55-1 24'5 I 3 -8 8*8 300 330 145 424 57-0 2 5 -3 14*3 9-1 310 34i 148 43i 59'o 26'2 14*8 9.4 320 352 150 438 61-0 27T i5'3 9-8 330 363 152 445 63-0 28'0 i 5 '8 io- 1 340 374 155 45 * 65*0 28*9 16-3 10-4 350 385 157 458 67-0 29'7 i6'8 10-7 360 396 159 465 68-4 30-4 17-1 10*9 370 407 161 47 1 7*3 31'2 17-6 11*2 380 418 164 477 72-2 32-1 18-1 n-6 390 429 166 484 74-1 32'9 18-5 11-9 400 440 168 490 76*0 33*7 19*0 13*1 The maximum speed is 50% higher. Speed. Working Speed* with Mirror System. 79 Gutta-percha 20% heavier than Copper strand. Weights of d D Speed of working in words per minute for following lengths. Copper Gutta- in mils. in mils* 1000 1500 2OOO 2500 strand. percha. knots. knots. knots. knots. Ibs. Ibs. IOO I2O 84 254 2O*O 8-9 5' 3*2 no 132 88 267 22'0 9-8 5'5 3'5 120 144 92 279 24*0 10-7 6-0 3'8 130 I 5 6 96 290 26'0 11-5 6-5 4'2 140 168 99 301 28-0 12-4 4*5 150 1 80 103 312 30*0 !3*3 7*5 4'8 160 192 106 322 32-0 14-2 8-0 170 204 109 332 33'5 14-9 8-4 5'4 1 80 216 "3 34i 35'5 15-8 8*9 5*7 190 228 116 37'4 16-6 9*3 6-0 200 240 119 360 39-4 *7*5 9*9 6-3 2IO 252 122 369 41-4 18-4 I0'4 6-6 220 264 124 377 43*3 19-2 io-8 6-9 230 276 127 386 45*3 20'I 11-3 7-2 240 288 130 394 47*3 2I*O 7-6 250 300 133 402 49'3 21-9 12-3 7*9 260 3" 410 51-2 I2'8 8'2 270 324 138 418 23-6 13-3 8-5 280 336 140 426 55-2 24-5 13-8 8-8 290 348 143 433 14-3 9-1 300 360 145 441 59*1 26'2 14*8 9'5 3 IO 372 148 448 6i-r 27-1 15*3 9'8 320 384 150 455 63*0 28'0 15-8 330 396 152 462 65-0 28-9 16-3 10-4 340 408 155 469 67-0 29*7 16-8 10-7 350 420 157 476 69*0 30*6 17-3 11*0 360 432 483 71-0 3 J *5 17-8 II -4 370 444 161 490 73-0 32*4 18-3 n7 380 456 164 496 33*3 18-8 I2'0 390 468 166 503 77*o 34-2 19-3 12-3 400 480 168 509 79-0 19-8 12-6 The maximum speed is 50% higher. 8o Speed. Table of actual Speeds attained in working through existing Cables. CABLE AND SECTION. Date of Exp. Log 5 Length in Knots. Actual Speed in Words per Minute. System. i. RED SEA : Suakin-Aden section . . 1860 0-5322 629 ii Morse 2. MALTA-ALEXANDRIA : Malta Tripoli . . 1861 0-4809 230 3 1 Morse Tripoli Bengazi . 57 2 4 do. Bengazi Alexandria 597 17 do. Alexandria Malta . .. .. 1330 do. 3. PERSIAN GULF: Fao Bussire . . 1864 0*5384 155 2 5 Morse Bussire Mussendom 329 17-5 do. Mussendom Gwadur tt ] t 358 16*7 do. Gwadur Manora . f 266 20 do. Fao Mussendom . tt >t 547 12*1 do. Mussendom Manora .. .. 624 9-64 do. 4. ATLANTIC CABLE (1865) . . 1867 0-5020 1896 17 Mirror 5. ATLANTIC CABLE (1866) . . 1867 0*5020 1857 17 Mirror 6. MALTA-ALEXANDRIA (1867) 1868 0-5107 925 19 Mirror 7. FRENCH ATLANTIC (1869) : Brest St. Pierre . . . 1869 0-4468 2584 f'inv Mirror St. Pierre Duxbury . . 0-5107 749 f Any I speed do. The following Table, extracted from a more detailed one by Sir W. Thomson, gives the relative speeds of working similar lengths of cables having different ratios - when D is given. a d D Speed = d D Speed = id \* D D d 200e (^) l g Galvanometers. a ) ' Cfa . Instead of observing the two maximum deflections on the same side, the velocities at the moments when the needle makes alternate returns to the zero line may be observed. GALVANOMETERS. The mirror galvanometer, as arranged by Professor Thomson, shows the deflections of the needle by the reflection of a ray of light upon an equally divided scale. As the angular deflections which produce the movements of the ray of light upon the scale are small, it is assumed that the values which are read off, and which are pro- portional to the tangents of twice the angles of deflection, are also proportional to the currents producing them. The sine galvanometer is turnable about a pin in its centre. When the needle is deflected from the zero, the coils are turned after it until the zero point is brought again to coincide with the needle. The strength of current producing the deflection is then directly pro- portional to the sine of the angle through which the coils are turned. The tangent galvanometer has its coil always placed in the plane of the magnetic meridian, and has a diameter at least ten times the length of the needle. When the needle is deflected, the current producing the deflection is directly proportional to the tangent of the angle. In absolute measure the current strength, I, producing he deflection a, is r* I = 1764 tan -i>-'MM^^'^'A-<-^-^viU ; v TVVO O vO v> r~ r- r~oo CO eo CT* O> CT< wMr>r~vMTM-M-.~MrM-N>rvt-M-i^M-M-i'^UM^CM-iM ? 3 8 8 s 5 vci^oo<\oo<^ao<^>oor~MvOwvOO^'r-M -rft vO O -^oo w 1^00 PI p p'g, *, 2, $ E^SSl.^ JTfTS J?J?"pfN S S S 8 8 w >- O t O GSOO t-\0 |8?J '"SI r! "r* t^ U ^" &* C jj HH o t^oo r^ t^-vO r\ - ^ ^ CO oocoooeo 3 IO2 Voltameter. Voltameter. The volume of gas developed, per second, is directly proportional to the strength of the current. Let v h be the volume of gas developed. / its temperature in deg. Centigrade. k the barometric pressure in millimetres. then the volume # at o Cent, is 760 (i + 0-003665 /) The B.A. unit of current develops 10-32 cubic centi- metres of mixed gas per min. at a temperature of o C., and a pressure of 76o mm mercury. , Jacobi defined his unit of current to be that current which, in one minute, at a temperature of o Cent., and under 760 millim. barometric pressure, develops one cubic centimetre of explosive gas. It is therefore equal - vebers per second. Electrolysis. When part of the circuit of an electric current is composed of a fluid conductor, decomposition of its elements takes place, the constituents resolving themselves in the vicinity of the one or other pole ac- cording to their relative electro-positiveness. In a circuit containing water through which an unit of current is circulating (one veber per second), a volume of mixed gases equivalent to 0-00142 grains of water will be generated per second. Therefore, in a circuit in which the quantity of current circulating is equal to n vebers per second, the weight, W, Copper. 103 of water decomposed in / seconds will be W = 0*00142 n t grains, of which the weight w of hydrogen gas will be w = -. 0*00142 n t = 0*000158 n t grains. 9 If instead of water we have a solution of some metal whose atomic weight is a, the weight vf of this metal deposited upon the negative electrode in / seconds, whilst a strength of current of n farads circulates will be it? = 0*000158 an /"grains. Heat produced in a Conductor by a current = 0*2405 R C 2 / . . (units of heat), R = Resistance of wire in ohms. C = Current strength, in vebers, per second. / = time in seconds. = heat (in units of heat). Example. In a circuit in which is contained a battery of galvanic elements the current strength is equal to one B A unit (or about equivalent to that of a circuit containing one Daniell's element and I unit resistance). This current circulates through a coil of thin wire, which has i'2 ohm's resistance, during 5 seconds. What amount of heat (6) is thereby developed in the wire ? Answer. 6 = 0*2405 x 1*2 x 5 = i'443 units of heat. That is to say that, had this wire coil been plunged into water during the time that the current was circulating in it, the heat developed would have been sufficient to raise 1*443 grammes of water i Cent, from its point of greatest density'. COPPER. The specific gravity of copper wire, according to the best authorities, is about 8*899. One cubic foot weighs about 550 Ibs. IO4 Copper. One cubic inch weighs 0*32 Ibs. The ordinary breaking weight^ of copper wire is about 17 tons per square inch, varying, however, greatly according to the size and degree of hardness. The weight, per nautical mile, of any copper wire is d* about Ibs., d* being the diameter in mils. The weight, per knot, of a copper strand is about 4 ibs. 70-4 The weight, per statute mile, of any copper wire is Ibs. A mile of No. 16 wire weighs in practice from 63 3 to 66 Ibs. The diameter of any copper wire weighing w Ibs. per nautical mile is 7*4 \Xze7mils. The diameter of any copper wire weighing w Ibs. per statute mile is 7*94 \/w . . mils. The diameter of a copper strand weighing w Ibs. per nautical mile is about 8-4 <\/w .... mils. The resistance of a nautical mile of pure copper weighing i Ib. is at 32 Fahr. 1091-22 ohms, at 60 1155-48 at 75 1192-43 The resistance per nautical mile of any pure copper wire or strand weighing w Ibs., is at 75 Fahr. Copper. 105 The resistance per nautical mile of any pure copper wire trails in diameter, is ? 2 ohms at 75 Fahr. The resistance per statute mile of any pure copper wire is 54 92 ohms at 60 Fahr. The resistance per nautical mile of any pure copper strand is 3 ? 2 4 ohms at 75 Fahr. The resistance, per knot, of a cable conductor is equal to 120,000 divided by the product of the per- centage conductivity of the copper and its weight, per knot, in Ibs. The resistance of a statute mile of pure copper weigh-, ing i Ib. is 1 002 *4 ohms at 60 Fahr. No. 16 copper wire of good quality has a resistance of about 19 ohms. The resistance of a statute mile of pure copper weigh- ing w Ibs., is - - ohms at 60 Fahr. The resistance of any pure copper wire / inches in length, weighing n grains = 001516 X / 2 , - ohms. n The conducting power of a pure metal wire, at o Cent., being C , its conducting power, at t Cent, is C, = C (i - -003765 /+ -00000834 / 2 ) The resistance of copper increases as the temperature rises 0-2 1 per cent, for each degree Fahr., or about 0-38 per cent, for each degree Centigrade. A table of re- sistances at different temperatures is given below. io6 Copper. TABLE for Calculating approximately the Resistance of Copper at different Temperatures Fahr. To increase from lower temperature to higher, multiply the Resistance by the Number in Column 2. To reduce from higher temperature to lower, multiply the Resistance by the Number in Column 4. No. of No. of No. of No. of De- Column 2. De- Column 2. De- Column 4. De- Column 4. grees. grees. grees. grees. . 16 0341 O I' 16 0*9670 I OO2I 17 '0363 I Q'9979 17 0-9650 2 0042 18 0385 2 0-9958 18 0-9629 3 0063 *9 0407 3 0-9937 19 0-9609 4 0084 20 0428 4 0*9916 20 0-9589 5 OIO5 21 0450 5 0*9896 21 0-9569 6 0127 22 0472 6 0-9875 22 0-9549 7 "0148 23 0494 7 0-9854 23 0-6529 8 0169 24 0516 8 0-9834 24 0-9509 9 Oigi 25 0538 9 9813 25 0-9489 10 O2I2 26 0561 10 0-9792 26 0-9469 ii 0233 27 0583 n 0-9772 27 0-9449 12 0255 28 0605 12 0-9751 28 0-9429 13 0276 29 0627 13 0-9731 2 9 0-9409 14 0298 30 .0650 14 0-9711 3 0-9390 15 0320 15 0-9690 The conductivity of any copper wire is obtained by multiplying its calculated resistance by 100, and dividing the product by its actual resistance. Pure copper is taken as = 100. The conductivity of any copper wire, / inches in length, weighing w grains, and having a resistance of r ohms, is 0-1516 / 2 wr The conductivity of any copper may be determined by taking a standard having a resistance equal to 100 inches pure copper, weighing 100 grains at 60 Fahr. Copper. 107 ( = 0*1516 ohms). The conductivity of any other wire of similar resistance will be as the square of its length in inches, divided by its weight in grains. To find the weight (w) of copper in Ibs. per knot required for a given speed of working through a given length of cable. Let s be the speed determined upon, in words per minute ; / the length in knots ; and a the ratio which is intended to be employed between the weights of G. P. and copper strand.* 1. When the speed s is obtained with the reflecting galvanometer, s! 3 w - - - Ibs. per knot. log ( i -05 \/ 1 -f- 6 -8 a) 600000 2. When the speed s is obtained with the Morse apparatus, si 2 Ibs. per knot. log (1-05 V i + 6-8a) 36500 When the cable is to be insulated with Hooper's india- rubber, the data having been determined upon as before, 1. With the reflecting galvanometer, si 2 w = - - Ibs. per knot. log (1*05 \/i -j- 57 a) 810,000 2. With Morse, si 2 w = - - Ibs. per knot. tog ('95 V J + 57 *) 49o * In the Malta- Alexandria cable, o ( = ) = i ; in the Atlantic V W io8 Copper. Example. In a proposed cable it is determined to take equal weights of copper strand and gutta-percha (therefore a = i); the length is 1792 knots ; and it is required to work with the reflecting galvanometer at the maximum rate of 14 words a minute. The quantity of copper required will therefore be 14 x I792 2 log (1-05 */6'8) 610000 = 1 68 Ibs. per knot. Table for Calculating Resistance and Conducting Power of (pure) Copper. (Temperatures in deg. Cent.) Temp. Cent. Resistance. Conducting power. Temp. Cent. Resistance. Conducting power. I'OOOOO I ' OOOOO 16 06168 0*94190 I 1*00381 0-99624 17 06563 0-93841 2 1*00756 0*99250 18 06959 0-93494 3 1-01135 0-98878 19 07356 0*93148 4 1-01515 0-98508 20 07742 0*92814 5 1*01896 '98139 21 08164 0*92452 6 02280 0*97771 22 08553 0-92121 7 02663 0*97406 23 08954 0*91782 8 03048 0*97042 24 09356 0*91445 9 03435 0*96679 25 09763 O-gillO 10 03822 0-96319 26 IOl6l 0-90776 ii 04199 0-95970 27 10567 0-90443 12 04599 0*95603 28 10972 0-90113 13 04990 0*95247 29 11382 0-89784 14 05406 0*94893 30 11782 0-89457 15 05774 0*94541 The percentage decrement in the conducting power of an impure metal, between o C. and 100 C., is to that of the pure one, between oC. and 100 C., as the con- ducting power of the impure metal at 100 C. is to that of the pure one at 100 C. (Matthiessen.}* Phil. Trans., 1864, p. 167. Copper. 109 TABLE of RESISTANCES of PURE COPPER WIRES. (Halt.) Diameter in inches. Diameter in millimetres. Number of yards per Ib. Number of metres in i kilo. Resistance in ohms of pure copper (unit of length 1760 yds. or 1609-31 mtrs). 2302 5-847 2*095 4*223 i-oo 226 5-740 2-175 4-384 1-038 198 5 029 2-834 1-352 183 4-648 6-680 1*583 175 160 4-064 3*628 4*350 7*314 8-75 1*731 2-o68 136 3-454 6-007 12-11 2-867 128 3 251 6*781 I3-67I 3*237 107 2-717 9*705 19*555 4-623 10 092 2-54 2-336 ii-n 13-125 22-398 26-46 5-300 6-266 08 2-032 35*00 8-288 07 778 22-67 45-71 10-82 065 651 26-29 53-00 12-25 0625 587 28-472 57-40 13*59 06 521 30-864 62-223 I4*73 058 473 33*03 66-588 15*76 056 422 71-431 16-91 054 371 38-104 76-818 18-18 052 32 41-091 82-839 19-61 05 048 274 219 44-444 48-225 89-60 97 '222 21-21 23-02 046 168 52-51 105-86 25-06 044 042 117 066 57*39 62-98 II5-70 126-96 27-39 30-06 04 038 036 016 965 914 69-444 77-16 85-766 140-00 I55-50 172-91 33*14 36-72 40-92 034 864 95-29 292-70 45*48 032 813 108-5 218-74 51-79 03 762 123-46 248-90 58-93 028 026 660 141-72 164-36 285-71 331-35 67-65 78-46 024 609 192-9 380-26 92-08 022 558 229-56 462-80 109-58 02 508 277-78 560-01 132-59 018 016 : 342*94 434; 03 691-36 875-00 163-69 207-17 014 *355 1148-10 270-58 OI2 305 771-60 I555-50 368-30 oi 254 ini-ii 2239-80 530-35 0095 241 1231-10 2481-90 587-64 009 228 ; 1371* 7 2765-30 0085 216 1537*8 3100-20 734'05 008 203 1736-1 3500-00 828-67 0075 190 1975*3 3982-20 942-84 007 177 2267-6 4571-00 1082-4 0065 165 2629-9 5300-00 1225-3 006 152 3086-4 6222-30 1473-1 0055 139 3673*1 7404-90 1753-2 005 127 4444*4 8960-00 2121-4 0045 '"J 5487-0 11062-00 2619-0 004 106 6944*4 14000-00 3314-7 0035 003 088 076 9070-3 12346-0 18285-09 24890-00 4329-4 5892-7 0025 063 17777*0, 35838 -oo 8485-6 no Copper. RESISTANCE (R) in ohms of a knot-pound of COPPER WIRE of various CONDUCTIVITY at different TEMPERATURES. (Ftiller.) ! PERCENTAGE OF CONDUCTIVITY. 100-0% 98-0% 96-0% 94-0% 92-0% 90-0% 88-0% 86 -0% 84 '% 82-0% F. R. R. R. R. R. R. R. R. R. R. 32 1091 i"3 "37 1161 1186 1212 1240 1269 1299 1331 33 1094 1116 "39 1163 1189 1215 1243 1272 1302 1334 34 1096 1118 1142 1166 1191 1218 1245 1274 1305 1337 35 1098 II2I "44 1168 "94 I22O 1248 1277 1307 1339 36 IIOI 1123 1146 1171 1196 1223 1251 1280 1310 1342 37 1 103 1125 1149 "73 "99 1226 1253 1283 1313 1345 38 1105 1128 "5i 1176 I2OI 1228 1256 1285 1316 1348 39 1108 1130 "54 1178 I2O4 1231 1259 1288 1319 1351 4 IIIO "33 1156 1181 1207 1233 1261 1291 1321 1354 41 III2 "35 "59 "8? 1209 1236 1274 1293 1324 1357 42 i5 "37 1161 1186 1212 1239 1267 1296 1327 1359 43 1117 1140 1164 "88 I2I 4 I2 4 I 1269 1299 13 ?o 1362 44 1119 1142 1166 1191 1217 1244 1272 1302 1333 1365 45 1122 "45 1169 "93 I2ig 1246 1275 1304 1335 1368 46 1124 "47 1171 1196 1222 1249 1277 1307 1338 1371 47 1126 "49 "73 "98 I22 4 I2 5 2 1280 1310 1341 J374 48 1129 1152 1176 1201 1227 1254 1283 1313 1344 1377 49 H3I "54 1178 1203 I2JO 1257 1285 1315 1347 1380 5 "34 "57 "81 1206 1232 I26o 1288 1318 1349 1382 51 1136 "59 "83 1208 1235 1262 1291 1321 1352 1385 52 53 Ilj8 1141 1161 1164 1 186 1188 I2II 1213 1237 1240 1265 1267 1293 1296 1324 1326 1355 1358 1388 1391 54 114? 1166 "91 1216 1242 1270 1299 1329 1361 1394 55 1145 1169 "93 1218 1245 1273 1301 1332 1363 1397 56 1148 1171 "95 1221 1247 1275 1304 1334 1366 1400 57 1150 "73 "98 122J 1250 1278 1307 1337 1369 1402 58 1152 1176 1200 1226 1253 I28o 1310 1340 1372 1405 59 "55 1178 1203 1228 1255 1283 1312 1343 1375 1408 60 1157 "81 1205 1231 1258 1286 1315 1345 1377 1411 61 "59 1183 1208 1233 1260 1288 1318 1348 1380 1414 62 1162 1185 I2IO 12^6 1263 1291 1320 1351 1383 1417 63 1164 1188 1113 1238 1265 1293 1323 1354 1386 1420 64 1166 "90 1215 1241 1268 1296 1326 1356 1389 1423 65 1169 "93 1218 I2 4 ? 1270 1299 1328 1359 1391 1425 66 1171 "95 I22O 1245 1273 1301 "31 1362 1394 1428 67 1174 "97 1222 I2 4 8 1276 1304 1334 1365 !*97 1431 68 1176 1 200 1225 1251 1278 1307 1336 1367 1400 H34 69 1178 1202 1227 1253 1281 1309 1339 137 1403 M37 7 1181 I2O5 I23O 1256 1283 1312 1342 1373 1405 1440 71 1183 1207 1232 1258 1286 13 14 1344 1376 1408 1443 72 1185 1209 1235 I26l 1288 I?i6 1347 1378 1411 1445 73 1188 1212 1237 1263 1291 1320 135 1381 1414 1448 74 1190 1214 I2 4 1266 1293 1322 1352 138^ 1417 1451 75 1192 1217 I2 4 2 1268 1296 1325 1355 1386 1419 1454 To find the resistance, per knot, in ohms, of Copper in a Cable : Rule. Divide the value of R given, in the above Table, by the weight of Copper, per knot. The quotient is the resistance required. Example. The Copper of the Persian Gulf Cable weighs 225 Ibs. per knot ; its conducting power was 88% of pure Copper : what is its resistance, per knot, at 75 Fahr. ? In coL 88%> opposite 75, we find 1355. The resistance is therefore ^^ = 6*02 ohms per knot at the given tempera- ture. Copper. ill The resistance of any copper wire may be found for any temperature from its known resistance at any other temperature. Refer to the column giving the percentage of con- ductivity in the Table. Divide the known resistance by the figure opposite the given temperature, and multiply by the figure in the same column, opposite the required temperature. Example. A conductor with 90% conductivity has a resistance of 130 ohms, at 60 F. ; its resistance at 75 F. is therefore TABLE of No. of Yards per Ib. of small Copper Wire. (Culky.) Birming- ham Wire Gauge. Diameter. No. of yards in i pound. Inches. Milli- metres. 24 02 5 635 177*7 25 023 584 210-0 ^- - 26 -019 483 307-8 v 27 018 457 342-94 /" 28 -016 406 29 015 381 493-8 30 -014 355 569-51 f / 31 *OI2 305 771-6 32 oio 254 IIII'II 34 0096 -244 1205-6 35 0087 -221 146^*6 ' *-.,,, 36 0079 200 1780-3 37 0067 170 2475*2 0058 147 3302-9 39 -OO42 106 6298-7 40 0039 099 7305-0 41 0033 084 IO2O2*O A strand of 7 No. 16 copper wires weighs 2*017 oz. per yard, 221-87 Ib. per mile. 112 Copper. A strand of 7 No. 2 2 copper wires weighs "944 oz. per yard, 103-81 Ib. per mile. Hooper's Tinned Copper Wire. The coefficient corresponding to i Fahr. for Hooper's tinned copper wire is '208 per cent, of its resistance at 75 Fahr. ; consequently, to ascertain the resistance at any temperature, we have to add or subtract / times '208 per cent of the resistance at 75 Fahr., according as the temperature is above or below 75 Fahr. By the table, multiply the resistance at 75 Fahr. by the coefficient corresponding to the number of degrees for temperatures above 75 Fahr., or divide by the same number for the number of degrees below 75 Fahr. Diffs. of Temp. F. Coefficient. Diffs. of Temp. F. Coefficient. Diffs. of Temp. F. Coefficient. 1 00208 16 03328 31 06448 2 00416 *7 03536 32 06656 3 00624 18 03744 33 06864 4 00832 J 9 03952 34 07072 5 01040 20 '04160 35 07280 6 01248 21 04368 36 07488 7 01456 22 04576 37 07696 8 01664 23 04784 38 07904 9 01872 2 4 04992 39 08112 10 02080 2 5 '05200 40 08320 ii 02288 26 05408 4i 08528 12 02496 27 1*05616 42 08736 13 02704 28 1*05824 43 08944 14 02912 29 1-06032 44 09152 15 03120 30 I'o624O 45 09360 Gutta-percha. 113 The conducting power of the following coppers have been determined by Matthiessen (chemically pure copper = 100). 1. Lake Superior, native, not fused . . 98*8 at 15*5 2. fused, as it comes in 92-6 at 15*0 commerce. 3. Burra Burra ....,... 887 at 14*0 4. Best selected ,..*,. 81*3 at 14*2 5. Bright copper wire 72*2 at 157 6. Tough copper 71-0 at 17*3 7. Demidoff 59-3 at 127 8. Rio Tinto 14*2 at 14-8 Conducting power and resistance of copper. The con- ducting power of pure copper is taken as 100. The copper used in telegraphy usually has a conducting power of 85 to 95 per cent, of that of pure copper. A wire of pure copper I inch long, and weighing i grain, has a resistance of '001516 ohms, at 60 F. The resistance of any other wire of pure copper will be, at 60 F. 001516 ohms x square of length in inches weight in grains GUTTA-PERCHA. The specific gravity of gutta-percha is between 0*9693 and 0-981. One cubic foot weighs between 60-56 and 61-32 Ibs. i Gutta-percha. One nautical mile by i circular inch weighs about 2036 Ibs. Unstretched gutta-percha begins to elongate per- manently at a strain of 6 cwt. per square inch. The following are a few of the sizes and weights of solid gutta-percha cylindrical band : No. Diameter iii Mils. Weight of Percha per Statute Mile. Ibs. 143 36 8 161 46 7 171 5 2 6 194 66 5 214 81 4 221 86 3 247 108 2 2 7 6 134 I 289 147 340 204 The weight of gutta-percha per knot is i Ib. for each 491 circular mils of sectional area ; or for a solid cylinder, 49 1 The weight of gutta-percha per knot in any core is Ibs. where d is the diameter of the copper and D* 491 D the diameter of the gutta-percha, both in mils. The weight of gutta-percha per statute mile D 2 - d 2 554*5 The exterior diameter of any gutta-percha core = \/7 '4 ^ + 491 W mils, where w is the weight, in Gutta-percha. 115 Ibs., per nautical mile of copper strand, and W that of gutta-percha. With a solid conductor the diam. = w _|_ 4 Q! w . . mils. The electro-static capacity per nautical mile of any gutta-percha core is approximately 0-1877 r j . microfarads. . . Log D log a The electro-static capacity of gutta-percha core as compared with india-rubber core of similar size is as 120 to 100 nearly. The resistance per knot of a gutta-percha core of the best quality = 769 (Log D log d) megohms at 75 Fahr. The resistance of gutta-percha under pressure increases in the following ratio : Let R be the resistance at atmospheric pressure, the resistance under the pressure / Ibs. per square inch = R (i -f- o '00023 /). The resistance of gutta-percha diminishes as the tem- perature increases j the rate of decrease is as follows : Let R = resistance at the higher temperature ; r resistance at the lower temperature ; / = the difference of temperature in degrees Fahr., then log of R = log r - t log 0-9399, and log of r = log R -f- / log 0-9399. Tables of resistance of gutta-percha at different tem- peratures are given on the following pages. Gutta-percha. Table of the relative resistance (after i minute) of Gutta- percha at different temperatures, by Bright and Clark's experi- ments with Persian Gulf core (1863). Fahr. Resist- ance. Fahr. Resist- ance. Fahr. Resist- ance. Fahr. Resist- ance. 32 14*38 47 5-675 6i 2-239 77 883 33 I3-52 48 5 '334 63 2-104 78 830 34 I2- 7 I 49 5-013 64 978 79 7 80 35 ii*94 5 4-712 65 859 80 *733 3.6 H'22 5i 4-429 66 '747 81 689 37 I0'55 52 4*162 67 6 4 2 82 648 38 9-917 53 3-912 68 *543 83 609 39 9T32 54 3-680 69 451 84 572 40 8*760 55 3-456 7 364 85 53 8 4i ' 8-233 56 3-248 7 1 282 86 506 42 7'738 57 3'053 72 204 87 475 43 7'273 58 2-869 73 132 88 447 44 6-835 59 2-697 74 064 89 -420 45 6-425 60 2'535 75 1*00 90 '394 46 6-038 61 2*382 76 940 The ratio of resistance for each degree Fahr. is given in the above table, taking that as the standard tem- perature of 75 Fahr. at i. To reduce any resistance from any temperature to 75, multiply it by the cor- responding number in the table. For reduction to other temperatures, the case must be treated as one of simple proportion. Mr. Willoughby Smith considers that for cables upon which the gutta-percha exceeds o'n inch in thickness, the above values are those still found experimentally. For cables whose thickness of gutta-percha, however, does not exceed o-ii inch, Mr. Smith has found the following table to be more correct : Gutta-percha. 117 Table of the relative resistance (after i minute) of Ordinary Gutta-percha at different temperatures, for all cores in which the thickness of G. P. does not exceed O'li inch. (W. Smith.) Temperature. Resist- ance. Log Resistance. Temperature. Resist- ance. Log Resistance. Fahr. Cent. Fahr. Cent. 32 O'O 23*622 373317 6 7 I9'4 801 2555H 33 0-5 21-947 341375 68 20 -O 6 73 223496 34 1*1 20-391 309439 6 9 20-5 "555 191730 35 1-6 I8'945 277495 70 2I'I 444 159567 36 2'2 17-602 245562 7 1 21-6 342 0I 27753 37 2'7 16-354 213624 72 22*2 247 095867 38 3*3 15-195 181701 73 22'7 158 063709 39 3-8 14-117 149742 74 23'3 076 031812 40 4*4 13-116 117801 75 23-8 1-000 oooooo 4i 5'0 I2-I86 085861 76 24-4 9418 '973959 42 5*5 II-322 053923 77 25-0 8870 947924 43 6-1 10*52 022016 78 25-5 8354 921895 44 6-6 9'774 990072 79 26-1 7867 895809 45 7'2 9-081 958134 80 26-6 7410 869818 46 7'7 8'437 926188 81 27'2 6978 843731 47 8'3 7'839 '894261 82 27-7 6572 817698 48 8-8 7-283 862310 83 28-3 6190 791691 49 9*4 6-767 830396 84 28-8 5829 765594 5 10 'O 6-287 798444 85 29-4 5490 739572 5 1 10-5 5-841 766487 86 30-0 5171 713575 52 ii'i 5'427 734560 87 30-5 4870 687529 53 u-6 5-042 702603 88 31-1 4586 661434 54 I2'2 4-685 670710 89 31-6 4319 635383 55 12-7 4'353 638/89 90 32-2 4068 609381 56 *3*3 4-044 6o68ll 9 1 32-7 3831 583312 57 13-8 3'757 574841 92 33'3 3608 557267 58 14-4 3'49i 542950 93 33-8 3398 531223 59 15-0 3*244 511081 94 34'4 3200 505150 60 15-5 3-013 478999 95 35-0 3014 *479 r 43 61 16-1 2-800 447158 96 35-5 2839 453 J 65 62 16-6 2*601 415140 97 36-1 2674 427161 63 17-2 2-417 383277 98 36-6 2518 401056 64 17-7 2-245 35I2I6 99 37-2 2371 '374932 65 18-3 2-086 3I93H IOO 37*7 2233 348889 66 18-8 1-938 287354 iiS Gutta-percha. Table for reducing Resistance of Gutta-percha to 24 Cent, or 75 Fahr. From Experiments with French Atlantic Cable core (1869). (Hockin.) Col. 3 gives Logarithm of Ratio of Resistance at Temperatures in Cols. I and 2 to Resistance at 24 Cent., &c. Resistance after current has been kept on for one minute. LOGARITHMS. NATURAL NUMBERS. Temp. R t **% Diff. for One Deg. Temp. R t Diff. for One Deg. R? Diff. for One Deg. Cent. Fahr. ^24 Cent. Fahr. 1 2 3 4 5 6 789 10 11 i! 21 2O 3 11 15 13 12 II 10 I I 5 75-2 ft 68-0 66-2 64-4 62-6 60-8 59-0 57-2 55-4 53-6 51-8 50-0 48-2 46-2 44-6 42-8 41-0 o-oooo 0-0519 0-1040 0-1564 0-2090 0-2618 0-3149 0-3682 0-4217 0-4755 0-5295 0-5838 0-6383 0-6930 0-7479 0-8131 0-8585 0-9142 0-9701 1-0262 o-oooo 1-9481 1-8960 1-8436 1-7910 1-7382 1-6851 1-6318 1-5783 1-5245 1-4705 1-4162 1-3618 1-3070 1-2521 1-1969 1-0858 1-0299 2-9738 0519 0521 0524 0526 0528 0531 0533 0535 0538 0540 0543 0545 0547 0550 0552 0554 0557 0559 0561 24 23 22 21 20 11 11 15 13 12 II 10 9 8 I * 75-2 ]\-t 69-8 68-0 66-2 64-4 62-6 60-8 59-0 57-2 55-4 5r6 51-8 50-0 48-2 46-2 44-6 42-8 41-0 i-ooo 1-127 1-271 1-433 1-618 1-827 2-065 2-335 2-641 2-989 3-385 3-835 4-348 5-597 6-355 7-220 8-207 9-334 10-62 0-127 0-144 0-162 0-185 0-209 0-238 0-270 0-306 0-348 0-396 0-450 0-513 0-583 0-666 0-758 0-865 0-987 1-127 1-286 I-ooo 0-8874 0-7870 0-6976 0-6181 0-5472 0-4843 0-4283 0-3787 0-3346 0-2954 0-2607 0-2300 0-2028 0-1787 0-1573 0-1385 0-1218 0-1071 0-0942 0-1126 0-1004 0-0894 0-0795 0-0709 0-0629 0-0560 0-0496 0-0441 0-0392 0-0349 0-0307 0-0272 0-0241 0-0214 0-0188 0-0167 0-0144 0-0130 4 1-0826 2-9175 0564 nefih 4 12-09 1 47 0-0827 3 n-t 33-8 32-0 30'2 28-4 26*6 24-8 23 '0 1-1396 i 1960 1-1530 1-3103 1-3679 1-4257 1-4837 1-5419 1-6004 1-6591 2-8609 2-8040 2-7470 2-6897 2-6321 2-5744 2-5163 2-4581 2-3996 2-3409 0568 0571 0573 0575 0578 0580 0582 0585 0587 J 2 O -I 2 -3 -4 -5 -6 37-4 35-6 33-8 32-0 30-2 28-4 26-6 24-8 23-0 2I'2 I3-78 15-70 17-91 20-43 23-33 26-65 30-46 34-83 45-61, 1-92 2-21 2-52 2-90 3-32 3-8i 4'37 5-01 5-77 0-0726 0-0637 0-0558 0-0489 0-0429 0-0375 0-0328 0-0287 0-0251 0-0219 0-0089 0-0076 0-0069 0-0061 0-0053 0-0047 0-0041 0-0036 0-0032 o Formula. Log: = (0*054598 0*0001175 /) (24 /) K-24 Gutta-percha. 119 Table for reducing Resistance of Gutta-percha to 24 Cent. or 75 Fahr. From Experiments with French Atlantic Cable core (1869). (^K&.) CoL 3 gives Logarithm of Ratio of Resistance at Temperatures in Cols. I and 2 to Resistance at 24 Cent, &c. Resistance after Current has been kept on for an indefinite period. LOGARITHMS. NATURAL NUMBERS. Temp. Rt R24 Diff. for One Temp. Rt Diff. for O_ R24 Diff. for One Cent.' Fahr. >g Rt Deg. Cent Fahr. R 24 Deg. Rt Deg. 1 2 3 4 5 6 7 8 9 10 11 24 23 22 21 20 18 11 15 14 13 12 II 10 I 5 4 3 2 I O -2 -3 -4 -5 -6 75-2 73-4 71-6 69-8 68-0 66-2 64-4 62-6 60-8 59-0 57-2 55-4 53-6 51-8 50-0 48-2 46-2 44-6 42-8 41-0 39-2 37'4 35-6 33-8 32-0 30-2 28-4 26-6 24-8 23-0 21'2 0-0550 O-III2 0-I685 O-2287 0-2864 0-3470 0-4088 0-4716 0-5356 0-6007 0-6669 0-7342 0-7027 0-8722 0-9429 0147 0876 1616 2368 3130 3904 4689 5485 6292 7011 7940 8781 6933 0496 1370 1-9450 T-8888 T-83I5 T-773I 1-7136 T-6530 T-59I2 1-5284 1-4644 T-3993 T-333I T-2658 T-I973 T-I277 T-057I 2-9853 2-9124 2-8384 2-7632 2-6870 2-6096 2-53" 2-4815 2-3708 2-2889 2-2060 2-1219 2-0367 3-9504 3-8630 0550 0562 '0573 0584 33 0617 0629 0640 0651 0662 0673 0684 0696 0707 0718 0729 0740 0751 0763 0774 0785 0796 0807 0818 0830 -0841 0852 0863 0874 24 23 22 21 20 18 s 15 M 13 12 II 10 I I 5 4 3 2 I O I -2 -3 75-2 73-4 71-6 69-8 68-0 66-2 64-4 62-6 60-8 59-0 57-2 55-4 53-6 51-8 50-0 48-2 46-2 44-6 42-8 41-0 39-2 37-4 35-6 33-8 32-0 30-2 28-4 26-6 24-8 23-0 21-2 ooo 135 292 3* 934 223 2-962 3-4J 2 4-644 5-423 6-348 T45i 8-768 10-34 12-24 14-71 17-25 20-56 24-57 29-44 35-36 42-57 51-41 62-24 75-52 91-89 II2-I 1137-1 0-135 0-157 0-182 0-212 0*248 0-289 0-340 0-399 0-470 0-555 0-657 0-779 0-925 1-103 I-3I7 1-56 l-8o 2-47 2-54 3-31 4-01 4-87 5-92 7-21 8-84 10-83 13-28 16-37 20-2 25-0 i-ooo 0-8810 0-6785 0-5931 0-5172 0-4498 0-3902 0-3376 0-2914 0-2508 0-2152 0-1844 0-1575 0-1342 0-1140 0-0967 O'OSl; 0-0689 0-0580 0-0486 0-0407 0-0340 O-O283 0-0235 0-0195 0-0161 0-0130 0-0109 0-0089 0-0079 0-1190 0-1069 0-0854 0-0759 0-0674 0-0596 0-0526 0-0462 0-0406 0-0356 0-0308 0-0269 0-0233 O-02O2 0-0173 0-0149 :o-oi28 o-oiio 0-0093 0-0079 0-0067 0-0057 0-0048 0-0040 0-0034 0-0028 0-0024 0-0020 o-ooio R* Formula. Log ^- = (0-06788 0-0005588 /) (24 - /). This table is calculated from experiments made on a I2O Gutta-percha. knot of core such as was used for the French Atlantic Cable 400 Ibs. gutta-percha and 400 Ibs. copper. Three observations were made at temperatures o f o C, 117 C., and 24 C. Loss of Charge. TABLE showing the measured Rate of Fall of Tension in a Gutta- percha Cable (at a Temperature of 11*7 C.), when charged for many hours, and then insulated. From Experiments with French Atlantic Cable core. Time. Potential. Time. Potential. Time. Potential. Minutes. Minutes. Minutes. IOO*O 21 50*8 42 33-0 I 95-8 22 49 '5 43 32-5 2 91-9 23 48-3 44 31-9 3 88'3 24 . 46'9 45 3i-3 4 85-0 25 45-0 46 30-9 5 81-9 26 45-0 47 30-5 6 79' 27 44*o 48 29-9 7 76-4 28 43-2 49 29-6 8 73-6 29 42'2 5 29-1 9 71-3 3 41*3 5i 28-7 10 69*2 31 40-5 S 2 28-3 n 67-1 32 39-6 53 27*9 12 64-8 33 39 -o 54 27*4 13 62-8 34 38-2 55 27-1 14 61-2 35 37'4 56 26-6 *5 59*5 36 36-8 57 26*0 16 57-8 37 36-0 58 25-9 17 56-4 38 35*4 59 25*7 18 54*8 39 34'7 60 25-4 19 53*4 40 34'i 20 52-0 4i 33'7 Gutta-percha. 121 TABLE of ratio of .. f rg ( = ) and of loss per cent, of charge discharge \ c } by ordinary gutta-percha core, at temperatures between 32 and 90 Fahr. (After I minute's insulation.) Temp. Fahr. C c Loss Temp. Fahr. C c Loss o/ /o Temp. Fahr. c c Loss Temp. Fahr. C c Loss 32 029 2-8 47 076 7-1 62 204 16-8 77 601 37*5 33 031 3'o 48 081 7'5 63 218 17-9 78 650 39-4 34 033 3'2 49 086 7-8 64 234 18-9 79 704 41-1 35 035 3'4 50 092 8-4 65 251 20- 1 80 763 36 038 099 9-0 66 269 21-2 81 828 45-0 37 040 3-8 52 105 9'5 67 288 22-4 82 899 47-0 38 043 4' 1 53 112 IO'O 68 309 23-6 83 979 49-0 39 047 4'5 54 120 ID- 7 69 332 24*9 84 2-068 5i-4 4 049 4*1 55 128 11-4 70 356 20-2 85 2-165 53-7 4 1 052 4'9 56 137 12-0 383 27-7 86 2-273 55'9 42 055 5-2 57 146 12-7 72 412 29-1 87 2-398 58-1 43 44 059 063 067 071 5;6 6-3 6-6 58 59 60 61 156 169 178 191 13-5 14-3 'I' 1 16-0 73 n 76 443 dffi 1-556 30-7 32-4 34'0 35'7 88 89 90 2-533 2-690 2-871 60-4 62-8 65-1 The resistance of a cube FOOT of gutta-percha, = 1 2 '8 x io 6 megohms at 75 F. Its electro-static capacity = 11*3 x io~ 6 microfarads. The resistance of a cube KNOT of gutta-percha, = 2100 megohms at 75 F. Its electro-static capacity '0687 microfarads. A PLATE of gutta-percha, i square foot surface and i mil thick has a Resistance = 1066 megohms at 75 F., and its electro- static capacity = "1356 microfarads. The insulation resistance in megohms at 75 F. of any ordinary gutta-percha cable or condenser multiplied by its electro-static capacity in microfarads = 144 '4. 122 Gutta-percha. TABLE to find Resistance, after I minute, and Capacity per Knot, of any ordinary Gutta-percha core, from the relative Weights or . / Insulator \ Diameters of . V Conductor/ w D d Resistance per knot at 24 C. in Electro- static capacity per knot W w D d Resistance per knot at 24 C. in Electro- static capacity per knot megohms. in micro- farads. megohms. in micro- farads. oo 2-80 360 4007 26 3'io 395 3657 01 2-81 36l 3995 27 3-n 396 3647 02 2-82 363 3982 28 3'I2 397 3638- 03 2 83 364 3969 29 3-13 398 3628 04 2-85 360 '3945 '30 3-14 399 3619 05 2-86 367 3934 31 3-15 400 3611 06 2-87 368 3921 32 3-17 402 3593 07 2-88 369 3910 '33 3'i8 403 3583 08 2-90 372 3886 '34 3-19 404 '3579 09 2-91 374 3864 '35 3'2o 405 3569 10 2-92 375 3853 36 3-21 406 3559 ii 12 2-94 376 377 3841 3830 38 3-22 3-23 407 408 3538 13 2'95 378 3820 39 3-24 409 3531 14 2-96 379 3808 40 3-25 410 3521 15 2-98 38i 3788 '4 1 3-26 411 3512 16 2-99 382 '3777 42 3-27 412 3502 17 3'oo 383 3766 '43 3-28 '3493 18 3-oi 38 4 3756 "44 3-29 414 3484 19 3-02 386 3746 "45 3-30 4 I 5 3476 20 3 '03 387 37?5 46 3'3I 416 3467 21 *'i 388 3725 47 3-32 418 '3459 22 3-06 39 3705 48 3'33 419 3450 23 3-07 391 3695 49 3-34 420 3441 24 3-08 392 3686 50 3'35 421 3433 25 3-09 393 3675 5i 3'36 422 3425 When the ratio between the weights ( W} of percha and of copper (w) are given, the resistance and capacity of the core are the same, whatever be the absolute value of these weights. The same is true of the relative diameters D and d. In using the above table we have only to ascertain the quotient weight of percha or the weight of copper diameter of percha , . , = and the table gives by inspection the diameter of copper resistance at 24 Cent, in megohms, and the electro-static capacity in microfarads. Gutta-percha. 123 - - Mtr*w\qi o Q O So0 * * * r- 'A "-N lalSS S a ? 2* r- PoSSTSS-^os O n M 1*1 M M .so rt Weight of Copper per kno Weight of G. P. per knot c* l. ^o *' 3i illl &** ^ rftro t~- CO 124 Gutta-percha. WILLOUGHBY SMITH'S IMPROVED GUTTA- PERCHA. The specific gravity of gutta-percha prepared by Mr. Willoughby Smith's process is the same as that of ordinary gutta-percha. The mechanical strength of this material is about 12% greater than that of ordinary gutta-percha. The electro-static capacity (F) per knot of a core of Smith's G. P. is approximately 0*15163 f = =r . . microfarads. Iog 7 (Log 0*15163 = 0*1807851 i). The electro-static capacity of Smith's G. P. core, as compared with Hooper's core of similar size, is as 100 to 98, about. The resistance (R) per knot, of Smith's G. P. core at 75 F. (= 24 Cent.) is approximately R = 350 log . . megohms after one minute's electrification. The resistance after the ist minute, of Smith's G. P. at 32 Fahr. is about the same as that of ordinary G. P. After a long application of the battery at this tempera- ture the ratio falls to 72 : 100, about. The resistance after the ist minute, of Smith's G. P. at 75 Fahr., compared with that of ordinary G. P., is as 67 to 100 ; or about 30% inferior. Gutta-percha. 125 Table of the relative resistance (after I minute) of Willoughby Smith's improved Gutta-percha at different temperatures, for all cores in which the thickness of G. P. does not exceed 0*110 inch. (W. Smith.) Temperature. Resist- ance. Log Resistance. Temperature. Resist- ance. Log Resistance. Fahr. Cent i"ahr. Cent 32 o-o 27-913 445807 67 19*4 858 269046 33 o'5 25-834 412192 68 20*0 719 235276 34 i-i 23-91 378580 69 20-5 591 201670 35 1-6 22T28 344942 70 2I-I 473 168203 36 2-2 20-48 311330 7i 21-6 363 134496 37 2*7 18-954 277701 22*2 261 100715 38 3*3 17-542 244079 73 22-7 167 067071 39 16-235 210452 74 23-3 080 033424 40 4'4 15-025 176815 75 1-000 oooooo 4 1 5-0 13-906 143202 76 24*4 9375 971971 42 5'5 12-87 109579 77 25*0 8789 943940 43 6-1 II*9II 075948 78 25 "5 8240 915927 44 6-6 11-024 042339 79 26*1 7725 887899 45 7'2 10-203 008728 80 26-6 7242 859859 46 7*7 9*442 975064 81 27-2 6789 831806 47 8-3 8-739 941462 82 27-7 6365 803798 48 8-8 8-088 907841 83 28*3 -5967 775756 49 9'4 7-485 874192 84 28-8 5594 747723 50 lO'O 6-928 840608 85 29*4 5245 719746 51 10-5 6-412 806994 8fr 30*0 4917 691700 52 ii'i 5 "934 773348 87 30-5 4609 663607 53 n-6 5-492 739731 88 31-1 4321 635584 54 I2'2 5-083 706120 89 31-6 4051 607562 55 12*7 4-704 672467 90 32-2 3798 '579555 56 r 3*3 4-354 638888 91 32*7 3561 551572 57 13-8 4-029 605197 92 33*3 3338 523486 58 14-4 3-729 571592 93 33-8 3130 '495544 59 15-0 3*45! 537945 94 34*4 2934 -467460 60 15-5 3*194 504335 95 35-0 2751 439491 61 16-1 2-956 470704 96 35*5 2579 411451 62 16-6 2-736 437116 97 36-1 2417 383277 63 17-2 2-532 403464 98 36-6 2266 355260 64 17-7 2'343 369772 99 37-2 2125 327359 65 18-3 2-169 336260 IOO 37'7 1992 299289 66 18-8 2*007 -302547 126 Gutta-percha. The resistance (R,) at any temperature (/) of Smith's G. P. may be found from its known resistance (R^) at 24 C., after i minute, by the formula, log R, = log R 24 -f- (0-06447 0-00017 /) (24 t) Table for reducing Resistance of Willoughby Smith's improved Gutta-percha to 24 Cent. (Resistance after Current has been kept on for one minute.) LOGARITHMS. NATURAL NUMBERS. Temp. & ^r **t Diff. for One Deg. Temp. ** K Diff. for One Deg. R24 ** Diff. for One Deg. Cels. Fahr. Cels Fahr. 1 2 3 4 5 6 7 8 9 10 11 24 23 22 21 20 i! 3 15 H 13 12 II 10 I I 5 4 3 2 I O I 2 3 -4 -5 6 75-2 ? 69-8 68-0 66-2 64-4 62-6 60-8 59-0 57-2 55-4 53-6 51-8 50-0 48-2 46-2 44-6 42-8 41-0 39-2 37'4 35-6 33-8 J2-o 30-2 28-4 26-6 24-8 23-0 21-2 o-oooo 0-064? 0-1283 0-1919 0-2552 0-3181 0-3807 0-4430 0-5049 0-5665 0-6277 0-6886 0-7492 0-8094 0-8693 0-9288 0-9881 1-0469 1-1054 i-i6;6 1-2214 1-2789 i-336i I-3929 1-4494 1-5055 1-5613 i -6168 1-6719 1-7267 1*7811 o-oooo T'9*57 1-8717 1-8081 1-7448 1-6819 i-6i 9 j 1-5570 1-4951 I-4J35 1-3723 1-3114 1-2508 1-1906 1-1307 1-0712 1-0119 2-9531 2-8946 2-8364 2-778? 2-7211 2-6639 2-6071 2-5506 2-4945 2-4J8 7 2-3832 2 3281 2-2733 2-2I89 0-0643 0640 0636 0633 0629 0626 0623 0619 0616 0612 0609 0606 0602 0599* 0595 059? 0588 0585 0582 0578 0575 0572 0568 0565 0561 0558 0555 0551 0548 0544 24 23 22 21 2O J 9 18 3 15 J 4 13 12 II IO I 7 6 5 4 3 ^ i o i 2 3 4 -1 75-2 73-4 71-6 69-8 68-0 66-2 64-4 62-6 60-8 59-0 57'2 y;-i 51-8 50' o 48-2 46-2 44-6 42-8 41-0 39-2 37-4 35-6 33-8 32-0 30-2 28-4 26-6 24-8 23-0 21'2 ooo 160 344 556 800 080 403 77? 3-198 3-685 4-24? 4-882 5'6i3 6-447 7-401 8-487 9-729 11-14 12-75 14-57 16-65 19-01 21-68 24-71 28-14 32-03 36-41 41-38 46-98 53-29 60-41 0-160 0-184 O-2I2 0-244 0-280 0-323 0-370 0-425 0-487 0-5 5 8 0-639 0-73I 0-834 0-954 1-076 I-242 I-4II i-6i 1-82 2-08 2-36 2-57 3-03 3-43 3-89 ! 4-38 i 4-87 ; 5-6o 6-31 ! 7-12 i-oooo 0-8624 0-7443 0-6429 0-5557 0-4807 0-4162 0-3606 0-3127 0-2714 o-2?57 0-2048 0.1782 0-1551 0-1351 0-1178 0-1028 0-0898 0-0785 0-0686 0-0601 0-0526 0-0461 0-0405 0-0355 0-0312 0-0275 0-0242 O-02IJ 0-0188 O-OI66 0-1376 0-1181 0-1014 0-0872 0-0750 0-0645 0-0556 0-0479 0-0413 0-0457 o-o?o9 0-0266 0-0231 0-0200 0-OI73 0-OI50 0*0130 0-0113 0-0099 0-0086 0-0074 0-0065 0-0056 0-0050 0-0043 0-0037 0-0033 0-0029 0-0025 O-0022 "D Formula = Log =-^ = (0*06447 0-00017 /) (24 /). Gutta-percha. 127 Table to find Resistance, after 1 minute, and Capacity per Knot of W. Smith's Gutta-percha core, from the relative Weights . / Insulator \ or Diameters of I - 1. VConductor/ w w D d Resistance per knot at 24 C. in Electro- static, capacity per knot W w D ~d Resistance per knot at 24 C. in Electro- static capacity per knot megohms. in micro- farads. megohms. in micro- farads. oo 2-80 164 3238 26 J-IO 179 2962 oi 2'8l 164 3228 27 180 2947 02 2-82 165 3217 28 3-12 181 2939 03 83 165 3207 29 3*13 181 2932 04 85 166 3188 '30 3-14 182 2924 3 86 87 '$ 3178 3171 31 3-15 3-17 182 183 2917 2902 07 88 168 3159 33 J-I8 183 2895 08 90 169 3140 34 3-19 184 2888 09 91 170 3122 '35 3-20 184 "Z88i 10 II 92 2-93 170 I7i 3113 3104 36 '37 3-21 3-22 185 185 2874 2867 12 2-94 171 3095 38 3'23 186 286o I? 2-95 172 3086 '39 3-24 186 2853 14 2-96 172 3077 40 3-25 186 2846 ' 2-98 173 3060 3-26 187 2839 16 2-99 ^74 3051 42 3*27 187 2833 17 3-00 '74 304? '43 3*28 188 826 18 19 20 j-oi 3-02 3-03 175 a 3035 3026 3018 ;44 3-29 3-30 188 189 189 2819 2806 2800 21 3-04 176 3010 47 3'32 190 2793 22 3-06 177 2994 48 3'33 190 2787 2? 3-07 178 2986 49 3;34 191 278! 24 3'08 178 2978 50 191 25 3-09 179 2970 3-36 192 2768 When the ratio between the weights ( W) of percha and of copper (w) are given, the resistance and capacity of the core are the same, whatever be the absolute value of these weights. The same is true of the relative diameters D and d. In using the above table we have percha only to ascertain the quotient or the weight of copper diameter of percha diameter of copper and the table &"* ** ms P ectlon the resistance at 24 Cent in megohms, and the electro-static capacity in microfarads. 128 India-rubber. TABLE of Cpefficients for reducing Silvertown Gutta-percha to 75 F. (F. Hawkins.) Temp. Coefficient. Log of Coefficient. Temp. Coefficient. Log of Coefficient. 75 ooo o-ooooooo 53 5-494 7398887 74 018 0-0077478 52 5-908 7714405 054 0-0228406 51 6-330 8014037 72 108 0-0445398 50 6-770 8305887 180 0-0718820 49 7-238 8596186 70 270 0-1038037 48 7-724 8878423 69 378 0-1392492 8-228 9152946 68 504 0-1772478 46 8-740 9415114 8 648 810 0-2169572 0-2576786 45 44 9-280 9'8?8 9615480 9929068 65 990 0-2988531 43 10-414 0176176 64 188 0-3400473 42 11-008 0417084 63 394 0-3791241 11-610 0648322 62 618 0-4179696 40 I2-2JO 0874265 61 2-860 0-4563660 39 12-868 1095111 60 3-120 0-4941546 38 I3-524 1301052 59 3-398 0-5312234 37 14-198 1512272 58 3-704 0-5686710 36 14-890 1728947 11 4-028 4-360 0-6050895 0-6394865 35 34 15-600 16-328 1921246 2129330 55 4-720 0-6739420 33 17-074 2323353 54 5-098 0-7073998 32 17-838 2513462 INDIA-RUBBER. The specific gravity of Hooper's india-rubber com- pound is about i 'i 76. One cubic foot of india-rubber compound weighs 73*44 Ibs. The weight of Hooper's india-rubber compound per knot is i Ib. for every 401 circular mils of sectional area. The weight of Hooper's india-rubber per knot in any D 8 d z cable is about -- Ibs. D being the external dia- 401 meter of the core and d that of the conductor. The weight of Hooper's india-rubber per statute mile 462-3 ' The exterior diameter of any core of Hooper's india- India-rubber. 129 rubber is = v 70-4 w -f- 401 W; W being the weight in Ibs. per knot of the compound, and w that of the copper strand. The resistance per knot of any core of Hooper's india-rubber is about 15400 (log D log d) megohms at 75 Fahr. The resistance per knot of any of Hooper's core at 75 F- is i. With a solid conductor, / W 15400 log \J i + 7-3 megohms. 2. With a strand conductor, 15400 log ^\/i + 57 J megohms. Where W is the weight of the dielectric and w the weight of the copper. The electro-static capacity per knot of any core of Hooper's india-rubber is approximately 0-1485 -- ~ microfarads. Log D log a The electro-static capacity per knot of any core of Hooper's india-rubber is 1. With a solid conductor, T - microfarads. / W log V 1 + 7-3- 2. With a strand conductor, 0-1485 C A/ 1 + 57 microfarads 130 India-rubber. Resistance (Comparative) of Gutta-percha and Hooper's Insulator, at different Temperatures, showing the Decrease of Resistance due to the Increase of Temperature. RESISTANCES. TEMPERATURE. Gutta-percha Persian Gulf Cable. Hooper's core Ceylon Cable. Centigrade. Fahrenheit. Observed. Calculated. Observed. Calculated. o 32-0 100-00 100-00 100 OO 100-00 2 4 39*2 84-14 64-66 80-00 64-00 90-10 80-60 88-73 78-62 6 42-8 47-65 51-20 72-90 68-30 8 46-4 37*15 4 V 9 6 65-30 61-20 10 50-0 28-97 32-77 58-80 54-81 12 51-6 23-18 26-22 52-90 48-56 3 57-2 60-8 16-89 20-97 16-78 49-40 44-50 4? -07 38-18 18 64-4 11-05 13-42 33-85 20 68-0 8-4? 10-74 29-10 30-01 22 71-6 6-82 8-59 26-40 26-51 24 75-2 5-51 6-87 24-50 23-59 2O 78-8 4'47 5-50 22-30 20-91 28 82-4 4-40 18-60 18-55 30 32 86-0 89-6 2-99 2-48 3-52 2-82 16-00 16-44 14-58 34 93-2 1-92 2-26 14-40 12.93 36 96-8 1-68 I -80 13-00 ii'4b 38 100-4 i*4J 1-44 10-60 10-16 The calculated values for gutta-percha are from Messrs. Bright and Clark's published table ; those for Hooper's insulator have been furnished by Mr. Hooper. EFFECTS OF TEMPERATURE ON HOOPER'S MATERIAL. The rate of variation in its insulation is, according to Mr. Warren's experiments, 0*026 for i Fahr. A difference of 27 above any temperature Fahr. reduces its insulation one-half, or the same difference below any temperature increases its insulation twofold, or according to table of coefficients : When from the resistance at a given temperature, the India-rubber. resistance corresponding to a lower temperature is re- quired, multiply the resistance at the given temperature by the number opposite to the degrees of difference. When the correction is required for any higher temperature, divide by the number opposite to the degrees of difference, the result in either case is the resistance required. Coefficients for Temperature corrections for Hooper's Material. (Warren.) Diffs. of Temp. F. Logarithms. Nat. Numbers. Diffs. of Temp. F. Logarithms. Nat. Numbers. 1 01115 026 26 28990 1-949 2 02230 053 27 30105 2'000 3 03345 080 28 31220 2-052 4 04460 108 29 32335 2-I05 5 *5575 137 30 33450 2-160 6 06690 167 31 34565 2'2l6 7 07805 197 32 35680 2-274 8 08920 228 33 36795 2'333 9 10035 260 34 37910 2-394 1C 11150 293 35 39025 2-456 ii 12265 326 36 40140 2*520 12 13380 361 37 41255 2-586 13 14495 396 38 42370 2-653 M 15610 '433 39 43485 2-722 15 16725 470 40 44600 2-796 16 i 7840 508 4r 457 r 5 2-865 17 18955 '547 42 46830 2-940 18 20070 587 43 '47945 3-OI6 *9 21185 629 44 49060 3-09I 20 22300 671 45 50175 3'i75 21 23415 7'5 46 51290 3-258 22 24530 '759 47 52405 3-342 23 25645 '805 48 53520 3-429 24 26760 852 49 54635 3-518 2 5 27875 900 50 55750 3-610 Example. A length of Hooper's core at 60 Fahr. was found to have an insulation resistance of 16124 megohms. Its resistance at 75 Fahr. is therefore 16124 = 10968 megohms. 1 3 2 India-rubier. Relative Resistance of Hooper's Material at different Temperatures.- ( Warren.) Temp. Fahr. Resistance. Temp. Fahr. Resistance. Temp. Fahr. Resistance. 32 301-6 56 162*9 80 87-95 33 294-0 57 158-7 8l 85-72 34 286-5 58 154-7 82 35 279-6 59 150-8 83 81-44 36 272-2 60 147-0 84 79-37 37 265-3 6 1 143*3 85 77-36 38 258*6 62 139-6 86 75-40 39 252-0 63 136-1 87 73 '49 40 245-6 64 132*6 88 71-62 41 239-4 65 129-3 89 69-81 42 233*3 66 126*0 9 68-04 43 227-4 67 122-8 91 66-31 44 221-6 68 II9-7 92 64*63 45 216*0 69 116-7 93 62-99 46 210-5 70 113-7 94 61*40 47 2O5-2 no-8 95 59-84 48 2OO-O 72 108*0 96 58-32 49 194-9 73 105-3 97 55*4i 5 I9O-O 102-6 98 54-00 5i 185-2 75 100-00 99 52-63 52 180-5 76 97-46 100 51-30 53 I75-9 77 95-00 101 50*00 54 I7I-5 78 92-59 134 25*00 55 167*1 79 90-34 The resistance of a cube FOOT of Hooper's material, = 249 x io 6 megohms at 75 F. Its electro-static capacity - 8*92 x io~ 6 microfarads. The resistance of a cube KNOT of Hooper's material, = 40950 megohms at 75 F. Its electro-static capacity = 0*0543 microfarads. A PLATE of Hooper's material, i square foot surface and i mil thick, has a Resistance = 20770 ohms at 75 F. India-rubber. 133 Its electro-static capacity - 0*1073 microfarads. The insulation resistance (in megohms, at 75 F.) of any perfect cable or condenser of Hooper's material multiplied by its electro-static capacity in microfarads = 2 2 20. TABLE to find Resistance, after I minute, and Capacity per Knot of any Hooper's Core from the relative Weights or Diameters of / Insulator \ VConductor/ * w 11} D d Resistance per knot at 24 C. in Electro- static capacity per knot W w D d Resistance per knot at 24 C. in Electro- static capacity per knot megohms. in micro- farads. megohms. m micro- farads. 0-85 2-42 6072 3669 II 2-71 6822 3266 0-86 2-43 6098 3652 12 2-72 68^6 3254 0-87 2-44 6124 3639 13 2-73 6869 3244 0-88 2'45 6149 3624 14 2-74 6891 3233 0-89 2-46 6174 3609 15 2'75 6914 3223 0-90 2-48 6225 3580 16 2-76 6930 3212 0-91 2-49 6259 3565 17 2-77 6959 3202 0-92 2-50 6299 3537 18 2-78 6981 3192 0-93 2-51 6324 3523 19 2-79 3182 0-94 2-52 6359 3501 20 2'80 7026 3172 0-95 2'53 6373 3496 21 2-81 7047 3162 0-96 0-97 l-lt 6398 6446 3 4 82 3456 22 23 2-82 2'83 7070 7092 3152 0-98 2-57 6470 3444 24 2-84 7113 3132 0-99 2-58 6495 3431 25 2-85 7137 3I2J oo 2-59 6 5 i8 3418 26 2-86 7J57 3113 oi 02 2-60 2-61 %& 3406 3394 28 2-87 2-88 7200 3104 3095 03 2-62 6590 338! 29 2-89 7221 3085 04 2-63 6614 3369 30 2-9^ 7265 3067 05 2-64 66?8 '3357 31 2-91 7281 3058 06 2-65 6660 3345 32 2-92 7307 3049 07 2-67 6708 3322 33 7328 3040 08 2-68 6731 3310 34 2-9} ? 7349 3032 09 2-69 6755 3299 35 7370 3023 10 2-70 6800 3277 36 2-96 3015 When the ratio between the weights ( W) of rubber and of copper (w) are given, the resistance and capacity of the core are the same, whatever be the absolute value of these weights. The same is true of the relative 134 Vulcanite. diameters D and d. In using the above table we have weight of rubber only to ascertain the quotient ~ - or the weight of copper diameter of rubber -r. 7 - and the table gives by inspection the diameter of copper resistance at 24 Cent, in megohms, and the electro-static capacity in microfarads. VULCANITE. Vulcanite, when pure, should consist only of india- rubber and sulphur. Its specific gravity is about 1-31. It should present a clean conchoidal surface when broken ; a granular fracture is due to admixture of other materials. Its surface, when polished, should be free from specks or indentations. By friction with a black silk rubber, it becomes strongly excited with negative electricity, which in a dry atmosphere it should retain for some hours. In thin strips it is very elastic, and when heated it may be bent and will retain its new shape or form permanently when cooled. The surface of vulcanite becomes conducting, partly by the condensation of moisture, and a slight film of sulphurous acid, which is produced by the oxidation of sulphur. On this account, all vulcanite supports and connections should be repeatedly washed with boiling water, and rinsed well in distilled water, and dried. This Hemp. 135 is the most effectual way of dealing with vulcanite apparatus when found leaky, as friction will not remove entirely the film of acid. It is, however, better to keep its surface varnished with shellac. HEMP. In a cable, as ordinarily applied in serving One cubic foot of (Russian or Italian) hemp weighs about 39 Ibs. One cubic foot of tarred hemp weighs about 56 Ibs. One cubic foot of Manilla weighs about 41 Ibs. The number of cubic inches of hemp space divided by one of the following constants gives approximately the weight of hemp in Ibs. Italian or Russian ... 44 Tarred hemp 30 Manilla 4 1 The transverse area of the hemp section in a cable, in square inches, multiplied by one of the following con- stants, gives approximately the weight of hemp serving, per knot, in cwts. Italian or Russian . . . . 14 Tarred hemp 21 Manilla . . .... 15 136 Hemp. The weight of hemp serving in a calk. Let D! be the diameter of the centre line of the iron wires, in inches (see Table, page 149) D the diameter of the dielectric in inches ; d the diameter of a single iron wire also in inches ; and n the number of iron wires. Then The transverse sectional area of the hemp is / n \ 07854 ( Di* D 2 d- } square inches. And the weight, per knot, of serving is approximately as follows : Hemp ... 12 ( D^ - D 2 - - r^ t^ ON M r-Tj- OO ON VTN r* o oo M t> r~. r>. w-> ^- OO KH ff\ rA rA r* oo ro O - t ON r~\O *^ ON *M- r< oo * t> > OXT*- 0^~ S _ r . SO Tf M r^ 00 ^\00 o 2 s r- t^ vr\ r^^i- s r- O ON r^ ONOO ON u% - M ON s < o r o oo sO r* vr\ M vr\ vr> 2 8 K Th S r^oo V/N. > ON tA 00 U (S (S M sO 00 NO VO ^l M HI M M 81/NVO 00 NO ir\ vr>o vr\ ^- r^ ON Tt-00 Ci M -t 00 ? roO W r*. t-x r T}- >r\ M M 00 ON O r/N. g\o M r* rA t^OO r^ n r~ r< r M CA ON r^ M H PQ D 2 r so ^r* rAOOOO M O *A r M t ^-ThOO * VA o ^ U f* C M s oo O TT M M M M rNr< f oo r-~ vri r--oo ^- r^ v^ U"\ O VTN v\ r ^ - 15 . r^OO Tj- O f M M O 00 M rA O ON HH M SO NO M t^sO vrs rA *r\CO ^- mis r^ ON * r< M M 1-1 00 NO M 00 H iv> M OA r M vr\ w o > "* O r > M r^ rv> U >H M OO OO iv\ M ONOO M M O t^ r^NO TJ- ON fS VO v> fA C M t^. (V> 'i O ^NO 1-1 00 ONNO O NO ON sO OO r\ ON ? M ro CN r^ ON >-^ ** (VN. ir\OO N*> ON >^\ M ON\O vr\ 0?^^ Diameter J S .s 3-8 iv> rA r^ T*- ONOO OO >r\ r^ M r N^^ WNO t^ OO ON O M r r/N, <4- v^\vO & pq 142 Iron. TABLE of the Sizes and Weights of Iron Wire. Size of Wire B. W. G. Diam. in Mils. PER STATUTE MILE^ Nautical Mile Weight in Cwts. Breaking Weight at 20 Tons per sq. in. Weight in Lbs. Weight in Cwts. Resistance in Ohms. i sq. in. . . 17645 r 57*54 0-340 181-63 4OOO- i circ. in. IOOO 13858 i23'73 '433 142-65 314-16 oooo 454 2854 25-48 2-10 29-38 64-40 000 425 2502 22-33 2-40 25^5 56-40 oo 380 2OOI 17-86 3'OO 20-59 45-36 o 340 I6OO 14-28 3' 74 16-47 36-31 i 300 I2 45 11-12 4-8! 12-82 28-27 2 284 III7 9-97 5'37 11-49 25*33 3 259 928 8-28 6-46 9'55 20-07 4 238 783 6-99 7-65 8-06 I 7 -79 5 220 670 5-98 8-96 6-90 15 *2O 6 203 570 5-09 10-52 5'86 12-94 7 180 448 4-00 13-38 4'6i 10-17 8 165 376 3'35 16-39 3-86 8-55 9 148 303 2- 7 l 19-79 3-12 6-88 10 134 249 2'22 24-14 2-55 5'6 4 ii 120 199 I- 7 8 30-10 2-05 4-52 12 ICQ 164 1*46 36-49 1-68 3*73 13 95 124 1*11 48-01 1-28 2-83 14 83 95 0-85 62-93 0-98 2-16 15 72 7 2 0*64 83-65 0-73 1-62 16 65 58 0-52 102*6 0-59 1-32 17 58 46-38 .. .. 18 49 33'*7 19 42 24*35 .. 20 35 17-93 .. .. .. 21 32 14-11 .. .. .. 22 28 10-76 Iron. 143 00 HI oo oo oo O^ ** oo f"* r* t^** u^ O O M r-* r< M r^* c^ 00 oo SO r< * NO OO vO ^|o?l^^^^23 ,S^^^^^S M NO ^ 1 a M OO NO ^" NO <^ O O -* OO O "* f^ NO ON f^ vr\ ON NTS < ^- NO * ^ s r-o^OMo%Mn^-o^M^o^t^ S a M 1 ONr-^Tl-r^M M ONOO t^ND NO VTN Tj- Tj- ^ ro H D 2 * r^ M i ^ o o M O ^" ^^ O ON O ^NO NO ON r< NO O NO O ^TN O ^ * ON oo ON JJ . 000^^0-O^^^OON^^ o oo * " r^ ro r* r* s j5 _________ 1 'f. 25 1 144 Iron. Stranded Wires. When 3 or 4 wires are twisted together to form a strand, as in the outer wires of very heavy shore end cables, and in the cores of multiple cables, it is some- times necessary to know the space they occupy. When 3 wires are used, the diameter of each being i , the diameter of the circumscribing circle is 2*155. When 4 wires are laid together the diameter of the circumscribing circle is 2 '4 14. When 7 wires are used it is 3. IRON WIRE (Culley). .- Diameter Area of Sec- tion, 1 WeightjWeight of loo of 1760 Weight of 2029 Length of i Breaking Strain. ,i 8 .A8J &$ g "^ w square yards. yards. yards. cwt. Soft Hard i0 c ^5 inches. Wire. Wire. 1 j Ibs. Ibs. CO 0-363 9-21 O'IO3 I02-OO 1794 2068 no 8600 6000 oo 0-331 8-40 0-086 84-72 1490 1718 132 7100 4750 i o I 0-300 7-61 0-071 88-75 1210 1395 162 6000 4000 ; 2 0-280 7-11 0-062 59-90 1054 1215 187 4850 3400 2 3 0-260 6-60 0-053 51-65 909 1048 215 4000 2900 3 4 0-240 6-10 0-045 44-00 775 895 255 3400 2500 4 5 c22o; 5-59 0-038 37-00 651 750 303 2950 2200 5 6 0-200 5-08 o-oji 30-56 538 620 361 2500 l800 6 7 0-185 4-69 0-026; 26-15 461 531 428 2200 1520 I 8 0-170 4'3i 0-023 22-10 389 448 509 1750 I2OO 8 9 10 0-155 0-140 3'93 3'55 0-0195 0-016 18-36 14-97 323 264 37* 305 609 747 1500 I2OO 950 820 9 10 n 0-125 3-17 0-0125 11-95 211 244 939 82O 650 ii 12 o-iio 2-79 O'CIO 9-24 163 188 1244 710 510 12 13 0-095 2-41 0-0071 7-05 124 M3 1589 640 400 13 14 0-085 2-15 0-0057 5-5I 97 112 2031 510 35 14 15 0-075 1-92 0-0044 4' 29 76 87 2608 410 300 15 16 0-065 1-65 o-ooj3 f 3-22 57 66 3473 350 20O 16 17 0-057 1-44 0-00261 2-48 44 50 4515 280 150 17 18 0-050 1-27 0-0020 1-91 34 39 5600 200 115 18 19 0-045 1-14 0-0016 1-55 27 7246 150 85 19 20 0-040 I -01 0-0013! 1*22 21 24 9168 110 65 20 21 0-035 0-88 o-ooioi 0-94 17 20 11980 85 5 21 22 0-030 0-76 0-0007 0-69 12 14 l63OO 65 40 22 The breaking strains of iron wire were supplied by Iron. 145 Messrs. Johnson and Nephew, of Manchester : the soft wire is that manufactured expressly for telegraphic purposes. Specification for Iron Wire. Wire supplied to the Electric Telegraph Company. The wire to be highly annealed, and very soft and pliable ; it is not required to possess great tensile strength, but must be capable of elongating 18 per cent, without breaking after being galvanized. To be supplied in not less than Ibs. pieces, and to be warranted not to contain any weld, join, or splice whatsoever, and to be free from all imperfections, flaws, sand splits, and other defects. The whole of the wire to be passed under and over three or more studs or pulleys placed in two lines the wire passing over the pulleys in the upper line and under the others. The whole of the wire to be stretched 2 per cent by machinery in the presence of the company's en'gineer or his representative, and to be tested, examined, and approved by him before leaving the works. The wire after being stretched to be coiled carefully, so as to con- tain no bends, but to resemble newly drawn wire in its straightness. If, during the process of testing the wire between the studs or pulleys, or during the process of stretching it, more than 5 per cent, of the bundles break, crack, or show any defect, the whole of the broken bundles to be rejected. If less than 5 per cent prove defective, the L 146 Clark's Asphalte. wire will be accepted. The makers are not to attempt to weld, join, or otherwise splice any wire that may break or prove defective, but deliver it as it comes from the testing. Binding. No. 16 charcoal wire best. When No. 4 wire is used for line, two servings required, and Culley remarks that it is necessary that the turns of the binding round the main wire should be all in one direction. CLARK'S COMPOUND. i cubic inch of asphalte covering weighs (approx.) o'o; Ib. Clark's compound for the outer casing of the iron sheathing of cables is composed of about 65 parts of mineral pitch] 30 of silica > by weight. 5 of tar J This is laid on with coarse hemp ; the proportion of hemp to bituminous compound being as i to 2 in bulk, nearly. The specific gravity of solid pitch is 1*65; one cubic foot weighing about 103 Ibs. The specific gravity of silica is 17; one cubic foot weighing about 106 Ibs. The specific gravity of tar is 1*02; one cubic foot weighing about 63^ Ibs. The specific gravity of Clark's compound varies ac- cording to the proportions ; one cubic foot of it weighing about 100 Ibs. The transverse area of asphalted section in a cable, in Asphaltc. 147 inches, multiplied by 36, gives (approx.) the weight in cwts. of the asphalte covering per knot length. To find the weight of hemp and asphalte casing (Clark's compound}. Let D 2 be the exterior diameter, in inches ; D! the diameter of the centre line of the iron wires in inches (see Table, page 149) ; d the diameter of the iron wire in inches ; and n the number of iron wires. i Then The transverse sectional area of the asphalte casing is 0785 f D< 2 - D, 2 - - d* J square inches. And the weight, per knot, of casing is approximately 28- cwt. Another way. Let a and b (in inches) be the two parts into which the 148 Asphalte. exterior diameter of the cable is divided by the centre line of the iron wires on one side ; and d the diameter, in inches, of a single iron wire. Then the transverse sectional area of the casing is a b - d z \ square inches. And the weight, per knot, of casing is approximately 112 (a& g^ 2 ) cwt. Chatterton's Compound. The compound, by means of which the alternate coatings of gutta-percha upon a cable conductor are cemented together, is composed of the following in- gredients : Stockholm tar ... i part Resin i ,, by weight. Gutta-percha ... 3 parts This compound is used also for filling up the inter- stices of strand conductors. Its specific gravity is about the same as that of ordi- nary gutta-percha; its insulating capacity, however, is much less. Asphalte. 149 OO OO OO OO vr% r Or^ONi-^Or *^- ^..NOOO M -00 ^r.^-00 r^^oo r* ^so M rA Js o oo NO w^, ^j- OO *$- OO NO OO ss^J^s" S^^^^s:^trs:^?r^^ C *M M M M M .00 k/N ^0 VTNSO S^SSSSMESS:? M " - " " " H K * -+ . ON ON ON r~~ ir\ y O f< -^- I-^O O O'-P^ONM r\r< O O r-N.rAr}-r* MOOOOOOOOOOOO g ^ ^ ^ n ^ o rf ONOO C* ONOO ON M -r\ r^* r o^ *^ M t^. o oo * r< ^^-^trg'S ONOO^ r-o o WN. TN^- Tj-^ rrs r< JC c %, OOOOOOOOOOOOO H '_C >^v M O O ON (jN i_i i_, oO >-r\vO \O t-^r^rNvO M ^C M M I-H M O OOOOOOOOOOOOO d-8S.?^ 2SSSSSS-S32 J= M M O O O OOOOOOOOOOOOO ON O **\ r^o n r<^ r< >-" ONQO rr\ o O j= - b b b b O O O O.O OOOOOOOO glgfi j O O O * CN X> O <-^O ^r\30 -^-Q ONwx~N.r* xr\ r>r\ r* O OO NO ^ *^ n O ON^i r^vO .!' a ~S Q *O ^* ^C O O O O O OOOOOOOOOOOOO O 8O M n rr, * ^NO r^x, ON ~ c, ^ ^. ^o ^M 1 50 Submersion. SUBMERSION OF CABLES. Approximate velocity of sinking. v= 2*51 <\y d( i j .... feet per second. v = the velocity with which a cable descends towards the bottom, at ordinary angles. d = the diameter of the cable, in inches. s = the specific gravity of sea water = 1-028. s' = the specific gravity of the cable. Example. Atlantic cable. Diam. = 1*128"; specific gravity = i '6. Rate of sinking therefore v = 2*51 A / 1*128 I i j = 1*98 feet per second. Angle of descent (a) with the horizon. V = sin a v = the velocity, in feet per second, with which the cable sinks. V = the velocity, in feet per second, of the ship. a -- the angle sought. Example. A cable falls freely in sea water at the rate of 1*78 feet per second. Vessel sails 10*4 feet per second (average). Therefore = 0*17115 = sin 9 50' (the angle of descent). 1 0*4 Tension on cable when paying out stopped. '' = ' 536 7-^ ' ' ' ' (cwt) " /' = tension on cable hanging over stern. h = depth in fathoms. w = weight of a foot of cable in water in Ibs. Slack. 151 ft angle of cable (hanging in water, with the horizon). Example. Atlantic (1866), h = 2000 fathoms; "W - '242 Ibs. ; )8 = 45, and another time 90. 2000 x '242 1) /' = -0536 x t _ 7<>7 = 367 cwt 2OOO X '242 2) ? = -0536 X - ~_ Q = 25-9 CWt. Tension of cable when payed out at different angles. (Airy.) Angle made by the cable Tension of the cable at the at the ship with the ship, expressed in terms horizontal line. of the minimum tension. 10 .......... 65-8 15 .......... 2 9*4 20 .......... 16*6 25 .......... 10-7 30 .......... 7*47 35 .......... 5'5? 40 .......... 4' 27 45 ......... 3'47 50 .......... 2*80 55 .......... 2 '35 60 ... * ...... 2'OO The unit is the weight in water of a piece of cable whose length is equal to the depth of the sea. To ascertain roughly during submersion the amount of Slack. /6ooo \ Slack = f - -- 100 J per cent. t time in minutes of one knot going out. s ~ speed of ship in knots per hour by log line. Example. In paying out the Atlantic, a knot passed out in 10-2 minutes, whilst the speed of the ship was 5-4 knots. Slack therefore = (IO I00) = 9 per cent - Speed of Ship. O >^Oi^O^\O>r\Ow\O^O^O O w w M r m -^ rt- ^- UMTNXO vo r~ Strain. 153 Strain during Submersion * (/). (Longridge.) , cosajl t - 0*0536. h \ \z/' / i ... in cwts. ( sin a J h = the depth in fathoms. w = the weight, in water, of one foot of cable in Ibs. v = the velocity, in feet per second, with which the cable leaves the ship. v' = the velocity of the ship, in feet, per second. a = the angle which the cable makes with the surface. k = the so-called coefficient of friction, that is, the resistance, in Ibs., which the water opposes to the motion of each foot of cable drawn lengthways, at a speed of one foot a second. For the (1866) Atlantic cable, which was covered with hemp, k = 0-0085. t Example. The (1866) Atlantic deep-sea cable. Depth 2000 fathoms. Weight of one foot in water = '2576 Ibs. Velocity of cable running out =12 feet per second. Velocity of ship = 10*4 feet per second, k = 0*0085 ^s. And tne angle under which the cable entered the water = 9 30', f * / 12 yj / = 0-0536 X 2000 J -2576 -0085 x io-4 2 \ 10 '4 3/ l_ { -16504 ~ J io'8 cwt. * See also Tables, pp. 248, 250. f For hemp covered cables k 0*007 d iron covered ,, k = O'ooi d approximately. d being the diameter in inches. 154 Tanks. Approximate Capacity of Cable Tanks. Let C circumference of tank in feet ; c = circumference of eye in feet ; n = number of turns between eye and circum- ference, then (C -f c) x n \ number of rings X (circumference of tank + circum- ference of eye) = length in each flake. In a tank with straight sides and circular ends, the length in each flake is = n 2 / -| D + // n being the number of rings in each flake. For circular tanks the length in each flake is D-f d = mr -- . Number of flakes in tank = -.. depth of tank diameter of cable X ro8. Cable Tanks. 155 In coiling from outside to inside, the bight has at the end of each flake to be brought back, thus reducing the room. This reduction may be found by laying the cable loosely across the bight, and let a equal the distance from the cross to the spot where cable touches the remainder, then the reduction = . circ. of eye The total length of cable in any tank is, there- fore, V.-? I '00\ to I i'iS/ <) ' *J I Where L = total length. N - number of rings in a flake. C = circumference of tank. c = circumference of eye. H = depth of tank. d' = diameter of cable. 1*00 = coefficient for circular tanks. 1*15 = coefficient for oval tanks. a = crossing of cable. (Hocking To find the capacity of a Circular Tank. -R Let r = radius of the eye. R = radius of the tank. d = diameter of the cable. n = number of coils in one flake. 156 Distances. Then R - r . x n = __ (i.) The length of the first coil is - and the length of the nth coil is Therefore, summing this arithmetic series, of which the first and last terms are given by substituting for n its value (i.) length of one flake = ^(R 2 - r 1 } (2.) Let h be the height of tank or coil, then Total length of cable - (R 2 - r 2 ). (3.) Distances. 157 Greatest Distances of visible Objects at Sea. Let h = the height in feet of the object above the h' = the height in feet of the observer j water. d = the distance of the object ) r I from the point d' = the distance of the observer j where the line joining both touches tan- gentially the water's surface (horizon). D = d -j- d 1 = the distance of the observer from the object. d = 1-31 \/h d 1 = i '3 1 \/Ji > in statute miles. D = 1-31 d = 1-23 d 1 = 1*23 v m nautical miles. D = 1-23 The Admiralty standard height, #, of the observer is = 10 feet. Example. The lantern of the Eddystone lighthouse is 72 feet ( - h) above the sea-level. An observer on the deck of a, ship> ififeet (= h') above the water would just see the light at a distance D = 1-23 (Jh + J~h } ) = 1-23 U/72 + Vl6) = I5'3 knots from the lighthouse. The distance in knots of a visible object at the sea- level is approximately equal to the square root of the height of the observer, in feet. I S 8 Distances. DISTANCE OF THE VISIBLE HORIZON. The distances are in knots, the heights in feet. Height of Ob- server. Distance of Horizon. Height of Ob- server. Distance of Horizon. Height of Ob- server. Distance of Horizon. Height of Ob- server. Distance of Horizon. Feet. Knots. Feet. Knots. Feet. Knots. Feet. Knots. 1 1-06 30 5-82 59 8-17 800 30-08 2 1-50 31 5-92 60 8-24 900 3i-9 3 1-84 32 6-or 65 8-58 1000 33-63 4 2-13 33 6-n 70 8-89 1100 J5-27 5 2-38 34 6-20 75 9-21 1200 36-84 6 2-6o 35 6-29 80 9-51 1300 38-34 1 2'8l 36 6-38 85 9-80 1400 39' 79 8 j-oi 37 6-47 90 10-09 1500 41-19 9 3-19 38 6-56 95 10-36 1600 42-54 10 3-36 39 6-64 100 10*63 1700 4r85 11 3 '51 40 6-73 110 11-15 1800 45-12 12 3-68 41 6-81 120 11-65 1900 4^-35 13 3-83 42 6-89 130 12-12 2000 47*56 14 3-98 43 6-97 140 12-58 2100 48-73 15 4-12 44 7-05 150 13-03 2200 49-88 16 4-25 45 7-13 160 ir45 2300 51-00 17 4-38 46 7-21 170 13-87 24DO 52-10 18 4'5i 47 7-29 180 14-27 2500 53-17 19 4'53 48 7*37 190 14-66 2600 54-22 20 4-78 49 7*44 200 15-04 2700 55-25 21 4-87 50 7-52 250 16-81 2800 56-77 22 4'99 51 7'59 300 18-42 2900 57-27 23 5-10 52 7-67 350 19-90 3000 58-25 24 5-21 53 7'74 400 21-27 3250 60-62 25 5-32 54 7-81 450 22-66 3500 62-91 26 5-42 55 7-89 500 23-78 3750 65-12 27 5-52 56 7-96 550 24-94 4000 67-26 28 5-62 57 8*03 600 26-05 4500 71-34 29 5-72 58 8-10 700 28-14 5000 75-20 Distance Sound. 1 59 Distance from Shore. Measurement by Sound. It sometimes happens that the distance of the ship from shore is required to be known, and a measurement by sound may be resorted to. For this purpose a gun is fired, and the interval between the flash and the sound noted. Let D = distance in knots ; T = temperature of air in deg. Centigrade ; S = interval in seconds. then "' _ D = 0*179 S \/i + 0-00374 T* Example. A ship fired a cannon, and the sound was heard 6 seconds after the flash was seen. The temperature of the air was 15 D C. Required the distance (D) of the ship. D = 0-179 X 6^ i + 0-00374 X 15 = 1-2 knots. Descriptions of Sound. Audible at a distance of Powerful human voice . . .200 yards Drum ...... 2 knots Horn . .... 3 Musket ...... 3 Cannon. . . . . 10 to 90 Velocity of Sound. Velocity of sound in air = i, 142 ft. per second. Ditto ,, water = 4,900 Ditto ,, iron = 17,500 Ditto ,, copper = 10,378 Ditto ,, wood = 12,000 to 16,000 1 60 Distance. To find the distance from ship to shore by the sextant. Let an assistant on shore set up two staves so as to form a base line at right angles to the position of the vessel, and signal their distance apart ; the observer on board ship measures the angle subtended in degrees and minutes, and multiplies the distance by the constant in the subjoined table. Example. The distance between two staves on shore is 420 yards, and the angle measured from the ship is 26 30', the distance of the nearer staff is 2*01 X 420 = 844 yards. Distances. 161 To find the distance from ship to shore by the sextant. Pegs. DISTANCES. 0' 10' 20' 30 40' 50' 5 11-43 ii'o6 10-71 10-39 io'o8 9*79 6 9-51 9-26 9'oi 8-78 8-56 8-34 7 8-14 7-95 Til 7*60 7'43 7-27 8 7-12 6-97 6-83 6 69 6-56 6-43 9 6-31 6'20 6-08 5-98 5-87 5*77 10 5-67 5-58 5-48 5-40 5'3i 5*23 ii 5*!4 5-07 4'99 4-92 4-84 4*77 12 4-70 4-64 4*57 4-5i 4*45 4*39 13 4'33 4*27 4-22 4'i7 4'ii 4' 06 14 4'oi 3-96 3-91 3-87 3-82 3-78 15 3 '73 3-69 3-65 3'6i 3'57 3'53 16 3 "49 3 '45 3'4i 3-38 3'34 3'3i 17 3*27 3-24 3'20 3-17 3*i4 3-11 18 3-08 3-05 3-02 2'99 2-96 2'93 19 2 '90 2-88 2-85 2-82 2 '80 2'77 20 2'75 2-72 2-70 2-67 2-6 5 2-63 21 2-61 2-58 2-56 2-54 2-52 2-50 22 2-48 2'45 2'43 2-41 '39 2-38 23 2-36 2-34 2-32 2-30 28 2-26 24 2-25 2-23 2*21 2-19 18 2-16 25 2-14 2-13 2-II 2-10 08 2-07 26 05 2*04 2-02 2-01 "99 98 27 96 *95 1-93 92 91 89 28 88 87 1-85 84 'S3 82 29 .80 '79 1-78 '11 7 6 *74 30 '73 72 1-71 70 6 9 68 31 66 65 1-64 63 62 61 32 60 *59 1-58 '57 5 6 55 33 '54 *53 1-52 '5 1 'SO '49 34 48 *47 1-46 46 45 *44 35 43 42 1-41 40 "39 38 36 38 "37 1-36 '35 '34 34 37 '33 32 1-31 30 30 29 38 28 27 1-26 26 25 24 39 23 23 1*22 21 I'2I 20 40 19 18 I'l8 17 1-16 16 162 Soundings. SOUNDINGS. To reduce Soundings to Low Water. Letters denote T = Interval in hours between low and high water. / = Interval in hours from low water to the time when the sounding is taken. H = Vertical rise of tide, in feet, from low to high water. h = Height, in feet, to be subtracted from the sounding taken at the time, /, ( l8 oi) cos 180 J when / < ^ T j = ' cos cos ( 1 80 ~ j when / > i T. Example. High water at loh. I5m. p.m. Low water at 3h. 45111. ,, Interval (T) = 6h. 3om. ,, -= 6*5 hours. The sounding taken at ijh. 3om. ,, was 16 feet 6 inches. Interval (t} = ih. 45111. = I '75 hours. Vertical rise H = 9-75 feet, Required the reduction and true sounding at low water. o - ) = I8 x '75 = 4 o 30 cos 48 30' = 0-66262. h = (I - 0-66262) = 1-6447 feet. Sounding taken at 5h. 3om. was 16*5 ,, (subtract) h = 1*6447 True sounding at low water 14*8553 ,, Soundings. 163 u n n eui s auiq nB >2 2 IH ON auiq vo O < : ^^- 3 p >* $ I IUEA-OA\ ins tp vo ir\ ^- >4- ^- f^ 8B8888888888 M^OooOrl^-xdooOcJ^- pOQOQOOoODO ooooooooooo nri-oooO^^-voooOw 164 Steering Across Currents. SOUNDING LINES. LINE. Number of Threads. Weight per 100 Fathoms. Circum- ference. Breaking Strain. Dry. Wet* Deep sea (Portsmouth) .... 27 Ibs. oz. 18 9 Inches. I'O Ibs. 1,760 Ibs. i559 Deep sea, hawser laid (Devonport) 27 24 6 i -066 1,176 952 Medium (Portsmouth) .... 18 12 8 0-8 1,402 1,211 Ordinary deep sea, cable laid 7 (Devonport Dockyard) . . j Cod (Portsmouth) ... 18 9 9 23 14 6 4 7 1*065 o-55 0*565 815 74 494 630 777 469 Cod (Devonport) Ordinary cod (Devonport) . . . 6 6 2 0-540 254 252 * After soaking 24 hours. Steering Across Currents. If it be required to lay a cable from two given points, A and c, between which a current runs (in the direction shown by the arrows) with a known velocity, the direction in which the ship must be steered in order to pay out the cable with the least possible loss is found by constructing the parallelogram of forces, A B D E. Let Steering. 165 the A E line, in the direction of the current, represent its velocity in knots per hour ; let A c be the cable in knots ; and A B, measured off from the point A, be the rate at which it is determined to pay it out per hour. We then construct the parallelogram, A B D E, in which A D gives the direction and required rate of the ship. A convenient diagram card is in use by the naval officers for this purpose. Around the centre of a com- pass card are described six or more concentric and equidistant circles, each representing a knot of distance. When it is required to find the rate and direction of a ship across a current, it is done by making the centre the starting-point, and laying off from it the direction and velocity of the current, and the resultant direction, and velocity of the ship, with which a parallelogram is 1 66 Sea Water. constructed, the new side, starting from the centre, giving at once the direction and rate. Example. A current is setting towards the S.W., at the rate of 3 knots an hour, whilst it is required to make good an E.S.E. course, at the rate of 4 knots an hour. Where the S.W. line intersects the 3 -knot circle, we mark off the point D; and where the E.S.E. line inter- sects the 4-knot circle, the point C. Between these two points we draw the straight line, C D, and parallel to this, and to the line joining D with the centre A, we draw the remaining lines A B and C F, which complete the parallelogram. The course in which the ship is to steer is given by the line A B, in this case E J N ; and the rate at which she must go through the water by the distance of F from the centre, in this case 5f knots. SEA WATER. The specific gravity of sea water is ordinarily 1-028. One cubic foot weighs 64-24 Ibs. One cubic foot of distilled water weighs 62*5 Ibs. The pressure of the ocean is equal to 2-676 Ibs. per square inch per fathom, or one ton one cwt. per statute mile of depth. Hence, in the Atlantic, where the depth is about two miles, the pressure will be two tons two cwt. for each square inch of surface. The temperature of the ocean below a depth of 1200 Water. 167 fathoms is believed to be about 4 Centigrade, that is to say, the temperature of water of maximum density. Force of the Waves. From experiments made by Mr. A. Stevenson, at the Skerryvore Lighthouse, on the west coast of Scotland, exposed to the whole fury of the Atlantic, it appears that the average pressure of the waves during the summer is equal to 611 Ibs. weight ou a square foot of surface, while in winter it was 2086 Ibs., or three times as much ; during the storm on the 9th of March, 1845, ^ amounted to 6013 Ibs. The effect of a gale descends to a comparatively small distance below the surface. The sea is probably tranquil at the depth of 200 or 300 yards. MEMORANDA CONNECTED WITH WATER. I cubic foot of water =62 "5 Ibs. = iooo oz. at 60 F. I cubic inch . . = '036 Ibs. I gallon . . . . = 10 Ibs. or . . . . = o'i6 cube feet. I cube foot of water 6*2355 gallons. or, approximately = 6| ,, I cwt. of water. . = i'8 cube ft. = ii'2 gals. I ton of water . . =35-9 cube ft. = 224 ,, Absorption of Water by Insulators. In Fresh Water. In Salt Water. Raw india-rubber ... 25 percent. 3 percent. Unvulcanized block india-) rubber j* 3 " 3 ' 8 " India-rubber and mica .19 ,, 3*9 Vulcanized india-rubber . 10*14 > 2 '9 > Gutta-percha, t , , , 1*5 ro 1 68 Length of Cable. Determination of the Height and Velocity of the Waves off the Cape of Good Hope, 1847. By Commander Dayman, R.N. Date. No. of Obser- vation. Speed of Ship. Height Wave. Length of Wave. Speed of Sea per Hour. Remarks. I8 47 Knot. Feet. Fath. Knot. Ap. 21 7*2 22 55 27-0 23 8 6-0 2O 43 24' 5 Before the wind, 24 6 6-0 20 50 24*0 with a heavy > 25 9 i\ * O 37 22*1 following sea. 26 6-0 33 22 'I May 2 6 7 7-0 7'8 22 17 57 35 26-2 22'O ) S ea irregular and ) on port quarter. Mean 20 44 24- o To find the length of cable required to join two given points. The rough way is to draw a straight line between the two places upon the chart, and measure off its length with that of a degree ( = 60 knots) taken from the margin at about the latitude of the middle. In high latitudes when the distances are great, however, this method will give very fallacious results, and we must have recourse to spherical trigonometry. Let the lower latitude be /, and longitude L, the higher latitude be /', and its longitude L'. The shortest distance, d, in degrees of the great circle between these two places is found by the equation sin /'. cos n . cos d - in which cos m tan m = cot /' cos (L L'), n - 90 / m. In the value of. , the latitude / is + when the places Course of Ship. 169 are on opposite sides of the equator, and when both are on the same side of it. Example. Required the shortest distance between the Lizard in latitude 49 57' N., longitude 5 14' W. t and the -west end of the island of Madeira in latitude 32 30' N. y longitude 17 26' W. According to the above (L - L') = 17 26'- 5 14' = 12 12' tan m = cot 49 57' X cos 12 12' = 0-8406 x 0-9775 = 0*817 = tan 39 14' n = 90 - 32 30' - 39 24' = 18 6' and d _ sin 49 5 7' X cos 18 6' _ 0-7655 X 0-9505 _ ~~cos 39 24' 0-7727 0*9412 = cos 19 45' The shortest distance is therefore 19 X 60 + 45 = 1185 knots. In specifying deep-sea cables it is safe to provide 20 to 25 per cent, more than the direct distance; and for shallow-sea cables 5 to 7-r per cent. To find the course of the Ship. Adopting the designations given above, the course from the lower latitude to the higher is obtained by sin (L L') sm C = - ^ - '- cos /' sin a and that from the higher latitude to the lower, by . sin L - L' sm C = - : ; cos /. sin d Example. Let us take again our supposed line. We have the course from Madeira given by sin 12 12' = COS49 57' = sm2 3 "44 The ship would therefore start from Madeira North (23 44') East. From Lizard the course is given by sin 12 12 I/O Log-line. the ship must therefore approach the English station in a course South (31 30') West. The course of a ship is usually given in points of the compass east and west of true north and south. A point is equal to 11 15' of arc, To find the difference of time between two places. Each 15 difference of longitude represents one hour difference of time. Therefore divide the difference of the longitudes of two given places by 15, and the quotient gives the dif- ference in time. The longitude of Greenwich is o o', and that of New York 74 7' W. The difference in time between them is therefore THE LOG-LINE AND HALF-MINUTE GLASS. The principle of the log-line is this : The length of each knot upon the line bears the same proportion to the length of a sea-mile as half a minute does to an hour. Therefore the length of each knot of the line is, or should be, the T J-g- part of a sea-mile. The length of a sea-mile is generally taken at 6120 feet, so that the length of a knot on the line is 51 feet. In submarine telegraph work, however, a sea-mile is assumed to be 6087 feet only (or 2029 yards), and as the telegraph cable is measured in this unit of length, the speed of the ship should be mea- sured to it also, or an error will arise in the amount of Log-line. l/i slack paid out. The length of a knot of the log-line of a cable-ship must therefore be- -==50723 feet for the half-minute glass. A correction for the glass is sometimes necessary, the length of the knot on the line being increased or de- creased in the same ratio as the glass takes a longer or shorter time than 30 seconds to run out. Thus, if the glass run out in 28 seconds, the knot lengths would be 28 only 50723 x = 47'34 feet, 172 Weights of Cables. TABLE for reducing weights of cables, per foot, to weight, per knot, of 2029 yards = 6087 feet. (Forde.) Weight of EQUIVALENT OF KNOT. Lbs. Cwt. Pounds. I 6-087 54-348 2 3 12-174 18-261 108 696 163-045 4 24-348 217-39? 5 30-345 271-741 6 36-522 326-089 7 42*6OQ 380*45*7 8 48-696 > 454-786 9 54^83 489-IJ4 10 60-870 543-482 Ounces. I 380 3*307 2 760 6-794 3 II 4 I 10-190 4 1522 13-587 1902 16-984 6 2282 20-381 7 2663 23-777 8 3043 27-174 9 10 3423 3804 30-571 33-9^8 ii 4184 27-364 12 4565 40-761 13 4945 44-158 14 5326 47-555 15 5706 5-0-951 16 6087 54-348 Weight of i loot Specimen. EQUIVALENT OF KNOT. Lbs. Cwt. Grains. I 0-8696 0078 2 I-739I 0155 3 2-6087 0233 4 3-4783 0310 5 4-3479 0388 6 5-2174 0466 7 6-0870 054J 8 6-9566 0621 9 7-8261 0699 10 8-6957 0767 20 I7-39I4 155? 30 26-0871 2329 40 34-7828 3106 50 43-4786 2882 60 52-I743 4650 70 60-8700 5435 80 69-5657 6211 90 78-2614 6988 ICO 86-957I 7665 200 173-9142 1-5528 300 260-8713 2-3292 400 347-8284 ! 3-1055 To find the weight, per knot, of a given cable by the above Table : Weigh a length of one foot of the cable and add together the equivalents for Ibs., oz., and grains. Example. A foot length of cable weighed 2 Ibs., 5 oz., and 74 grains. Its weight, per knot, is therefore obtained as follows : 2 Ibs. . . io8'696cwt. 5 oz. . . 16-984 7ogrs. . . . -544 4 <0 3i Total = 126-255 ^wt., per knot. Overland Lines. 173 Extra material required by twisting helically. L = length of finished cable or strand in yards. / = length of one wire required to lap it helically in yards. D = outside diameter in inches. 8 = diameter of helical wire in inches. h = lay in inches. . T / = L. (D - . m yards. OVERLAND LINES. Strains of suspended wires. The suspended wire may be regarded as a parabola. It is usually stretched so as to allow, in a distance, / = 240 feet between the supporting insulators, a sag, h - i \ feet in mild weather, which is on the average equivalent to h = o'oo6 /. The length L of the suspended wire is 174 Overland Lines. The vertical strain S r or weight upon each insulator is L d^ira S P = -- Ibs. 4 in which 00 r-ooco 3VOO O JH g 1 I- tJSIISIf lisf Or- ^^^.^^.^^^^5:^:3: -f^iA^vOO r^r-oooo <>o H, ?vgs-^g;^Ss^5?^s H i^^^oo rTvS ^Sv CO VN *> r- M ?oo C4VO O^-oo * ^OO HOO t'O r~f^a\iriM rO O\ r* \O O -4-r^iH TTOO M Jg ^?5^^^S:?r^3i^s .g P.8^5^82,5S^-P.S 3 S ST * " \ 5000 Varas . . J 46*5 do. 563 ?5 do. 37-97 Swabia. . . Mile . . . 10126 do. 275-4 do. 17-58 Sweden . . Mile . . . 11700 do. 664-77 do. 15 04 Switzerland . Mile . . . 915? do. 520-05 do. 19-2; 1826 do. do. 06 " ?8 Tuscany . . Mile . . . 1808 do! 102-72 do! 9" "34 Westphalia . Mile . . . 12151 do. 690-39 do. 14-48 i8o Statistics. Statistics of some Telegraph Systems. Scudamore's Report. In Belgium. In Switzerland. In the United Kingdom. (186$.) Miles of tele- graphic line to every Miles. Miles. Miles. 100 square miles of 1 71 137(5 II^j territory. Number of telegra- phic offices to every > Offices. Offices. Offices. 100,000 persons . ) 3 "TO JTS Increase per cent, in 1866 over 1865 : Per cent. Per cent. Per cent. Miles of line 9 3i 3* Miles of wire 15 10 4 Telegraph offices 16 - I2j 7 Instruments . 1 S% J 3i ii Proportion of Inland! Telegrams to Inland) Letters . . 1860) Telegrams Letters i to 218 Telegrams Letters I to 84 Telegrams Letters i to 296 Ditto Ditto 1 86 1 195 87 273 Ditto Ditto 1862 187 80 221 Ditto Ditto 1863 114 74 197 Ditto Ditto 1864 88 70 I6 9 Ditto Ditto 1865 73 69 Ditto Ditto 1866 37 69 121 Cost per mile of' line of working and 1 * d. s. d. s. d. maintaining Tele- 1 4 18 4 550 4 10 o graph. . . 1865] Ditto Ditto 1866 5 7 6 532 4 10 2 Number of messages] Messages per Mile. Messages per Mile. Messages per Mile. per mile of line 1862 97 128 47 Ditto Ditto 1865 124 159 61 Ditto Ditto 1866 181 163 78 Thermometers. 181 COMPARATIVE TABLE of the Degrees of the three Thermometrical Scales. To convert the Degrees of Fahrenheit into those of Reaumur and Celsius (the Centigrade) ; and conversely. F 32 Fahrenheit into Reaumur X 4 = R. 9 F 32 Fahrenheit into Celsius X 5 = C. Reaumur into Fahrenheit -j- 3 2 = F. 4 Celsius into Fahrenheit ^ + 32 = F. 1 82 Thermometers. TABLE of Comparison of different Thermometers. Fah. Reau. Cent. Fah. Reau. Cent. Fah. Reau. Cent. Fah. Reau. Cent. 212 80-0 lOO'O 153 53-7 67-2 94 27-5 34'4 35 I'3 1-6 211 79' 5 99*4 152 53'3 66-6 93 27-1 33-8 34 0-8 I " I 210 79-1 98-8 151 52-8 66-1 92 26-6 33'3 33 0-4 0-5 209 78-6 98-3 150 52-4 65-5 26-2 32 o-o O'O 208 78-2 97*7 149 52' 65-0 9 25-7 32-2 3' 0-4 0-5 207 77;7 97-2 148 51' 64-4 89 25-3 31-6 30 0-8 i-i 206 96-6 5i * 6j-8 88 24-8 ?I " I 2 9 1*3 1-6 205 76-8 96-1 146 50- 63-3 87 24-4 30-5 28 i'7 2'2 204 76-4 95-5 145 50- 62-7 86 24-0 30-0 27 2'2 2-7 203 76*0 95-0 144 49' 62-2 85 2J-5 29-4 26 2*6 3'3 202 75-5 94'4 14? 49'3 61-6 84 23-1 28-8 25 3'I 3-8 201 75-1 93-8 142 48-8 61-1 83 22-6 28-3 24 3'5 4*4 20O 74-6 93-3 141 48-4 60-5 82 22-2 27-7 23 4-0 199 74'2 92-7 140 48-0 60-0 81 21*7 27-2 22 4'4 5'5 198 73-7 92-2 47'5 59'4 80 21-3 26-6 21 -4-8 6-1 I 9 7 196 73-3 72-8 91-6 91-1 I3 ? 7 ^ 58-8 58-3 79 78 20-8 20-4 26-1 25; 5 20 19 5'3 - 5'7 6-6 7*2 195 72-4 90-5 136 46-2 57'7 77 20'0 18 6-2 7-7 I 94 72-0 90-0 135 45'7 57'2 76 19-5 24-4 17 6-6 8-3 19* 71-5 89-4 134 45-3 56-6 75 19-1 23-8 16 7'i 8-8 192 7I'I 88-8 133 44-8 56-1 74 18-6 23'3 15 7'5 9'5 191 70-6 88-3 132 44'4 55'5 73 18-2 22-7 8-0 lO'O 70-2 87-7 131 44-0 72 17-7 22-2 13 -8-4 10-5 189 69-7 8 7 -2 130 54'4 71 17-3 21-6 12 8-8 ii'i 188 69-3 86-6 129 4 ? * I 5r8 70 16-8 21 * I II 9'3 11-6 187 68-8 86-1 128 42-6 69 16-4 20-5 10 9'7 12'2 186 68-4 85-5 127 42-2 52-7 68 16-0 2O'0 9 10-2 12-7 185 68-0 85-0 126 41-7 52-2 67 J 5'5 19-4 8 10-6 13-3 184 67-5 84-4 125 51-6 66 15-1 18-8 7 ii-i 13-8 183 67-1 83-8 124 40-3 51-1 65 14-6 18-3 6 H'5 14-4 182 66-6 83-3 123 40-4 5o-5 64 14-2 17-7 5 12-0 15-0 181 1 80 66-2 65-7 82-7 82-2 122 121 40*0 39'5 50-0 49'4 62 13-7 13-3 17-2 16-6 4 3 12-8 -Iti 179 65*3 81-6 1 2O 39' i 48-8 61 12-8 16-1 2 13-3 16-6 178 64-8 81-1 119 38-6 48-3 60 12-4 15-5 I 13-7 17-2 177 64-4 80-5 118 38-2 47'7 59 12-0 I5'o O 14-2 17-7 176 64-0 80-0 117 37'7 47-2 58 11-5 14-4 I -14-6 -18-3 175 63-5 79'4 116 37'3 46-6 57 n-i I3'8 2 15-1 18-8 63-1 78-8 115 36-8 46-1 56 10-6 I3'3 3 i5'5 19-4 173 62-6 78-3 114 36-4 45'5 55 I0'2 12-7 4 16-0 20-0 172 62-2 77'7 "3 36-0 45-o 54 9-7 12-2 5 16-4 20-5 171 170 61-7 61-3 ?n 112 III 35'5 35-1 44'4 43-8 53 52 9'3 8-8 II-6 II'I 6 7 16-8 17-3 21 -I 21-6 169 60-8 7 6-i no 34-6 43-3 5i 8-4 10-5 -8 17-7 22-2 168 60-4 75'5 109 34'2 5o 8-0 io-o -9 18-2 22-7 '67 6o m o 108 33'7 42-2 49 7'5 9'4 10 18-6 23-3 1 66 59;5 74'4 107 33'3 41*6 48 7-1 8-8 ii 19-1 23-8 165 73-8 106 32-8 41-1 47 6-6 8-3 12 19-5 -24-4 164 58-6 73-3 105 32*4 40-5 46 6-2 7'7 13 20-0 -25-0 163 58-2 72-7 104 32-0 40-0 45 5'7 7-2 14 20-4 25-5 162 57'7 72-2 103 31*5 39'4 44 5'3 6-6 2o-8 26-1 161 160 56-8 71-6 71-1 102 101 3O'6 38-8 38-3 43 42 4-8 4'4 6-1 5'5 17 -21-3 21-7 26-6 27-2 159 56-4 7o-5 IOO 30-2 37'7 5-0 18 22-2 27-7 158 56-0 70*0 99 29-7 37-2 40 3'5 4'4 19 22-6 28-3 157 55'5 69-4 98 36-6 39 3-8 20 23*1 28-8 156 68-8 97 28-8 36-1 38 2-6 3'3 155 54-6 68-3 96 28-4 35'5 37 2'2 2'7 154 67-7 95 28-0 J6 1-7 2'2 Wind Air. 183 Velocity and Force of the Wind. (Smeaton.) Miles per hour. Feet per second. Direct force per square foot in Ibs. avoirdupois. Expression. I i'47 005 Hardly perceptible. 2 3 2-93 4*40 O2O| 044/ Just perceptible. 4 5 5-87 7*33 '79l 123! Gentle, pleasant wind. 10 15 14-66 22-OO 492) IT07I Pleasant, brisk gale. 20 25 29-34 36-67 1-968} 3'075/ Very brisk. 30 35 44-01 5^34 4'429\ 6-027/ High wind. 40 45 58-68 66*01 7-873) 9-963; Very high wind. 50 73*35 12*300 Storm, or tempest. 60 88-02 17-715 Great storm. bo 117-36 31-490 Hurricane. 100 146-66 49-200 ( Hurricane that tears up trees, and \ carries buildings before it. Weight of a Cubic Foot of Air. To find the weight in pounds of a cubic foot of air at different tem- peratures, and under different pressures (Molesworth) W = 459 + T Where B is the height in inches of mercury in barometer, and T temperature Fahrenheit. The Barometer. If the barometer differ from 30 inches, the boiling point of water will differ from 212. According to Wollaston, i Fahr. corresponds to a dif- ference of 0*589 inches of barometric pressure. When the barometer stands at 29 inches, water boils at 1 84 Barometer. 210-38 Fahr. When it stands at 31 inches, water boils at 213-57. To Measure Vertical Heights by the Barometer. Letters denote H = column of mercury . , at the lower station. T = temperature of the air h = column of mercury . J . at the higher station. / = temperature of the air / = latitude of the place. /= vertical height, in feet, between the higher and lower station. H _ _\ -/)/ (T f 60345-51 X (l -f- O'00255I COS 2 /) (l -(- O'OO2O8 (T + / - 64)). If the atmosphere be very calm the observations may be made one after the other by one barometer and detached thermometer; but the least disturbance of wind requires the observations at the upper and lower stations to be made at the same time. The reduction of the columns of mercury is included in the formula. If a measure of a height rather greater than the Aneroid will commonly show, be required re-set it, thus : When at the upper station (within its range), and having noted the reading carefully, touch the screw behind so as to bring back the hand a few inches (if the instrument will admit), then read off and start again. Reverse the operation when descending. This may add some inches of measure approximately. Barometer. i8 S TABLE. Barometer Inches. Height in feet. Barometer Inches. Height in feet. Barometer Inches. Height in feet. 31-0 26-8 3829 22-7 8201 30-9 85 26-7 3927 22-6 8317 30-8 170 26-6 4025 22'5 8434 30-7 255 26-5 4124 22-4 8551 jo-6 341 26-4 4223 22-3 8669 30-5 427 26-3 4323 22-2 8787 30-4 26-2 4423 22-1 8906 30-3 600 26-1 45M 22-O 9025 JO- 2 JO'I 30-0 687 m 26-0 25-9 25-8 4625 4726 4828 21-9 21-8 21-7 3% 9*88 29-9 29-8 950 1038 25-7 25-6 4930 5033 21-6 21-5 9510 9632 29-7 29-6 1126 1215 25-5 25-4 5136 5240 21-4 2I-J 9755 9878 29-5 1304 25-3 5344 21-2 IOOO2 29-4 1393 25-2 5448 2I'I 10127 29-3 i 4 82 25-1 5553 21-0 10253 29-2 1572 25-0 5658 20-9 10379 29-1 1662 24-9 5763 20-8 10506 29-0 28-9 1844 24-8 24-7 20-7 20-6 10633 10760 28-8 1935 24-6 6083 20-5 10889 28-7 28-6 2027 2119 24-5 24-4 6190 6297 20-4 20-3 11018 11148 28-5 2211 24-3 6405 20-2 11278 28-4 2303 24-2 6514 20-1 11409 28-j 2396 24-1 6623 20-O 11541 28-2 2 4 8 9 24-0 6733 19-9 "673 28-1 2582 23-9 6843 I 9 -8 11805 28-o 27-9 2675 2769 23-8 23-7 6953 7064 19-7 19-6 11939 12074 27-8 2864 2J-6 7175 J9-5 I22IO 27-7 2959 23-5 7287 19-4 12346 27-6 3054 23-4 7399 19-3 12483 27-5 27-4 3H9 3245 23-3 23-2 7512 7625 I9-2 I9-I 12620 12757 27-3 3341 23-1 7729 J9-0 12894 27-2 3438 23-0 7854 18-9 12942 27-1 3535 22-9 7969 18-8 13080 27-0 3633 22-8 8085 18-7 I32I9 26-9 3731 1 86 Conducting Powers. TABLE of Conducting Powers and Resistances. (Jenkins.} b 11= O O & III .S b "8 *>'M O 1> s si-si w^-S '*? d f Resistan one foot ing o: Resistan one m weighing Ji!" 1| llll ft bX)*-3 o Silver annealed . . . Silver hard drawn . . 100-00 0-2214 0-2421 0-1544 0-1689 9-936 9-151 0-01937 0-02103 0-377 Copper annealed . . 0-2064 0-1440 0*388 Copper hard drawn . Gold annealed . ... 99 '55 0-2106 0-5849 0-1469 0-4080 9-9400-02104 12-52 0-02650 0-365 Gold hard drawn . . 77-96 0-5950 0-4150 12-74 ,0-02697 Aluminium annealed . 0-06822 0-05759 17-72 |o-0375i Zinc pressed .... 29-02 0-5710 3-536 0-3983 2-464 32-22 55-09 0-07244 ii'jb 0-365 Platinum annealed . . Iron annealed . . . 16*81 1-2425 0-7522 59-40 1251 Nickel annealed 13-11 1-0785 0-8666 75-78 1604 Tin pressed .... 12-36 8-32 I-3I7 3-236 0-9184 2-257 80-36 II9-39 1701 2527 0-365 0-387 Lead pressed Antimony pressed . . 4-62 3-324 2-3295 216-0 4571 0-389 Bismuth pressed 1-245 5-054 3 ' 525 798-0 1-689 0-354 Mercury liquid . . . 18-740 13-071 600-0 1-270 0-072 Platinum, Silver, alloy, ) hard or annealed . 5 .. 4-243 2-959 143-35 0-3140 0-031 German Silver, hard or ) annealed .... 5 .. 2-652 1-850 127-32 0-2695 0-044 Gold, Silver, alloy, hard 7 or annealed ... 5 2'39l 1-668 66-10 0-1399 0-06, CONDUCTING POWERS OF METALS. Coefficients for temperature (t) in deg. Cels. (Mattkiessen.) METALS. COEFFICIENTS. Silver. . . IOO - o 38278 1 + o 0009848 1 2 Copper . C = 100 0*38701 / + 0-0009009 f 2 Gold . . . c = IOO - 0-36745 / + 0-0008443 1* Zinc . C IOO - o- 37047 t+ o- 0008274/2 Cadmium c IOO - 0-36871 1 + 0-0007575 1 2 Tin ... C IOO - 0-36029 / + 0-0006136 1 2 Lead . . . c = IOO - 0*38756 / + 0-0009146 / 2 Arsenic . . c = IOO - 0-38996 1 + 0-0008879 p Antimony c = IOO - o- 39826 1 + o- 0010364/2 Bismuth . c = IOO - 0-35216^+ 0-0005728 / 2 Mean of all . c = IOO - o 37647 1 + o - 0008340 / 2 Solutions. i8 7 CONDUCTING POWERS OF SOLUTIONS. Comparison with Pure Copper = 100,000,000. SOLUTIONS. f Conducting Power. I. Sulphate of Copper cone. (sp. gr. = 1*171) . Ditto, with an equal volume of water . Ditto, with 3 volumes of water . 9 5*42 3'47 2*08 Ditto, with an equal volume of water . Ditto, with 2 volumes of water . Ditto, with 3 volumes of water . 3. Sulphate of Zinc cone, (sp.gr. 1*441) . . Ditto, with i volume of water . . Ditto, with 3 volumes of water . : 13*58 5*77 7*i3 5*43 DILUTE SULPHURIC ACID. Resistances of different strengths. Specific gravity. SO 3 HO, n 100 parts by weight. Tempera- ture C. Resistance. 003 0*5 16*1 16*01 018 2*2 15*2 5*47 053 7*9 13*7 1*884 080 12*0 12-8 1*368 '*47 20*8 I3'6 0*960 190 26-4 13*0 0*871 215 29*6 12*3 0*830 225 30*9 13*6 0*862 252 34*3 13*5 0*874 277 37*3 .. 0*930 -348 45*4 17*9 0*973 *393 50*5 *4*5 i* 086 492 60-6 13*8 1*549 638 73*7 I4'3 2*786 726 8l'2 16*3 4*337 827 92*7 14*3 5*320 188 Chemical Equivalents. At very high temperatures the resistances of metals are increased, according to Miiller, as follows : IRON WIRE. COPPER WIRE. PLATINUM WIRE. Temperature. .>!. 4> 5 c Temperature. |8 Temperature. |8 < rt ri O Q C. . 21 C 640 o C. . . oC 1870 285 C. . Commencing to ) colour . 5 091 1660 2250 Scarcely incan- \ descent . } Carmine red 004 2100 2450 Barely incan- ) descent. . 5 Red hot . . 4300 4700 Dark grey Scarcely incan- ) descent. ) 2460 3050 Brick red . Bright red 21 C. . . 3300 4700 910 Light red . . Orange . . Light Yellow 5400 6000 Dark red . 3200 21 C.. . . 1984 Bright red 3650 Red hot . 455 White hot 4880 21 C. . . 727 Simple Substances, with their Symbols, Equivalents, and Specific Gravities. NAME. 1 CO 1 Sp. Grav. NAME. *o CO 1 Sp. Grav. Aluminium Al ir7 2-56 Molybdenum Mo 47 '9 8-60 Antimony Sb 64-6 6-70 Nickel . Ni 29-5 8-80 Arsenic . As 37'7 5-70 Nitrogen . N 14-2 0-972 Bismuth . Bi 71-5 9-82 Osmium . Os 99'7 10-00 Bromine . Cadmium Br, Cd 78-4 55-8 8-65 Oxygen . Palladium Pd 8-0 I -102 11-35 Calcium . Ca 20-5 58 Phosphorus P 15-9 1-77 Carbon . C 6-1 3-50 Platinum . Pt 98-8 21-50 Chlorine . Cl 35-5 2-44 Potassium K 39-2 0-865 Cobalt . Co 29-5 8-53 Rhodium . R 52-2 11-00 Copper Cu Ji-,7 8-80 Selenium . Se 40-0 4'5 Fluorine . F 18-7 1-32 Silver . . Ajr 108-3 10-5 Gold (Anrum Au 196-6 19^0 Sodium . Na 23-5 0-972 Hydrogen H I'D 0-069 Strontium Sr 2-54 Iodine. . I I26-5 4' 94 Sulphur . S 16-1 1-99 Iridium . Ir 9 8-5 18-68 Tellurium. Te 64-2 6-30 Iron . . Fe 28-0 7*75 Tin . . Sn 58-9 7-29 Lead . . Pb 103-7 Titanium . Ti 24-5 5-28 Magnesium Manganese J}g Mu 12-7 26-0 1-75 8-00 Tungsten . Uranium . W U 92-0 60-0 17-00 10-15 Mercury . Hy 2OO-O 13-50 Zinc . . Zn 32-3 7-00 Table of Weights. 189 TABLE containing the weight of a cubic inch, and a cubic foot, in ounces and pounds avoirdupois, and also the number of cubic inches in one pound, of the substances most used in construction. NAMES OF BODIES. Weight of a Cubic Foot. Weight of a Cubic Inch. Number ol Cubic Inches in a Pound. InOz. In Lbs. InOz. In Lbs. Copper, sheet. Brass, cast Iron, cast . . Iron, bar . Lead .... Steel, soft . . . Zinc, cast . Tin, cast . Bismuth Mercury . 8,915 8,393 7.271 7.631 11,344 7.833 7,190 7.292 9,880 *3.595 557-18 524'75 445*43 476-93 708-75 489*56 449*37 455*75 619*50 850*00 5*159 4-857 4-207 4-416 6-356 4-533 4-161 4-219 5-710 7-870 3225 3037 26 3 2 7 6 4103 2833 26 2636 355 "4908 3*IOI 3-294 3-802 3*623 2-438 3'53* 3-845 3-792 2- 7 9 2-037 Sand . Coal .... Brick .... Slate .... Glass .... 1,520 1,250 2,000 2,672 2,880 95-00 78-13 125 -oo 167-00 180*00 8777 7234 1-157 1-546 1-664 055 0452 0723 0967 1042 18*190 22-118 13-824 10*347 9-600 Larch .... Beech .... Teak .... Mahogany. Oak .... 544 696 745 852 970 34-00 43.50 46-56 53-25 60-62 3i5 403 43i '493 561 0197 0252 0269 0308 0351 50-823 39*724 37-111 32-449 28-503 Paraffin . . . Gutta-percha . India-rubber . Hooper's material Asphalte . Clark's Compound Hemp .... Hemp, tarred . 870 981 903 1176 1650 1760 1232 1776 54-38 61-31 56-44 73-50 103-12 IIO'OO 77-00 in-oo 503 508 523 681 *955 1-019 713 1-028 0315 0355 0327 0425 0597 0637 0446 0405 31*779 28*184 19-318 23*510 16*756 13*709 22*422 24-673 Olive Oil . . . Linseed Oil Spirits, proof . Water, distilled . Water, sea Tar .... 915 932 927 1,000 1,028 1,015 57-19 58-25 57-93 62-50 64-25 63*44 529 539 536 578 594 587 0331 0337 03352 0362 0372 0367 30-216 29*655 29*288 27*648 26*895 27-242 B. W. G. TABLE of the Birmingham Wire Gauge. No. B.W.G. rf= diam. in inches. d* Sect, area in sq. ins. No. B.W.G. d diam. in inches. d* Sect, area in sq. ins. I circ. in. I'OOO I'OOOO 7854 13* 089 0079 00622 oooo '454 2061 16188 M 083 0069 00541 000 425 1806 14186 I4i 077 0059 00466 oo 380 1444 11341 15 072 0052 00407 o 34 1156 09-579 15* 068 0046 00363 I 300 0900 07068 16 065 0042 00332 2 284 0807 06335 17 058 00336 00264 3 259 0671 05268 18 049 00240 00188 4 238 0566 04449 19 042 00176 00138 5 220 0484 03801 20 035 00123 00096 5* 211 0445 o?497 " 21 032 OOIO2 00080 6 203 0412 03236 22 028 00078 00061 6* I 9 I 0365 02865 23 025 00063 00049 7 180 0324 02545 24 022 00048 00038 7* 172 0269 02324 25 O2O 00040 oooji 8 165 0272 02138 26 018 '00032 00025 8* 156 0241 01911 27 016 OO0256 00020 9 148 0219 01720 28 014 000196 00015 9* 141 0199 01561 29 013 000169 00013 10 iM 0180 01410 JO 012 000144 ooon 10* 127 0161 01267 31 oio oooioo 000078 II 120 0144 01131 32 009 000081 000063 ii* 114 0130 0102 I 33 008 000064 000050 12 IOQ 0119 00913 34 007 000049 000038 12* 102 0104 00817 35 005 000025 000019 U 095 0090 00708 36 004 000016 000012 Decimal Equivalents of Inches, &c. 191 Decimal Equivalents of Inches, Feet, and Yards. Fractions Decims. Decims. of an of an of a Inch. Inch. Foot. Ins. Feet Yards. ^ 0625 00521 I = 0833 = -0277 1 125 = OI04I 2 = 1666 = -0555 * 1875 = 01562 3 = 25 = -0833 \ 25 = 02083 4 = 3333 = -mi A 3125 = 02604 5 = 4166 = -1389 I '375 = 03125 6 = 5 = -1666 T ? 5 "4375 = 03645 7 - 5833 = *I944 I "5 = 04166 8 = 6666 = '2222 & 5625 = 04688 9 = 75 = .25 I 625 = 05208 10 = 8333 = .2778 ti 6875 = 05729 ii = 9166 = "3055 3 75 = 06250 12 = I'OOO = '3333 ii 8125 = 06771 1 875 = 07291 if '9375 = 07812 linchroo = 08333 TABLE OF RECIPROCALS. No. Recip- rocal. No. Recip- rocal. No. Recip- rocal. No. Recip- rocal. No. Recip- rocal. 1 0-5000 22 0-0455 42 0-0238 62 0-0161 82 0*OI22 J O"3?33 23 o-04?5 4* O-02?? 6? 0-0159 83 0-0120 4 0-2500 M 0-0417 44 0-0227 64 0-0156 84 0-OII9 5 0-20OO 0-0400 0-0222 "5 0-0154 85 0-OII8 6 0-1667 26 0-0385 4 0*0217 66 0-0152 86 0-0116 7 0-1429 27 0-0370 47 O-O2I3 6 7 0-0149 7 0-0115 8 O'I250 28 o-o?57 48 0-0208 68 0-0147 88 0-0114 9 o-iin 29 i 0-0345 49 0*0204 69 0-0145 89 0-OII2 10 o-iooo 30 o-o??? 5 0-0200 7 0-0143 90 O'OIII ii 0-0909 31 ! 0-032? 51 0-0196 71 0-0141 91 O'OIIO 12 o-o8?3 32 ; 0-031? 52 0-OI92 72 0-0139 92 0-0109 13 0-0769 33 0-030? 5? 0-0189 73 0-0137 9* 0-0108 0-0714 34 i 0-0294 54 0-OI85 74 0-0135 94 0-0106 15 0-0667 35 i o*r286 55 0-OI82 75 0-OIJ3 95 0-0105 16 0-0625 36 0-0278 56 O-OI79 76 O-OI?2 96 0-0104 17 18 0-0588 0-0556 37 0-0270 38 j 0-026? 57 58 0-0175 0-OI72 3 0-0130 0-0128 98 o-oio? 0-0102 0-0526 39 j 0-0256 59 0-0169 79 o 0127 99 O'OIOI 20 0-0500 40 0-0250 60 0-OI67 80 0-0125 100 o-oioo 21 0-0476 41 ; 0-0244 61 0-0164 81 0-0123 192 Knots into Miles. CJ J^&^'&'^-Oi^o" 00 ^.^eaiACOM^voO* t- O^MvOwr-wr-r* O I * a C/3 >S P (/. ^ O ^i \b M eo b | - * o M 2'IS >v ,S.SJtl<5f^ > fi !j ~s - - s - PC H cTSa^gS- 00 ^ * ^ oo M Tf- r^ Miles into Knots. 193 co o rt ^ r^ o M 8 00 OS , % S & ET ^ kr\ p s t ~ "w J? j; q- s, s S p oo 00 C* ^ . S-* >/- r- ^JS O "^f" s S R ^ f 5 f o 3- P 11 O 00 S fi- oo t- III II 1 \r\ S 1 X vO J- ~> "\ * < n S [C. 3" ? ~ ~ ?. S" K S^ 5. 1 I? CD c* OO tr\ w OO 00 O r rs S f R ^ f 1 1 * S 1 S S^ 2T ? , O Si 00 5 ? 2" ^r vO eo O =? ir C* 00 >O r\ ^. w es N r^ ^- l SO *"" oo 00 HI ^ c^ S" "^ M O r^ -O CO CM 1 1 oo r- r\ ^r ^A j^ o M f, -^- lr> *"* 00 eo M * si? S 1 1 * ^c oo r- i ^ t^ M M c> rH lit 5 S S S o? ^ 3 Sv 1- M 3 J O O oo ^ tJJ ^ 5 - CO < r^ M ^ cc s: r^ C^ r- ** O <5 ^> o p. % 1 S oo r- $ 2C ^ & C 00 O " T- rt ^ O O a * & 5 g. S o o 194 Yards into Knots. TABLE to convert Yards into Knots. Yards. Knots. Log. Yards. Knots. Log. Yards Knots. Log. I 00049 6901961 51 02513 4001925 101 04978 6970549 2 00099 9956352 52 02563 4087486 102 05028 7015953 > 1702617 53 02612 4169732 103 05077 7056072 4 00197 2944662 54 02661 4250449 104 05126 7097786 5 00246 3909*51 55 02710 4329693 105 05175 7139104 6 00296 4712917 56 02760 4409091 106 05225 7180863 7 00345 5*78191 57 028 9 4485517 107 05274 7221401 8 00394 5954962 58 02858 4560622 108 05525 7261565 9 00444 6473850 59 02908 4635944 109 05*7* 7302168 10 00493 6928469 60 02957 4708513 no 05421 7340794 II 00542 '7**999f 61 03006 4779890 in 05470 7?7987? 12 00592 7725217 62 03056 4851535 112 05520 7419391 Ij 00641 8068580 63 05105 4920616 113 05569 7457772 14 15 00690 00739 8388491 8686444 6J 03154 03203 4988617 5055569 115 05618 05667 7495817 7533532 16 00789 8970770 66 03253 5122841 116 05717 7571682 '7 00838 9252440 67 03502 117 05766 7608746 18 00887 9479236 68 05551 5251-44 118 05815 7645497 19 00937 9717*96 69 05401 5*16066 119 05865 7682680 20 00986 9938769 70 03450 5378191 120 05914 7718813 21 01035 0149403 71 03499 '54*94*9 121 05963 7754648 22 01085 0354297 72 05549 5501060 122 06013 7790912 23 01154 0546151 7* 05598 5560612 123 06062 7826159 24 25 01183 01232 0729847 0906107 74 75 05647 03696 5619558 5677320 I2 4 125 o6in 06160 7861123 7895807 26 01282 1078880 76 05746 57*5678 126 06210 79*0916 27 01331 1241781 77 03795 5792118 127 06259 7965050 28 01380 1398791 78 03844 5847854 128 06508 7998917 29 01450 1553*60 79 -05894 '59^*950 I2 9 06558 803*205 30 01479 1699682 80 03943 5958268 130 06407 8066547 31 01528 1841234 81 03992 6011905 131 06456 8099635 01578 1981070 82 04042 6065965 132 06506 81*3141 j-j 01627 2113876 83 04091 6118295 133 06555 8165727 ^4 01676 2242740 84 04140 6170005 134 06604 8198071 35 01725 2367891 85 04189 6221104 135 06653 8230175 36 01775 2491984 86 04259 6272654 i?6 0670? 8262692 a 01824 01873 2610248 2725378 87 88 04288 04557 6522548 6571894 137 158 06752 06801 8294*24 8*25728 39 01923 283979* 89 04587 6421670 1*9 06351 8557540 40 01971 2946866 90 04436 6469,15 140 06900 8388491 4 1 0202O 305*514 91 04485 6517624 141 06949 8419223 42 02070 3'59705 92 04,55 6565:75 142 06999 8450360 43 02II9 3261310 9* 04584 6612446 14? 07048 8480659 44 02168 3360593 94 04635 | '6658625 144 07097 -8510748 45 02217 3457657 95 04682 67043 4 145 07146 -8540630 46 02267 3554515 96 04752 6750447 146 07196 -8570912 47 023l6 3647386 97 04781 6795187 147 07245 i -8600384 48 02365 37*8311 98 04850 6859471 148 07294 -8629658 49 02415 3829171 99 04880 6884198 149 07344 ' -8659*27 5 02464 -39 l6 47 100 04929 6927588 150 07393 j '8688207 1 Yards into Knots. TABLE to convert Yards into Knots continued. 195 Yards.! Knots. ! Log. Yards. 1 Knots. Log. Yards.) Knots. Log. 151 07442 8716897 201 09906 995?933 25 1 12370 0923697 152 07492 8745978 202 09956 9980849 252 12420 0941216 153 07541 8774289 203 10005 0002171 253 12469 0958316 154 07590 8802418 204 10054 0023389 254 125-8 0975349 155 07639 8830365 205 '1OI03 0044504 255 12567 0992316 156 07689 8858699 206 IOI53 0065944 256 12617 100956* 157 -07738 8886287 207 ' 10202 0086853 257 : -12666 1026395 158 07787 8913702 208 M025I 0107662 258 12715 1043164 159 07837 8941498 209 I030I 0128794 259 12765 io6o2oa 160 07886 8968568 210 10350 0149403 260 12814 1076847 161 07935 89954^9 211 10399 0169916 261 12863 1093423 162 07985 9022749 212 -10449 0190747 262 12913 1110272 163 08034 9049518 213 i '10498 0211066 263 12962 1126720 164 08085 9075726 2I 4 10547 0231289 264 13011 1143107 165 08132 9101974 215 10596 0251419 265 13060 1159432 166 08182 912*595 216 10646 0271865 266 13110 1176027 167 08251 9154526 217 10695 0291808 267 13159 1192229 168 08280 9180303 218 10744 0311660 268 13208 1208371 169 08330 9206450 219 10794 0331824 269 13258 1224780 170 08379 9231922 220 10843 035H95 270 13307 1240802 171 08428 9257245 221 10892 0371076 271 13*56 1256764 T 08478 222 10942 0390967 272 13406 1272992 08527 9307965 223 10991 0410372 27* '1*455 1288837 n4 08576 9332848 224 i 1040 0429691 274 13504 1304624 175 08625 9*575,1 225 11089 0448924 275 13553 1320354 176 086-75 9382695 226 IH39 0468462 276 13603 -1*36347 08724 9407157 227 11188 048-525 277 13652 1351903 178 , -08773 9431481 228 -11237 -0506504 278 I370I 1367523 179 -08823 9456163 229 -11287 "0525785 279 I575I 1383343 180 08871 9479726 230 11336 0544598 280 13800 1398791 181 08920 9503649 231 11385 0563330 281 13849 1414184 182 08970 9527924 232 11434 i -0586158 282 13899 1429836 183 9551584 233 ..484 0600932 283 1445119 184 09068 9575"5 234 II553 0619423 28 4 13997 1460350 185 09117 .9598520 235 1.582 0637836 28 5 14046 1475527 186 09167 9622272 236 1.632 0656544 286 | -14096 1490959 187 09216 -9645425 237 j "11681 ! -0674806 287 i -14145 1506030 188 09265 ; -9668454 238 j i 17*0 i -0692980 288 i -14194 1521048 189 190 09515 09364 9691829 9714614 239 j -1.780 -0711453 240 i -11828 -072^113 289 1 -14244 290 -14293 1536320 1551234 191 09413 9737281 241 11877 0747068 291 ! -14342 1566097 192 ! -09463 9760288 242 i 927 -0765312 292 j -14392 1581212 19* 09512 9782718 243 -11976 ! -0783118 293 -14441 1595^73 194 09561 9805033 244 -12025 -080085I 294 -14490 1610684 195 09610 9827234 245 | -12074 0818512 295 "M539 1625345 196 -09660 9849-171 246 12124 -0836459 296 ! -14539 1640255 197 ! -09709 9871745 247 M2I73 1 -0853^6 297 '14638 1654817 198 i -09758 -989360-. 248 12222 i -08T 423 298 -14687 1669331 199 09808 9915805 249 12272 i -0889153 299 ; -147*7 1684091 200 09857 9937448 250 1232J 0906460 300 . -14786 16118507 1 1 196 Yards into Knots. TABLE to convert Yards into Knots continued. /ards. Knots. Log. Yards. Knots. Log. Yards. Knots. Log. 301 148*5 1112876 35i 17299 2380210 401 19763 2958529 302 14885 1727488 352 17*49 2392744 402 19813 -2969502 303 149*4 1741761 353 I7J98 2404,93 403 19862 '2980230 304 1498? 1755988 354 17447 2417208 404 19911 '2990931 305 15032 l-;70l68 355 17496 2429388 405 19960 3001605 306 15082 1784589 356 17546 2441781 406 200IO 3012471 307 151*1 1798676 357 '17595 2453893 407 20059 3023093 308 15180 1812718 358 17644 2465970 408 20108 3033689 309 15230 I 826999 359 17694 2478260 409 '20158 3044474 JIO 15278 1840665 360 1774* 2490271 410 20207 3055018 3ii 15527 1854572 J6i 17792 2502248 411 20256 3065537 312 15*77 1868716 362 17842 25I4425 412 2O3O6 3076244 313 15426 1882533 363 17891 2526346 4!3 20355 3086711 314 3^5 15475 15524 1896307 1910036 364 365 17940 17989 2538224 2550070 414 -20404 415 -20453 "3097153 3107570 3i6 5 43815 6411269 6416228 790 38935 5903402 840 41400 6170003 fc90 4*864 6421082 791 38984 5908864 841 41449 6175141 891 4*913 64259*1 792 39-34 59144?! 842 41499 6180376 892 43963 6430873 793 39083 5919879 843 41 49 6185606 893 44012 64357" 794 795 39132 39181 5925320 '59*755 844 845 '4*597 41646 6190620 6195733 894 895 44 61 44110 644054? 6445371 796 392*1 5936294 846 41696 6200944 896 44160 6450291 797 39280 5941715 847 -41745 '62 6045 897 44209 6455107 798 39*29 5947"9 848 ; -41794 i -6211139 898 44258 6459918 799 i -39*8* 595*o83 849 -418^4 i -6216332 899 44308 "6464821 800 39428 -5958047 8TO 4ity3 6221415 900 '44357 6469622 2OO Yards into Knots. TABLE to convert Yards into Knots continued. Yards Knots. Log. Yards Knots. Log. Yards. Knots. 1 Log. 901 44406 6474417 951 46870 6708950 ICO! *49*H 6931463 902 44456 6479304 952 46920 6713580 1002 49384 6935863 903 44505 6484088 953 46969 6718113 1003 '494H 6940170 904 '44554 6488867 954 47018 6722642 1004 49482 6944472 905 44603 6493641 955 47067 6727165 1005 '49531 6948771 906 44 6 53 6498506 956 47117 .6731776 1006 49581 6953153 907 44702 6503270 957 47166 6736290 1007 -49630 -6957443 908 44751 6508027 958 47215 6740800 1008 49679 6961728 909 910 44801 44850 -6512877 6517624 959 960 47265 47**4 6745397 6749 8 97 1009 1010 49729 49778 6966097 6970374 911 44899 6522*67 961 47363 6754392 IOII 49827 6974647 912 44949 6527200 962 '474 1 * 6758974 1012 49877 "6979003 9** 44998 6531932 963 47462 6763460 1013 49926 6983268 914 45047 6536659 964 47511 6767942 1014 '49975 6987528 9i5 45096 6541*80 965 47560 6772418 1015 50024 6991784 916 45146 6546193 966 47610 6776982 1016 .50074 6996123 917 45195 6550904 967 47659 6781449 1017 50123 7000371 918 45244 655.5610 968 47708 6785912 1 01 8 50172 7004614 919 45294 6560407 969 47758 6790461 1019 50222 7008940 920 45343 6565103 970 47807 6794915 1020 50271 7013175 921 M5?92 6569793 971 47856 6799364 102 1 50320 7017406 922 45442 6574574 972 -47906 6803899 1022 50370 7021720 923 454/1 6579255 973 '47955 68o8*39 J023 50419 7025942 924 '4554 6583930 974 48004 6812774 1024 50468 7030161 925 45589 6588601 975 48053 6817205 1025 50517 7034376 926 '456?9 6593361 976 48103 6821722 1026 50567 7038672 927 45688 -6598021 977 48152 6826143 1027 50616 7042878 928 '457*7 6602677 978 48201 6830560 1028 50665 7047080 929 45787 6607422 979 48251 68 55063 1029 50715 7051364 93 45835 6611972 980 48300 6839471 1030 50764 7055558 9*i 45884 6616613 981 48349 6843875 1031 50813 7059743 9*2 '459?4 662134? 982 -48399 6848364 1032 50863 i -7064020 933 4598? 6625973 98? 48448 6852759 103* 50912 7068202 9?4 46032 6630598 984 48497 6857149 1034 50961 7072379 935 46081 6635^19 985 4^46 686i535 1035 51010 7076553 936 46131 6639929 986 48596 6866005 1036 51060 7080808 937 46180 6644579 987 M8645 6870382 1037 51109 708497^ 938 46229 6649145 988 48694 6874755 1038 51158 7089136 939 940 46279 46328 6655840 -6658436 989 990 48744 48793 687^212 6883575 1039 1040 51208 51257 7093378 7097532 941 46377 6663027 991 48842 6887934 1041 51306 7101682 942 '4''427 -6667706 992 48892 6892578 1042 51356 7105912 94* 46476 6672287 993 48941 6896728 1043 51405 7110054 944 46525 -6676864 994 48990 6901074 1044 5M54 7114191 945 '4 6 574 6681435 995 49039 6905416 1045 51503 7118325 946 46624 6686095 996 49089 6^9842 1046 51553 7122539 947 46673 6690657 997 49n8 6914175 1047 51602 7126665 948 46722 669:214 9>8 49187 6918503 1048 51651 7130787 949 46772 6699859 999 '49 '17 6922916 1049 51701 7134989 950 46821 6704407 IOCO 49285 6927148 1050 51750 7139104 Yards into Knots. TABLE to convert Yards into Knots continued. 201 Yards. Knots. Log. Yards. Knots. Log. Yards. Knots. Log. 1051 51799 7143214 IIOI 54263 7345038 1151 56727 7537898 1052 51849 7147404 1 102 54313 7349038 1152 56777 j -7541724 1053 51898 7151506 1103 54362 -7352954 "53 56826 ; -7545471 1054 51947 7155605 1104 544" 7356867 "54 56875 ; -7549214 1055 51996 7159699 1105 54460 7360776 "55 56924 7552954 1056 52046 7163874 1106 54510 7364762 1156 56974 7556767 1057 52095 7167960 1107 '54559 7368664 "57 57023 7560501 1058 52144 7172043 1108 54608 -7372563 1158 57072 7564231 1059 1000 52194 52242 7176206 7180198 1109 IIIO 54658 54707 7376537 7380429 "59 1160 57122 57171 7568034 7571758 1061 52291 7184269 .mi 54756 7384317 1161 57220 '7575479 1062 52341 7188420 III2 54806 -7388281 1162 57270 757927- 1063 52390 7192484 i"3 54855 7392162 1163 57319 7582986 1064 524*9 7196544 1114 549~4 7396040 1164 57368 7586697 1065- 52488 7200600 1115 '54953 73999H 1165 57417 7590405 1066 1067 1068 52538 52587 52636 7204735 7208784 7212829 1116 1117 1118 55003 55052 55101 7403864 7407731 "74" 595 1166 1167 1168 -57467 57516 57565 7594185 7597887 7601585 1069 52686 7216952 1119 55151 7415534 1169 57615 7605356 1070 52735 7220990 II2O 55200 7419391 1170 -57664 7609048 1071 52784 7225023 II2I 55249 7423244 1171 57713 7612737 1072 52834 7229135 1122 55299 7427173 1172 57763 ^616497 1073 52883 7233161 1123 55348 7431019 "73 57812 7620180 1074 1075 529*2 52981 7237183 7241202 II2 4 1125 55417 55446 7436430 7438702 "74 1175 57861 57910 7623859 7627536 1076 53031 7245298 1126 55496 7442617 1176 57960 7631284 1077 -53080 7249309 1127 '55545 7446450 "77 58009 7634954 1078 -53129 7253316 1128 55594 7450279 1178 58058 -638621 1079 -53179 725740: 1129 55644 7454183 "79 58108 7642359 1080 -53228 7261401 IIJO 55692 7457928 1180 58157 - 7646020 1081 -532-7 1082 -53327 7265398 "269472 1131 1132 55741 5579 1 7461748 7465641 1181 1182 58206 58256 7649678 7653407 1083 -53376 7273460 "33 55840 7469454 1183 58305 1084 -53425 7277445 H34 55889 7473263 1184 58354 7660706 1085 '53474 7281427 "35 55938 7477069 1185 58403 7664352 1086 53524 7285486 1136 55988 7480950 1186 58453 7668068 1087 -53573 7289460 "37 56037 7484749 1187 58,02 7671707 1088 -53622 1138 56086 7488545 1188 58551 7675343 1089 -53672 7297478 H39 56136 7492415 1189 58601 7679050 1090 -53721 7301441 1140 56185 7496204 1190 58650 7682680 1091 -53770 7305400 1141 56234 7499990 1191 58699 7686307 1092 -53820 1 -7309437 1142 56284 7503850 1192 58749 | -7690005 1093 -53869 , -7313389 "43 56333 7507629 H93 58798 i -7693626 1094 -53918 -7317338 1144 56382 7511405 "94 58850 7696505 1095 -53967 7321283 "45 56431 75I5I77 "95 58896 7700858 1096 i -54017 7325305 1146 56481 7519024 1196 58946 7704543 1097 -54 66 -7329242 1147 -56530 -7522790 "97 -58995 7708152 1098 -54"5 -7333177 1099 -54 l6 5 "7337 l8 7 1148 "49 56579 '7526553 56629 -75303^9 1198 -59044 "99 -59094 7711758 7715434 noo -54214 7341115 1150 56678 7534145 1 200 59142 7718960 1 2O2 Yards into Knots. TABLE to convert Yards into Knots continued. Yards. Knots. Log. Yards. Knots. Log. Yards. Knots. Log. 1201 59191 7722557 1251 61656 7899753 1301 64120 8069935 1202 59241 7726224 1252 61706 7903274 1302 64170 8073320 I2O3 59290 7729815 1253 61755 7906721 1303 64219 8076635 1204 7735402 1254 61804 7910166 1304 64268 8079948 1205 59388 7736987 1255 61853 7913608 1305 64317 8083258 1206 59458 7740642 1256 61903 7917117 1306 64*67 8086633 1207 59487 7744221 1257 61952 7920553 1307 64416 8089938 1208 59556 '7747797 1258 62001 7923987 1308 64465 809*240 I2O9 59586 7751442 1259 62051 79274*8 1309 64515 8096607 I21O 59635 7755012 1260 62100 79*0916 1310 '64564 8099904 I2II 59684 7758579 1261 62149 7954541 I3 64613 8103199 1212 '59734 7762216 1262 62199 7937854 1312 64663 8106558 1213 59783 7765777 1263 62 .'48 7941254 1313 64712 8109848 1214 59852 1264 62297 7944671 1314 64761 8113135 1215 59881 7772890 1265 62346 7948086 1315 64810 8116420 12l6 59951 7776515 1266 62396 7951567 1316 64860 8119769 1217 59980 7780065 1267 62445 '7954977 1317 64909 8123049 1218 60029 7783611 1268 62494 7958J8? 1318 64958 8126326 1219 60079 7787227 1269 62544 7961857 1319 65008 8129668 I22O 60128 7790768 1270 62592 7965188 1320 65057 8132940 122 1 60177 7794*05 1271 62641 7968587 1321 65106 8136210 1222 60227 7797912 1272 62691 7972052 1322 65156 81*9544 1223 60276 7801444 1273 62740 '7975445 1323 65205 8142809 1224 60325 7804973 1274 62789 7978836 1324 65254 8146071 1225 60374 7808500 1275 62838 7982224 1325 65303 8149331 1226 60424 7812095 I2 7 6 62888 7985678 1326 65*53 8152655 1227 60473 7815615 1277 629*7 7989060 1327 65402 8155910 1228 60522 7819133 1278 62987 799250) 1328 65451 8159163 1229 60572 7822719 1279 6?o?6 7995886 1329 65501 8162479 1230 60621 7826231 1280 63085 7999261 1330 65550 8165727 1231 60670 7829740 I28l 63134 8002633 1331 65599 8168972 1232 60720 78*3318 1282 63184 8006071 1332 8172281 1233 60769 78*6821 1283 632?? 80094*8 1333 65698 8175521 1234 60818 7840321 1284 63282 8012802 1334 65747 8178759 1235 60867 7843819 1285 63331 8016163 IJJ5 65796 8181995 1236 60917 7847385 1286 6*381 8019591 1336 65846 8185294 1237 60966 7850877 1287 6*4*0 8022262 1337 '65895 8188525 1238 61015 7854*66 1288 63479 8026301 1338 65944 8191753 1239 61065 7857924 1289 63529 8029720 1339 65994 8195045 1240 61114 7861407 1290 63578 8033069 134 66042 8198202 1241 61163 7864888 1291 63627 8036414 1341 66091 8201423 1242 61213 78^84*7 1292 63677 8039^26 1342 66141 8204708 124* 61262 7871912 1293 63726 804*167 1343 66190 8207924 1244 61*17 7875809 1294 63775 8046505 1344 662*9 8211138 1245 61360 7878854 1295 63824 8049840 1345 66288 8214349 1246 61410 7882391 1296 63874 805*241 1346 663*8 8217624 1247 1248 61459 61508 7885855 7889*16 1297 1298 63923 6*971 8056571 8059899 1547 1548 66*87 664*8 82208*0 8224166 1249 61558 7892845 1299 64022 8063292 1549 66486 8227302 1250 61607 7896301 1300 64071 8066615 1350 66535 8230502 Yards into Knots. TABLE to convert Yards into Knots continued. 203 Yards. Knots. Log. fards. Knots. Log. Yards. Knots. Log. 1351 66584 82*3699 1401 69049 8391574 1451 7I5I3 .854*850 1352 666*4 8236959 1402 69099 8394718 1452 71563 8546885 135? 6668? 8240151 140? 69148 8397796 H53 71612 8549858 1354 667*2 824*341 1404 8400873 M54 71661 8552829 1355 66781 8246529 1405 69246 8403947 1455 71710 8555797 1356 668*1 8249780 1406 69296 8407082 1456 71760 8558824 1357 66880 8252963 1407 8410152 M57 71809 8561789 1*58 66929 825614? 1408 69*94 841*219 1458 71858 8564751 1359 66979 8259*87 1409 69444 8416347 M59 71908 8567772 1360 67028 8262563 1410 69492 8419348 1460 71957 8570730 1361 67077 8265736 1411 69541 8422409 1461 72006 8573687 1362 67127 8268972 1412 69591 8425531 1462 72056 8576701 1363 67176 8272141 1413 8428588 1463 72105 8579654 1364 67225 8275*08 1414 69689 84*1642 1464 72154 8582604 1365 67274 8278473 M'5 69738 8434695 1465 72203 8585552 1366 67*24 8281699 1416 69788 84*7808 1466 72253 8588559 1367 1*68 67373 67422 8284859 8288016 1417 1418 698*7 69886 8440856 844*902 1467 1468 72*02 72351 859150? 1369 67472 8291236 1419 699*6 8447008 1469 72391 859 846 67521 8294389 1420 69985 8450050 1470 72450 8600384 1371 67570 82975*9 1421 700*4 845?o89 1471 72499 860*320 1372 67620 8*00752 1422 70084 8456189 1472 72549 8606314 U73 67669 8*0*898 1423 701?? 8459224 1473 72598 8609247 1374 67718 8*07041 1424 70182 8462257 H74 72647 8612177 1375 67767 8310183 1425 70231 8465289 1475 72696 8615105 1376 67817 8313386 1426 70281 8468379 1476 72746 8618091 1377 67866 8*16523 1427 703 ?o 8471406 1477 72795 8621016 67915 8*19657 1428 70379 84744?! 1478 72844 86239*8 1379 1380 67965 68014 832285? 8325983 1429 1430 70429 70478 8477515 8480536 1479 1480 72894 72942 8626918 8629777 1381 68063 8329111 1431 70527 848*554 1481 72991 86*269? 1382 68113 8*32300 1432 70577 8486632 1482 73041 8635667 138* 68162 83*5423 70626 8489646 1483 73090 8638580 1384 68211 8338544 14*4 70675 8492658 1484 73139 8641490 1385 68260 8*41663 1435 70724 8495668 1485 73188 8644399 1386 68310 834484? I4?6 70774 8498737 1486 73238 8647365 1387 68*59 8H7957 1437 70823 850174? 1487 73287 8650269 1388 68408 8*51069 14*8 70872 8504747 1488 73336 8653172 1389 68458 8*54242 14*9 70922 8507810 1489 73386 8656132 1390 68507 8357349 1440 7^971 8510809 1490 '73435 8659031 1391 68556 8360455 1441 71020 8513807 1491 73484 8661928 1392 68606 8*6*621 1442 71070 8516863 1492 73534 8664882 i?93 68655 8366722 1443 71119 8519856 1493 73582 8667716 68704 8369820 T 444 71168 8529848 1494 736*2 8670666 1395 68753 8372917 1445 71217 8522837 1495 73681 8673555 1396 68803 8376074 1446 71267 8528885 1496 '73731 8676501 1397 68852 8*79166 71*16 85*1870 1497 73780 8679?87 1398 68901 8*82255 ^448 71365 85*485? 1498 73829 8682270 1399 68951 8385406 1449 71415 8537894 1499 73879 8685210 1400 69000 8338491 1450 71464 8540873 1500 7?928 8688090 2O4 Yards into Knots. TABLE to convert Yards into Knots continued. Yards Knots. I Log. .Yards Knots. Log. Yards Knots. Log. 1501 '73977 8690967 I55i 76441 8833264 1601 78966 8971100 1502 74027 8693901 1552 76491 8836103 1602 78956 8973851 150? 740-? 6 8696775 1553 76540 8838885 1603 79005 8976546 1504 74125 8699647 1554 76589 8841664 1604 79054 8979238 1505 74 J 74 8702517 1555 76638 8844442 1605 79103 8981930 1506 74224 8705444 1556 76688 8847274 1606 79153 8984674 1507 74 2 73 8708310 1557 767J7 8850048 1607 79202 8987361 1508 74322 8711174 1558 76186 8852820 1608 79251 8990048 1509 74*72 8714095 1559 76836 8855647 1609 79?oi 8992787 1510 74421 8716955 1560 76885 8858416 1610 79349 8995415 1511 74470 8719814 1561 76934 8861183 1611 79398 8998096 1512 74520 8722728 1562 76984 8864005 1612 79448 9000830 1513 74569 8725583 1563 77033 8866768 1613 '79497 9003507 1514 74618 8728436 1564 77082 8869530 1614 79546 9006183 1515 74667 8731287 1565 77I3I 8872290 1615 '79595 9008858 1516 74717 8734I94 1566 77181 8875104 1616 79645 9011585 1517 74766 8737041 1567 77230 8877860 1617 79694 9014256 1518 74815 8739887 1568 77279 8880615 1618 '79743 9016926 1519 74865 8742788 1569 77329 8883424 1619 79793 9019648 1520 749H 8745630 1570 77378 8886175 1620 79842 9022314 1521 74963 8748470 1571 77427 8888924 1621 79891 9024979 1522 75oi3 8751365 1572 77477 8891728 1622 79941 9027696 1523 75 62 8754201 1573 77526 8894474 1623 79990 9030357 1524 75111 8757055 1574 77575 8897218 1624 08039 9033017 1525 75160 8759868 1575 77624 ; 8899960 1625 80088 9035674 1526 75210 8762756 1576 77674 8902757 1626 80138 9038385 1527 75259 8765584 1577 77723 8905496 1627 8 187 9041040 1528 75308 8768411 1-578 77772 8908233 1628 80236 9043693 1529 75358 8771294 1579 77822 8911024 1629 80286 9046398 1530 '754-7 8774"7 1580 77871 8913758 1630 80335 9049048 1531 75456 8776938 1581 77920 8916489 1631 80384 9051696 1532 75506 8779815 1582 77970 8919275 1632 80434 9054397 1533 '75555 8782632 1583 78019 8922004 1633 80483 9057042 1534 75604 8785448 1584 78068 8924731 1634 80532 9059685 1535 75653 8788262 1585 78117 8927456 1635 80581 9062327 1536 1537 75703 75752 8791131 8793941 1586 1587 78167 78216 8930234 8932956 1636 1637 80631 80680 9065020 9067659 1538 75801 8796749 1588 78265 8935676 1638 80729 9070296 1539 75851 8799613 1589 78315 8938450 1639 80779 9072985 1540 75899 8802361 1590 78364 8941166 1640 80828 9075618 1541 75948 8805163 1591 78415 8943991 1641 80877 9078250 1542 75998 '8808022 1592 78463 8946649 1642 80927 9080934 1543 76047 8810821 1593 78512 8949360 1643 80976 9083563 J 544 76096 8813618 J 594 78561 8952070 1644 81025 9086190 1545 76145 8816414 1595 78610 8954778 1645 81074 9088816 1546 1547 1548 1549 1550 76195 76244 76293 76343 76392 8819265 8822057 8824847 8827692 8830479 1596 1597 1598 1599 1600 78660 78709 78758 78808 78857 8957539 8960244 8962947 8965703 8968403 1646 1647 1648 1649 1650 81124 81173 81222 81272 8I32I 9091494 9094116 9096737 9099409 9102027 Yards into Knots. TABLE to convert Yards into Knots continued. 205 Yards. Knots. Log. Yards. Knots. Log. Yards. Knots. Log. 1651 81370 9104643 1701 83834 9234202 1751 86298 9360007 1652 81420 9107311 1702 83884 9236791 1752 86348 9362523 165? 1654 81469 81518 9109924 9112535 1703 1704 839?? 83982 9239327 9241862 1753 1754 86397 86446 '9364987 9367449 1655 81567 9115145 1705 84031 9244395 1755 86495 9369910 1656 81617 9117806 1706 84081 9246979 1756 86545 9372420 1657 81666 9120413 1707 84130 9249509 1757 86594 9374878 1658 81715 9123018 1708 84179 9252038 1758 86643 9377335 1659 81765 9125674 1709 84229 9254616 1759 86693 9379840 1660 81814 9128276 1710 84278 9257142 1760 86742 9382294 1661 8186? 9130877 1711 84327 9259667 1761 86791 9384747 1662 81913 9133528 1712 84*77 9262241 1762 86841 9387248 1663 81962 9136125 1713 84426 9264702 1763 86890 9389698 1664 82011 9138721 1714 '84475 9267282 1764 86939 9392146 1665 82060 9141315 1715 84524 9269800 1765 86988 9394593 1666 82110 9143961 1716 84574 9272369 1766 87038 9397089 1667 82159 9146551 1717 84623 9274884 1767 87-- 87 9399533 1668 82208 9149141 1718 84672 9277398 1768 87136 9401976 1669 82258 9151781 1719 84722 9279962 17 9 87186 9404468 1670 823-7 9154368 1720 84771 9282473 1770 87235 9406908 1671 82356 9156952 1721 84820 9284983 1771 87284 9409346 1672 82406 9159588 1722 84870 9287542 1772 87334 94"834 167? 82455 9162170 1723 84919 929C049 i"73 87383 9414270 1674 82504 9i 6 47 5o 1724 84968 9292554 1774 87432 9416704 1675 82553 9167329 1725 85017 9295058 1775 87481 9419137 1676 82603 9169958 1726 85067 9297611 1776 87531 9421619 1677 82652 9172534 1727 85116 9300112 1777 87580 9424049 1678 82701 9175108 1728 85165 9302612 1778 87629 9426479 1679 82751 9177733 1729 85215 9305160 1779 87679 9428956 1680 82799 9180251 1730 85264 9307657 1780 87728 9431382 1681 82848 9182820 1731 85313 9310152 781 87777 9433807 1682 82898 9185441 1732 85363 9312697 782 87827 9436280 1683 1684 82947 82996 9188007 9190572 1733 1734 85412 85461 9315189 9317680 ?4 87876 87925 9438703 9441124 1685 83045 9193135 1735 85510 9320169 785 87974 9443543 1686 83095 9195749 1736 85560 9322708 786 88024 9446011 1687 83144 9198309 1737 85609 9325194 787 88073 9448428 1688 83193 9200868 1738 85653 9327679 788 88122 945084; 1689 8324? 92^3477 1739 85-08 9330214 1789 88172 9453307 1690 83292 9206033 1740 85757 9332696 1790 88221 9455720 1691 83341 9208587 1741 85806 9335I77 1791 88270 9458i3i 1692 83391 9211192 1742 85856 9337707 1792 88320 9460591 1695 83440 92IJ74? 174? 85905 9340184 179? 88369 9462999 1694 83489 9216293 1744 85954 9342661 1794 88418 9465407 1695 83538 9218841 1745 86003 9345136 1795 88467 946:813 1696 83588 9221439 1746 86053 9347660 1796 88517 9470267 1697 83637 9223984 1747 86102 9?5or32 1797 88566 9472670 1698 83686 9226528 1748 86151 9352' 03 1798 88615 94-5072 iGgg 83736 9229122 1749 86201 9355123 1799 88665 9477522 1700 8J785 9231663 1750 86249 9357541 1800 88714 9479922 , J 2o6 Yards into Knots. TABLE to convert Yards into Knots contimted. Yards. Knots. Log. Yards. Knots. Log. Yards. Knots. Log. 1801 88763 9482320 1851 91227 9601254 1901 95691 9716979 1802 88813 9484765 1852 91277 9605614 1902 95741 9719296 1803 88862 9487161 1855 91526 9605944 1903 95790 9721565 1804 88911 9489555 1854 91375 9608274 1904 93839 9T25834 1805 88960 9491948 1855 91424 9610602 1905 93888 9726101 1806 89010 9494588 1856 '9*474 9612977 1906 93958 972841? 1807 89059 9496778 1857 91523 9615502 1907 95987 9750678 1808 89108 9499167 1858 91572 9617627 1908 94056 9752941 I8r 9 89158 9501603 1859 91622 9619998 1909 94086 9735250 1810 89207 9503989 1860 91671 9622320 1910 94135 97375 1811 89256 9506574 1861 91720 9624640 1911 94184 9739771 I8l2 89506 9508806 1862 91770 9627007 1912 94254 9742076 1813 89355 9511189 1863 91819 9629326 1913 94283 9744554 1814 894-4 9513569 1864 91868 9651645 1914 945*2 9746590 1815 89453 9515949 1865 91917 9633958 1915 94381 9748846 1816 1817 8950; 89552 9518376 9520755 i8'6 1867 919*7 9:016 9656520 96586*4 1916 1917 94451 94480 9751146 '9755599 1818 89601 9523129 1868 92065 9640946 1918 94529 9755651 1819 1820 89651 89699 9525551 9527876 1869 1870 92115 92164 964*504 9645613 1919 1920 '94579 94628 '9757947 9760197 1821 89748 9550248 1871 92215 9647922 1921 94677 9762445 1822 89798 9552667 1872 92263 9650276 1922 94727 9764758 1823 89847 9555056 1875 92512 9652582 1923 94776 9766984 "1824 89896 9557404 1874 92361 9654886 1924 94825 9769229 1825 89945 9539770 1875 92410 9657190 1925 94874 9771472 1826 89995 9542184 1876 92460 9659539 1926 94924 9773760 1827 90044 9544548 1877 92509 9661840 1927 '94973 9776002 1828 90093 9546910 1878 92558 9664140 1928 95022 9778242 1829 9014* 9549520 1879 92608 9666485 1929 95072 9780526 1830 90192 9551680 1880 92656 9668735 1930 95121 9782764 1851 90241 9554059 1881 92705 9671052 1951 95170 9785001 1852 90291 9556445 1882 92755 9675573 1952 95220 9787282 185? 90*4 9558801 1885 92804 9675667 1953 95269 9789516 1854 90? 89 9561156 1884 92855 9677959 1954 955i8 9791749 I8J5 90438 9563509 1885 92902 9680251 1935 95367 9793981 1856 90488 9565910 1886 92952 9682587 1956 '954 J 7 9796258 1857 905*7 9568261 1887 95001 96*4876 J 957 95466 9798487 1858 90586 9570611 1888 95050 9687164 19*8 95515 9800716 1859 9o'>36 9575007 1889 95100 9689497 1959 95565 9802989 1840 90685 '9575355 1890 93149 9691782 1940 95614 9805215 1841 907*4 9577701 1891 9U98 9694066 1941 95663 9607440 1842 90784 9580095 1892 '9524< 9696162 1942 95713 9809709 184} 908?? 9582457 1895 95297 9698677 1945 95762 9811952 184^ 90882 9584779 1894 9J?46 9:00957 1944 95811 9814154 I8 4 5 90931 9587120 1895 93395 9703236 1945 95860 9816374 1846 90981 9589507 1896 9?445 9705561 1946 95910 9818659 1847 91050 9591845 1897 9H94 9707857 1947 '95959 9820857 1848 91079 9594185 1898 95545 9710115 1948 '9'82 16 35-2969 29 6?"9757 42 92-6545 4 8-8242 17 37-5029 30 66-1818 94-8605 5 II'0?OJ 18 39-7090 31 68-3878 44 97-0666 6 13-2364 19 41 9150 32 70-5939 45 99-2726 1 15-4424 17 6485 20 21 44-1212 46-3272 33 34 72-7999 75-0060 46 47 101-4787 10? -6847 9 19-8545 22 48-5??; 35 77-2120 48 105-8908 10 22-0606 23 50-759? 36 79-4181 49 108 0969 ii 24-2666 24 52-9454 37 81-6241 50 lio- jojo 12 26-4727 25 55-I5I4 38 83-8302 112-5090 " 28-6787 26 57'3575 39 86-0363 52 114-7151 TRIGONOMETRICAL FORMULAE. 1 Sinus 2 Cosinus 3 Sinus-versus 4 Cosinus-versus 5 Tangent 6 Cotangent j Secant ' 8 Cosecant abbre iated sin.C. cos. C. sinv. C. cosv. C. tan.C. cot. C. sec.C. cosec.C. r Radius of the circle, which is the unit by which the functions are me sured. r* = sin 2 C-fcos 2 C, I sec C "= . tanC sin C cosC' cos C cosecC = . sinC tanC ~~ cotC' sinv C = i cos C, cosv C = i sin C, cotC _ cosC -sin 2C = 2 sin C cos C, sin C* sin 1C = |vTsin 2 C+sinv 2 C), p I sin (C + B) = sin C cos B+ tan C' sin B cos C. Trigonometrical Formula. 213 A, B, C, angles. a, b, c, sides. Q, area. 4. a / Q = 2 \/ sin 2 C' 5. * = cos0^jl 7. * = a SU&, 8. = c tan X 9. 6=. : = sin A : sin B, and b : c sin B : sin C : : c = sin A : sin C, and Q : ab = sin C : 2. I. 2. 3- 4- c sin A c sin A 5- 6. 7- 745 6771 6796 6822, '6847 6873 68 99 6924 6950 6976 7002 55 35 7002 -7028 7054 7080' '7107 '7i 33 7159 7186 '7212 '72?9 7265 54 37 7265 -7292 75?6 -7563 7719 7*46 '7'7* '740 7618 -76461 -7673. 7701 7454 : -7481; -7508 7729! '77571 "11*9 78H 5* 38 781? -7841 7869 7898 -7926 --7954 7983 8012 -8040 -8069 8098^51 39 8098 -8127 8156 8185 -8214 8243 8273 8302 8332 8?6i 8391 5 40 8?9i 8421 8451 8481 8511 8541 8571 8601 8632 8662 869? 49 869? -872.1 8754 8785 -8816 8847 8878 8910 '8941 '8972 9004 48 42 9004 -9036 9007 9099 -91 ji 9163 9195 9228 -9260 -929?! -9?25 47 4? 9*25 -9*58 Q?QI 9424 -9457 9490 9523 9556 -9590 -9623 -9657 46 44 9657 -9691 9725 9759 ( 9793 9827 ^861 9896 -9930 -9965 i -ooo 45 1-0 9 5 7 6 5 4 3 2 1 DEG. Natural Cotangents (r i). Natural Tangents. , Natural Tangents (r = i) contimted. 217 Dw. 1 2 3 4 5 6 7 8 9 45 i-ooo 1-003 1-007 I'OII 1-014 I'OlS' I'O2I 1-025 I -028 1-032 I o?6 44 I i-oj-6 1-072 i-in 1-039 1-076 1-115 1-043 1-046 i -080; 1-084 I-II8, I-I22 1-050 i -081 1-126 1-054 1*057 I'o6x 1-065! -069 1-091 1-095 1-099 1-103 -107 1-130' X-I34 I-I38 1-142! -146 1-072 i-iii 1-150 43 42 41 49 1-150 1-154 I-J59J 1-163 1-167 I-I7I 1-175 1-179 X'l83 188 1-192 40 5 1-192 1-196 1-200 1-205 1-209 I 213 1-217 1-222 1-226 230 1-235 39 1-235 I 2?9 1-244 1-248 1-25? 1-257 1-262 i "266 1-271 "275 i-28o 38 52 5? 1-280 1-327 i 285 1-332 I ' 289 I ' 294 1-3371 1-342 1-299 1-303 I-35I 1-308 1-356 I-3I3 I-3I7 I-36I 1-366 322 1-327 i 376 3 54 1-376 1-381 I-387| I-392 1-397 1-402 I 47 I-4I2 1-418 423 1-428 35 55 1-428 1-4?? i'4?9 1-444 1-450 J "455 1-460 1-466 1-471 '477 I-483 34 56 1-483 1-488 1-494 i"499 1-505 1-511 1-517 1-522 1-528 534 1-540 33 1-540 1-600 1-546 1-607 1-552 1-61? 1-558 1-619 1-564 1-625 1-570 1-632 1-576 1-582; 1-588 l-6?8 1-645 1-651 3 1-600 1-664 32 31 59 1-664 1-671 1-678 1-684 1-691 1-698 1-704 1-711 I- 7 i8 -725 X'732 30 60 1-732 1-739 1-746 x-75? 1-760 1-767 1-775 1-782 1-789 "797 1-804 29 61 1-804 I*8xi 1-819 1-827 1-834 i 842 1-849 1-857 1-865 873 1-881 28 62 1-881 1-889 1-897 1-905 1*913 1-921 1-929 1-937 1-946 '954 1-963 27 6? 1*963 1-971 1-980 1-988 1-997 2-006 2-014 2-023 2-032 041 2-050 26 64 2-050 2-059 2-069 2-078 2-087 2-097 2-106 2-II6 2-125 135 2-145 25 65 2-145! 2-154 2 164 2-174 2-184 2-194 2-204 2-215 2-225 236 2-246 24 66 2-246 2-257 2-267 2-278 2-289 2-300 2-311 2-322 2-333 344 2-356 23 67 2-356! 2-367 2-379 2-391 2-402 2-414 2-426 2'4?8 2-450 -463 2'475 22 68 69 HS 2 488 2-619 2-500 2-633 2 5*3 2-646 2-526 2-660 2-539 2-675 2-552 2-689 2-703 2-578 2-718 592 2 733 2-747 21 20 70 2-747 2-762 2-778 2-793 2-808 2-824 2-840 2-856 2-872 2-888 2 904 19 71 72 73 2-904 3-078 3-271 2-921 3 096 3-291 2-937 3-115 3-312 2-954 3-133 3-333 2-971 3-152 3-354 2989 3-172 3-376 3-006 3-024 3-2II 3-420 3-042 3-230 3-060 3-251 3-465 3-078 3-271 3-487 18 \l 74 3-487 3-5" 3-534 3-558 3-582 3-606 3-630 3-655 3-681 J-706 3-732 15 75 3-732 3-758 3-785 3-8I2 3-839 3-86? 3 895 3-9t3 3-952 3-981 4-OII 14 76 4-011 4-041 4-071 4*102 4-134 4-165 4*198 4-25-0 4*264 4-297 4'33I 13 77 4-331 4-366 4-402 4-437 4'474 4 511] 4-548 4-586 4 625 4-665 4-705 12 78 4-705 4-745 4-829 4-872 4'9i5j 4-959 5-005 5-050 5-097 5-145 II 79 5-I45 5-I93 5*242 5-292 5-343 5-396 5-449 5-503 5-614 5-67I IO 80 81 5-671 6-314 5-730 6-386 5-789 6-460 5-850 6'5?5 5912 6-612 5-976 6-041 6-691 6-772 6-107 6-855 6-174 6-940 6-243 7-026 6-3I4 7-II5 1 82 7-115 7-207 7-3oo| 7-39* 7-495 7'596! 7*700 7 806 7-916 8-028 8 144 7 8? 8-144 8-264 8-386| 8-513 8-643 8-777 8 915 9 058 9-205 9"357| 9-5M 6 84 9-514 9-677 9-845 10-02 10-20 10-39 10-58 10 78 10-99 11-20 11-43 5 85 11-43 ii 66 11-91 12 'l6 12-43 12-71 13-00 13-30 13-62 13-95 .14-30 4 86 14-30 14*67 15-06 15-46 15-89 16-35 16-83 I7-34 17-89 18-46 [19-08 3 87 19-08 19-74 J20-45 88 28-64 30-14 J3I-82 21-20 22-02 35-80 22-90 38-19 23-86 40-92 24-90 44-07 26-03 27-27 52-08 28-64 57-29 2 I 89 57-29 1-0 63-66 171-62 1~ 81-85 95-49 114*6 5 4 191-0 3 286-5 573-0 OO o 7 6 2 1 DEG. Natural Cotangents (r = i). 2 1 8 Squares of Diameters. TABLE of Squares of Diameters, for finding the value of d* and -J <. No. Square. No. Square. No. i Square. No. Square. No. Square. I t 51 2601 101 I020I I5i 22801 201 40401 2 4 52 2704 12 \ 10404 152 2*104 202 4 8--H 3 9 53 2809 103 : 10609 153 23409 203 41209 4 16 54 2916 I.-4 10816 154 23716 204 41616 $ 25 55 3025 105 II025 155 24025 205 42025 6 36 56 3136 106 II236 156 24336 206 42456 7 57 3249 107 11449 157 24649 207 42849 8 04 58 3364 108 11664 158 24964 208 45264 9 81 59 3481 109 11881 159 25281 209 45681 10 100 60 3600 no I2ICO 160 25600 210 44100 ii 121 61 3721 in I232I 161 25921 211 44521 12 144 62 3844 112 12544 162 26244 212 44944 13 169 63 3969 113 12769 163 26569 213 45369 14 196 64 4096 114 12996 164 26896 214 45796 J*5 225 65 4225 "5 13225 165 27225 215 46225 16 256 66 4356 116 13456 166 27556 216 46656 *7 289 67 4489 117 13689 167 27889 217 47089 18 324 68 4624 13924 168 28224 218 19 361 69 476i 119 14161 169 28561 219 4796? 20 400 70 4900 120 14400 170 28900 220 48400 21 441 7 1 5041 121 14641 171 29241 221 48841 22 484 72 122 14884 172 29584 222 49284 23 529 73 5329 123 I5I29 173 29929 223 49729 24 576 74 5476 124 15376 174 30276 224 50176 25 625 75 5625 125 15625 175 30625 225 50625 26 27 676 729 76 77 57/6 5929 126 127 15876 16129 176 177 30976 31*29 226 227 51076 51529 28 784 78 6084 128 16384 178 31684 228 i 51984 29 841 79 6241 129 I '.641 179 32041 229 52441 30 900 80 6400 130 16900 180 32400 230 52900 ?I 961 81 6561 131 I7l6l 181 32761 231 53361 32 1024 82 6724 132 17424 182 33124 232 55824 33 1089 83 6889 133 17689 183 33489 233 54289 34 1156 84 7056 134 17956 184 33856 234 54756 35 1225 85 7225 135 18225 185 34225 235 55225 36 1296 86 7396 136 18496 186 34596 236 55696 37 1369 87 7569 137 18769 187 34969 237 ! 56169 38 1444 88 7744 138 19044 188 35?44 238 56644 39 1521 89 7921 139 I932I 189 35721 239 ; 57121 40 l6oo 90 8100 140 19600 190 36100 240 i 57600 4 1 1681 91 8281 141 19881 191 36481 241 58081 42 1764 92 8464 142 20164 192 36864 242 58564 43 1849 93 8649 M3 20449 I9J 37249 243 1 59049 44 1936 94 8836 144 20736 194 37636 244 i 595 ?6 45 2025 95 9025 21025 195 38025 245 ; 60025 I 46 2116 96 9216 146 2I3l6 196 38416 246 60516 47 2209 97 9409 21609 197 38809 247 1 61009 48 2304 98 9604 148 21904 198 39204 248 I 61504 49 2401 99 9801 149 222-1 199 39601 249 62001 5 2500 100 'I-OOOO 150 22500 200 40000 250 62500 | Squares of Diameters. TABLE of Squares of Diameters continued. 219 No. Square. No. ! Square. No. Square. No. ! Square. No. Square. 251 63001 301 90601 351 I 23 201 401 160801 45 203401 252 63504 302 91204 352 123904 402 161604 452 204304 253 64009 303 91809 35* 124609 403 - 162409 45 J ) 205209 254 64516 304 92416 354 125116 44 ; 163216 4*4 206116 255 65025 305 93025 355 126025 405 i 164025 455 207025 256 655*6 306 93636 356 126736 406 164836 456 207936 257 66749 307 94249 357 127449 407 : 165649 457 208849 258 66564 308 94864 3S8 128164 408 166404 458 I 209704 g 67081 67600 309 3 10 95481 96100 359 360 128881 129*00 439 i 410 167281 168100 459 210681 460 211600 261 68121 311 96721 36l 130321 4" 168921 461 212521 262 68644 312 97344 362 131044 412 169744 462 213444 26? 69169 313 97969 363 131769 4'3 170569 463 214369 264 69696 314 98596 364 132496 414 171396 464 215296 265 70225 315 99225 365 133225 4^5 172225 465 216225 266 70756 3i6 99856 366 133956 416 173056 466 217156 267 71289 317 100489 367 134689 4n 173889 467 218089 268 71824 318 101124 368 135424 418 1:4724 468 219024 269 72361 319 1 101761 369 136161 419 175561 469 219961 270 72900 320 102400 370 136900 420 176400 470 220900 271 73441 321 103041 371 137641 421 177241 47 r 221841 272 7?984 322 103684 372 i}8!84 4 2J 178084 472 222784 27? 74529 323 104329 373 139129 423 178929 473 22'729 274 75076 324 104976 374 139876 424 179776 474 224676 275 75625 325 105625 375 140625 425 180625 475 225625 276 76176 326 106276 376 I4I376 426 181476 476 226576 277 76729 327 106929 377 142129 427 182329 477 227529 278 77284 328 107284 378 142884 4 28 183184 478 228484 279 77841 329 108241 379 14*641 429 184041 4"9 229441 280 78400 330 108900 380 144400 430 184900 480 230400 281 78961 331 109561 38f 145161 431 1857 *>! 481 231161 282 79524 332 110224 382 145924 432 186624 482 232324 283 80089 333 I 10889 383 ! 146689 4" 187489 483 23*289 284 80656 3H i"556 384 ! 147456 434 188356 484 234256 285 81225 335 112225 385 148225 435 189225 485 235225 286 81796 J36 112896 386 148996 436 190096 486 236196 287 82369 3*7 113569 387 14^769 4'7 190969 487 237169 288 82944 33* 114244 388 , 150544 438 191844 488 238144 289 83521 339 114921 389 | 151321 439 I9272I 489 239121 290 84100 340 115600 390 152100 440 ! 193600 490 240100 291 84681 341 116281 39i 152881 441 | I944BI 491 241081 292 85264 342 116964 392 ; 153664 442 i 195*64 492 24:064 29? 85849 34* 117649 393 1 154449 44* 196249 49* 2430-19 294 86436 344 H8J36 394 ! 155236 444 197U6 494 244036 295 87025 345 119025 395 156025 445 198025 495 745025 296 87616 346 119716 396 156816 446 198916 496 246016 297 88209 347 120409 ?97 ; 157609 447 i 199809 497 247009 298 88804 348 121104 398 158404 448 ; 200704 498 248 04 299 89401 349 ! 121801 399 159-01 449 201601 499 249001 300 90000 350 I 122500 400 ; 160000 450 102500 530 250000 22O Squares of Diameters. TABLE of Squares of Diameters continued. No.' | Square. No. Square. No. Square. No. Square. No. Square. 501 j 251001 551 303601 601 361201 651 423801 701 491401 502 252004 552 304704 602 362404 652 425104 702 492804 5* 25*009 553 305809 603 363609 653 426409 703 494209 504 254016 554 306916 604 364816 654 427716 704 495616 505 255025 555 308025 605 366025 655 429025 705 497025 506 256036 556 3091*6 606 3672*6 656 4303*6 706 4984*6 507 257049 557 310249 607 368449 657 431639 707 499849 508 258064 558 311*64 608 369664 658 4*2964 708 501264 509 259081 559 312481 609 370881 659 434281 709 502681 510 260100 560 313600 610 372100 660 4356oo 710 504100 5" 261121 561 314721 611 373321 661 436921 711 505521 512 262144 562 315844 612 374544 662 438244 712 506944 513 26*169 563 316969 613 375769 663 439569 713 508369 5*4 264196 564 318096 614 376996 664 440896 714 509796 515 265225 565 319225 615 378225 665 442225 715 511225 516 266256 566 320*56 616 379456 666 44*556 716 512656 517 267289 567 321489 617 380689 667 444899 717 514089 518 268324 568 322624 618 381924 668 446224 718 515524 519 269361 569 619 383161 669 447561 719 516961 520 270400 570 324900 620 384400 670 448900 720 518400 521 271411 57i 326041 621 385641 671 450241 721 519841 522 272484 572 327184 622 386884 672 451584 722 521284 523 273529 573 328*29 623 388129 673 452929 723 522729 524 274576 574 329476 624 389376 674 454276 724 524176 525 275625 575 330625 625 390625 675 455625 725 525625 526 276676 576 331776 626 391876 676 456976 726 527076 527 277729 577 3*2927 627 393129 677 458*29 727 528529 528 278784 578 3*4084 628 394384 678 459684 728 529984 529 279841 579 335241 629 395641 679 461041 729 53I44I 530 280900 580 336400 630 396900 680 462400 730 532900 531 281961 581 33756i 631 398161 68 1 46*761 731 53436i 532 28*024 582 3*8724 632 399424 682 465124 732 535824 5*3 5*4 284089 285156 583 584 339889 341056 633 634 400689 401956 683 684 466489 467856 733 734 537289 538756 535 286225 585 342225 635 403225 685 469225 735 540225 536 287296 586 343*96 636 404496 686 470596 7*6 541696 537 288369 587 344569 637 405769 687 471969 737 54*169 538 289444 588 345744 638 407044 688 473344 738 544644 539 540 290521 291600 589 590 346921 348100 639 640 408321 409600 689 690 474721 476100 739 740 546121 547600 541 292681 591 349281 641 410881 691 477481 741 549801 542 29*764 592 350464 642 412164 692 478864 742 550564 543 294849 593 351649 643 413449 693 480249 743 552049 544 2959*6 594 352836 644 694 4816*6 744 55*5*6 545 297025 595 354025 645 416125 695 483025 745 555025 546 298116 596 3552i6 646 417*16 696 484416 746 556516 547 299209 356409 647 418609 697 485809 747 558009 548 300304 598 357604 648 419904 698 487204 748 549 301401 599 358801 649 421201 699 488601 749 561001 550 302500 600 360000 650 422500 700 490000 750 562500 Squares of Diameters. TABLE of Squares of Diameters continued. 221 No. Square. No. Square. No. Square. No. Square, j No. Square. 751 564001 801 641601 851 724201 901 811801 951 904401 752 565504 802 643204 852 725904 902 813604 952 906304 753 567009 803 644809 853 727609 903 815409 953 908209 154 568516 804 646416 854 729316 904 817216 954 910116 755 570025 805 648025 855 731025 905 819025 955 912025 756 57i5?6 806 649636 856 732736 906 820836 956 91*936 757 573049 807 651249 857 7J4449 907 822649 957 915849 758 574564 808 652864 858 1 736164 908 824464 958 917764 759 576081 809 654481 859 737881 909 826281 959 919681 760 577600 8io 656100 860 739600 910 828100 960 921600 761 579121 811 657721 861 741321 911 829921 961 923521 762 580644 812 659344 862 743044 912 831744 962 925444 763 582169 813 660969 863 744769 913 833569 963 927369 764 58*696 814 662596 864 746496 914 835396 964 929296 765 585225 815 664225 865 748225 915 837225 965 931225 766 586756 816 665856 866 749956 916 839056 966 933156 767 588289 817 667489 867 751689 917 840889 967 935089 768 769 770 589824 59u6i 592900 818 819 820 669124 670761 672400 868 869 870 753424 755i6i 756900 918 919 920 842724 844561 846400 968 969 970 937024 938961 940900 771 594441 821 674041 871 758641 921 848241 971 942841 772 773 595984 597529 822 823 675684 677329 872 873 760384 762129 922 923 850084 851929 972 973 944784 946729 774 775 599076 600625 82 4 825 678976 680625 874 i 763876 875 765625 924 925 853776 855625 974 975 948676 950625 776 602176 826 682276 876 767376 926 857476 976 952576 777 603729 827 683929 877 769129 927 859329 977 954529 778 605284 828 685584 878 i 770884 928 861184 978 956484 779 606841 82 9 687241 879 i 772641 929 863041 979 958441 780 608400 830 688900 880 774400 930 864900 980 960400 781 609961 831 690561 881 776161 931 866761 981 962361 782 611524 832 692224 882 777924 932 868624 982 964324 783 61 5089 8*3 695889 883 i 779689 933 870489 983 784 614656 834 695556 884 781456 934 872356 984 968250 785 616225 835 697225 885 i 783225 935 874225 985 970225 786 617796 836 698896 886 784996 936 876096 986 972196 787 6ig?69 857 700569 887 ( 786769 937 8*77969 987 974169 788 620944 8?8 702244 888 i 788544 9?8 879844 988 976144 789 790 622521 624100 8 59 840 703921 705600 889 790321 890 ; 792100 9*9 940 881721 883600 989 990 978121 980100 791 625681 841 707281 891 : 795881 941 885481 991 982081 792 627624 842 708964 892 795664 942 887364 992 984064 793 628849 8 4 3 710649 893 797449 943 889249 993 986049 794 650456 844 712336 894 799236 944 891136 994 988056 795 632025 845 714025 895 801025 945 893025 995 990025 796. 653616 846 715716 896 802816 946 894916 996 992016 797 655209 847 717409 897 801609 947 896808 997 994009 798 636804 848 719104 898 806404 ! 948 898704 998 996004 799 658401 849 720801 899 808201 ; 949 900601 999 998001 800 640000 850 722500 900 810000 950 902500 IOOO 1000000 222 Sundry Recipes. SUNDRY RECIPES. 1. Shell-lac varnish for glass (Harris). Put i oz. of the shell-lac of commerce into a wide- mouthed 8-ounce phial, containing 5 oz. of well-rectified naphtha, wood or spirit. Close the bottle with a cork, and let it stand in a warm place until perfectly dissolved. Shake the mixture frequently, and pass the fluid through a paper filter ; add rectified naphtha to the solution from time to time in such quantities as will enable it to percolate freely through the filter. Change the filter when necessary. 2 . Varnish for paper, for insulating. Dissolve i oz. of Canada balsam in 2 oz. of spirits of turpentine. Put into a bottle and digest at gentle heat, and filter before being cold. 3 . Varnish for silk. Boiled oil, 6 oz., and 2 oz. of clear spirits of turpen- tine. 4. Electrical cement. Harris prefers the best sealing-wax. 5. Amalgam for electrical machines. Tin i. Zinc 2. Mercury 4. The best and cheapest plan for amalgam is to buy it ready made at an electrical instrument maker's. For ebonite places the amalgam should be softer than for glass. Stindry Recipes. 223 6. Solder* For line wires, Tin i, Lead i J ; or Tin i, Lead i. 7. Marine glue. Much used in batteries. In 12 parts of benzole dissolve i of india-rubber, and to the solution add 20 parts of powdered shell-lac, heating the mixture cautiously over a fire. Apply with a brush. 8. Printing solutions for Bains. i part ferro-cyanide of potassium saturated solution ; i part nitrate of ammonia saturated solution, i part of each solution to 2 parts of water. 9. Cement for insulators. Sulphur, lead, plaster of Paris, with a little glue to prevent it setting quickly. 10. MuirheacFs cement. 3 Ib. Portland cement, 3 Ib. rough sand, 4 Ib. smith's ashes, 4 Ib. resin. n. Black cement. i Ib. rough sand, i Ib. smith's ashes, 2 Ib. resin. 12. Siemens' cement. 12 Ib. black iron rust or iron filings, 100 Ib. sulphur. * Soldering (Culley). Connections in apparatus and test-boxes must never be soldered with acids or chloride of zinc. These liquids cannot be entirely removed, and will corrode the metal. If spilled on wood, or even on ebonite, chloride of zinc never dries, and injures the insulation. Resin must always be used. 224 Logarithms. LOGARITHMS. To convert Common into Hyperbolic Logarithms. TABLE. Common Hyperbolic Logarithms. Logarithms. I" 2-3025851 2* 4-6051702 3* 6-9o?7<;53 4* 9-2103404 5' 11-5129255 6- 13-8155 106 r 16*118095 7 8- 18-4206^07 9' 20-7232658 Write the common logarithm (as shown in the follow- ing example), and then take from the table the equiva- lent value of each figure in the hyperbolic logarithms, taking care that the latter are each moved as many places to the right as the corresponding numbers in the common logarithms are. The sum of the whole will be the hyperbolic logarithm required. Example. Required the hyp. log. of 3156. The common log. of 3156 is 3*499137 ; therefore Common Log. Hyp. Log. 3* 6-907755 OOOO3 "000069 5'499 r 37 8-057061 To convert common into Napierean logarithms, mul- tiply the common logarithms by 2 '3 025851. Logarithms. 225 On the following pages will be found a table of Napierean logarithms from i to 6, calculated to the second decimal place for finding the exact value of log for various sizes of telegraph conductor. In the table of common logarithms will be found a column giving the arithmetical complement of each logarithm ; this gives great facility for working sums in proportion, and other calculations in which division becomes necessary ; the addition of the arithmetical complement giving the same figures as the subtraction of the original logarithm would have done. Thus I4 X 386 becomes 924 log 140 = -14613 log 3 86 '5 86 59 A. Comp. 924 -0343 2 76704 = 585. 226 Natural Logarithms. Table of natural or Napierean logarithms from I to 6, for finding the values of log. . + '00 + 0!! + 02 + 03 + 04 + 05 + 06 + 07 + 08 + 09 I'O o-ooo o-oio O'O2O 0-030 039 049 058 068 0-077 0-086 I'l 0-095 104 O'H3 122 131 140 148 157 0-166 0-174 1-2 0-182 191 0-199 207 215 223 231 0-247 0-255 l'3 0-262 270 0-278 285 293 300 307 -315 0-322 329 0-336 '344 0-351 358 365 372 378 385 0-392 399 1-5 0-405 .412 0-419 425 432 438 '445 451 '457 464 1-6 0-470 476 0-482 489 '495 501 507 513 0-519 525 1-7 0-531 536 0-542 548 554 560 565 571 0-577 582 1-8 0-588 '593 0-599 604 610 615 621 626 o-6?i 1-9 0-642 647 0-652 658 663 668 673 678 0-683 688 2'O 0-693 698 0-70? 708 713 718 723 728 0-732 737 2* I 0-742 '747 0-751 756 761 765 77o '775 0-779 784 2'2 0-788 793 0-798 802 806 811 815 820 0-824 829 2'3 0-833 837 0-842 846 850 854 859 86j 0-867 871 0-875 880 0-884 888 892 896 -900 904 0-908 912 2-5 0-916 920 0-924 928 932 936 940 '944 0-948 952 2-6 0-956 '959 0-963 967 971 '975 9/8 982 0-986 990 2-7 0*993 '997 I'OOI 004 008 012 015 019 1-022 026 2-8 i'o?o oj? 1-037 -040 044 047 051 054 1-058 061 2-9 1-065 068 1-072 075 078 082 085 089 1-092 095 3-o 1-099 102 1-105 109 112 115 118 122 I -125 128 3*1 1-131 135 1-138 141 " I 44 147 151 154 I-I57 160 3-2 1-163 166 1-169 172 170 179 182 185 1-188 191 3'3 1-194 197 i -200 20} 206 209 212 215 1-218 221 3 '4 1-224 227 1-230 233 235 238 2 4 I 244 1-247 250 3'5 1-253 256 1-258 26l 264 267 270 273 1-275 2 7 8 3'6 1-281 284 1-286 289 292 295 297 300 1-3-3 ?o6 3'7 1-308 1-314 316 319 322 32 4 327 1-330 332 1-335 338 1-340 343 345 348 351 353 1-356 358 3'9 1-361 364 1-366 369 371 '374 376 '379 1-381 38 4 4-0 1-386 389 1-391 394 396 399 401 404 1-406 409 1-411 1-416 418 421 423 4 26 4 28 1-430 433 4'2 437 1-440 442 445 '447 '449 452 1 '454 456 4'3 I- 459 461 1*463 466 468 470 472 ! '475 1-477 '479 4'4 1-482 484 1-486 488 491 '493 '495 497 1-500 502 4*5 1-504 506 1-509 511 513 515 517 520 1-522 524 4-6 4'7 1-526 1-548 528 550 1-530 1-552 '533 554 535 556 '537 558 5?9 560 541 562 1-564 545 567 4-8 1-569 571 1-573 575 577 '579 58i 583 1-585 587 4'9 1-589 591 1-593 595 597 599 601 603 1-605 607 5-o 1-609 1-629 6ir 631 1-613 1-633 615 635 617 637 -619 639 621 641 38 1-625 627 647 5'2 1-649 651 1-652 654 656 658 660 "602 i "664 666 1-668 670 1-671 673 675 677 679 j 681 1-68? 685 5'4 1-686 683 1-690 692 694 696 697 699 I' 7oi 703 5'5 1-705 707 1-708 710 712 714 716 717 1-719 721 5-6 1-723 725 1-726 728 730 732 '733 735 1-737 739 5'7 5-8 1-740 1-758 742 760 1-744 1-761 '?$ '76*5 ?66 751 768 ; 1*753 1-770 1-754 1-772 756 '773 5'9 1-775 H 1-778 780 782 783 785 1-787 1-788 790 Common Logarithms. I to 150. 227 Num. Log. A. Comp. Num.1 Log. A. Comp. Num. Log. A. Comp. 00 i 00 1 'OOOOO i 0000 5 1 70757 29243 101 004*2 99568 3010? 69897 52 71600 28400 102 00860 99140 47712 522ti8 " 72428 27572 IOJ 01284 98716 60206 39794 54 7*239 26761 104 01703 98297 69897 30103 55 74036 25964 105 02119 97881 6 77815 22185 56 i 74819 25181 106 025*1 97469 7 84510 15490 57 ! 75587 24413 107 029*8 97061 8 90509 09691 58 i 7634? 23657 108 0*342 96658 9 95424 04576 59 77085 22915 109 o?74? 96257 10 ooooo ooooo 60 77815 22185 no 04139 95861 ii 041*9 95861 61 785*3 21467 III 045*2 95463 12 07918 92082 62 792*9 20761 112 04922 95078 11 14 11*94 1461? 88606 85387 63 64 '.&& 20066 193M2 H3 "4 05308 05690 94692 94310 15 17609 82391 65 81291 18709 "5 06070 93930 16 20412 79588 66 81954 18046 116 06446 93554 17 2*045 76955 67 82607 17393 117 06819 93181 18 25527 74473 68 8*251 16749 118 07188 92812 19 27875 72125 69 83885 16115 119 07555 92445 20 30103 69897 70 84510 15490 1 2O 07918 92082 21 32222 67778 71 85126 14874 121 08270 91721 22 34242 65758 72 85733 14267 122 086*6 91364 21 36173 63827 73 86?32 13668 I2 08991 910i'9 24 38021 61979 74 86923 13077 124 09:42 90658 25 39794 60206 75 87506 12494 125 0-^91 90309 26 41497 58503 76 88081 11919 126 100*7 89963 27 4?U6 56864 77 88649 11351 127 10*80 89620 28 447i6 55284 73 89209 10791 128 10721 S9279 2 9 46240 53760 79 8976J 10237 129 11059 88941 JO 47712 52288 80 90309 09691 130 '"394 88606 *I 49n6 50864 81 90849 09151 1*1 11727 8*273 22 50515 49485 82 91381 08619 1*2 12057 87943 3? 51851 48149 83 91908 08092 133 12*85 87615 34 55148 46852 84 92428 07572 1*4 12710 87290 35 54407 45593 85 92942 07058 135 13033 86967 36 556?o 44370 86 9*450 06550 136 13*54 86646 37 56820 43180 87 9*952 06048 *37 13672 86328 38 57978 42022 88 94448 05552 1*8 i *988 86012 39 59106 40894 89 94919 05061 i*9 14 ?oi 85699 4 60206 39794 90 95424 04576 140 14613 85387 4i 61278 38722 91 95904 04096 141 14922 85078 42 62*25 37675 92 96*79 03621 142 15229 84771 4* 6?J47 36653 93 96848 03152 14? 15554 84466 44 64H5 35655 94 97 n* 02687 144 15876 84164 45 65321 34679 95 97772 02223 M5 i6ij7 P3863 46 66276 33724 96 98221 01773 146 164*5 83565 47 67210 32790 9^ 98677 01323 J 47 16732 83268 48 68124 31876 98 99123 00877 148 17026 82974 49 69020 30980 99 99564 00436 149 11319 82681 5 69897 30103 100 ooooo oouoo 150 17609 82391 228 Common Logarithms. 151 /6?6i 63639 28l 44871 55129 182 26007 73993 232 36549 63451 282 45025 54975 18? 26245 73755 2?? 3'7?6 63264 283 '45*79 54821 184 26482 73518 234 36922 63078 284 45*32 54668 185 26717 73283 235 37107 62893 28 5 45484 54515 186 26951 73049 2?6 37291 62709 286 456*7 54363 187 27184 72816 237 '37475 62525 287 45788 542.2 188 27416 72n84 238 37658 62342 288 '459 9 54061 .189 27646 72354 239 378-10 62160 28 9 460.0 53910 190 27875 72125 2 4 o 38021 61979 190 46240 53760 191 2810? 71897 2 4 I 38202 61798 291 46389 53611 192 28330 71670 242 * j8 ?82 61618 292 53462 28556 71444 243 58561 61439 29? 46687 53313 194 28780 71220 244 38739 61261 294 53165 '95 29003 7(996 245 38917 61083 295 46982 53018 196 29226 7(774 2 4 6 79094 60906 296 47129 52871 197 29447 70553 247 39270 60730 297 47276 52724 198 29^67 7( 333 2 4 8 39445 60555 298 47422 52578 29885 70115 249 39620 60380 299 47567 52433 200 30103 69897 250 J9794 60206 300 -47712 52288 Common Logarithms. 301 to 450. 229 Num. Log. A. Comp. Num. Log. A. Comp. Num. Log. A. Comp. 301 47857 52143 351 '545*1 45469 401 60314 39686 302 48001 51999 J52 54654 45?46 402 60423 39577 303 48144 51856 35 J '54777 45223 403 60531 39469 304 48288 51712 354 54900 45100 44 60638 39362 305 48450 51570 355 55023 44977 405 60746 39254 306 48572 51428 356 55145 44855 406 60853 39147 507 48713 51287 357 55267 447*3 407 60959 39041 308 48855 51145 358 55*88 44612 408 61066 38934 309 3io 48996 49136 51004 50864 *59 360 55590 55630 44491 44370 409 410 61172 61278 38828 38722 3ii 49276 50724 361 '55751 44249 4" 61384 3*616 JI2 49415 50585 362 55871 44129 412 61490 38510 31 J '49554 50446 363 55991 44009 4*3 6i595 38405 315 49^93 49831 50307 50169 365 '56110 56229 43890 43771 414 415 61700 61805 38300 35195 316 49969 50031 366 56348 43652 416 61990 38091 |I* 50106 49894 367 56407 43633 4*7 62014 37986 318 50243 49757 368 56585 43415 418 62118 37882 519 50579 49621 369 56703 43297 419 62221 37779 320 -50515 49485 370 56820 43180 420 62325 37675 321 -50651 49349 371 569*7 43063 421 62428 37572 322 -50786 49214 372 57054 42946 422 62551 37469 32? 50920 49080 373 57171 42829 423 62634 37366 1*4 51055 48945 374 57287 42713 424 62737 37263 325 51188 48812 375 57403 42597 425 62839 37161 326 i -51322 48678 37^ ;575i9 42481 426 62941 37059 327 | -51455 48545 377 42366 427 "63043 36957 328 51587 48413 378 '57749 42251 428 63144 36856 329 51720 48280 379 57864 43136 429 6324? 36755 330 51851 48149 380 57978 42022 430 36653 3U -51983 48017 38i 58093 41907 4*1 65448 36552 332 52114 47886 382 58206 41794 4*2 65548 36452 3?3 52244 47756 383 58320 41680 4*3 65649 36351 334 52375 47625 384 58433 41567 4*4 65749 36251 335 52504 47496 385 58546 41454 435 63849 3t>151 3*6 52654 47366 386 -58659 41341 4*6 63949 36051 3*7 52763 47237 387 -58771 41229 437 64048 35952 338 -52892 359 5 7020 47108 46980 ?88 i -58883 389 -58995 41117 41005 438 -64147 459 -64246 35853 35754 340 -53148 46852 390 59106 40894 44 64345 35755 341 5*275 46725 391 59218 40782 44 1 64444 35556 342 -53403 46597 392 59*29 40671 442 -64542 35458 343 1 -55529 46471 393 ; 594*9 40561 44* 64640 35360 344 ' '5*656 46344 394 40450 444 64738 35262 345 -53782 46218 395 59660 40340 445 64836 35164 346 53908 46092 396 59770 40230 446 64953 35066 3! 54035 54158 45967 45842 397 59879 59988 40111 40012 447 448 65051 .65128 34969 34872 349 -54283 -45717 399 -60097 39903 449 65225 34775 350 -54407 45593 400 -60206 39794 450 65321 34678 I 230 Common Logarithms. 451^600. Num. Log. A. Comp. Num. Log. A. Comp. Num. Log. A. Comp. 45i 65418 34582 501 69984 30016 551 74115 2:>885 452 65514 34486 502 70070 29930 552 '74 I 94 25806 453 65610 34390 503 70157 29843 553 74273 25727 454 65706 34294 504 70243 29757 554 74?5i 25649 455 65801 34199 505 70329 29671 555 74429 25571 456 457 65896 34104 34008 506 507 70415 70501 29585 29499 556 557 74507 74586 25493 25414 458 66087 33913 508 70586 29414 558 74663 25337 459 66181 33319 509 70672 29328 559 74741 25259 460 66276 33724 510 70757 29243 560 74819 25181 461 66370 33630 5ii 70842 29158 561 74896 25104 462 66464 33536 512 70927 29073 562 "74974 25026 463 66558 33442 5U 71012 28988 563 75051 24949 464 66652 33348 5M 71096 28904 564 75128 24872 465 66745 33255 515 71181 28819 565 75205 24795 4 ? 66839 33161 516 71265 28735 566 75282 24718 467 66932 33068 517 71349 28651 567 75358 24642 468 67025 32975 518 714*3 28567 568 75435 24565 469 67117 32883 519 71517 28483 569 75511 24489 470 67210 32790 520 71600 28400 570 75587 24413 471 67302 32698 521 71684 28316 571 75664 24336 472 67394 32606 522 71767 28233 572 75740 24260 473 67486 32514 523 71850 28150 573 75815 24185 4'4 67578 32422 524 71933 28067 574 75841 24109 475 67669 32331 525 72016 27984 575 75967 24033 476 67761 32239 526 72099 27901 576 76042 23958 477 67852 32148 527 72181 27819 577 76118 23882 478 67943 32057 528 72263 27737 578 76193 23807 479 68034 31966 529 72346 27655 579 76268 23732 480 68124 31876 530 72428 27572 580 76343 23657 481 68215 31785 53i 72590 27491 581 76418 23582 482 68305 31695 532 72591 274H9 582 -6492 23508 48? 68395 31605 533 72673 27327 583 76567 2M433 484 68485 31515 534 7 2 754 27246 584 6641 23359 485 68574 31426 535 72835 27165 585 76716 23284 486 68664 31336 536 72916 27084 586 76790 23210 487 68753 31247 537 72997 27003 587 70864 23136 488 68842 31158 538 73078 2H922 588 76938 23062 489 68931 31069 539 73159 26841 589 77012 22988 490 69020 30980 540 73239 26761 590 77085 22915 491 69108 30892 541 73320 26680 59i 77159 22841 492 691^7 30803 542 73400 26600 592 77232 22768 493 69285 30715 543 73480 26520 5^3 77305 22694 494 69373 30627 544 7?56o 26440 594 77379 22821 495 69461 30539 545 73640 26360 595 77452 22548 496 69548 30452 546 73719 26281 596 77525 22475 497 69636 30364 547 7^99 26201 597 '77597 22403 498 6^723 20277 548 '7?873 26122 5/8 77670 22330 499 69810 30190 549 7*957 26043 599 '7774* 22257 500 69897 30103 550 74036 25964 600 77815 22185 Common Logarithms. 601/0750. 231 Num. Log. A. Comp. Num. Log. A. Comp. Num. Log. A. Comp. 601 77887 22113 651 81*58 18642 701 84572 15428 602 77960 22040 6 5 2 81425 18575 702 15366 603 78032 21968 653 81491 18509 703 84690 15304 604 78104 21896 654 8,558 18442 704 84757 15243 605 78176 21824 655 81624 18376 705 84819 15181 606 78248 21752 656 81690 18310 706. 84880 15120 607 78*19 21681 657 81757 18243 707 84942 15058 608 78*90 21610 658 81823 18177 708 85003 14997 609 78462 21538 659 81889 18111 709 85065 14935 610 78533 21467 660 81954 18046 710 85126 14874 611 78604 21396 661 82020 17980 711 85187 14813 612 613 78675 78-46 21325 21254 662 663 82086 82151 17914 17849 712 713 85248 85309 14752 14691 614 78817 21183 664 82217 17783 85370 14630 615 78888 21112 665 82282 17718 7*5 85431 14569 616 78958 21042 666 82347 17653 716 85491 14509 617 79029 20971 667 82413 17587 717 85552 14448 618 79099 20901 668 82478 17522 718 85612 14388 619 79169 20831 669 82543 17457 719 85613 14327 620 79239 20761 670 82607 17393 720 85733 14267 621 79390 20691 671 82672 17328 721 85794 14206 622 '79379 20621 672 827*7 17263 722 85854 14146 623 79449 20551 82802 17198 723 85914 14086 624 79518 20482 674 82866 17134 724 85m 14026 625 79588 20412 675 82930 17070 725 86034 13966 626 79657 20343 676 82995 17005 726 86094 13906 627 79727 20273 677 8*059 16941 727 86153 13847 628 79796 20204 678 8*123 16877 728 #6213 13787 629 79865 20135 679 8ji87 16813 729 86273 13727 630 '79934 20066 680 83251 16749 730 86332 13668 631 80003 19997 68 r 83315 16685 731 86392 13608 632 80072 19928 682 *8**78 16622 732 86451 13549 633 80140 19860 683 8*442 16558 733 86510 13490 634 80109 19791 684 8*506 16494 734 86570 13430 635 80277 19723 685 83569 16431 735 86629 13371 636 80346 19654 686 85632 16368 736 86688 13312 6*7 80414 19585 687 8*696 16304 737 86747 13253 6*8 80482 19518 68 8*759 16241 738 86806 13194 6*9 -80550 19450 689 8?822 16178 739 86864 13136 640 80618 193S2 690 83885 16115 740 86923 13077 641 80686 19314 691 83948 16052 74 1 86982 13018 642 80754 19246 692 84011 15989 742 87040 12960 6 4 3 80821 19179 693 84073 15927 743 87099 12901 644 80889 19111 694 841*6 15864 744 87157 12843 645 80956 19044 095 841^8 15802 745 87216 12784 646 8102* 18977 696 84261 15739 746 87274 12726 647 8io9o 18910 697 84*2* 15677 747 87332 12668 648 81158 18842 698 84*86 15614 748 87390 12610 649 81224 18776 699 84448 15552 749 87448 12552 650 j -81291 18709 700 j -84510 15490 750 87566 12494 232 Common Logarithms. 751 to Num. Log. A. Comp. Num. Log. A. Comp. Num. Log. A. Comp. 751 87564 12436 801 9036? (9637 851 02993 07007 752 87622 12378 802 90417 09583 852 "9?044 ! -06956 75? 87680 12320 803 90472 09528 853 93095 | -(,6905 754 877?7 12263 804 90526 09474 854 9?M 06854 755 87795 12205 805 90580 09420 855 93197 06103 756 87852 12148 806 90634 09366 856 93247 06753 757 87910 12090 807 90687 09313 857 93298 06702 758 87967 12033 808 90741 09259 858 93349 06651 759 88024 11976 809 90795 09205 859 9?*99 06601 760 88081 11919 810 90849 09151 860 9*4*o 06550 761 88138 11862 811 90902 09198 861 9*500 -06500 762 88196 11804 812 90956 09044 862 93551 i '06449 76? 88252 11748 813 91090 0*991 863 93601 '06399 764 88390 11691 814 91062 08938 864 93651 06349 765 88J66 11634 815 91116 08884 865 9370Z 06293 766 8842? 11577 816 91169 T8831 866 9*752 T6248 767 88480 11520 817 91222 08778 867 93802 06198 768 88536 11464 818 91275 08725 868 9?852 06148 769 88593 11407 819 91328 08672 869 95902 '06098 770 88649 11351 820 91381 OS619 870 93952 '06048 771 88705 11295 821 9I4H 08566 871 94002 ; '05998 772 88762 11238 822 91487 08513 872 94052 i '05948 77* 88818 11182 82J 91540 08460 873 94101 | -05899 774 88874 11126 82 4 91593 08407 874 94151 '05849 775 88930 11070 82 5 91645 08355 875 94201 '05799 776 88986 11014 826 91698 08302 876 94250 '05750 777 778 89042 89098 10958 10902 827 828 91751 9180? 08249 08197 877 878 94300 ; '05700 9 4 ?49 -05651 779 89154 10846 82 9 91855 08145 879 94599 '05601 780 89290 10791 830 91908 08092 880 94448 ' -05552 781 89265 10735 831 91960 08040 881 94498 ! '05502 782 89321 10679 832 92012 07988 882 94547 '05453 78? 89377 10623 833 92065 07935 88* 94596 '05404 784 89432 10568 834 92117 07883 884 94645 -05355 785 89487 10513 835 92169 07831 885 '94694 '05306 786 89542 10458 836 92221 f7779 886 -94743 -05257 787 89597 10403 837 92273 07727 887 '94792 1 -0520* 788 8965? 10347 8;8 92324 07676 888 94841 05159 789 89708 10292 839 -.,2376 07624 889 94890 05110 790 89763 10237 840 92428 07572 890 94939 05061 791 89818 10182 841 92480 07520 8 9 I 94988 05012 792 89873 10127 842 92531 07469 892 95056 04964 79? 89927 10073 843 92583 07417 89? 95085 04915 794 89982 10018 844 926M 07366 894 95134 04866 795 90037 09963 845 92686 07314 895 95182 04818 796 90091 09909 846 927f7 07263 896 95231 1 -04769 791 90146 09854 847 92788 07212 897 95279 -04721 798 90200 09800 848 92840 07160 898 95?28 04672 799 9025* 09745 849 -92891 07109 899 95376 04624 800 SQjgo 09691 850 -92942 07058 900 95424 04576 Common Logarithms. 901 to 999. 233 Num. Log. A. Comp. Num. Log. A. Comp. Num. Log. A. Comp. 901 95472 04528 94 970J5 02965 967 9854* 01457 902 95521 04479 935 97081 02919 968 98588 01412 90? 95569 04431 936 97128 02872 969 98632 01368 904 95617 04383 937 97*74 02826 970 98677 013-'3 905 95665 04333 938 97220 02780 971 98722 01278 906 95713 04287 939 97267 02733 972 98767 01233 907 95761 '04239 94 97313 02687 97* 98811 01189 908 95809 04191 941 '97359 02641 974 98856 01144 909 910 95904 04144 04096 942 943 97405 97451 02595 02549 975 976 98900 98945 01100 Olu55 911 95952 04048 944 '97497 02503 977 98989 01011 912 95999 04001 97543 02457 978 99034 Od966 913 <3953 946 97589 02411 979 99078 00922 914 | -96095 039H5 947 02365 980 99123 00877 915 j -96142 03358 948 9?6sf 02319 981 99167 00833 916 I -96190 03810 949 97727 02273 982 99211 00789 917 ; -96237 j '03763 950 l -97772 02228 98? 99255 00745 918 j -96284 03716 95i 97818 02182 984 99*oo 007i)0 919 ; -96332 03668 952 97864 02136 985 '99*44 00656 920 -96379 03621 953 97990 02091 986 99388 00612 921 | -96426 (3574 954 '97955 02045 987 '994*2 00568 922 i -96473 923 -96520 (3527 03480 955 956 98000 93046 02000 01954 988 989 99476 99520 00524 004*0 924 ; -96567 03433 957 98091 01909 990 99564 00436 925 ; -96614 03386 958 98137 01863 991 99607 00393 926 ! -96661 (3339 959 93182 01818 992 99651 00349 927 96708 (3292 960 98227 01773 993 ^9695 00305 928 96755 (3245 961 93272 01728 994 997*9 00261 929 96802 03198 962 98318 01682 995 99782 00218 930 96848 03152 963 98363 01637 996 99826 00174 931 96895 03105 964 98408 01592 997 99870 00130 932 96942 03C53 965 98453 01547 998 99913 00087 933 96988 03012 966 98498 01502 999 '99957 00043 ALPHABETS FOR PRINTING AND SINGLE NEEDLE INSTRUMENTS- RULES FOR SPACING AND SIGNALLING. 236 Alphabets for Printing and A mm ___ x/ , ____ ___ a (se) _ __ x/x/ K. ~- ^_ B _ mm _ /xxx L C t __>_ __ /x/x M D /xx N E ~ \ F xx/x 6 (ce) G //x P -, . - H \\\\ Q I \\ R s \\\ T / U XX/ ii (ue) xx// V xxx/ W x// X /xx/ y _ _ _ /x// Z //xx Ch //// Single Needle Instruments. 237 . (French accented 6 - V\X/\\) Italian n - N.B. Ch is always sent _ _ _ and never as separate letters. I mm mm X//// 2 xx/// 3 \\\// 4 xxxx/ \\x\\ /xxxx *j ^^ //xxx 8 //As 9 ///A ///// 238 A Iphabets for Printing and Full Stop (.)-- -- -- Colon (:) Semicolon ( ; ) - Comma ( > ) " - Note of Interrogation ( p ) - _ Note of Admiration ( \ ) _ Hyphen (-) Apostrophe ( ' ) - ' Parenthesis ( ) Inverted Comma (" ") Begin another Line Bar of divi- 1 sion H) f " V\ \\ \\ //Axx AAA xAA/ xx/Ax /Ay/ Axxx/ X////X /X//X/ x/xx/x x/x/xx Call Signal Understand Message Correction, or rub out - - End of Message Cleared out, ) & all right ) A/x/x/ \\\/ \ \\\\\\\\\ x/x/x/x \/ \\\ \/ \\/ \\/ \ Single Needle Instruments. 239 RULES FOR SPACING. The length of a dot being taken as unit. i st. A dash is equal in length to 3 dots. 2nd. The space between the elements of a letter is equal to i dot. 3rd. The space between two letters of a word is equal to 3 dots. 4th. The space between two following words is equal to 6 dots. The above rules are illustrated by the words below, "at the hour named " at the : | | : : | | i I | : : | | :::: O u : | I : : : : : : | | e d : : : : | | : : : : | | :. : : : | | : : | | : : : : : : N.B. For long circuits, especially underground wires, the dots must ' be made firmly and distinctly, thus, And not thus .... As dots are shortened by transmission through the Line, Clerks must make them a little longer and closer together than indicated. ( 240 ) RULES FOR SIGNALLING. i st. Give the Call Signal, and 2nd, the name of "Station to" and " Station from," with the letter V between them : thus if LY call MR MR V L Y M Manchester will reply, R G To get a word repeated, say _. _ To get remainder of Message repeated, say _ - - (word) all after_ If the whole must be repeated, or' you cannot read, send ? all. To signify all is understood, give To signify wait, give the Signal Wait ~ If you require wait for any time, send the number of minutes after Wait, thus : 5 _ .,_ Wait 5 minutes. To signify that you have made an error, give the correction signal repeat the last correct word, and continue. To signify that you have finished a Message, give- _ - (equivalent to PQ of Double Needle Alphabet). When you have cleared out, and want to signify everything is right, give Rides for Signalling. 241 Always give the Call Signal before sending anything, to give time to start the Machine ; thus, to give Understand Instead of the double-needle colon use - - ; and . instead of DQ. Initial letters must be separated by the full stop ; thus, J. W. Schcene would be sent J W S ch ce n e Ch must always be sent thus, _ , and never as c, h. Long lines must never be made : if necessary to hold on, give _ _ instead of a continuous line. All figures, doubtful words, and unknown proper names in a message, must be repeated back, followed by the _ . - signifying Is this correct P The Sending Station will reply if correct, and go on with the next message. Fractions are sent thus, 98 10 / 16 . 98 1 1 6 leaving a good space between the figures and the fractions; and in repeating them, spell the Enumerator always thus 9 8- ten 242 Rides for Signalling. 1 6 - _ _ _ _ ^_ (this is to ensure correctness). o n e 2 \ would be repeated &c. 100 ten th o us for brevity and for greater certainty. A good space must always be left between whole numbers and their 1 fractions; 1 15-1-5- would be sent thus ______ 1 5 1 1 5 - _ _ _ _ ..... to distinguish it from 1,151^ The Numerator 1 1 being spelled in the Collating. c o The word " couche " would be sent thus, . . n ch e When a Station does not read you, send the letters ... ... _ ... _ to enable him to adjust his Apparatus. In a circuit containing one or more translating Stations, if there be necessity for calling the attention of those Stations to the translators, give the letter h .... several times, which is to be understood by the Translating Clerk to signify that there is something wrong and re- quiring his immediate attention. Rules for Signalling. 243 The call for " all Stations " (C Q) is the letter s _ _ _ &c., given during one minute. When the number of words in a received message is incorrect, the Receiving Station must repeat the actual number to the Sending Station, thus : 2 If 28 W. be telegraphed, and only 27 received, say - ^ _ _ 7 w P 2 Should 27 be right, the Sending Station will reply, 7 ... _ _ _ _ _ _ _ but if there still be 28 words, the Sending Station will say 28 W., and repeat the first letters of every word, when the Receiving Station can easily detect the erro'r or omis- sion, and get the word repeated. N.B. For the Single Needle Alphabet, the Beat to the right \/ ) is equivalent to the ( ), and the Beat to the left (\) is equivalent to the dot ( ). The " understand," and not " understand," are the same as in the Double Needle Alphabet. The end of a word is expressed by a pause. In Single Needle, the code signals FI before, and IF after the figures are to be used (but not in printing). Figures are to be made very distinctly. N.B. As all Figures contain 5 signals, and all Stops 6, the receiver can read them off with great accuracy. The following Signals are much used on the Continent, though not (Officially recognised : Telegraph. - _ Drahtantwort. ia for ja or yes, and is used in place of and 244 Tables for Deciphering. Tables to assist the reading of Telegraphic Despatches. (Sir Charles Wheatstone, F.B.S.*) The same telegraphic alphabet has, by universal agree- ment, been adopted by all the countries of the world in which telegraphic communication exists. At present, its use is however almost exclusively limited to the clerks whose business it is to send and receive the messages. If it were deemed important or desirable that the message should be transmitted to the person to whom it was addressed in the exact manner in which it was received, so as not to incur the intermediate errors of translation, it would become necessary that the receiver should be acquainted with the language in which it was written. Now this is by no means a difficult thing to attain, and it would require but little time if resolutely set about. But the preliminary task of committing the meaning of the signs to memory, comparatively easy as it is, may be con- siderably lightened by a very simple expedient. To refer to a table of 26 characters in order to translate a despatch, letter by letter, is a very tedious matter, and the process may be much abridged by forming a table showing the formation of the more compound characters from the more elementary ones. Such a table can be much more rapidly referred to ; and it will be found that, by its aid, a telegraphic despatch can be read accurately without any previous knowledge, and without much loss of time. After a little practice in thus deciphering, the Tables for Deciphering. 245 meanings of the signs will, without any great effort, become fixed in the mind, and the messages be read in future fluently and without aid. i Element 2 Elements i a n m 3 Elements ; s u r w d k g o 4 Elements h V * ii 1 a P 3 b X C y z n O ch 246 Tables for Deciphering. The manner of using the above tables is as follows : The person wishing to translate the despatch commences at the first letter, noticing of how many elementary signs (dots or dashes), it is composed. When it consists of one element only, its meaning is given directly by re- ference to the first table ; when of two elements, by the second table, the first element on the left being found in the front vertical column, and the second at the heading of the columns containing the letters ; when the letter consists of three elements, it is found by refer- ence to the third table, the first two elements being in the front, and the last one at the head, of the columns ; when of four elements, the first two are found in the front of the fourth table, and the last two at the head of the columns. As an example, suppose we wish to translate the word . . . . Here the first letter consists of four elements; we look, therefore, in the corresponding table for the two first elements as they stand in order in the front, and find them opposite the second horizontal line of letters, which we follow across until at the head of the third vertical column we see the remaining two elements of the letter "/," which is written at the point of inter- section. The next letter consists of two elements, the first being a dot ; we refer to the table of two elements, and find the letter corresponding to be " a." The third letter has three elements, all dots ; we refer to the table of three elements, and find this to be "s." The fourth letter is a single dash, which the table of one element Tables for Deciphering. 247 informs us is "/." The last letter is also a single element, "^ s o ^ R . ..^or^O^r^O-^^Sa | .PH iH 4> 1 " g . . M0 ^r~0^^K r^ < ^ 3 r* u flj "8 O o . . oo ^1-sO O^^'^'S oo ?\ fS Ooo d g H. 5 Q o . .vOO^OCOO^-^sg^S^^aoTP ,0 3 c cfl ^ . o f ^^M Mvg^S ^"S S-ooTP?.i8 c c$ 0^00^^fwHW g g o M v\ M- o r-oo O * O ^> oo ooo g G VO r~^TC^ M M 55 "i o ^^O.S ^^-^^^-S gsg: RS , K,^-^ *-^fM M M | o ^r-soS'ftS'5^SJS,^55-S^S5 CO 00v0-f~sw M M -a o r^r^^2 I?P.^o7vo N 5^.2:^^^^ 3-S s rjO^f^N M M * 10 Nl^Tf-lH O^^lN O "tO\C> ~>M OOO \O *** O^WSNM MM ^!- d j ^S" CA) 18 Submersion Tables. 251 VMfvOO <7s*M N I^^VOOO 10M* OM^S 2" O^CO *-O IT ^wxf^M **???? . Jrrr^PT O CT>^< ^ M c ^ r4 O oo t~-O i^**t*f^sr4r4MMH]OOO T}- irvO r-OO C^O >i (4 iw, -^i 252 Data of Cables. ELECTRICAL TESTS OF VARIOUS Length Laid Diameters. Logarithm of CABLE. D (G.P. Core.) Date. Knots. Copper Core D ~d (approx.)* mils. mils. r. Persian Gulf . . . 1864 1148 no 380 53781 2. Atlantic .... 1865 1896 147 467 52763 3. Persian Gulf .... 1866 160 110 3 80 53781 4. Atlantic .... 1866 1852 147 467 52763 5. England and Hanover. 1866 224 87 280 -53 6 55 6. Placentia Bay and Syd-1 ney . 1 1867 Jri2T | \i88'7 / 102 348 55266 7. Cuba and Florida : Havannah to Key West| Key West to Punta Rassa/ 1867 (125-4 \ \n 9 -9 / 87 290 '5575 8. Anglo-Mediterranean . 1868 927 103 327 52763 9. French Atlantic. . .} Do. St. Pierre . . / 1869 / 2584 I 749 168 87 470 282 47129 -53655 10. British Indian : Suez- Aden ... .'I Aden-Bombay . . . j 1870 / 1461 \ i8 I7 92 H3 304 358 -54530 52763 ii. Falmouth and Gibraltar 1870 1431 92 304 54530 12. Gibraltar and Malta 1870 1025 92 304 "54530 13. Marseilles, Algiers and Malta : Marseilles to Bona . . 1 Bona to Malta . . . j 1870 /447'6 \378-4 87 87 272 2 7 2 50242 50242 14- Anglo-Mediterranean 1 Duplicate . . . ./ 1870 - 15 . .British Indian Extension 1756 92 304 54530 1 6. China Telegraph . . 2640 92 304 54530 1 7. British Australian . . 2526 92 304 54530 * The value of -j is increased 5% in these instances in which the con- ductor is a strand. Data of Cables. RECENT TELEGRAPH CABLES. 253 Resistance of Conductor at 24 Cent. Resistance of Dielectric at 24 Cent. Electro-static Capacity. Approximate Resistance when laid irrespective of temperature and pressure. Resist- ance per knot. Ohms. Specific Conduc- tivity, Pu. Copper = IOO. Resist- ance per knot, Meg- ohms. Specific Resist- ance. Meg- ohms-f Electro- static Capacity per knot, Micro- farads. Specific Inductive Capacity, Micro- farads.}: Resistance of Con- ductor, Ohms, per knot. Resist- ance of Dielectric. Megohms, per knot. Fao-Bushire 6*46 495* Bushire 7 , MussendumjO* 21 326- 6-25 84-79 I9O IOO2 0-3486 O66l Mussendum ) , Gwader { 6 '4O 342* Gwader | * ^Kurrachee J 6 '3 239- 4-27 93-09 349 1805 o-3535 0684 4-01 2945 6-oi 88-17 395 2084 0-3312 0628 . . 4-20 94-63 342 1768 o*3535 0684 3-89 2437 12*07 92-32 239 1213 0*3447 0679 11-71 IOIO 8-96 88-71 455 2237 0-3566 0725 [ Placentia & ) o . , - 1 St. Pierre J 8 32 1 St. Pierre & ) o . , , 4498 [ Sydney J tf > 4 4257 12-38 90-02 464 2270 0-3507 0717 / "'83 [ 12-37 1268 175*0 8'73 91-05 496 2565 0-4500 '0870 8-23 2631 3-16 94*33 235 I36l 0-4295 0742 2-93 5200 12*03 92-63 266 1350 0-3740 0737 II'I2 2910 10-42 95*35 329 l6 4 6 0-3580 "0716 IO-26 5700 7-02 94*36 278 1441 0-3610 '0696 6*52 1899 10-508 10-508 94*55 94*55 214 214 1070 IO7O 0-3645 0-3480 0729 '0696 | 10-13 1419 12-03 92-62 2/3 1482 0-286 0527 II-65 2329 12-17 9i*57 238 1291 0-286 0527 n-66 734 10-508 94*55 235 1176 0-3400 0680 10-907 91-20 194 970 0-2920 0584 ! ! ! '. 1 r The specific resistance is taken as that of a cube knot. t The specific capacity is taken as the capacity of a cube knot. This cable is made up of lengths of various cables. 254 Data of Cables. ELECTRICAL TESTS OF VARIOUS Length Laid. Diameters. /-I A T>T T7 Logarithm of UArJLiil,. (Hooper's Core.) Date. D 1? Knots. Copper d Core D (approx.) mils. mils. 1 8. Persian Gulf . . . 1868 525 JIO 309 46125 19. Anglo -Danish. 1868 365 no 290 43410 20. Anglo -Norwegian . 1869 240 no 290 43410 21. Moen Banholm . . 1869 82 80 241 '5373 22. Aland Cable . . . 1869 87 no 290 43410 23. Shetland Cables. . 1869 ( 69 I 9 80 110 2 4 l 290 50373 '43410 24. North China : Hong-Kong Shangai ] Shangai Posietta . . f 1870 f 1098 1 1 1198 I 147 3 I8 36169 Data of Cables. RECENT TELEGRAPH CABLES (continued). 255 Resistance of Conductor at 24 Cent. Resistance of Dielectric at 24 Cent. Electro- static Capacity. Approximate Resistance when laid irrespective of temperature and pressure. Resist- ance per knot. Ohms. Specific Conduc- tivity, Pu- Copper = IOO Resist- ance per knot, Meg- ohms. Specific Resist- ance. Meg- ohms. Electro- static Capacity per knot, Micro- farads. Specific nductive Capacity, Micro- farads. Resistance of Con- ductor, Ohms. Resist- ance of Dielectric, Megohms. 5 '60 93-64 3900 2580 0*349 0528 7'06 93-82 4430 2780 0-3680 0585 7-06 93-82 4500 2780 0-3680 0585 14-37 92-I9 400O 2I7O 0*3120 0576 7-06 93-82 4500 2780 0*3680 0585 14-37 7* 06 92-I9 92-82 4000 3890 2170 2440 0*3120 0-3690 0576 0587 4'23 93-96 4000 3O2O 0-4400 0583 Not yet laid. 2 5 6 MECHANICAL DATA OF VARIOUS CABLE. Date. Length laid. WEIGHT Copper. Insu- lator. Iron. Knots. Lbs. Lbs. Tons. i. Persian Gulf .... 1864 1148 225 275 3-060 2 Atlantic . 1865 1896 O " 6 2 2 3. Persian Gulf .... 1866 160 225 275 3-060 1866 18? 2 400 O " 632 5. England and Hanover 1866 224 107 150 \ 8-100 6. Placentia Bay and Sydney 1867 fri2-i \ \i88- 7 / 150 230 2" 150 7. Cuba and Florida . 1867 Havannah to Key West . | Key West to Punta Rassa/ - (125-4 \ \ri 9 -9 / I0 7 166 2"IOO 8. Anglo-Mediterranean . . 9. French Atlantic 1868 1869 927 150 200 Brest St. Pierre . . . . 1 r r y 795 5> 55 ' .. 2584 400 400 4*605 J 55 ' .. 1 I '79 St. Pierre Duxbury .. 1 (14-972 55 55 .. [749 107 150 4-753 55 55 .. 1 ( i"949 IO. British Indian .... 1870 Suez Aden .... . . ( 9*758 . . . . 1460*66 I2O 175 j i:in Aden Bombay . .. ( 9-759 55 55 ... 1 1 1 1 - 705 55 '5 ... ^1817-43 1 80 240 i 5-429 55 55 ... 1 i 2*851 55 55 ... J ( 1*186 II. Fal mouth and Gibraltar . 1870 Falmouth Lisbon . .. 27-75 1 2O !75 10*604 55 55 .. 144-80 .. .. 3-018 55 55 .. 6 5 1 06 .. .. 709 Lisbon Gibraltar . 12-00 120 175 10-604 5 55 .. 15 "oo .. .. 3-018 5 55 ' .. 274-00 .. .. 923 5 55 * * .. 45-00 .. .. 5-917 12. Gibraltar and Malta . . 1870 4-00 120 175 10-604 5 55 ' * 251-97 .. 3-018 ) J 846-29 .. .. 923 5 55 * 2-81 " 5-917 257 RECENT TELEGRAPH CABLES. PER KNOT. REMARKS. Hemp. Asphalte, Complete. Tons. Tons, Tons. .. .. 3*73 -80 55 None .. .. 3*73 -8055 None J "75 *3396 637 18-49 Shore ends. 4000 2-080 10-94 Main. 1804 None 2-50 (Placentia and St. Pierre, \St Pierre and Sydney, 2782 None 2*50 2I 7 2TIJ 20-447 Shore ends. 368 921 6-246 Intermediate, 104 487 1*652 Main, I0 9 1-563 16-760 Shore ends. -528 8 79 6-276 Intermediate. 1095 700 2*875 Main. 540 Q 2 " 11*412 Shore ends. "33 3-286 Intermediate, 189 "459 2*712 Main, -725 146 -325 i -080 698 691 "'737 12*737 6-633 Shore end (Aden). (Bombay), Intermediate (No. i). 083 "345 3*414 (No. 2). 146 -352 1*872 Main, 725 1-080 11*737 Shore ends. 090 350 3-420 ist Intermediate, M04 487 1*652 ist Main. 725 i -080 "*737 Shore ends. '090 350 3-420 ist Intermediate. 063 244 **535 2nd Main. 325 691 6-633 2nd Intermediate. 725 1-080 11-737 Shore ends. '090 350 3-420 ist Intermediate, 063 -244 I% 535 2nd Main. 325 691 6-633 2nd Intermediate, MECHANICAL DATA OF VARIOUS WEIGHT CABLE. Date. Length laid. Copper. Insu- lator. Iron. Knots. Lbs. Lbs. Tons. 13. Marseilles, Algiers and\ Malta / 1870 i Marseilles to Bona . . . . 16 107 166 IO'6O4 .. 486 1-054 .; Bona to Malta ... . . 24 107 166 10*604 99 >? * . . 336 a , 1*211 14. Anglo-Mediterranean Du-\ 1870 15. British Indian Extension . 1870 Penang Singapore . . .. j ; 9-518 .. [i447'i7 120 175 2-696 .. 1 2-761 Penang Madras. ;; } 387 I2O J 75 5-113 I f099 1 6. China Telegraph . . , I 9'5!4 > ... .. . 1632 107 140 2-831 > ... .. 1 1-913 $7. British Australian . . , 1870 Batavia and Singapore . > [ 579 107 140 / 9*5i4 \ 2-831 Batavia and Port Darwin .. .. 107 140 9'5i4 > - .. .. .. .. 1-193 1 8. Persian Gulf .... 1868 5 2 5 225 200 3*06 19. Anglo- Danish . . . 1868 365 1 80 1 80 2-40 20. Anglo-Norwegian . . . 1869 21. Moen-Banholm. . . . 1869 240 82 1 80 9 180 130 2*40 22. Aland Cable . . . . | 1869 87 180 1 80 2-40 2^. Shetland Cables . . . 1869 / 69 I 9 90 1 80 130 180 1-04 6*00 44. North China .... 1870 Hong-Kong Shanghai . .. 685 300 200 -10 > .. 272 .. .. 10 5> J .. in .. .. 60 > .. 30 .. .. *5 2 Shanghai Posietta . .. 990 300 200 jo 5 > - .. 92 .. .. 40 96 .. .. 6-60 ' ' 20 1-52 259 RECENT TELEGRAPH CABLES continued. PER KNOT. REMARKS. Hemp. Asphalte. Complete Tons. Tons. Tons. 725 I '080 II'737 Shore ends. 140 346 1-864 Main. 725 I'oBo 11-737 Shore ends. I 5 3 60 I -880 Main. 587 108 1-304 '443 11-521 3*375 Shore ends. Intermediate. 122 385 3*397 Main. 273 810 6-331 Shore ends. 066 * 3 47 1-541 Main. 666 1*371 11-412 Shore ends. 103 *443 3-286 Intermediate, 259 "459 2-712 Main. 666 1-371 11*665 Shore ends. 103 "443 3-490 Main. 666 1-371 11-665 Shore ends. 107 *393 1-796 Main. .. 3'73 . . -. .. 3-00 . . 3-00 . . " 3-00 J 45 260 1-64 . , 250 450 6- 95 . . . .. 1-50 Section A Hooper's India-rubber. . 3-00 , B . mi 8-00 , c . .. 18-00 , D . .. 1-50 A . 3-00 B . 8-00 , c 18*00 . D j INDEX. ABSOLUTE measure, determination of capacity in . ; . .. 61 ,, units, formulae of . . . . . 1 Absorption or electrification ... . . -7 ,, of water by insulators . . . . . 167 Accumulation joint test . , , - . 4 1 test . . . . . . .59 Accumulators or condensers ...... 69 Clark's 69 ,, ,, Smith's ..... 69 Varley's . ... 69 Acid, specific gravity of nitric . , , . . 101 - ,, ,, of sulphuric . , . . IOO Actual speed attained in working cable .... 80 Air, correction of throw for . > . - . , . - . 84 ,, weight of a cubic foot of , . , . . .183 Airy; submersion of cables . , , , . .151 Alphabets for printing and gingle-needle instruments . 336-238 Amalgam for electrical machines . . . . 22a Angle of descent of cable , . , . . . .150 Asphalte covering of cables - 146 Atlantic Cable, 1865, rate of working through , . .75 B. A. units 3 Bain's telegraph, printing solution for . , . . . 223 Balance, Wheatstone's . , y , . 23 Barometer , 1-83 vertical heights by . . . . 184, 185 Batteries, comparison of .90 ' Clark's method - . . * ' . 93 262 Index. PACK Batteries, comparison of, Law's method .... 94 ,, ,, method of equal deflections . . 9 ,, method with shunts . . 9 1 > Poggendorff's method . . 9 1 ,, Wiedemann's method ... 90 ,, Wheatstone's method . . 9 1 ,, when resistance of unknown . . 92 distribution of, to obtain maximum current . . 94 telegraphic ....... 95 ,, bichromate of potassium ... 96 ,, Daniell's ... -95 Faure's 95 Leclanche's 95 ,, Marie Davy's 95 ,, Minotti's. . 95 Beetz; laws . . 16 Binding wire ......... 146 Biot and Savart ; laws 18 Bituminous compound, Clark's ...... 146 Black cement for insulators . . . . .223 Bosscha j laws. ........ 13 Bound and free charge 22 Breaking- weight of copper wire . . . . .104 ,, of iron . . . . . .139 British Indian Cable, rate of working through ... 75 B. W. G ... 190 Cables, external diameter of 143 ,, faults in submerged ...... 47 ,, faults in 41 ,, paid out at different angles, tension of . . 151 ,, rates of working through 73 ,, speed of waves in . ...... 81 ,, submersion of ....... 15 ,, table of actual speed attained . . . , .'. ^ 80 ,, table for reducing weights of . . . . .172 Cable tanks, capacity of I54> 155, 1 S 6 to find length of 168 ,, when paying-out stopped, tension of . . . . 15 Capacity, B. A. unit of 4 of cable tanks 154,155,156 Index. 263 PAGE Capacity, comparison of electro-static ..... 62 ,, of cube foot of G. P 121 ,, of cube knot of G. P. 121 of a plate of G. P .121 ,, of a plate . . . . . . . .68 ,, of a cube knot ....... 68 ,, De Sauty's method of comparing . ... 62 ,, determination of, in absolute measure . . .61 of G. P. core . ... . . . 115 ,, Varley's method 63 ,, from insulation and fall of tension ... 65 ,, of two condensers or cables combined ... 66 ,, of a knot of cable ...... 66 , , of insulators (table of) , , . . .67 of an insulated cylindrical conductor . . .67 ,, of a plate .... . . . 67, 68 of a cube foot 121 ,, of a cube knot 121 ,, of plate of G. P. . . ... .121 of Smith's G.P 124 ,, by swing of needle . . . . . .64 Cement, black 223 ,, electrical . . . . . . . . 222 ,, for insulators . . . . . . . 223 ,, Muirhead's 223 ,, Siemens' . . . . . . . 223 Centimetres in inches, table of .. .. .. .211 Centre lines of sheathing wires, table of .... 149 Charge, laws of electro-static . . . . . .21 ,, free and bound 22 insulation by loss of 35 ,, electro-static . .... . .70 loss of, by G. P. cores 120 Chatterton's compound, composition of .... 148 Chemical equivalents of elements . . . . .188 Chromate of potassium element 96 Circle, measure of . 213 Circuits, shunt and derived . . . . .30 Circular current, effect of, upon a magnet .... 84 Clark's compound . . . . . . . .146 i, ,, -composition of ..... 146 264 Index* PAGE Clark's compound, specific gravity of . . . . 146 ,, to find weight in a cable . . . . 147 ,, ,, weight of . . . . . . 146 ,, method of comparing batteries .... 92 ,, potentiometer . ... . ... 92 Coils, magnetizing powers of . . . . . .21 Common logarithms, table of ..... 227-233 Compound, Chatterton's ....... 148 Claries .146 Coefficients for pure metal wires. ..... 105 Coefficients for temperature . . . . : , 186 Comparison of electro -static capacities . . . . 62 Condensers or accumulators . . . . .69 Clark's . . . . . 69 ,, Smith's . . . ... 69 Varley's .... . .69 Conducting powers of pure metals, coefficient of . . . 105 and resistances , . . . . . 186 ,, coefficients for temperature . . . 186 , ,, solutions 187 Conductivity of copper wire, to calculate .... 106 >, ,> to measure .. . . . 106 of iron wire . . . . . 140 Conductor, heat produced in a . . . , . . 103 ,, rupture of .... . . . .60 Constant galvanometer deflection with one cell and one megohm * . . 8$ ,, ,, resistance which produces unit deflection 86, 87 Constants of galvanometers ...... 85 Contact between two overhead wires, to find . . 53, 54, 55 , v a wire and earth ..... 56 Continuous testing ........ 50 Copper 103 ,, at fault, exposure of ...... 52 ,, breaking-weight of . , . . . ,104 conducting power of 105, 106 ., ,, powers of various kinds . . , .113,, diameter of conductors . . . . . 104 ,, Hooper's tinned wire . . . . . .112, ,, percentage decrement in conducting power . . ioS, j, , resistance in ohms of 9. knot pound . .. , .no Index. 26$ PAGE Copper, resistance of, per mile ... . . . .104 ,, specific gravity of . , . . . . . 103 ,, table of resistances for different temperatures . 106, 108 ,, ,, of resistances of pure wires .... 109 ,, ,, of yards per Ib. for small wires . , .ill to find the weight for a given speed of signalling . 107 .,, weight per mile . . . . . . . 104 ,, wires, weight of strand of No. 1 6 . . . .ill ,, ,, ,, of strand of No. 22 .... na Corrected resistance of line . . . . 57 Correction of throw for air . . . . . . 84 ,, for deflection in Wheatstone's bridge . . .29 ,, for different readings -f and currents in Wheat- stone's bridge. ....... 29 , , for Murray's loop method ..... 42 , , for strand conductor ...... 40 Corrections for loop methods ...... 44 Cosines, table of natural . ....... . 214, 215 Cotangents, table of natural . . . . . 216,217 Coulomb ; laws ........ 17 Course of ship .. ... . . . . 169 Culley ; contacts between line wires, &c. 55, in, 144, 177, 223 Current, B. A. unit of ....... 3 ,, heat produced by ......... . . 103 ,, Jacobi's unit of ....... 102 ,, maximum . . . . .94 ,, permanent through insulation . . . .70 ,, which produces unit deflection .... 88 Currents, steering across 164 ratio for strand and solid conductors ... . 40 Daniell's element . . ... . . . . 95- Dayman, Commander ; height and velocity of waves . . 186 Decimal equivalents of inches,. &c. . . . . .191 Deep sea sounding, velocity of descent . . . . 163 Deflection, insulation of cable by . . . . 31 ,, with one cell and one megohm . . . . 85 ,, current which produces unit of . . . . 8& ,, resistance which produces unit of . - . 86,88 Derived magnetical units . . . . .. ........ -.* I 266 Index. PAHS Derived mechanical units . . . . ; \-f-:?.^i4 ,, circuits and shunts ...... 30 Be Sauty's method for comparing electro-static capacities . 62 Descent of cable, angle of . . . . . . .150 of lead weights in the sea 163 Descriptions of sound . . . . . .159 Determination of capacity in absolute measure . . 6 1 Development of heat and work ...... 9 Diameter of copper wire calculated from weight . . . 104 ,, of G. P. calculated from weight . . . .114 external, of submarine cables, table of . . , 143 ,, of iron wires ....... 140 ,, of iron-covered cables 140 ,, of centre lines of sheathing ..... 149 ,, table of squares of ..... 218-221 Difference of time between places . . . . . 1 70 Different reading with + and - currents in Wheatstone's balance ......... 29 Differential method, insulation by 33 ,, galvanometer for comparing capacities . . 63 Distance of fault by tension . . . . , .49 ,, of visible objects at sea. . . . .157 >y , table .... 158 ,, from shore ........ 159 ,, from ship to shore by sextant . . . .160 Dub; laws 18 Dynamic electric circuits, laws of . . . .12 Earth and wire, contact between ..... 56 Earth's magnetism, horizontal component of . . .18 Edlund ; laws ......... 14 Effect of a circular current on a magnet .... 84 Electrical cement . . . ... . . 222 ,, machines, amalgam for ..... 222 ,, units of measurement ..... 3 ,, resistance, various units of . . . . . 5 table of ... a ,, tests of recent submarine cables, tables of . 252-254 Electrification of French Atlantic core at different temperatures 72 ,, notes on ....... 70 ,, . Smith's G, P, core ... . , . 124 Index. 267 PACK Electro-chemical unit . . . . . . * 5 Electrolysis . . IO2 Electro-magnetic system of units . . . . . I Electro-magnetism, laws of . . . .18 Electromotive force, B. A. unit of 3 ,, ,, Grove's element ..... 97 ,, ,, of elements formed by amalgams . . 97 ,, ,, of elements when heated ... 98 of useful elements .... 99 Clark's method 92 ,, Law's method ..... 94 . ,, . measurement of . . . . .90 ,, method of deflection .... 90 ,, method with shunts . . . 9! ,, PoggendorfFs method . . . 91 ,, Wheatstone's method . . . 91 ,, When resistance of battery is unknown . 92 ,, Wiedemann's method . . .90 Electro-static capacities, comparison of . . .62 ,, De Sauty's method . . . .62 ,, ,, from insulation and fall of tension . 65 ,, ,, method of swing .... 64 ,, specific . .65 ,, table of 67 ,, ,, of two joint cables or condensers . 66 ,, ,, Varley's method .... 63 ,, capacity of a cube knot . . .68 ,, of an insulated cylindrical conductor . 67 ,, of G. P. Core . . . . . 115 ,, of a plate . . . . 67, 68 charge .... . 70 ,, laws of 21 system of units 2 Element, chromate of potassium 96 ,, DanielPs . . 95 Faure's 95 ,, Leclanche's . . . ... -95 ,, Marie Davy's 95 ,, Minotti's . . ... . . . -95 Elements, arrangement of, to obtain maximum current . . 94 formed by amalgams . , . .... . . 97 268 Index. PAGE Elements, electro-motive, forces of useful . , ... 99 ,, when subjected to heat ..... 98 Elementary bodies, symbols, equivalents and specific gravities of 188 Elimination of leading wires on Wheatstone's balance . % 28 Equivalent, electro-chemical . . , . , 5 ,, of heat , . . . . , . . -4^. Equivalents of elements , , . . .... .188 Esselbach ; insulation of cable by loss of charge , . 3^ Exposure of copper at fault . , . ... .52 External diameter of submarine cables , . , .143 Extra material required by twisting helically , . , . 1 73 Fall of tension, insulation and inductive capacity from , , 65 Farad 4 Fault, distance of, by tension . , . , , .49 , , exposure of copper, at . . , . . 52 ,, resistance of . . . . . , , .49 ,, resultant ; in insulated wire 46 ,, in cable , , , . . . , .41 ,, jn line wires . . . . ... .53 in short lengths of insulated wire . , , .57 ,, in submerged cable . . . , . , -47 ,, Warren'g method of detecting . , , .58 Faure's element . , . , ,. , , -95 Figure of merit of galvanometer. . , . , .85 Force of waves , , , , . , , . 167 ,, of wind ...,.,.. 183 ,, unit of . , , . . . . . , . . . . . 2 Forde ; table for reducing weights of cables . , . 1 72 Formulae of absolute system of units, , . , , . ... . I Free and bound charge . , . . , , .22 French, and English measures ...... 209 ,, .Atlantic core, electrification of, at different temperatures 72 ,, unit of resistance , . .... , . 6 Fuller; resistance of copper wire , - . . , no Fundamental electrical units I Galvanic circuits, laws of . , , . , , . 12 ,, elements subjected to heat , . f , , 98 Galvanoscope, ordinary .,,... , , . , . . .83 Index. 269 PAGB Galvanometer constant deflection with one cell and one megohm . . . . . . . '85 M figure of merit ...... 85 ,, in Wheatstone's balance, sensibility of .24 method of vibration with . . . 83 . resistance, method of measuring ... 84 resistance which produces unit deflection . 86, 87 Galvanometers ......... 82 and shunts . .... . . 3 ! ,, constants of. ...... 85 ,, mirror ....... . 82 ,, sine .... . . . . .82 ,, tangent . . . . . . .82 Gas developed by current 102 Gauss ; laws . . . .... . 17 German mile, unit of resistance ...... 7 Glass, half- minute, and log line . . . . . .170' Glue, marine . ........ 223 Greatest distances of visible objects at sea 157 table of. . .158 Grove's element, electro-motive force of . . -97 G. P. and shellac condensers ...... 69 ,, cables, speed of working through .... 75 core ratio -^ ....... . . .40 1 1 decrease of resistance with temperature . . -US table of 1 16, 117, 118,119 M dimensions and electrical values of cores . . , 123 ,, electro-static capacity of . . . . . .115 ,, exterior diameter of . . , . . . .114 ,, loss of charge of ....... 120 ,, resistance and capacity of cable cores . . 122 ,, ,, of cube foot .... 121 of cube knot . . .121 of plate 12 1 ,, specific gravity of . . . . . , , 113 ,, (Silvertown), table of coefficients for . , . 128 ,, temperature and loss . . . . . .121 weight of cylindrical band . . , , , 1 14 per knot 114 Willoughby Smith's improved . . . . , .124 270 Index. PACK G. P., Willbughby Smith's improved electro-static, capacity of 124 ,, ,, ,, . table for temperature 125, 126, 127 ,, . ,, ,, mechanical strength of. 124 ,, ,, . ,, resistance at 75 F. of . 124 ,, . ,, ,, specific gravity of. . 124 Hall; table, of resistances of pure copper wires . . . 109 Harris j electrical cement . . . . . . . 222 Hawkins ; table of coefficients for reducing Silvertown gutta- percha , . . . . . . . . 128 Heat and work, development of 9 ,, galvanic elements subjected to . . . .98 . ,, produced in a conductor by a current . . . . 103 unit of . ... . .... . . 4 Height and velocity of waves 168 ,, . by barometer, to measure . . . . 184, 185 Helical twist, extra material required for 173 Hemp ........ -135 ,, ropes ....- . 136 ,, serving in a cable, weight of , . . . .136 Hockin ; correction for Murray's loop method, &c. 42, 86, 118 Hooper's cable, speed of working through .... 76 D ,, core ratio =. . 40 india-rubber, capacity per knot .... 129 ,, . coefficient of temperature of . . 131 resistance compared with G. P . . 130 diameter of core .... 128 effect of temperature on . . . 130 electro-static capacity of cube foot . 132 ,, ,, of cube knot . 132 ,, ,, of plate . . 132 resistance at different temps., table of. 132 ,, of a cube foot . . . 132 , r of a cube knot . . . 132 ,, of a plate .... 132 ,,. per knot .... 129 specific gravity of . . .128 table to find resistance after one minute and capacity per knot ..... 133 Index. '271 PACK Hooper's india-rubber, weight per mile . " . . . 128 ,, tinned copper wire . 112 Horizon, distance of visible, table of ... . . .158 Horizontal component of earth's magnetism . . . .18 India-rubber, capacity of a cube foot , . . . .132 ,, ,, of a cube knot ...... 132 of a plate . 132 ,, per knot of 129 ,, . coefficients for temperature . . . . 131 ,, effect of temperature on Hooper's . . .130 ,, exterior diameter of core. .... 128 ,, relative resistance at different temperatures . 132 resistance of a cube foot ..... 132 ,, ,, of a cube knot . . . . .132 ,, of a plate 132 ,, ,, per knot of , ..... 129 ,, specific gravity of ..... . . . 128" ,, table of comparisons with G- P. . . .130 ,, weight per knot of. . . . . .128 Induction and resistance of insulators, relation between . . 68 ,, volta, laws of . . ..... . .14 Inductive capacity from insulation and fall of tension . . 65 Insulation and fall of tension, inductive capacity from . . 65 ,, by differential method . . . . -33 ,, by loss of charge ...... 35 ,, of cable by deflection . . . . . 31 ,, resistance . . . 31 ,, specific .... -37 Insulated wire, faults in short lengths of . . . . 57 ,, resultant fault in , . . . .46 Insulators, absorption of water by . . . . . .167 ,, cement for . . . . . 223 ,, relation between resistance and induction . .68 Iron .......... . . . 139 ,, binding wire ........ 146 ,, breaking weight of . . . . . . 139 . ,, conductivity. of. . 140 ,, (Culley) table of wires 144 ,, diameter of cables . ... . . . . 146 ,, diameter of wires . . . . . . 146 272 Judex. PAGB Iron, specification for overhead lines . . . . 145 ,, specific gravity of ... . . . . 139 ,, stranded wires ...,..-.. 144 > table of external diameters of cables . . . .143 ,, ,, of sizes and weights of wires . . . .142 ,, weight of wire in a cable ...... 140 table of . . . .141 Italian hemp . . . 135 Jacobi's unit of current . . . . . . .102 ,, ,, of resistance ....... 5 Jenkin ; relative values of various units of electrical resistance, &c 8, 186 Joint electro-static capacity of two cables .... 66 ,, resistance of galvanometer and shunt , . , .31 ,, tension of two condensers or cables .... 66 ,, test by accumulation . . . . . 41 Joule's equivalent of heat . . . . . 4 ,, laws of heat 9 Kilogrammes in pounds, table of . . . . .212 KirchhofPs laws 12 Knot cube of insulating material . . . . 68 ,, of cable, specific capacity of ..... 66 Knots in degrees of longitude ...... 209 ,, into statute miles, table of . . . . .192 Laws > Joule's ...... ... 9 ,, Ohm's 10 Kirchhoff's 12 ,, of dynamic electric circuits . . . . .12 of electro-magnetism . . . . . .18 ,, of electro-static charge . . . . . .21 ,, of magnetism . ...... 16 ,, of volta induction . . .... . .14 Law's, J. C., method of comparing batteries ... 94 Leading wires in Wheatstone's balance, elimination of . . 28 ,, to test . 60 Lead weights, velocity of descent of . . . . .163 Leakage of insulating material ...... 70 Leclanche's element , 95 Index. 273 PAGE Length of cable, to find . . ' . ' " . . . 168 Leuz ; laws . . . . - . . . 15* *9 Line, contents of telegraph poles . . . . .178 ,, corrected resistance of . . . . -57 ,, statistics. ........ 180 Line wires, faults in . . . . . . -53 ,, solder for ....... 223 Lines for deep sea sounding 164 ,, measures of lengths . . . . . . 179 ,, overhead . . . . . . . 173 ,, strains of . . . . . . . . 173 table of 177 Log line and half-minute glass . . . . . .170 Logarithms . . . / . . . . . . 224 ,, common table of . . . * . 227-233 ,, Napierean ....... 224 table of 226 Longitude, degrees of, in knots ...... 209 Longridge; strain during submersion . . . . -153 Loop method, Murray's . . . . . . .41 ,, ,, ,, correction for . . . . .42 ,, Varley's .... -43 ,, test, correction for . . . . . . .44 Loss of charge by G. P. core . . . . . .120 ,, ,, at different temperatures . . 121 ,, insulation by ...... 35 ,, of tension ........ 39 Low water, to reduce soundings to . . . .162 Magnetical units, derived . . . . . . I Magnetising power of coils . . . . . .21 Magnetism, horizontal component of earth's . . .18 ,, laws 16 Manilla hemp ......... 135 Marie Davy's element ....... 95 Marine glue . . . . . . . . . 223 Materials, weights of . . . . . . .189 Matthiessen's unit of resistance ...... 7 Maximum current ........ 94. Mean horizontal component of earth's magnetism 18 Measurement, electrical units of . . . . . .3 2/4 Index. PAGE Measurement of electro-motive forces ..... 90 Measures: centimetres to inches, table of ..... .211 ,, French and English 209 ,, kilogrammes to pounds, table of . . . .212 ,, of lengths of overhead wires . . . 179 ,, of the circle 213 ,, of metres in feet, table of . . . . .211 Mechanical effect, unit of . . . . . . -2 ,, equivalent of heat . . . . . -4 ,, performance, unit of ..... 2 ,, units, derived ....... I Megafarad . . . . . . . 4 Megaveber ......... 4 Megavolt . . . . . . . . 3 Megohm / . . . . . . .3 Menzzer ; magnetising power of coils . . . . .21 Mercury unit ......... 6 Metals and fluids, polarization of . . . . .98 Method of continuous testing ...... 50 ,, of vibrations ....... 83 Mica condensers ........ 69 Microfarad ......... 4 Microhm . . . . . . . . . 3 Microveber . . . . . . . . -4 Microvolt . . . . . . . .3 Miles, statute, into knots . . . . . . .193 ,, to kilometres, table of . . . . .210 Minotti's element ... . . . . -95 Mirror galvanometer ....... 82 ,, system, tables of working speed with . . 77, 78, 79 Molesworth ; weight of cubic foot of air . . . .183 Morse alphabet 236-238 ,, ,, Wheatstone's tables for deciphering . . 244 Muirhead's cement ........ 223 Muller ; resistance of metals at high temperatures . .188 Murray's loop method ... ... . .41 ,, ,, correction for . . . . .42 Muschenbrock ; laws . . . . . . . 17 Napierean logarithms ....... 224 table 226 Index. 275 PAGE Natural cosines, table of . ... . . 214, 215 ,, cotangents, table of 216, 217 sines, table of . . . . . 214, 215 tangents, table of 216,217 Needle, method of swing of .... .64 Nickles; laws 20 Nitric acid, specific gravity of . . . . . IOI Notes on electrification ....... 7 Ohm (laws) 10 ,, unit of resistance ..... 3 Ordinary galvanoscope ....... 83 Overhead lines . . 173 ,, contents of poles . . . . .178 ,, measures of length of various countries . -179 solder for 223 ,, statistics of 180 ,, strains of ..- .173 table of 177 ,, to find contact between , .53, 54, 55 Paper and paraffin condensers . . . . . .69 ,, insulating varnish for ...... 222 Paraffin and paper condensers ...... 69 Parallel circuit, resistance of . . . . 3 1 ,, shunt circuits . ... . . . -3 Paying out, angle of descent . . . . . .150 ,, at different angles, tension of cables . . I 5 I ,, tension on cable when stopped -. .15 ,, to ascertain slack . . . . I5 1 table of .152 ,, strain during ....... 153 ,, velocity of sinking . . . . . .150 Performance, mechanical unit ...... 2 Permanent current through insulator . . . *. . .70 Plate, electro-static capacity of ... . . . 67, 68 Poggendorff 's method of comparing batteries . . .91 Polarization of metal and fluids . . . . . .98 Potential ; B. A. .unit of . , 3 Potentiometer, Clark's. . 92 Printing solution for Bain's telegraph ..... 223 276 Index. " PAGE Quantity, B. A. unit of . . . * * Y 4 Rates of working through cables . . . . . -73 Ratio-j 40 Recipes, sundry ........ 222 Reciprocals, table of . . . . . . .191 Relation between resistance and capacity . . . .121 ,. ,, ,, ,, of Hooper's material 133 ,, of resistance ; sensibility of galvanometer . .24 Relative electrical values of G. P. cores . . . .123 ,, resistance of Smith's G. P. at different temperatures 125, 126 ,, speed of working similar lengths of cable. . . 80 ,, values of resistance units ..... 8 Resistance and capacity after one minute, table of, for G. P. . 122 ,, ,, per knot of material, table of . . 133 ,, ,, relation between . . . .121 ,, and induction of insulators, relation between . 68 and loss of charge, table of . . . . .38 ,, B. A. unit of 3 , , electrical, various units of . . . . .5 table of ... 8 ,, in ohms of a knot pound of copper wire . . HO ,, of a cube foot of G. P 121 ,, of a cube knot of G. P 121 ,, of a plate of G. P 121 ,, of copper at different temperatures, Fahrenheit . 106 ,, ,, ,, ,, Centigrade . 108 ,, of fault 49 ,, of galvanometer, method of measuring . . . 84 ,, of G. P. core 115 ,, ,, in various temperatures 115, 116, 117, 118, 119 ,, ,, underpressure. .... 115 ,, of insulation . . . . . . 31 ,, specific 37 ,, of iron wire ....... 140 ,, of line composed of wire of different gauges . . 57 ,, of line corrected . . . . . 57 ,, of parallel circuits . . . . . .31 ,, of pure copper wires, table of . . . .109 Index. 277 PAGE Resistance per knot of Smith's G. P, core . . . .124 ,, per mile of copper wire . . . . 104, 105 ,, units, relative values of ..... 8 ,, which produces unit of deflection . . 86,87 Resistances and conducting powers of metals . . .186 ,, of metals when heated . . . . .188 ,, sulphuric acid .... .187 Resultant faults in insulated wire ..... 4^ Rules for signalling 240-243 spacing . . . 239 Rupture of conductor ....... 60 Russian hemp . ........ 135 Sabine, method of eliminating leading wires ... 28 ,, elements subjected to heat ..... 98 Salt, specific gravity of solutions of . . . . . 101 Schwendler ; sensibility of galvanometer . 24, 29, 44, 46, 54, 57 Scudamore ; statistics . ... . . .180 Sea water 166 ,, pressure of 166 ,, specific gravity of . . . . .166 ,, temperature of . . . . . . .166 Sensibility of galvanometer in Wheatstone's balance . . 24 Sextant, to find distance by . . . . 160 Sheathing wires, diameter of the centre lines . . . 149 Shellac and mica condensers ...... 69 ,, and parrafnn condensers ..... 69 ,, varnish for glass ....... 222 Ship, course of .... 169 ,, to shore, distance by sextant . . . . .160 Shore, distance from, measurement by sound . . 159 Short length of insulated wire, faults in . . . -57 Shunt, to prepare any given . . . . . 31 Shunts and derived circuits ...... 30 ,, and galvanometers . . . . . . 31 Siemens' cement for insulators ...... 223 ., mercury unit ....... 6 Signalling, rules for . . . . . . . 240-243 Silk, insulating varnish for ...... 222 Silvertown, table of coefficients for G. P. .... 128 Sine galvanometer ........ 82 278 Index. PAGE Sines, table of natural 214, 215 Sinking, velocity of . ... . . . . .150 Sizes and weights of iron wire, table of .... 142 Slack, to ascertain . . . . . . . 151 table of 152 Smeaton ; velocity and force of the wind . . . .183 Smith, Willoughby, capacity per Knot of prepared G. P. . 124 ,, ,, mechanical strength of prepared G. P . . 124 ,, ,, method of continuoxis testing . . . 50 ,, ,, resistance per knot of prepared G. P. . 124 ,, ,, specific gravity of prepared G. P. . .124 , , , , table of relative resistance at different temperatures . . . . . . . 125, 126 ,, ,, table to find resistance and capacity of core 127 Solder for overhead wires ...... 223 Solutions of common salt, sp. grs. of ..... 101 ,, conducting powers of . . . . . .187 Sound, descriptions of . . . . . 159 ,, measurement of distance by . . , . , . .159 ,, velocity of ........ 159 Soundings . . . . . . . . .162 ,, lines . .164 ,, to reduce to low water . . . . .162 ,, velocity of descent of lead weights . . .163 Spacing, rules for ........ 239 Specification of iron wire .... . . . . 145 Specific capacity of insulating material . . .66 ,, insulation resistance ... . . -37 ,, gravity of Clark's compound . . . . . 146 ,, ,, of copper wire ...... 103 ,, ,, of diluted sulphuric acid .... 100 G. P. 113 ,, ,, of iron . 139 ,, ,, of pitch ....... 146 ,, ,, of silica ....... 146 oftar 146 ,, ,, of Willoughby Smith's G. P. . . .124 ,, gravities of acid solutions ... . . 101 ,, ,, of elements ...... 188 ,, of salt solutions ..... 101 Speed of signalling, weight of copper required for given . 107 Index. 279 PAGE Speed of waves in cables . ... . . .81 ,, of working 1865 Atlantic cable .... 75 ,, ,, British Indian cable .... 75 ,, ,, through G. P. cables . . . -75 ,, ,, ,, Hooper's cable .... 76 Speeds attained in working existing cables .... 80 Speeds of working similar lengths of cable, relative . . 80 Squares of diameters, table of ..... 218-221 ,, table of . . . . . . 218-221 Statistics of some telegraph systems . . . . .180 Statute miles into knots . . . . - . .193 Stays and struts, positions of . . . . .174 Steering across currents . . . . . . .164 Strains of suspended wires. .... 173 ,, on cables, table of 250 Stranded wires . . . . . . . . 144 Strength, mechanical, of Smith's G. P 124 Submarine cables, external diameter of .... 143 Submerged cables, faults in ...... 47 Submersion of cables . . . . . . .150 ,, angle of descent . . . .150 ,, slack during .... 151, 152 ,, strain during . . . . . 153 ,, tension of, at different angles . . 151 ,, ,, when stopped . . .150 ,, velocity of sinking . . . .150 ,, tables of strain on grapnel rope . . 248 ,, ,, cables . . .250 Sulphuric acid, resistance of ...... 187 ,, ,, specific gravity of diluted . . . 100 Sundry recipes. . . . . . . . . 222 Suspended wires, strains of . . . . . -173 Swiss unit of resistance ....... 6 Symbols of elements . . . . . . .188 Tangent, galvanometer . . . . . . . 82 Tangents, table of natural . .. . . . 216, 217 Tarred hemp . . . . . . . . 135 Taylor, H. A. ; correction for loop test .... 45 Telegraph batteries ........ 95 Temperatures, electrification at different . . . -72 28o Index. PAGE Tension, B. A. unit of .... . . . -....? :^. , , distance of fault by ...... 49 ,, inductive capacity from fall of . . 65 ,, loss of ........ 39 ,, of cables paid out at different angles . . -151 ,, of two condensers or cables joined. ... 66 ,, on cable when paying out stopped . . . .150 Test by accumulation . . . . . . -59 ,, of joint by accumulation . . . . . . 41 , , of leading wires ....... 60 Thermometers, comparative table of . . . . 181, 182 Thompson's tables of relative speeds ..... 80 Throw, correction of, for air . . . . . 84 Time, difference of, between places . . . . .170 ,, of falling of charge 36 Trigonometrical formulae . . .. . . 212, 213 Twisting helically, extra material required for . . .173 Units, absolute system ....... i B.A 3 ,, current, Jacobi's ....... 102 , , deflection ; current which produces .... 88 ,, derived magnetical ....... \ ,, ,, mechanical. ...... i ,, electro-chemical . . . . . .5 ,, electro-magnetic, system of I ,, electro-static, system of . . . . . .2 ,, force . . . 2 ,, fundamental electrical . . . . . . i ,, heat ......... 4 ,, mechanical performance ...... 2 , , of electrical measurement . . . . . 3 ,, ,, resistance, various ..... 5 table of ... 8 ,, resistance, French . . . . . .6 ,, ,, German mile of copper .... 7 ,, ,, Jacobi's ... 5 ,, Matthiessen's . . . . . . 7 ,, ,, Siemens' mercury ..... 6 ,, ,, Sir Charles Wheatstone's . ... 5 Swiss 6 Index, 281 PAGE Units, resistance, Varley's. . . . ... 7 ,, work ......... 2 Values, relative, of resistance units 8 Various units of electrical resistance ..... 5 table of ...".. .8 Varley's loop method ....... 43 ,, condensers ........ 69 ,, unit of resistance ....... 7 Varnish for silk 222 , , insulating, for paper ...... 222 shellac, for glass 222 Veber, unit of quantity 4 Velocity and force of wind . . . . . . . 183 ,, of descent of lead weights . . . . .163 ,, of sinking ........ 150 of sound 159 ,, of waves ......... 168 Vibrations of needle ; method of ..... 83 Volt 3 Volta-induction, laws of . . . . . . .14 Voltameter 102 Volume of gas developed by current . . . . .102 Vulcanite 134 Warren's method of detecting faults . . . . -58 Water, absorption of, by insulators . . . . .167 ,, decomposition of, in voltameters .... 102 ,, memoranda connected with . . . . .167 sea . 166 Waves, force of ........ 167 ,, in cables, speed of. ...... 81 ,, velocity of ........ 168 Weber ; laws, &c 19, 84 Weight of a cubic foot of air . . . . . 183 ,, of cables; table for finding . . . . .172 ,, of Clark's compound on cable 147 ,, of G. P. per mile 114 ,, of hemp serving in cable . . . . .136 ,, of iron wire in cables ...... 140 ,, per mile , ... 140 282 Index. PAGE Weight of iron wire, table of .... 141, 142, 144 ,, per mile of copper wire strand . . . .104 Weights of material, table of . . . . . .189 Wheatstone's amalgam elements. . . . . -97 ,, balance ....... 23 ,, ,, arrangement for observing copper resist- ance per knot without calculation . 25 ,, ,, arrangement for observing insulation per knot without calculation . . .27 ,, ,, different readings with + and currents 29 ,, ,, elimination of leading wires . . . 28 ,, ,, estimation of true resistance . . . 29 ,, ,, for comparing electro-static capacities . 62 ,, ,, sensibility of galvanometer ... 24 ,, method of comparing batteries . . . 91 , , table for deciphering despatches . . . 244 ,, unit of resistance ...... 5 Wiedemann ; measurement of electro-motive forces . . 90 ,, method of comparing batteries ... 90 Wire and earth, contact between ...... 56 ,, copper 103 ,, ,, breaking strain of . . , . . . 104 ,, ,, diameter of . . . . . . . 104 ,, ,, Hooper's tinned ... . . .112 ,, ,, resistance per mile .... 104, 105 ,, weight per knot of 104 ,, of different gauges, resistance of . . . . -57 Wires, stranded . . . . . . . . .144 Wind, velocity and force of 183 Work and heat, development of 9 ,, unit of . 2 Working speed of G. P. cables 75 ,, ,, through Hooper's cable . . . . 76 ,, ,, with mirror system . . . . 7 7, 78, 79 ,, ,, through cables, rate of . . 73 Yards into knots, table to convert .... 194-208 INDEX TO TABLES. Actual speeds attained in working through existing cables . 80 Approximate cubical contents of wooden telegraph poles . 1 78 ,, electro-static capacities of various insulators . 67 Birmingham wire gauge ....... 190 Centimetres and millimetres to inches . . . . . 211 Coefficients for reducing Silvertown G. P. to 75 Fahrenheit . 128 ,, for temperature, corrections for Hooper's material 131 ,, of Hooper's tinned wire . . . .112 Common logarithms ...... 227-233 Comparison of different thermometers .... 182 Conducting powers and resistances . . . . .186 ,, of metals 186 ,, ,, of solutions. . ... . . 187 Conversion of knots into statute miles . . . . .192 Decimal equivalents of inches, feet, and yards . .191 Deep sea soundings average velocity of descent of lead weights in feet per second . . . . . .163 Determination of the height and velocity of the waves . .168 Diameters of centre lines of sheathing-wires, for calculating weights of hemp serving and asphalte casing . . . 149 Dilute sulphuric acid, resistance of . . . 187 Dimensions and relative electrical values of G. P. cores . 123 Distance of the visible horizon . . . . . .158 Electrical tests of cables . . . . . . 252, 253 Electro-motive force of Grove's element . . . 97 284 Index to Tables. PAGE Electro-motive forces of elements formed by amalgams . . 97 ,, ,, of elements when subjected to heat . 98 ,, ,, of useful elements .... 99 English miles to kilometres . . . . . .210 External diameters of submarine cables . . . .143 For ascertaining slack during paying out . . . .152 For calculating resistance and conducting power of pure copper in degs. Cent. 108 For Calculating resistance of copper at different temperatures, Fahr. ......... 106 For reducing resistance of G. P. to 24 Cent, or 75 Fahr. 118, 119 For reducing resistance of Willoughby Smith's improved G. P. 126 For reducing weights of copper per foot to weight per knot . 172 French and English measures . . . . . .210 ,, metres to English feet . . . . . .211 Iron wire 144 Kilogrammes to pounds avoirdupois . . . . .212 Knots into degrees of longitude 209 Loss of charge ........ 120 Measures in which the lengths of overhead lines are expressed in various countries . . . . . . .179 Mechanical data of cables . . . . . . . 256 Miles into knots . . . . . . . .193 Natural logarithms . . . . . . . .226 i sines 214, 215 tangents 216, 217 Number of yards per pound of small copper wire . . 1 1 1 Ratio _. , and loss per cent, of G. P. 121 Discharge Reciprocals . . . . . . . . .191 Relative resistance of Hooper's material at different temps. . 132 ,, ,, of G. P. . . . . . 116, 117 ,, ,, of W. Smith's improved G. P. . .125 ,, speeds of working similar lengths of cables having different ratios . 80 Index to Tables. 285 PAGE Relative values of various units of electrical resistance . . 8 Resistance and capacity per knot of G. P. core . . .122 of W. Smith's improved G. P. . . 127 ,, comparative, of G. P. and Hooper's insulator at different temperatures . . . . . .130 ,, in megohms of any dielectric .... 38 ,, in ohms of a knot pound of copper wire at different temperatures . . . . . no Resistances of metals when heated . . . . .188 ,, of pure copper wires ..... 109 Simple substances with their symbols, equivalents, and specific gravities ......... 188 Sizes and weights of iron wires ....... 142 ,, ,, of solid G. P. cylindrical band . . .114 Sounding lines . . . . . . . .164 Specific gravities of common salt solution .... 101 ,, ,, of diluted sulphuric acid .... 100 ,, ,, of nitric acid ...... 101 Squares of diameters ...... 218-221 Statistics of some telegraph systems . . . . .180 Strain corresponding to the sag or dip of a wire suspended at both ends ......... 177 ,, on grapnel rope 248 ,, on cables . ....... 250 To assist the reading of telegraph despatches . . . 245 To convert common into hyperbolic logarithms . . . 224 To find distance from ship to shore by sextant . . .161 To find resistance after one minute, and capacity per knot, of any Hooper's core . . . . . . .133 To measure vertical heights by the barometer . . .185 Velocity and force of the wind 183 Weight of iron per nautical mile in cables of different sizes . 141 ,, of substances most used in construction . . .189 Working speed with mirror system . . - . 77, 78, 79 Yards into knots ..... . 194-208 THE END. 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