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 the Cornell University Library. 
 
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 http://www.archive.org/details/cu31 9241 01 1 57893 
 
CORNELL UNIVERSITY LIBHAHY 
 
 3 1924 101 
 
■DIAGRAM OF CONNECTIONS. 
 
 Frontispiece. 
 
AN 
 
 ELEMENTARY TREATISE 
 
 ELECTRICAL MEASUREMENT. 
 
 FOR THE USE OF TELEGRAPH INSPECTORS 
 AND OPERATORS. 
 
 BY LATIMER CLARK. 
 
 LONDON: 
 
 E. & F. N. SPON, 48, CHARING CROSS. 
 1868. 
 
 Sight of Tiunslation reserved. 
 

 s^ 
 
 
 2>-f 
 
 LONDON : PRINTED BY WILLIAM CLOWES AND SONS, STAMFORD STREET 
 AND CHARING CROSS. 
 
PREFACE. 
 
 The Author having had occasion to write a little 
 Manual to accompany some instruments designed for a 
 special purpose, has thought that its publication might 
 be of use to students preparing themselves for the ser- 
 vice of the Electric Telegraph, and to others who might 
 desire an Elementary Treatise on the subject of Electrical 
 Measurement. The first half of the work is designed 
 for the use of the student, and the practical telegraphist 
 who has not given much time to the study of his subject, 
 and is therefore written in a somewhat colloquial style : 
 it is possible that from this cause it may prove more 
 readable and attractive than works of a more advanced 
 character, and may tend to awaken an interest in the 
 subject among many who have hitherto been content 
 to employ the services of electricity daily without caring 
 to acquaint themselves with the laws of its operation. 
 
 The Author believes that the form of galvanometer 
 herein recommended will be found a very useful and 
 convenient instrument for all the practical measure- 
 ments of telegraphy. Unlike ordinary^ galvanometers, 
 
iv Preface. 
 
 it is peculiarly suited for testing batteries, and the 
 measure of their internal resistance is perhaps more 
 easily and expeditiously obtained by this instrument than 
 by any other method.* 
 
 The latter half of the work is in the form of an 
 Appendix, which has been added to the original treatise 
 in order to make it useful to the practical electrician. 
 It contains a variety of formulae, tables, and data for 
 general use, chiefly taken from the author's note-book; 
 and also a description of the methods of measurement 
 usually employed in telegraphy, with the formulae relating 
 to them, which may often serve as an aid to the memory. 
 The algebraic expressions throughout the book are put 
 into a form especially intended for the use of those who 
 do not often have recourse to them. The book having 
 thus been written in two different portions, is necessarily 
 wanting in all unity of design, for which, as for other 
 imperfections, the author claims the indulgence of his 
 readers. His acknowledgments are due to Mr. J. C. Laws 
 for the assistance he has rendered in revising most of 
 the calculations in the work. 
 
 5 Westminster Chambers, 
 London, 1868. 
 
 * This instrument is made by Messrs. Warden and Co., of Church 
 Street, Westminster. 
 
CONTENTS. 
 
 CHAPTER 
 
 I. On Electrical Resistance 
 
 PAGE 
 I 
 
 II. 
 
 On Electromotive Force 
 
 . 6 
 
 III. 
 
 On Electrical Tension or Potential . 
 
 . lO 
 
 IV. 
 
 On Electrical Induction 
 
 . 28 
 
 V. 
 
 On Electrical Quantity 
 
 ■ 36 
 
 VI. 
 
 On Earth Connections .... 
 
 . 40 
 
 VII. 
 
 On Units of Measurement . 
 
 ■ 43 
 
 Clark's Double-Shunt Differential Galva- 
 nometer 47 
 
 VIII. To use the Instrument as an Ordinary 
 
 Galvanometer 50 
 
 IX. To use the Instrument as a Sending and 
 Receiving Instrument. 
 
 X. To use the Instrument as a Quantity Gal- 
 vanometer for Testing Batteries 
 
 XI. The Measurement of Resistances . 
 
 XII. The Measurement of Higher Resistances . 
 
 XIII. To Measure very High Resistances 
 
 51 
 
 53 
 54 
 56 
 57 
 
vi Contents. 
 
 CHAPTER PAGE 
 
 XIV. To Measure the Resistance of Short Wires, 
 
 &c 59 
 
 XV. To Measure the Internal Resistance of 
 
 Batteries 60 
 
 XVI. To determine the _ Electromotive Force of 
 
 A Battery 63 
 
 XVII. To ascertain the Specific Conductivity of 
 
 Copper 64 
 
 XVIII. Allowance for the Effect of Temperature 
 
 on the Conductivity of Copper. . . 67 
 
 XIX. To ascertain the Locality of Faults . . 6g 
 
 XX. The Method of taking the Loop Test . 72 
 
 XXI. Blavier's Formula for finding the Position 
 
 OF A Fault 75 
 
 XXII. On Shunts and Derived Circuits . . .78 
 
 XXIII. On the Multiplying Proportion of Shunts, 
 
 AND THEIR RESISTANCE . . . 8o 
 
 XXIV. On Measurement by the Electrical Balance 84 
 XXV. On THE Measurement of Gutta-percha Cables 88 
 
 Appendix, containing various Tables and Formulae . 91 
 
ON 
 ELECTRICAL MEASUREMENT. 
 
 The student of electricity in considering the various 
 phenomena which come under his notice must of neces- 
 sity form some theory in his mind as to the nature of the 
 element with which he has to deal ; and as philosophers 
 are not in accord as to its nature and the theory of its 
 action, the choice must to a novice be a difficult one. 
 Without therefore in the least offering any opinion upon 
 this point, I would advise him, until his views are more 
 matured, to regard electricity as a substance like water or 
 gas, having a veritable existence, and although easily 
 convertible into heat, and vice versct, in other respects 
 indestructible.* I would advise him to dismiss from his 
 mind all ideas about the existence of two different kinds 
 of electricity, and to regard the earth as a vast reservoir 
 highly charged with one kind of electricity (positive), and 
 to regard a telegraph or a battery as an arrangement by 
 which electricity is pumped out of the earth at one point 
 * See note a, page i68. 
 
viii Introductory Chapters. 
 
 and poured into it at another. When any object has less 
 electricity than the neighbouring earth it is charged mga- 
 tively, when it has more it is charged positively, and in 
 either case electricity will endeavour to flow from the 
 earth to it, or from it to the earth, until equilibrium is 
 established. 
 
 The laws which govern the propagation of the electric 
 current along conductors are so simple, and yet withal so 
 important, that every telegraphist ought to be familiar 
 with them. The most important of them was first enun- 
 ciated by Ohm in 1827, and is known as Ohm's law. 
 For a long time this remained entirely unappreciated ; 
 but its importance is now abundantly recognised, and 
 Ohm's law forms the foundation of all electrical measure- 
 ment. To understand its application it is necessary to 
 have a clear conception of the meaning of the terms 
 electromotive force, resistance, tension, and quantity, and 
 these will be unfolded in the following chapters. 
 
AN ELEMENTARY TREATISE 
 
 ELECTRICAL MEASUREMENT. 
 
 CHAPTER I. 
 On Electrical Kesistance. 
 
 Take the galvanometer described at page 45, and having 
 inclined it on its back support, join it up in the manner 
 described at page 5 1 ; that is to say, plug up the holes 
 B and C, and also the y^th shunts at A and B. Take 
 one cell of a battery, and putting one pole to earth,* 
 connect the other pole to the terminal A ; then connect 
 
 * It is not essential to make any connection to earth, but the 
 battery may be joined directly to the resistance coil (see Chapter VI. ) ; 
 nor is it necessary to employ this particular instrument ; any galva- 
 nometer with very short and thick wire will suffice for this experi- 
 ment: these are commonly called "quantity galvanometers," because 
 they are capable of measuring larger quantities of current electricity 
 than ordinary fine wire galvanometers. 
 
 B 
 
2 Introductory Chapters. 
 
 the resistance coil to the terminal D, its other end being 
 to earth ; the arrangement will then be as follows : 
 
 Fig." I- 
 
 Heslslanoe 
 
 Sartk. 
 
 Now short circuit the resistance coil by inserting all the 
 plugs, and observe the deflection on the galvanometer; 
 it wiir be found to be very great, probably 50° or more, 
 depending on the resistance of the battery cell. Now 
 gradually withdraw the plugs from the resistance coil, 
 so as to interpose greater and greater resistance into the 
 circuit ; as this is done the needle will fall gradually back 
 as the resistance is introduced, and its deflection will at 
 last become scarcely visible. The construction of the 
 galvanometer is such that its deflections are not truly 
 proportioned to the force of the current ; but when this is 
 measured by suitable instruments the law is found to be 
 simply this — that the electromotive force being constant, the 
 quantity of electricity which flows through any circuit is 
 inversely proportional to the resistance; that is to say, 
 the greater the resistance, the smaller the current. Call- 
 
On Electrical Resistance. 3 
 
 ing the quantity Q, the electromotive force E, and the 
 resistance R, this is expressed by the formula 
 
 which is known as Ohm's law. 
 
 Hence if in any circuit with a given resistance, one 
 farad of electricity* passes per second, then with twice 
 that resistance we shall get a current of only half a 
 farad per second ; and with twenty, or one hundred and 
 twenty times that resistance, we should get ^'^th or x^th 
 of a farad per second. Again, with one-tenth of the re- 
 sistance we shall get ten farads per second ; it being un- 
 derstood that the electromotive force remains unchanged. 
 
 It is important to observe, that in speaking of the 
 resistance in any circuit, we speak of the whole resist- 
 ance, including that of the galvanometer, of the connect- 
 ing wires or line circuit, and of the battery itself, which 
 last is frequently a very important part of the whole 
 resistance, and must on no account be forgotten. 
 
 This resistance may in practice originate in a variety 
 of ways J a small cell gives much more resistance than a 
 large one ; and if the plates be far apart, the resistance 
 is greater than when near together. If two similar 
 batteries be joined up together in parallel circuit, or " for 
 quantity " as it is sometimes termed, as shown in fig. 2, 
 the resistance is only one half what one of them would 
 give singly j and ten cells so joined up only give -^th the 
 
 * The farad is a certain definite measure or quantity of electricity, 
 see page 43. 
 
4 Introductory Chapters. 
 
 resistance of one of them : they are, in fact, in every way 
 equivalent to one very large cell. On the other hand. 
 
 two or ten cells joined up in series as in fig. 3, give twice 
 or ten times the resistance of one cell. 
 
 Fig. 3- 
 
 'HI 
 
 A partially dried or otherwise defective battery cell 
 will often cause great resistance in a circuit, so will im- 
 perfectly soldered joints in a line wire; the soil itself, 
 especially if dry and sandy, or rocky, will often oppose 
 great resistance to the current : this is technically called 
 " bad earth '' (see page 40). Pure water offers a very 
 high resistance, but if it contains any acids or saline 
 matters in solution the resistance is much smaller : hence 
 it is that clean rain in the country does not greatly injure 
 the working of a line, but in towns, where the atmosphere 
 is less pure, the insulation often becomes very imperfect 
 in wet weather. It is from a similar cause that batteries 
 
On Electrical Resistance. 5 
 
 when first set up give a very weak current, and thus 
 create the supposition that the electromotive force is 
 feeble. This, however, is not so, as the addition of a 
 little salt or acid will at once show : the real cause is the , 
 great resistance interposed in the circuit by the pure 
 water before it has yet had time to become saturated 
 with salts. 
 
 If an insulated line of telegraph ninety miles in length 
 gives a resistance of, say 10,000 units, the resistance per 
 mile will be ninety times 10,000, or 900,000 units ; that 
 is to say, each mile of the line conveys a certain quantity 
 of electricity to the earth by reason of its imperfect in- 
 sulation, and therefore the greater the number of miles 
 the smaller is the total resistance ; the average resistance 
 of a single mile is therefore obtained by multiplying the 
 total resistance by the number of miles. 
 
 The case is just the reverse when the line is con- 
 nected to the earth at the distant end : the leakage or 
 escape, which was before the only measure we dealt with, 
 becomes in this case unimportant, and we measure the 
 resistance of the metallic wire, instead of the resistance ^ 
 of the i nsulato rs. The greater the length of the wire the 
 greater the resistance ; and to obtain the average resist- ' 
 ance of a single mile we have now to divide the total 
 resistance by the number of miles. Thus if a ninety- 
 mile line of No. 8 wire gave a resistance of 12 15 units, 
 
 1215 
 the resistance of each mile would be — — - or 13 -5 units. 
 
Introductory Chapters. 
 
 CHAPTER II. 
 On Electromotive Force. 
 
 We now pass on to the second part of the question, that 
 of the electromotive force. Let us again take the galva- 
 nometer, joined up as before with one cell (fig. i), and 
 withdrawing all the plugs of the coil insert the whole of 
 the resistance into the circuit, viz., ten thousand ohms. 
 The deflection, as we noticed in the last experiment, will 
 be extremely small. Now add a second cell to the 
 battery and it will be found that the deflection is doubled ; 
 increase the cells to three _ and it will be trebled, and so 
 on. The galvanometer, as before remarked, will not 
 continue to give truly proportional deflections after the 
 needle leaves its central position, but when proper means 
 of measurement are employed, it is found that with a 
 constant resistance the quantity of electricity which flows 
 through any circuit is directly proportional to the electromo- 
 tive force. 
 
 This is expressed by the formula above given, viz. : — 
 
 If then with any given resistance one cell gives a 
 
On Electromotive Force. 7 
 
 current of ten farads per second, two cells will give 
 twenty farads, and ten cells one hundred farads. It is 
 scarcely necessary to say that in this case, as in the last, 
 the resistance of the cells themselves must not be for- 
 gotten. 
 
 As an instance of calculation we will suppose now that 
 with ten cells and a total resistance of ten units we get 
 a current of one farad per second, and we desire to know 
 from this what current would pass through a circuit of six 
 units with one hundred and forty-four cells — we may 
 reason thus : 
 
 If ten cells give one farad, then one hundred and forty- 
 four cells will give 14 '4 farads, or, 
 
 10 : 144 : : I : i4'4. 
 And again, if with ten units' resistance we get 14 "4, with 
 six units we shall get more than this, viz. : — 
 
 10 
 i4"4 X — = 24, or, 
 
 6 : 10 : : i4'4 : 24 
 
 The electromotive force does not in the least degree 
 depend on the size of the cell, but is as great with a very 
 minute pair of elements as with an immensely large pair ; 
 and if the one be opposed to the other, not the slightest 
 current will pass. 
 
 We will now make another experiment, and it is 
 one which the student should on no account neglect to 
 perform for himself, as a great deal is to be learned 
 from it. 
 
 Take the galvanometer still connected up as before 
 
8 Introductory Chapters. 
 
 (fig. i), and plug up all the resistance coil, so that there 
 
 is no resistance in circuit except that of the galvanometer 
 
 and the battery ; or the resistance coil may be removed 
 
 altogether. Note the deflection with one cell, and then 
 
 add a second cell to the circuit ; the result will perhaps 
 
 be unexpected, for the deflection will be but very slightly 
 
 increased. Add a third and fourth cells, and still there 
 
 will be little or no increase in the deflection of the needle, 
 
 and the same will be the case if we add one hundred cells, 
 
 or five hundred cells ! But how is this? We have just been 
 
 taught that the quantity of current passing varies directly 
 
 as the electromotive force (and we actually saw proof of 
 
 it in the last experiment), and yet now we suddenly find 
 
 that increasing the electromotive force one hundred or 
 
 five hundred times has had scarcely any effect whatever. 
 
 But let us look a little closer into the matter, and the 
 
 anomaly will vanish. 
 
 Let us apply the two laws we have just learned to the 
 
 case, and see whether the phenomena are, or are not, in 
 
 E 
 accordance with the formula Q = — . 
 
 Let us suppose the resistance of each cell of the battery 
 to be thirty units, and the resistance of the shunted gal- 
 vanometer four units ; we have then in the first case — 
 
 E _ I i_ 
 
 R ~ 30+4 " 34 
 and in the second case, with two cells, we have — 
 2 E 2 I 
 
 2 R 6o-)-4 32 >. 
 
On Electromotive Force. 9 
 
 and in the case of five hundred cdls we have — 
 500 E 500 I 
 
 500 R ,15000 + 4 30-008 
 
 Although then we have doubled the electromotive 
 force we have only increased the quantity of electricity 
 flowing in the circuit from -^ to ^, and even when we 
 increase the electromotive force five hundred times we 
 only increase the current to ^V; the fact being that each 
 battery brought as much resistance to the circuit as it 
 brought electromotive force. 
 
 To make this still clearer, let us suppose the galva- 
 nometer taken away altogether and the batteries alone 
 left in circuit : our calculation would then be in one 
 
 E I 
 
 500 E 500 
 
 case -^ — — , and in the other case — 
 R 30' 
 
 500 R 15000 30 
 
 or, in other words, we get exactly the same current in 
 one case as in the other. There arises from this the 
 curious result, that if one or any number of similar cells 
 be joined up on short circuit, without external resistance 
 there will in every case be the same quantity of current 
 flowing through them. 
 
lo Introductory Chapters. 
 
 CHAPTER III. 
 On Electrical Tension or Potential. 
 
 Having spoken of resistance and electromotive force, 
 we will now treat of electric tension or potential. The 
 two terms are perfectly synonymous, but the word poten- 
 tial is generally preferred by mathematical writers. There 
 is often much confusion in the way in which the terms 
 electromotive force and tension are indiscriminately 
 employed, and it is well to endeavour to gain a clear 
 idea of the distinction between them. We shall see as 
 we go on that in a battery the electromotive force is the 
 origin of the tension, and that the sum of all the electro- 
 motive forces is always equal to the sum of all the ten- 
 sions, but their distribution is in every way different. 
 To make the meaning of the term intelligible, we will 
 cite a few cases of the effect of extreme tension, or 
 potential, and then descend to more ordinary cases. 
 Lightning is the most extreme case of tension with which 
 we are acquainted (if we except perhaps the aurora 
 boreaUs), and we may often see a flash a quarter of a mile 
 in length. With an electrifying machine we may easily 
 
On Electrical Tension. 
 
 II 
 
 obtain a tension high enough to make sparks leap across 
 a space of six inches or a foot ; descending to lower 
 tensions, a Daniell's battery of five hundred cells will, 
 when the circuit has once been established, maintain 
 an arc of flame across a space of a quarter or half an 
 inch; with still lower tensions, the electricity will traverse 
 conducting substances freely, but will not pass across 
 the air. 
 
 Degrees of tension are only relative, and we have no 
 means of ascertaining the zero point of tension. The ten- 
 sion of the earth is called zero ; but this tension varies 
 slightly at different times and places, and we have no 
 means of judging of its tension relatively to that of other 
 planets and celestial bodies : just as a person enclosed 
 within an electrified chamber has no means of ascertain- 
 ing to what tension he is electrified, or whether his elec- 
 tricity is positive or negative ; but taking the tension of 
 the earth for the time being as a standard, we have no 
 difficulty in comparing other tensions with it, with the 
 most minute precision. 
 
 Fig. 4. 
 
 100 ^ 
 
 H I I I I 
 
 £ar(h 
 
 Take a battery of, say one hundred cells, and placing 
 
12 
 
 Introductory Chapters. 
 
 it on a well-insulated stand, connect one pole of it, say 
 the zinc or negative pole, to earth, and leave the other 
 pole free, as in fig. 4 : the end which is connected to 
 the earth will now have a tension of o, and the opposite 
 end will have a tension of 100 positive, or above that of 
 the earth ; and if a wire were connected from it to the 
 earth, a powerful current would flow from it to the 
 earth. 
 
 Now reverse the connection, and place the other pole 
 to earth, as in fig. 5. The copper end of the battery- 
 Fig. S- 
 
 I I I I 
 
 JEarBi 
 
 will now have a tension of o, and the zinc or negative 
 end will have a tension of 100 minus, or below that 
 of the earth ; and if a wire were connected from it 
 to the earth, a powerful current would flow fi-om the 
 earth to it. In each of these cases the degree of tension 
 is the same, but in one case it is higher than that of the 
 earth, and in the other lower; the one is positive, the 
 other negative. 
 
On Electrical Tension. 
 
 n 
 
 Now take the same battery and connect it up, as in 
 the first instance, with the zinc or negative pole to earth ; 
 but instead of leaving the positive pole free, join a short 
 and thick wire across from the one pole to the other, as 
 in fig. 6. An important change now occurs. We know 
 
 Fig. 6. 
 
 fi 
 
 I I I I 
 
 SarBi, 
 
 from previous experiments that a powerful current will 
 circulate through the wire from c to z, and knowing the 
 resistances we have the means of calculating the strength 
 of this current ; we know also that the electromotive 
 force is not in any way affected by thus putting the 
 battery into action. But although the electromotive force 
 has not changed, we shall find on examination that the 
 exterior tension has almost entirely disappeared : the wire 
 at c, which in fig. 4 was at a tension 100 degrees above 
 that of the earth, has now a tension but little above that 
 of the earth. 
 
 If we now change the short and thick wire which 
 
14 
 
 Introductory Chapters. 
 
 connects the poles c and z for a wire offering greater 
 resistance, we shall soon find the tension at c begin to 
 rise, although the tension of z is constantly kept at o by 
 its connection Avith the earth at that point : as we 
 increase the resistance of this connecting wire so does 
 the tension at c rise, until at last, when we have made 
 the resistance infinitely great, as in fig. 4, we find it 
 again 100 : the tension is now equal to the electromotive 
 force, but it can never under any circumstances exceed it. 
 Let us now imagine a battery of, say one hundred cells, 
 connected to a perfectly insulated line of, suppose one 
 hundred mUes in length, as shown in fig. 7, not con- 
 
 zoo Cells 
 
 ril 
 
 Sarth 
 
 Fig- 7- 
 
 7S 
 
 SO 
 
 SS 3Iiles o 
 
 nected to earth at the distant end. The line will 
 instantly obtain a tension of one hundred throuo-hout 
 its whole length (this being equal to the electromotive 
 force of the battery), and it would do so equally if it 
 were a thousand, or a million times that length : after 
 this no current will flow from the battery. 
 
 Let us now imagine the distant end of the line con- 
 nected to the earth; the battery will now come into 
 
On Electrical Tension. 
 
 IS 
 
 action, and a current will flow through the line. This 
 will not in any way affect the electromotive force of the 
 battery, but it will entirely change the tensions every- 
 where. The end connected to earth will of course at 
 once assume a tension of o, and from this point all 
 along the line up to the battery the tension will rise 
 regularly and, gradually ; at the battery itself it will be 
 something less than one hundred ; but without at present 
 stopping to calculate what, we will assume it to be 
 eighty. Having ascertained the tension at this or any 
 other spot, we can easily calculate it for every other part 
 of the line, for in a circuit of uniform resistance the 
 tension varies directly as the distance from the zero end of 
 the line. Thus if it is equal to eighty cells at one 
 hundred miles, it will be equal to forty cells at fifty 
 miles, to twenty cells at twenty-five miles, to sixty cells 
 at seventy-five miles, and so on. The tension will, in fact. 
 
 Fig. 8. 
 
 100 Cells 
 
 Earth, 
 
 ---Jffo 
 
 ClOO 
 I) 
 
 73 
 
 50 
 
 
 25 
 B 
 
 
 
 Hari 
 
 I 
 
 be represented at every point by the diagonal Hne in 
 fig. 8 ; and knowing the tension at any spot in the line. 
 
i6 
 
 Introductory Chapters. 
 
 as D, we can obtain the tension at any other point, 
 B or C, by simple proportion, viz. : — 
 
 Length AD : A B : : tension P : tension B. 
 
 or, loo : 25 : : 80 : 20. 
 
 The tension thus spoken- of has been /^j-z/Zz'i? tension, 
 
 but the law is just the same with negative tension, or a 
 
 tension less than that of the earth. We will take a case 
 
 in which both tensions come into play. We have here 
 
 Fig. 9. 
 
 ■Ear A. 
 
 —^^f/AVeJ^^ 
 
 Sjotls 
 
 75 
 
 SI) 
 
 
 SS Miles 
 
 ..J. 
 
 
 
 two parallel wires one hundred miles in length joined to- 
 gether at the distant end. The earth is. connected now 
 for the sake of illustration only at the centre of the 
 battery, which has therefore a tension of o, and may be 
 considered as divided into two halves, the upper half 
 giving a positive tension to the upper line, and the lower 
 half giving a negative tension to the lower line. In the 
 one case the tension falls, as before, regularly from the 
 battery to o, and in the other half it rises as regularly 
 from the battery to o. If a wire were connected from 
 
On Electrical Tension. 17 
 
 the earth to the upper line at any part, a current of 
 electricity would flow from the line to the earth, with an 
 energy proportionate to the degree of tension. On the 
 other hand, if the same wire were connected to the lower 
 or negative line, a current would flow from the earth to 
 the line with the same energy ; and here it may be stated 
 generally that the quantity of electricity flowing along any 
 conducting wire between any given points is directly pro- 
 portional to the difference of tension between those points. 
 It does not in the least depend on the actual tension, 
 which may be positive or negative, high or low, but 
 purely on the difference of tension at the two points. 
 
 In the illustration above given there are two zero 
 points, one in the centre of the battery which is con- 
 nected to earth, and one in the centre point of the two 
 lines : this arises from our having a negative current on 
 one half the line, and a positive on the other. In 
 practice it is usual to have either all positive tensions 
 or all negative tensions, or else to alternate them one 
 after the other. 
 
 We will now see how to measure these tensions ; there 
 are several methods, but perhaps the most ^useful for 
 linework is the following : 
 
 Fig. 10 shows a line with a battery of one hundred 
 cells connected to it, the distant end being to earth 
 The galvanometer is connected to it at any point, 
 together with a second battery; its pole being also to 
 earth ; each battery is now trying to send a current into 
 the line, and if both be attached at the same point, and 
 
 c 
 
1 8 Introductory Chapters. 
 
 both of equal tension, both will send a current into the 
 line, and the galvanometer will be deflected, say to the 
 right. Now gradually reduce the number of cells in 
 the secondary battery, and a point will soon be found 
 at which no current will pass through the galvanometer 
 either one way or the other, and the needle will be at 
 zero. The number <jfiells now in circuit in the secondary 
 lattery will represent tlie actual tension of the^line at that 
 spot. If we take away another cell, the principal battery 
 
 JOO CMs 
 
 Fig. 10. 
 
 r-^II 
 
 c wo Miles. 
 
 JSarih. 
 
 will send a current back through the secondary one, and 
 the needle will deect to the left ; and if we add another 
 cell, the smaller battery will begin to send a current into 
 the line, and it will deflect to the right. ^Vhen the 
 tensions are equal, it will remain at zero. The number 
 of cells in the secondary battery will always be smaller 
 than in the principal battery, even when attached close 
 to it, and as we get farther away from the station, 
 the number of cells will diminish gradually, till near the 
 
On Electrical Tension. 
 
 19 
 
 distant end where the line makes earth, even one pell 
 will send a current into the linej in fact, the tension there 
 becomes o. This experiment may be easily performed 
 in a room, using a resistance coil to represent the line, 
 and three or four cells for the principal battery, and it is 
 a most instructive one. 
 
 We have seen at p. 15 how to derive the value of the 
 tension at any one point from that at any other, we will 
 now see how to calculate it from the electromotive force 
 of the battery. Perhaps a diagram will make this clearer 
 than any other method of explanation. Let A B (fig. 1 1) 
 
 Fig. II. 
 
 
 14 
 
 ^^C 
 
 represent a battery of, say one hundred cells, and let B C 
 be a line of any length. Let the length of the line A B 
 be drawn so as to represent the internal resistance of the 
 battery (see page 60), and let the length of B C represent 
 the resistance of the line. Let the height of the line A D 
 represent the electromotive force of the battery, which we 
 may call one hundred; then the height of the line B E will 
 represent the tension of the line at its junction with the 
 battery, and the height of the line F G will represent the 
 tension at any other point, as F. The following rule will 
 
20 Introductory Chapters. 
 
 therefore enable us to determine the tension at any point 
 of the line, as, for example, F. As the whole resistance of 
 the line and battery is to the resistance, measured from the 
 distant end of the line (C F), so is- the electromotive force 
 of the battery to t/ie tension at the spot F ; or, 
 
 AC:FC::AD:FG. 
 As an example, let a line four hundred miles long have 
 a resistance of three units per mile, and let it be con- 
 nected to a battery of fifty cells, each having a resistance 
 of twenty units, and let us ascertain the tension at the 
 middle of the line, or two hundred miles from its con- 
 nection to earth. The total resistance in circuit will be 
 400 X 3 + 5° X 20, = 2200 units; and the resistance 
 measured to the centre of the line will be 200X3 =600 
 units. The tension at that point will therefore be 
 
 2200 : 600 : : 50 cells : i3'64 cells ; 
 and the tension close to the battery wiU be 
 
 2200 : 1200 : : 50 : 27^27 cells; 
 being, of course, according to the rule at p. 15, equal to 
 twice the tension at the centre of the line. It is evident 
 that if the resistance of the line be exactly equal to that 
 of the battery, the tension at the point where they join 
 will be half the electromotive force; and the resistance 
 of a battery may be ascertained in that way, wz., by 
 varying the external resistance until the tension at the 
 point of junction is half that of the battery when insulated : 
 when this is the case the two resistances will be equal. 
 
 The following diagram will give some idea of the dis- 
 tribution of the tensions within the battery itself, where. 
 
On Electrical Tension. 
 
 21 
 
 as far as regards the internal resistance, they follow the 
 same law as elsewhere. 
 
 Fig. 12. 
 
 4 4 
 
 JSoLrth. 
 
 Fig. 1 2 shows a battery of four cells attached to a line 
 of infinite resistance, that is to say, having its distant end 
 insulated. The tensions are indicated by the upper line, 
 atid are in this case equal to the electromotive force. 
 At each junction of the zinc with the hquid the latter 
 rises in tension one cell, the whole tension attained being 
 four cells. 
 
 Fig. 13 shows the same battery connected up to a line 
 having exactly the same resistance as itself; the tension 
 at the distant end, instead of being four, is zero; the 
 tensions at the other points are figured on the diagram, 
 
22 
 
 Introdtictory Chapters. 
 
 and according to the law before given, since the resist- 
 ance of the line is equal to that of the battery, the tension 
 at the junction will be half the electromotive force. It 
 
 Fig- 13- 
 
 zh 
 
 1/3 
 
 ■•-,2 
 
 Earfh. 
 
 Earth 
 
 will be seen that the tension falls in the liquid contained 
 in the cells of the battery in proportion to the resistance, 
 just as it does on the line. 
 
 Fig. 14 shows the same battery short-circuited, that is 
 to say, connected to a thick wire connected to the 
 earth, and which is supposed to offer an infinitely small 
 resistance, and therefore to maintain both ends of the 
 battery almost rigidly at zero. Here we see that the 
 tension rises within the cells themselves as in the previous 
 examples, the maximum point of tension being in the 
 liquid which is in immediate contact with the zinc plate ; 
 it falls, however, to o at each copper plate, and this is the 
 
On Electrical Tension. 
 
 23 
 
 case however many cells there be in the circuit. Within 
 the cells the tensions fall in proportion to the resistances. 
 
 Fig. 14. 
 a a. 
 
 ^ 
 
 IBartTx 
 
 It c"^ 
 
 tEarfh 
 
 z 
 
 Fig. IS- 
 
 1 S 
 
 , N 
 
 C 
 
 Fig. 15 shows a single cell of copper and zinc short- 
 circuited by a wire a b, supposed to be 
 so thick and so directly connected to 
 earth as to maintain both plates almost 
 rigidly to the tension of o : in this case 
 the tension exists only within the liquid, 
 as shown by the diagonal line. The 
 tensions of the opposite ends of a and b, and conse- 
 quently of z and c, are here assumed to be so nearly the 
 
 same that they may be neglected. In all these cases 
 
 "p 
 
 we find the current conforming rigidly to the law 0,=-^^ 
 
 is. 
 
 and we find also, as first .stated, that tke sum of all the 
 
 electromotive forces is equal to the sum of all the differences 
 
 of potential. 
 
 It may be remarked that tensions always tend to 
 
 equalise themselves j all electrical currents are produced 
 
 solely by differences of tension, and whenever the tension is 
 
 greater at one spot than another, a current will commence 
 
Introductory Chapters. 
 
 to flow from one to the other, and will continue until the 
 tensions have become equalised ; the quantity or strength 
 of the current being greater or less according to the 
 difference in the degree of tension, and the amount of 
 resistance : however great or small these be, the tensions, 
 if left undisturbed, will at length equaUse themselves. 
 
 The tension too is the same in the interior of any con- 
 ductor, whatever its form riiay be, as it is on the surface; 
 thus, if any insulated conductor have another electrified 
 
 Fig. i6. 
 
 body brought near to it, it is well known thai the electricity 
 in it will be disturbed according to well-understood laws 
 of electrical induction, and one side of it will become 
 charged positively and the other negatively; for example, 
 in fig. 1 6. A is a globe charged with positive electricity 
 and brought near to another insulated globe B ; the effect 
 is, that the distribution of the natural electricity in B is 
 disturbed, and the side c, nearest to A, becomes in 
 ordinary language negatively electrified, and the opposite 
 
On Electrical Tension. 25 
 
 side, d, .positively electrified; but here let the student 
 carefully consider what these terms mean as usually- 
 employed by writers on static electricity; they mean 
 that there is a larger quantity of free or indtued electricity 
 on the side d, and a smaller quantity on the side c; 
 they treat of the distribution of the free electricity, or 
 the charge as it is called, but do not usually refer to 
 electrical tension at all. As regards the tension, the 
 fact is that it is equal everywhere throughout B. There 
 is less electricity at c than at d, but the tension is precisely 
 the same at one point as the other : if it were not so, a wire 
 connected from d to c would convey a current from one 
 point to the other, which we know is not the case. In 
 short, the tension throughout all parts of a conductor is 
 uniform, or rapidly tends to become so. 
 
 As a further illustration of the importance of not con- 
 founding a positive or negative charge with positive or 
 negative tension, we will give a paradoxical case in which 
 a body is negatively electrified, and is charged with negative 
 electricity, and yet has 2. positive tension. 
 
 Fig. 17. 
 100 Pells 
 
 Earth JEar& 
 
 In fig. IT, a bis 3. bent plate, connected to the positive 
 
26 Introductory Chapters. 
 
 pole of a battery of one hundred cells, and having there- 
 fore a positive tension of one hundred. It entirely 
 envelops the plate d, which is in connection with the 
 positive pole of a battery of one cell. The positively- 
 charged plate a b acting inductively on the plate d gives 
 it a negative charge as regards its free electricity; but 
 the cell with which it is connected gives it a positive 
 tension of one cell, as regards its tension, and thus we 
 have the apparent paradox of a body negatively electri- 
 fied, or having less than its natural amount of elec- 
 tricity, but which has yet a positive tension, and is pre- 
 pared to give off a continuous stream of electricity to 
 the earth. This experiment is more easily demonstrated 
 with a length of cable immersed in an insulated tub of 
 water, as described in the next chapter ; the water being 
 raised to a tension of one hundred, and the cable to any 
 smaller tension. 
 
 Fig. i8. 
 
 3 
 
 While treating on tensions as affected by induction, 
 another instructive case may be referred to : « in the 
 figure is a ball suspended within the interior of a 
 conducting globe g : if this outer globe be now raised 
 or lowered to any tension, as, for example, loo plus or 
 
On Electrical Tension. 27 
 
 minus, the ball a will also assume the same tension : 
 this arises purely from induction, and all the changes 
 which occur in g are instantly reproduced in a, without 
 any alteration of the quantity in a, and without any 
 electricity passing from one to the other. If iJ be a fine 
 wire, it is easy to verify this by measuriiig the changes 
 on an electrometer : if, before starting, a have a charge 
 given to it equal to a tension of, say ten volts* plus 
 or minus, this difference of ten volts will remain constant 
 throughout all subsequent changes. 
 
 * The volt is a measure of tension, see p. 43. 
 
28 
 
 Introductory Chapters. 
 
 CHAPTER IV. 
 On Electrical Induction. 
 
 Although the phenomena of induction enter more or 
 less into every case df electrical action, they rarely come 
 within the cognizance of those who have charge of land 
 lines. An allusion was incidentally made to the subject 
 in the last chapter, and a few of its laws will be briefly 
 given here for the benefit of those who may have charge 
 of underground wires, or cables. 
 
 If a cable A B (fig. i8), perfectly insulated with gutta 
 
 Fig. 19. 
 
 V 
 
 Earth, 
 
 percha or other dielectric, be immersed in water or 
 buried in the earth, and a galvanometer and battery be 
 connected to it, as shown in the diagram, at the first 
 moment of contact a certain charge of electricity will be 
 seen to rush into the cable, causing a momentary deflec- 
 tion of the needle. After this all remains quiescent, and 
 the cable remains charged throughout its length to the 
 
On Electrical Induction. 29 
 
 full tension of the battery ; but if the insulation be per- 
 fect, no more electricity enters the cable. This is called 
 the charge, and its amount varies directly as the tension ; 
 that is to say, with a tension of ten cells it is exactly ten 
 times as great as with one. If the battery be now re- 
 moved, and the inside of the cable connected to earth, 
 the whole of the charge will return through the galvano- 
 meter to earth, deflecting the needle to the same extent as 
 before, but in the opposite direction : this is called the 
 discharge, and its amount is exactly the same as that of 
 the charge. 
 
 If a perfectly insulated mile of cable be charged to a 
 tension of, say ten, and then joined to a similar length of 
 one mile, the charge will instantly distribute itself uni- 
 formly throughout the whole two miles, and the tension 
 will be reduced to five ; and so if it be joined to a length 
 of nine miles, the tension will be one-tenth of what it was 
 before; but the quantity will be the same in the ten 
 miles as it was in the one, and will remain quite unaf- 
 fected by the change in tension : the quantity per mile 
 will of course be one-tenth of what it was at first. The 
 student will perceive that we are here for the first time 
 applying the term quantity to a static charge, and not to 
 current electricity. 
 
 If a charge be sent into a cable in the manner before 
 described, a precisely similar quantity of electricity of the 
 same kind leaves the outer surface and becomes distri- 
 buted in the earth. Thus if three Daniell's cells be con- 
 nected to a mile of ordinary submarine cable, a charge of 
 
30 Introductory Chapters. 
 
 about one farad of electricity will enter the cable, and if 
 so, exactly one farad of electricity will leave its outer sur- 
 face and flow into the earth : the outer surface is then 
 said to be negatively electrified, for it has less than its 
 natural amount of electricity. In the same way, if the 
 negative pole of the battery had been applied to the 
 cable the charge would have been negative, that is to 
 say, the cable would have one farad less than its natural 
 amount, and the outer surface of the cable would have 
 attracted one farad of electricity from the surrounding 
 earth, and would have been positively electrified. But in 
 either case these terms must not be understood to refer to 
 the tension of the exterior, but only to the quantity of 
 electricity collected there : whatever the tension of the 
 interior may be, that of the exterior is neither positive 
 nor negative, but remains rigidly zero. If the cable thus 
 charged, that is to say with a negative charge and a 
 negative tension inside, and with a positive charge and 
 zero tension outside, be lifted out of the water, its exte- 
 rior charge will come with it; and if it be dried, or 
 scoured, or washed, or treated in any way, this charge 
 cannot be removed from the surface, nor can its pre- 
 sence be in any way detected or made evident to the 
 senses : it remains, in fact, latent, and only when its 
 counterpoising charge in the interior is removed does it 
 spring again into activity and become once more elec- 
 tricity of tension. 
 
 If, instead of raising the tension of the inner wire of 
 the cable, we raise the tension of the water in which it is 
 
On Electrical Induction. 3 1 
 
 immersed, the same phenomena take place, that is to 
 say, a charge corresponding to the tension of the exte- 
 rior goes out of the cable (deflecting the galvanometer to 
 precisely the same extent as if it had been connected to 
 the interior), and the inside becomes negatively electrified, 
 that is to say, negative as regards the quantity of electricity 
 in it, but absolutely at zero as regards its tension. 
 
 The quantity of the charge depends on the difference 
 of tension between the interior and exterior, and not on 
 its degree : thus, if the exterior water have a tension of 
 ten cells, and the cable of thirteen, the charge is the same 
 as if the water were at zero and the cable at three. 
 
 We have already seen at fig. 8 that the positive tension 
 in a long telegraph line falls regularly from the battery to 
 the distant extremity of the line ; or, if the charge be 
 negative, it rises regularly from the battery to the end of 
 line, arid this directly in proportion to the distance. Now 
 since the charge varies everywhere as the difference be- 
 tween the internal and external tensions, it follows that 
 there is a constantly decreasing charge as we get further 
 from the battery j in fact, the diagram at fig. 8 would re- 
 present the charge as accurately as it does the tensions. 
 
 If the line be divided into any number of equal por- 
 tions, the proportion of charge in each length, commenc- 
 ing at the distant end, will be as the numbers i, 3, 5, 7, 
 9, 1 1, &c. ; and consequently, if the line be divided into 
 two portions, the quantity of the charges will be as one 
 to three respectively, or the half near the battery will con- 
 tain thrice the charge that the more distant half contains. 
 
32 Introductory Chapters. 
 
 The quantity of electricity contained in any given cable* 
 is called the electrostatic capacity, or sometimes the induc- 
 tive capacity. The length being constant, it depends on 
 the proportion between the surfaces of the copper con- 
 ductor, and of the dielectric or insulating material ; it 
 scarcely alters with temperature, but it differs with 
 different substances. It is about twenty-five per cent, 
 greater with gutta percha than with india rubber and its 
 compounds. Increasing the copper conductor increases 
 the quantity, and increasing the thickness of the dielectric 
 or insulating substance diminishes it ; in fact, the gutta 
 percha behaves in the same manner as air. Land lines 
 have so little charge because the thickness of the coating 
 of dielectric (which is in this case air) is so great. If we 
 double or treble the diameter of the copper, and also 
 that of the gutta percha, the quantity remains unchanged. 
 We obtain in that way a cable having four or nine times 
 as heavy a conductor with the same inductive capacity. 
 
 The electrostatic capacity of any insulated wire is 
 
 inversely proportional to the logarithm of — , where D is 
 
 d 
 
 the diameter of the dielectric or insulator and d that of 
 
 the conducting wire. Thus the diameter of the copper in 
 
 the Atlantic cable is 147 thousandths of an inch, and of the 
 
 gutta percha 467, and ^ff = 3'i77 ; and the logarithm 
 
 of 3 '17 7 is '5020, which is the logarithm required. 
 
 A short table of logarithms is given in the Appendix 
 
 for reference ; and we give below the dimensions and 
 
 ' With the unit tension of one volt, see p. 36. 
 
On Electrical Induction. 
 
 33 
 
 logarithms of two or three cables, and their calculated 
 inductive capacity : the diameters are given in inches :— 
 
 Name of Cable. 
 
 Diam. 
 
 of 
 
 Copper. 
 
 d 
 
 Diam. 
 
 of 
 Percha. 
 
 D 
 
 Logarithm 
 
 Calculated 
 Electro- 
 static 
 Capacity. 
 
 Malta and Alexandria 
 Atlantic Cable . . 
 Persian Gulf Cable . 
 No. 1 Gutta-percha 1 
 wire J 
 
 •153 
 
 •147 
 •no 
 
 •65 
 
 •463 
 •467 
 •380 
 
 •289 
 
 •4809 
 •5020 
 •5384 
 •6480 
 
 Farads. 
 ■3903 
 ■3739 
 •3486 
 
 ■2896 
 
 The electrostatic capacity of the Persian Gulf cable is 
 •3486 farads,* and from this datum we can, by means of 
 the logarithm, calculate the capacity of any other cable. 
 For example, the logarithmic equivalent for the Atlantic 
 cable is '5020, and that of the Persian Gulf is '5384 ; 
 and since the inductive capacity varies inversely in this 
 proportion, we have for the Atlantic cable — 
 
 •5020 : '5384 : : '3486 farads = '3739 farads. 
 
 The rule, in fact, is this : as the log. of the new cable is 
 to that of the Persian Gulf cable, so is '3486 farads to 
 the answer. It will be observed that the capacities in all 
 cases are about one-third of a farad per mile, and also 
 that the larger the logarithmic number, the smaller is the 
 capacity of the cable, f 
 
 * See pages 36 and 43. 
 
 t The following is a still simpler formula :— 
 
 •18769 
 Electrostatic capacity = — g — farads. 
 
 a D 
 
34 Introductory Chapters. 
 
 The obtaining of the logarithmic equivalent can be 
 done more easily by the following method than by that 
 previously given : — 
 
 Subtract the logarithm of the smaller diameter d from 
 that of the larger diameter D, and the remainder will be 
 the logarithmic number required. Thus in the instance 
 above given we have — 
 
 Log. of 467 = -6693 
 Log. of 147 = -1673 
 
 Logarithm required "5020 
 
 It will sometimes happen that the decimal part of the 
 logarithm of the smaller diameter d will be larger than 
 that of D ; the subtraction is nevertheless performed in 
 the same way, borrowing ten in order to make the left- 
 hand figure of D large enough for subtraction, and 
 disregarding all remainder. 
 
 This formula has another value : the logarithmic 
 
 number not only represents inversely the proportionate 
 
 inductive capacity of different cores, but it also represents 
 
 their insulation or resistance ; and that in a direct ratio, 
 
 the larger the logarithm, the higher the resistance. Thus, 
 
 assuming the quality of material the same, the Persian 
 
 Gulf core would give a higher resistance than the Atlantic 
 
 core in the proportion of 5384 to 5020.* 
 
 * As 5384 : 5020 : : res. P. Gulf : res. Atlantic. A still 
 simpler formula is the foUowitig : — Res. per statute mile of any 
 . D 
 
 , , , " d megohms. (See Appendix.) 
 
 gutta-percha cable = ■ 1 i-r / 
 
 13 
 
On Electrical Induction. 35 
 
 We saw at page 29 that the quantity of charge in a 
 cable was proportionate to the tension, and at page 17, 
 that the leakage or escape of electricity through any 
 conductor was also proportional to the tension. It arises 
 from this that a cable charged to a tension of two hundred 
 cells should fall to a tension of one hundred, in the same 
 time that it would fall from one hundred to fifty, or from 
 fifty to twenty-five; the escape per minute decreasing 
 just as the tension decreases. We know also that the 
 length of the cable does not aff"ect this result ; a cable 
 one mile long would fall to half its tension in the same 
 time as it would if it were one hundred miles long. 
 
 Lastly, we have just seen that the greater the inductive 
 capacity of a cable the smaller its resistance, or, in other 
 words, the greater its leakage. If we combine these 
 three laws we arrive at a somewhat curious general result, 
 viz., that at any given temperature, all gutta percha 
 cables should lose a given proportion of their charge by 
 leakage ; for example, they should fall from any tension 
 to half that tension in a uniform time ; and this irrespec- 
 tive of their length, or of the size of their conductor, or 
 of the thickness of their insulating coating, or of the 
 battery power employed.* In practice, the time of falling 
 from charge to half charge is found to be a very useful 
 method of comparing the insulation of a cable at difierent 
 periods of time. In fact, with extremely long cables it is 
 the only reliable metliod. 
 
 * See page 98. 
 
36 Introductory Chapters. 
 
 CHAPTER V. 
 On Electrical Quantity. 
 
 The meaning of this term has by this time become 
 apparent; it has been appHed to current electricity, 
 where it has been spoken of as a current of so many 
 farads per second ; and it has been spoken of as static 
 quantity, as an absolute static charge of so many farads. 
 If a cable contained a static charge of sixty farads, and 
 the whole charge were to flow out at a uniform rate in 
 one minute, we should have a current of one farad per 
 second. Ordinary telegraph cables usually have an 
 " Electro-static capacity," as it is termed, of about one- 
 third of a farad, that is to say, with the unit tension 
 (which is a little higher than that of one Daniell's cell) 
 they contain a charge of about one-third of a farad per 
 nautical mile. Consequently, one mile of cable, with a 
 tension of one hundred and eighty cells, would take a 
 charge of about sixty farads, and would, if discharged 
 during one minute at a uniform rate, maintain a current 
 of one farad per second. 
 
On Electrical Quantity. 37 
 
 The importance which attaches to quantity lies in the 
 fact that the influence of any electric current upon an electro- 
 magnet or galvanometer needle varies with the quantity 
 of the current passing round the coil: hence, if by aiiy 
 means we can get a greater quantity of current to pass 
 round our coil, we get our magnet or needle deflected 
 with a greater force. One obvious way of doing this is to 
 increase our electromotive force, and consequently our 
 tension : if we double this we get double the current 
 through our coils. Another usual expedient where we 
 have much resistance in the circuit, is to make the coil 
 wire circulate round the needle or magnet a great many 
 times, sometimes many thousand times, and each revo- 
 lution adds its influence to that of the others. We are 
 obliged, however, in this case to use very fine wire, or 
 else the outer coils get out of influence from their dis- 
 tance, for a long length of very small wire interposes 
 very great resistance, and therefore diminishes the quan- 
 tity. On short lines, where the resistances are small, it is 
 most convenient to use a few turns of very thick wire ; 
 and with a suitable battery it is easier to get a much 
 larger quantity of electricity to pass round a coil through 
 half a dozen turns of thick wire, than through six thou- 
 sand turns of thin wire, and hence to get a stronger de- 
 flection of the needle or of the electro-magnet. 
 
 It may be as well to remark here that the French 
 writers on electricity use the word intensity, as applied to 
 currents, in the same sense that we have used quantity • 
 and English translators frequently render the term by the 
 
38 Introductory Chapters. 
 
 word " intensity :'.' readers of French books or their 
 translations should therefore bear this in mind, and 
 remember that when the term " intensity " is applied to 
 electric currents, it usually has no relation to tension, but 
 should be understood to mea-n the quantity per second, 
 or strength of the current. 
 
 Not only does the influence of the current upon the 
 needle or electro-magnet depend on the quantity of the 
 current without any reference to its tension, but, generally 
 speaking, all the most important eff'ects of electricity vary 
 in magnitude as the quantity rather than as the tension. 
 The quantity of water or other substance decomposed in 
 a cell, or of metal deposited on an electrotype plate, 
 depends purely and only on the quantity of current which 
 passes through the cell. A battery of five hundred cells 
 will scarcely decompose more than a single cell, and if 
 resistances be interposed so as to make the quantity of 
 current the same, it will not decompose any more. 
 
 Faraday stated that a flash of lightning contains so 
 small a quantity of electricity that it probably would not 
 suffice to decompose more than a single drop of water ; 
 its enormous tension would be wasted, and only con- 
 verted into heat. There is one sense, however, in which 
 this statement would not be strictly accurate. Assuming 
 the tension of the lightning to be a million of cells, and 
 assuming the tension of one cell to be sufficient to de- 
 compose water, it is clear that by passing the flash 
 through a million vessels of water in a series we should 
 have tension enough to decompose a drop of water in 
 
On Electrical Quantity. 39 
 
 each vessel, and thus decompose a miUion drops. In 
 like manner, our battery of five hundred cells would de- 
 posit metal or decompose water in, say five hundied suc- 
 cessive vessels, losing a tension of one in each vessel ; 
 but in both these cases the quantity formed or decom- 
 posed would be precisely the same in each of the suc- 
 cessive vessels, and would depend only on the quantity 
 which had passed through them, without any reference 
 to the tension, which, as we know, would be much 
 greater at one end of the series than at the other. 
 
 In like manner, the amount of heat generated at any 
 point, or in any part of a circuit, varies as the quantity of 
 electricity passing multiplied by the difference of tension, or 
 (since these two things always vary in the same ratio) as 
 the square of the quantity of electricity passing. 
 
 An electric spark is a minute quantity of electricity 
 leaving a conductor at a high tension, and falling in 
 tension as it travels through the air, and giving out heat 
 and light at each point in proportion to the loss of 
 tension. A spark of electricity five or six inches long, 
 from an electrifying machine, contains so small a quan- 
 tity that it may be received on the knuckle with impu- 
 nity, but if a larger quantity be accumulated in a Leyden 
 battery to the same degree of tension, the shock would 
 destroy an ox. 
 
40 Introductory Chapters. 
 
 CHAPTER VI. 
 On Earth. Connections. 
 
 In most of the experiments hitherto described the 
 battery has had one pole to the earth, and the distaat 
 end of the hne has been placed to earth ; and even in 
 experiments performed in the room the terminations of 
 the arrangement have been, for the sake of perspicuity, 
 drawn and described as being connected to the earth. 
 In practice, however, this is not generally necessary, 
 most of the indoor experiments being equally well per- 
 formed on the table without any earth connection. 
 Wherever it is preferred to use the earth connection in 
 order to insure a tension of o as a starting point, a 
 single wire connected to any gas pipe, or to moist earth, 
 will serve for any number of earth connections. 
 
 The earth, being regarded as an inexhaustible reservoir 
 of electricity, offers no sensible resistance to the passage 
 into it, or out of it, of any quantity of electricity, in the 
 same way as the ocean would supply or receive at any 
 point an indefinite quantity of water ; and this is equally 
 
On Earth Connections. 41 
 
 true whether the points be close together or in different 
 parts of the globe. The earth is not, however, always or 
 even usually at the same tension at different points, and 
 - consequently currents are almost constantly circulating 
 through the earth, and also through the telegraph wires, 
 in their endeavours to equalise the tension. These are 
 sometimes so considerable as to show the existence of a 
 difference of tension of fifty or one hundred cells and 
 upwards between places not more than one or two 
 hundred miles apart. Such currents are, in fact, some- 
 times sufficient to deflect the needle of the mariner's 
 compass considerably : these extreme cases, however, only 
 occur during the prevalence of aurora, and are very 
 probably caused by the induction of the vast clouds of 
 electricity which are at such times seen travelling in the 
 upper regions of the atmosphere, and which, during their 
 passage over any part of the earth's surface, repel and 
 chase away by their induction the natural electricity at 
 that spot, thus causing temporary electric currents and 
 changes of tension. In such cases the telegraphist, 
 where possible, joins two parallel line wires together 
 into one circuit, without any connection with the earth, 
 and becomes thereby quite independent of its tensions. 
 
 In practice it is found that the earth connections, made 
 at stations where there are no gas or water pipes, are 
 often defective, and offer great resistance to the passage 
 of the current ; this is especially the case in dry seasons 
 and dry countries. The earth connections should there- 
 fore be carefully looked to occasionally. If a station 
 
42 Introductory Chapters. 
 
 have a defective earth, and have two wires leading to it, 
 the evil will generally disclose itself; for the current from 
 a distant station, finding a great resistance at the earth 
 plate, will partially return along the second wire, and will 
 exhibit feeble signals on the return wire, both at the 
 faulty station and at the station which sends the current. 
 Where, however, there is only one wire to a station, the 
 evil is not so easily apparent, and may exist for years, 
 - and cause bad working without discovery : the measure- 
 ment of the resistance of the circuit would disclose it, if 
 the evil were extreme, and this might be taken from 
 either station. The better way of discovering it is, how- 
 ever, to run a naked wire for a few hundred yards to the 
 nearest water or damp earth, and to connect it to the 
 line wire, interposing the galvanometer : if the earth offer 
 any sensible resistance, a portion of the current received 
 from a distant station will pass through the new earth 
 and show itself by slightly deflecting the galvanometer, 
 which would not be the case if the earth were perfect. 
 
On Units of Measurement 43 
 
 CHAPTER VII. 
 
 On Units of Measurement. 
 
 The measures now universally adopted are those of the 
 British Association. 
 
 1. The unit of resistance is called the ohm. One 
 million ohms = i megohm, and one millionth part of an 
 ohm = I microhm. 
 
 Before the use of the " British Association units," or 
 ohms, resistances were generally measured in Siemen's 
 units or Varley's units; i'0456 Siemen's units are equal 
 to one ohm. To convert Siemen's units into ohms, 
 multiply them by "9564. One Varley's unit is equal to 
 about twenty-five ohms. 
 
 The ohm is a resistance equal to 10', or ten million 
 absolute electromagnetic units, and the megohm is equal 
 to 10" absolute units. The ohm is often called the 
 B. A. unit. 
 
 2. The unit of tension, or electromotive force, is 
 called the volt, and it does not differ greatly from that 
 of a Daniell's cell. One million volts = i megavolt, and 
 one millionth of a. volt = i microvolt. According to 
 
44 Introductory Chapters. 
 
 the latest determination by Sir William Thomson, the 
 volt = -9268 the electromotive force of a Daniell's cell, 
 or the Daniell's cell = i"079 volt. 
 
 The volt is equal to 10°, or 100,000 absolute electro- 
 magnetic units of tension. 
 
 3. The unit of quantity is called a farad. One 
 million farads = i megafarad,' s.n.A one millionth of a farad 
 = I microfarad. The farad is that quantity of electricity 
 which, with an electromotive force of one volt, would flow 
 through a resistance of one megohm in one second ; and 
 since the quantity passing varies inversely as the resist- 
 ance, the megafarad is that quantity which would flow 
 through a resistance of one ohm in one second (see 
 p. 36). 
 
 10' I 
 
 The farad is equal — ^, or th part of the 
 
 10" 100,000,000 
 
 absolute electromagnetic unit of quantity. The mega- 
 farad, or quantity which flows through one ohm with one 
 
 volt in one second, is ■ — th part of the absolute unit. 
 100 
 
 4. The unit of current. — The current of electricity 
 is defined as the quantity of electricity which flows per 
 second. The British Association unit of current is a 
 current of one farad per second, or that which would 
 flow through one megohm with a tension of one volt, 
 or thrpugh one ohm with one microvolt ; it is equal to 
 
 10"' or ■ th part of the natural electromag- 
 
 100,000,000 
 
On Units of Measurement. 45 
 
 netic unit of current, or the unit tension, through the unit 
 resistance.* 
 
 5. The unit of work or dsoiamity. — The natural 
 unit of force in metrical measure is that which will pro- 
 duce a velocity of one metre per second in a mass 
 weighing one gramme (15 "44 grains) after acting on it 
 one second of time. Gravity would move a gramme 
 through 9'8o8 metres in a second ; therefore the natural 
 
 unit of work is — r— ^ of a gramme raised one metre in 
 9'8o8 
 
 one second. The conventional unit of work W ordi- 
 narily employed in metrical measure is, however, that 
 which will raise a weight of one gramme one metre in one 
 second, and is called the metre-gramme unit, and is of 
 course equal to 9 '8 08 absolute units of work. 
 
 * A unit current is one which, in a wire one metre long, bent so 
 as to form an arc of a circle of one metre in radius, or, which is the 
 same thing, an arc of 57J°, would repel a unit pole at the centre 
 of the circle with a unit of force. The whole circumference of a 
 circle, a metre in radius, is 6 "2832 metres, and would consequently 
 repel a unit pole at its centre with 6 '2832 units of force. If such a 
 circle be placed in the magnetic meridian, the deflection produced 
 by it on a small needle at its centre, as in the tangent galvanometer, 
 is due to the whole circumference, so that the strength of the current, 
 measured by only one metre of it, forms only -^i^ part of the 
 deflecting force. A unit current in a straight wire, measuring a 
 metre, repels another similar unit current, one metre distance, with a 
 unit of force. A unit magnetic field repels a metre's length of a 
 unit current held at right angles to the lines of magnetic force with a 
 unit of force. Hence in a unit magnetic field, a. metre of a unit 
 current, forming an arc of 57i°, and held in the magnetic meridian, 
 would cause a small needle at its centre to deflect 45°. — Ferguson's 
 Electricity. 
 
46 Introductory Chapters. 
 
 The work done is equal to the quantity of any current 
 per second multipHed by its fall of tension or difference 
 of potential ; it therefore varies as the number of farads 
 multiplied by the number of volts. The absolute unit of 
 work = 1000 volt-farads. The conventional or metre- 
 gramme unit of work W = 9808 volt-farads per second, 
 or 9808 farads falling through a tension of one volt. 
 
 6. The unit of heat H is taken as one gramme of 
 water raised 1° centigrade. The mechanical equivalent 
 of this unit is 423-8 metre-grammes, or grammes' weight 
 raised one metre (Paris), or H = 423'8 W. It is equal 
 to 4iS7'25 absolute units of work. It is proportional to 
 
 ■ the quantity of electricity multiphed by its fall of tension. 
 
 7. The electro-chemical unit. — It is found by ex- 
 periment that a unit quantity of current decomposes 
 ■142 grains of water, or generates i'o2 cubic inches of 
 mixed gas per second, the amount of zinc consumed in 
 each cell being '513 grains. The chemical equivalent 
 
 of zmc being - — ^»that of water. 
 
 One grain of zinc consumed in a Daniell's battery per- 
 forms 195,000 metre-gramme units of work, and one 
 grain consumed in a Grove's battery performs 365,000 
 units of work. (See also p. 115). 
 
 The tension necessary to decompose addulated water 
 is about 175 volts. 
 
47 
 
 CLARK'S DOUBLE-SHUNT DIFFERENTIAL 
 GALVANOMETER. 
 
 This instrument is a form of differential galvanometer, 
 that is to say, it is wound with two separate wires which 
 form distinct circuits around the needle ; one circuit ex- 
 tending from A to B and the other from C to D.* These 
 wires are both adjusted to have the same electrical re- 
 sistance, and also to have the same effect on the needle, 
 so that when a battery is connected to the two central 
 terminals B and C, the current divides itself into two 
 equal portions ; one flowing from B to A and tending to 
 deflect the needle to the left, the other from C to D 
 deflecting it to the right; but since the quantities and 
 forces are precisely equal, the needle remains quiescent : 
 if equal resistances be added on each side of the galva- 
 nometer the needle still remains motionless, but if unequal 
 resistances be added, taore electricity flows to that side 
 which has the lesser resistance, and the needle is deflected 
 to that side. The peculiarity of the instrument consists 
 
 * See Diagram of connections, Frontispiece . 
 
48 Double-Shunt Differential Galvanometer. 
 
 in the addition of a " shunt," or derived circuit, to each 
 half of the galvanometer : these shunts are marked on the 
 instrument " shunt y^ :'' they are short wires having a 
 resistance equal to exactly -^th of that of the half coil, 
 and when thrown into the circuit by the insertion of the 
 plug, -nnr'^s °f ^'^ current pass through them, and only 
 ■j-BTj- through the coils of the galvanometer : either one 
 or both half coils may be shunted at pleasure. The 
 instrument is supplied with a set of resistance coils vary- 
 ing from one to ten thousand ohms. 
 
 The instrument does not pretend to minute accuracy, 
 but is well suited for making all the ordinary practical 
 measurements required in telegraphy. Its daily and 
 hourly use cannot be too strongly recommended ; for a 
 constant reference to actual measurement is the very foun- 
 dation of telegraphy. The resistance of every principal 
 circuit should be measured every morning, and its varia- 
 tions recorded. In England it is generally considered 
 that even in bad weather a line should not give less 
 than one megohm (one million ohms) per mile, so that 
 a line of two hundred mUes should give not less than 
 
 1,000,000 _ ^. . . , , , . , 
 
 ■ = 5000 ohms. If It gives less than this, the 
 
 200 
 
 low resistance is due to defective insulation. The line 
 should now be tested in many separate sections, either 
 from the office (see Chapter I.) or by a visit to each 
 section. If the resistance per mile is the same for each 
 section the fault is probably in the nature of the insula- 
 tion, but if, as is usual, some sections are very much 
 
Double-Shunt Differential Galvanometer. 49 
 
 worse than others the fault will probably be found in 
 tunnels, in contact from branches of trees, from wires or 
 insulators touching the posts, from broken insulators, &c., 
 and a visit to the faulty locality will at once disclose the 
 cause of the evil. 
 
 The metalhc resistance of the line wire should also be 
 occasionally tested in sections in the finest weather : if 
 there is a uniformity in the sections all is well, but if 
 some give an unduly high resistance per mile, a closer 
 examination will almost certainly disclose imperfectly- 
 soldered joints, which oppose a great resistance to the 
 current and . interfere seriously with the working ; or the 
 earth connections may be out of order. It is difficult 
 for those who have not tried it to believe the improve- 
 ment that may be made in any line in a few days by 
 quantitative measurements, and by Un inspection of the 
 sections which give indications of being defective. 
 
 In the same way each battery should be tested for 
 resistance every few days, and those which are faulty 
 should be attended to. The operation is performed in a 
 few moments, and it will frequently be found that one dry 
 or defective cell or battery is sufficient to mar the work- 
 ing of a whole line. 
 
50 Double-Shunt Differential Galvanometer. 
 
 CHAPTER VIII. 
 To use the Instrument as an ordinary Galvanometer. 
 
 Plug up B and C and attach the hne wire and earth to 
 the terminals A and D. The current then passes through 
 half the coil from A to B, thence along the front bar to C, 
 and through the other half coil from C to D. The 
 instrument is now in the condition of an ordinary 
 " detector," and is suited for receiving a current, proving 
 the continuity of a circuit, or detecting a broken connec- 
 tion or loss of insulation in any apparatus. For these 
 purposes the instrument may sometimes with advantage 
 be inclined on its back support. 
 
Double-Shunt Differential Galvanometer. 5 1 
 
 CHAPTER IX. 
 
 To use the Instrument as a Sending and Receiving 
 Instrument. 
 
 Put the line to the terminal marked " key,'' at the back 
 of the instrument ; the battery to one of the small screws 
 on the front bar (the other pole being to earth) ; connect 
 the terminal marked " bridge " by a wire to A, and put 
 D to earth ; lastly, connect a short wire from B to C by 
 means of the flat-headed screws. In this condition, 
 when the key is pressed down, the battery current goes 
 direct from the front bar through the key to line without 
 passing through the instrument. When the key is resting 
 up against the bridge in its normal position, the current 
 received from the line passes from the key through the 
 bridge to its terminal, and thence by the connecting wire 
 to A, and through the galvanometer to D and earth. 
 
 If it be preferred that both the transmitted and received 
 current should pass through the galvanometer, the con- 
 nections are a little varied : join the battery as before to 
 the front terminal and connect a short wire from B to C as 
 
52 Double-Shunt Differential Galvanometer. 
 
 before ; connect a wire from the " key " terminal to A , 
 put the line to D and put " bridge " to earth. In this 
 condition both currents pass through the galvanometer. 
 On emergency the instrument may be used as a receiving 
 instrument by inclining it on its support, and by ex- 
 temporising stops out of pieces of wood or wire to limit 
 the movement of the needle. 
 
 Fig. 20. 
 
 3- P 
 
 tShwnt 
 
Testing Batteries. 53 
 
 CHAPTER X. 
 
 To use the Instrument as a Quantity Galvanometer 
 for Testing Batteries. 
 
 Incline the instrument and insert both the plugs 
 marked " shunt y^ ;" insert plugs at B and C, and con- 
 nect the poles of the battery to be tested at A and D, 
 and observe the deflection. The instrument is now 
 connected up in the manner shown at fig. 20, and 
 is adapted for measuring much stronger currents, and 
 also for testing the condition of batteries. Ascertain 
 the average deflection from a battery cell in good con- 
 dition, and then if any of the cells fall much below the 
 average standard it is a proof either that they offer too 
 great internal resistance or that the electromotive force 
 is become feeble, and in either case they should be 
 rejected. In this condition the instrument will give 
 nearly the same deflection with one cell as with ten cells 
 or one hundred cells, and it is sometimes convenierit to 
 test a whole battery at once instead of by single cells ; 
 the influence of a bad cell is not, however, so marked 
 when associated with other cells as when tested singly. 
 
 The testing of the individual cells may be done while 
 the battery is in use. 
 
54 
 
 Measurement of Resistances. 
 
 CHAPTER XL 
 The Measurement of Resistances. 
 
 To measure any resistance by direct measurement, insert 
 plugs at B and C, and connect the line to terminal A ; 
 
 JRe^ ColU 
 
 Fig. 21. 
 
 T 
 
 JJine 
 
 put the battery to the terminal marked " key,'' and the 
 resistance coil to D, their other ends being to earth. On 
 depressing the key, the battery current divides itself into 
 two parts, one part traversing half the galvanometer from 
 B to A, and through the Une to earth ; the other part 
 
Measurement of Resistances. 55 
 
 traversing the other half, and through the resistance coil 
 to earth. If the resistance of the coil and the line are 
 equal, the needle will remain motionless ; if they are not 
 equal, the needle will incline to one side or the other, and 
 the resistance must be varied till it remains unaffected. 
 The resistance unplugged will then equal that of the line. 
 If extreme accuracy be desired, it is advisable to repeat 
 the measurement, changing the line and resistance coil 
 to opposite sides, and taking the mean of the two 
 measures. 
 
56 Measurement of Resistances. 
 
 CHAPTER XII. 
 Tb.e Measurement of higher Resistances. 
 
 The resistance coils only range as high as ten thousand 
 ohms, and this, therefore, is the limit of their measure- 
 ment by the above plan. If it be necessary to measure 
 higher resistances, insert a plug between D and the block 
 marked " shunt -j-o-j-," all other connections remaining 
 unchanged. That portion of the current which traverses 
 the right-hand half of the galvanometer and the resistance 
 coil will now be divided into two parts, -,^ths traversing 
 the shunt and y^ passing through the galvanometer ; 
 it follows, therefore, since only y^ of its current affects 
 the right-hand portion of the galvanometer, while the 
 whole of its current affects the left hand, that in order to 
 produce no movement on the needle, one hundred times 
 more electricity must pass to the right hand than to the 
 left, or, in other words, the resistance of the right-hand 
 circuit must be one hundred times less than that of the 
 left. Hence the resistance unplugged on the coil must 
 be multiplied by one hundred to give the true resistance 
 of the line. By this method it is possible to measure 
 resistances as high as loo x 10,000 ohms, or one 
 million ohms (one megohm). 
 
Measurement of Resistances. 57 
 
 CHAPTER XIII. 
 To Measure very high Besistauces. 
 
 If it be necessary to measure still higher resistances, 
 the following plan may be resorted to. : Put the line to A 
 and the battery to D (its other pole being to earth), and 
 insert plugs at B and C. Note carefully the deflection, 
 the battery power being so arranged as to make this, if 
 possible, about 30° or 40°. Now disconnect the line 
 and insert in its place a resistance coil with its other end 
 connected to earth. Insert both the ^^ shunt plugs at 
 A and D, and reduce the number of battery cells to, say, 
 the tenth of its original number ; then, by varjdng the 
 resistance coils, reproduce exactly the same deflection as 
 before. This being the case, it is manifest that the same 
 quantity of electricity is passing through the galvanometer 
 coils as before ; but since the shunts convey -^■§^ of the 
 whole current, and therefore diminish its effect one hundred 
 times, and since the battery power is also diminished ten 
 times, we have to multiply the reading of the resistance 
 coil by 100 X 10, or one thousand times. By this method 
 
58 Measurement of Resistances. 
 
 we can measure resistances as high as looo x 10,000 
 ohms, or ten million ohms (ten megohms). For example, 
 suppose a line to have a resistance of 8,450,000 ohms; 
 this would give the same deflection with one hundred cells 
 direct as a resistance of 845 ohms through the shunted 
 galvanometer with one cell, or as 8,450 ohms with ten 
 cells. To obtain theoretical accuracy by this method 
 the resistances of the batteries ought also to be taken 
 into account, but this may be safely neglected in practice. 
 
Resistance of Short Wires. 59 
 
 CHAPTER XIV. 
 To Measure the Resistance of Sliort Wires, &c. 
 
 For measuring small resistances, such as one ohm or 
 less, the arrangements are the same in principle as in 
 Chapter 12;- that is to say, attach the wire to the 
 terminal A, and one pole of the battery to the "key" 
 terminal ; attach the resistance coil at D ; plug up B 
 and C, and also the y^ shunt at A ; finally, attach the 
 other pole of the battery and the other end of the wire 
 to be measured direct on to the opposite end of the 
 resistance coil without using any intervening connecting 
 wire. Press down the key, and, when the resistance 
 has been varied so as to bring the needle to zero, it will 
 be found that the resistance of the wire is -j^ of that 
 unplugged in the resistance coil. It therefore transmits 
 one hundred times more current; but since the effect 
 of this is diminished one hundred times by the shunt 
 at A, the effect on the needle is nil. This arrangement 
 is very useful for determining the specific conductivity of 
 specimens of copper and other metals. 
 
6o Resistance of Batteries. 
 
 CHAPTER XV 
 To Measure the internal Resistance of Batteries. 
 
 Connect the battery and a resistance coil in circuit 
 between tlie terminals A and D, and insert plugs in the 
 resistance coil so that it gives no resistance ; insert plugs 
 at A and C, and also both the shunt plugs at A and D. 
 The battery current will now flow through one half of the 
 galvanometer circuit only, being however reduced to 
 -j-^ th of its amount by the shunt D : the deflection of the 
 needle must be carefully read. The plug A must now be 
 removed to B, which causes the battery current to flow 
 through both halves of the galvanometer (each being 
 shunted). The circuit will now be as shown in Fig. 22, 
 and the needle will, of course, be deflected somewhat 
 inore than before. Now unplug the resistance coil which 
 is in circuit with the battery until the deflection of the 
 needle is reduced to its original amount, and the resistances 
 unplugged will be equal to the internal resistance of the 
 battery. For example, assuming the resistance of the 
 half coil to be ninety-nine ohms, and that of the shunt 
 
Resistance of Batteries. 
 
 6i 
 
 wire one ohm, the joint resistance of the two circuits will 
 
 Galvanometer x Shunt 99x1 
 
 = o"99 ohms. 
 
 be 
 
 Galvanometer + Shunt 99+1 
 Suppose the resistance of the battery to be four ohms, 
 the two together = 4-99 ohms, and the current acts on 
 the galvanometer needle through one half of its circuit 
 
 Fig. 22. 
 
 I^i.st Coils^ 
 
 only : when the second half of the galvanometer is thrown 
 in circuit by shifting the plug from A to B, the resistance 
 becomes 4-99 + o'99 = S'98, and therefore less current 
 passes ; but, since it acts upon the needle through both 
 coils instead of one, the deflection is greater than before. 
 The resistance coil is now varied until the needle recedes 
 to its original deflection, which will necessitate the un- 
 
62 Resistance of Batteries. 
 
 plugging of a resistance of four ohms, making the total 
 resistance now 5 '98 + 4 = 9'98, which is exactly double 
 the first resistance ; that is to say, in the one case we 
 had the current acting upon one coil through 4^99 ohms, 
 and in the other case acting upon the two coils through 
 9'98 ohms, the deflecting power on the needle having 
 been increased in the same ratio as the resistance. 
 
 Other methods of obtaining the resistance will be 
 found in the Appendix. 
 
Electromotive Force of a Battery. 63 
 
 CHAPTER XVI. 
 To detemune the Electroxuotive Force of a Battery. 
 
 This can only be done relatively in terms of some 
 other standard battery. The method is as follows : — 
 Determine the resistance of the standard and of the 
 other cells to be measured ; insert the shunt plugs at A 
 and D, and also at C and B, as in the former case, and 
 join up the standard cell in circuit with a resistance coil 
 to the terminals A and D, and unplug resistance until a 
 convenient deflection is obtained, say 1 5° ; note the sum 
 of the resistances in circuit, including that of the battery, 
 galvanometer, resistance coil, and connecting wires ; now 
 change the cell for another, and by unplugging the resist- 
 ance coils bring the needle again to the same deflection, 
 15°: having again found the total resistance in circuit, 
 the relative electromotive forces of the two cells will be 
 directly proportional to these resistances. 
 
 A table of the electromotive forces of different batteries 
 will be found in the Appendix. 
 
64 Specific Conductivity of Copper. 
 
 CHAPTER XVII. 
 To ascertain tlie Specific Conductivity of Copper. 
 
 The specific conductivity of pure copper is taken at 
 1 00 ; but the copper used in telegraphy being never 
 absolutely pure, has a lower conductivity, or, in other 
 words, gives a higher resistance : when carefully selected 
 its conductivity usually ranges from 85 to 95 per cent, 
 of that of pure copper. 
 
 One nautical mile (2029 yards) of pure copper, weigh- 
 ing lib., has a resistance of iiS5'5 ohms at 60° Fahr., 
 or of ii92'3 ohms at 75° Fahr. From these data we 
 can easily calculate the resistance of any other wire of 
 pure copper by dividing the above resistance by the 
 number of lbs. weight per mile. For example, a wire 
 weighing 180 lbs. per knot should, if pure, have at 60° 
 
 Fahr. a resistance of — %r^, or 6 '4 17 ohms per mile; 
 loo 
 
 and if its length were 3 J miles its resistance should be 
 
 3'5 X 6'4i7 = 22-26 ohms. If, however, the wire be 
 
 impure, and we measure its actual resistance by the 
 
The Specific Conductivity of Copper. 65 
 
 methods described at p. 54 or 59, and find it to be, say 
 
 26 ohms, we know that its conductivity is less than that 
 
 of pure copper in the inverse ratio of the resistances ; that 
 
 is to say — - 
 
 26 : 22'26 : : 100 : 8S'6 ; 
 
 or the copper has a conductivity of 85 '6 as compared 
 
 with pure copper. 
 
 For short lengths of wire the following data are 
 
 more suitable : — A wire of pure copper, one inch in length, 
 
 weighing one grain, has a resistance of 'ooi^iS ohms at 60° 
 
 Fahr., and the resistance of any other wire of pure copper, 
 
 , n _ , -,, , •001516 ohms X square of length 
 
 at 60° Fahr., will be ^-r---, — ^— ^ — ■ ^— > 
 
 Weight in grams 
 
 the length being taken in inches. To understand this 
 formula, imagine the above wire to be stretched to twice 
 its leiigth, without any alteration in its weight : being 
 twice as long as before, its resistance from this cause 
 must be twice as great ; but since it has been stretched 
 it has evidently been reduced to only half its original 
 size or sectional area ; its resistance therefore must be 
 again doubled from this cause. The wire will therefore 
 have 2 X 2, or four times its original resistance ; and simi- 
 larly, if stretched to three times its length, it would have 
 3 X 3, or nine times its resistance. In other words, the 
 weight being constant, the resistance of a wire varies as 
 the square of the length. 
 
 Let us now suppose the wire to retain its original 
 length, but to be (jiouble in weight; the wire having 
 twice the substance that it had before will evidently have 
 
 F 
 
66 Conductivity of Copper. 
 
 only half the resistance, and if it had four times the 
 weight it would have only one-fourth the resistance. In 
 other words, the resistance of a wire varies inversely as the 
 weight. Compounding these two rules together, we get 
 the before-mentioned formula for the resistance of any 
 wire of pure copper, viz. : — 
 
 ■001516 X L'^ 
 
 Resistance = —t-Tj 
 
 W. , 
 
 Having, therefore, calculated the theoretical resistance 
 of any wire, we have only to compare it with the actual 
 resistance, as before, to give its conductivity. 
 
 Thus 25 inches of wire, weighing 360 grains, should 
 
 •001516x25 X 25 
 give a resistance of 7 ohms, or '263 
 
 ohms ; but if it actually gives a resistance of "290, the 
 conductivity of the copper will be — 
 
 •290 : '263 : : 100 = 907 per cent. 
 
Allowance for Temperature. 67 
 
 CHAPTER XVIII. 
 
 Allowance for the Effect of Temperature on the 
 Conductivity of Copper. 
 
 We have hitherto neglected the effect of temperature, 
 
 and spoken of resistances only at a temperature of 60° ; 
 
 but since the resistance of copper increases "2 1 per cent. 
 
 for every degree Fahr., while the German silver of the 
 
 resistance coils scarcely changes perceptibly (about '024 
 
 for each degree Fahr.), it is necessary to make allowance 
 
 for this. For instance, in the first example the resistance 
 
 of the 3'S miles of pure copper was calculated as 22-26 
 
 ohms, at 60° (page 64) ; but if the actual temperature 
 
 at the time had been 90° we should have to add thirty 
 
 times '21 per cent, to the 22*26 ohms, or 
 
 30 X '21 X 22-26 
 
 = 1-40, 
 
 100 ^ ' 
 
 making the calculated resistance at 90° = 23-66 ohms; 
 
 and since the resistance of our tested wire actually was 
 
 26 ohms at 90°, the conductivity of the wire was — 
 
 26 : 23-66 : : 100 : = 91 per cent. 
 
68 
 
 Conductivity of Copper. 
 
 as compared with pure copper, instead of 85 '6, as first 
 stated. 
 
 The following table gives these relations still more 
 
 accurately : as an example of its use, suppose a wire 
 
 to give a resistance of 22-26, at 60° Fahrenheit, what 
 
 will it give at 90° ? or with a difference of 30 degrees : — 
 
 22'26 X i'o65 = 23707. 
 
 TABLE for calculating the Besistance of Copper at 
 different Temperatures. 
 
 To increase from lower Temperature to 
 
 To reduce from higher Temperature to 
 
 higher, multiply the Res. by the num- 
 
 lower, multiply the Res. by the num- 
 
 ber in Column 2. 
 
 1 
 
 ber in Column 4. 
 
 1 
 
 No. of 
 
 Column 2. 
 
 No. of 
 
 Column 2. 
 
 No. of 
 
 Column 4. 
 
 No. of 
 
 Column 4. 
 
 degrees. 
 
 
 degrees. 
 
 
 degrees. 
 
 
 degrees. 
 
 
 
 
 I' 
 
 
 
 
 
 I- 
 
 
 
 I 
 
 I -0021 
 
 16 
 
 1-0341 
 
 I 
 
 0-9979 
 
 16 
 
 0-9670 
 
 2 
 
 I '0042 
 
 17 
 
 1-0363 
 
 2 
 
 0-9958 
 
 17 
 
 0-9650 
 
 3 
 
 1-0063 
 
 18 
 
 1-0385 
 
 3 
 
 0-9937 
 
 18 
 
 0-9629 
 
 4 • 
 
 1-0084 
 
 19 
 
 1-0407 
 
 4 
 
 0-9916 
 
 19 
 
 0-9609 
 
 5 
 
 1-0105 
 
 20 
 
 I • 0428 
 
 5 
 
 0-9896 
 
 20 
 
 0-9589 
 
 6 
 
 1-0127 
 
 21 
 
 1-0450 
 
 6 
 
 0-9875 
 
 21 
 
 0-9569 
 
 7 
 
 1-0148 
 
 22 
 
 1-0472 
 
 7 
 
 0-9854 
 
 22 
 
 0-9549 
 
 8 
 
 1-0169 
 
 23 
 
 1-0494 
 
 8 
 
 0-9834 
 
 23 
 
 0-9529 
 
 9 
 
 I-O191 
 
 24 
 
 1-0516 
 
 9 
 
 0-9813 
 
 24 
 
 0-9509 
 
 10 
 
 I-02I2 
 
 .25. 
 
 1-0538 
 
 10 
 
 0-9792 
 
 ^5 
 
 0-9489 
 
 II 
 
 1-0233 
 
 26 
 
 1-0561 
 
 II 
 
 0-9772 
 
 26 
 
 0-9469 
 
 12 
 
 1-0255 
 
 '27 
 
 1-0583 
 
 12 
 
 0-9751 
 
 27 
 
 0-9449 
 
 ^3 
 
 1-0276 
 
 28 
 
 1-0605 
 
 13 
 
 0-9731 
 
 28 
 
 0-9429 
 
 14 
 
 1-0298 
 
 29 
 
 1-0627 
 
 14 
 
 O-9711 
 
 29 
 
 0-9409 
 
 15 
 
 1-0320 
 
 30 
 
 1-0650 
 
 15 0-9690 
 
 30 
 
 0-93.90 
 
Testing for Faults. 69 
 
 CHAPTER XIX. 
 To ascertain the Ijocality of Fatilts. 
 
 When a line is broken down at any spot, one of four 
 cases generally occurs : — 
 
 a. Either the line is broken, and makes full, or nearly 
 
 full earth at the fault ; 
 
 b. Or the line is unbroken, but makes a partial earth, 
 
 nearly sufficient to make the signals imperceptible ; 
 
 c. Or the fault is caused by two wires being in metallic 
 
 contact, so that the signals sent on one wire are 
 communicated to both ; 
 
 d. Or the line is broken asunder without making con- 
 
 tact with earth. 
 In all cases it is essential to record frequent 
 measurements of the resistance of each circuit, so that 
 when a fault occurs the resistance per mile may be known. 
 If the broken line makes full earth, the resistance of the 
 broken line, divided by the resistance per mile, gives the 
 distance of the fault from the station ; and if the distant 
 station obtains a corresponding result the confirmation is 
 
yo Testing for Faults. 
 
 complete. Thus, in a line of one hundred miles in length, 
 if the tests from the two extremities indicate distances of 
 forty-five and fifty-five miles respectively, the locality is 
 clearly indicated. 
 
 Usually, however, the fault gives a very considerable 
 resistance where the line makes contact with earth, so 
 that the sum of the two resistances greatly exceeds the 
 resistance of the line itself when perfect. In such cases 
 it is usual to estimate the fault midway between the two 
 points indicated ; thus if the respective resistances indicate 
 eighty-^ix miles and twenty-six miles, the sum of these 
 exceeds one hundred miles by twelve, and therefore half 
 this excess, or six, is deducted from each of the measures. 
 The same rule appKes in testing submarine cables, and \<. 
 is worthy of remembrance that the resistance at the fault 
 will often make the distance appear five, ten, or even 
 fifty or more miles farther off than it actually is ; even in 
 the largest faults in submarine cables, where the copper 
 is fully exposed, it is prudent to allow from two to five 
 miles for the resistance of the fault itself The nearest 
 approximation is obtained by first applying the positive 
 current, which clothes the fault with an insoluble salt of 
 copper, and increases the resistance enormously ; the 
 application of the negative current then dissolves the salt 
 and rapidly reduces the resistance : at the moment when 
 the copper is bright and clean, the resistance is at a 
 minimum, and gives -the' truest approximation to the 
 real resistance of the line ; if the negative current be 
 continued beyond this, hydrogen gas is formed, and this 
 
Testing for Faults. 7 1 
 
 resistance increases, and rises and falls capriciously as the 
 bubbles of gas escape. 
 
 The author has pointed out that the resistance of a 
 small fault is much greater with a small battery power, 
 say five cells, than with a higher power, say fifty cells ; 
 but if the fault be a large one the resistance will be more 
 nearly equal ; and if a great length of copper be exposed 
 the resistances will be the same : this fact affords a 
 valuable means of obtaining the approximate resistance 
 of a fault. 
 
 If the line is unbroken, but yet makes a partial 
 earth at the fault sufficient to weaken signals, two or 
 three methods present themselves. The first plan is that 
 of direct measurement from both ends alternately, as 
 given above, the distant end of the line being in «ach 
 case insulated; in this case the resistance of the fault is 
 measured twice over, and is roughly allowed for by the 
 method of calculation above given. 
 
72 
 
 Testing for Faults. 
 
 CHAPTER XX. 
 The Method of taking the Loop Test. 
 
 The second and more accurate plan is that known as 
 the "loop test,'' which gives a measure entirely inde- 
 pendent of the resistance of the fault. It can, however, 
 only be employed when there are two or more parallel 
 'wires to the circuit. To make this test, first ascertain 
 the resistance of the faulty wire (before it was injured) 
 and that of any other perfect wire running parallel with 
 it. This should be taken from previous records, but, if 
 unknown, the sum of the two resistances may be obtained 
 as follows : — 
 
 Fig. 23. 
 
 IPerfect yVtrc too 
 
 Feuddbj -Wire 76 
 
 33 
 
 Ji^artJv 
 
 Plug in B and C, and -attach one pole of the battery to 
 
Testing for Faults. 73 
 
 the "key" terminal. Have the twoHnes joined together 
 at the distant station, and attach one of them to D and 
 the other to the remaining pole of the battery. Connect 
 also one end of the resistance coil to the same battery 
 pole, and the other end to terminal A. When this is 
 done, the connections will be as shown in fig. 23, and, 
 on depressing the key and varying the resistance coil, 
 the sum of the resistances of the two lines may be correctly 
 ascertained. Although the fault makes earth at E, this 
 will not affect the measurement, since there is no other 
 earth connection in the circuit. 
 
 Having thus ascertained the resistance of the double 
 line, alter the connections as follows : put one poje 
 of the battery to earth and the other to the " key " 
 terminal ; plug in B and C ; attach the perfect wire to 
 the terminal D, and connect the faulty wire to the terminal 
 A, interposing, however, a resistance coil in circuit between 
 the terminal and the line. The connections will then be 
 as shown in fig. 24 : — 
 
 Fig. 24. 
 
 f\ 
 
 And on depressing the key, the battery current will flow 
 into both lines simultaneously, passing to the earth at the 
 
74 Testing for Faults. 
 
 fault E, and by varying the resistance so as to bring the 
 needle to zero, we shall make the sum of the resistance 
 of the perfect wire A and the portion x, equal to the sum 
 of the resistances of the other portion z and the coil R, 
 or, R + ir = A + X. 
 
 When this is the case, the position of the fault is at 
 once determined, for we have only to add together all 
 the resistances in circuit, viz.. A, x, z and R, and one 
 half the sum will indicate the position of the fault as 
 measured from the instrument in either direction through 
 A and X, or through R and z. 
 
 For example, let the resistance of the perfect line 
 be one hundred, and of the injured Une ninety-eight, and 
 suppose the fault to be at thirty-two ohms from the 
 distant station. Now, to obtain equilibrium of the 
 needle, we shall require on one side of the instrument 
 ICO + 32 = 132, and on the resistance coil side of the 
 instrument 56-^76= 132, and the needle will remain 
 at zero whatever be the resistance of the fault or however 
 it may vary at different times. The sum of these four 
 resistances is 264, and the half sum is 132, which, 
 measured in either direction, indicates the position of the 
 fault. If the resistance of both lines be equal, the 
 resistance unplugged at the coil will be always tvrice the 
 resistance of the fault measured from the distant station, 
 or twice x. 
 
Testing for Faults. 75 
 
 CHAPTER XXI. 
 Blavier's Formula for finding tlie Position of a Fault. 
 
 Where there is only one line, and it has a fault in it, 
 the following method may be resorted to with advantage, 
 and it has the merit that it only requires an unskilled 
 assistant at the other end of the line. Three tests have 
 to be taken for the operation, viz. : — 
 
 Let R = the resistance of the line before it was 
 defective (this must be obtained from pre- 
 vious records). 
 S = the resistance of the line when to earth at 
 
 the distant end. 
 T = the resistance of the line when disconnected 
 from earth at the distant end. 
 Having obtained these three resistances, multiply 
 S by S, and T by R, and add the products together ; 
 subtract from this amount T times S, and also R times S. 
 Whatever the remainder be, find its square root, and 
 subtract it from the resistance S ; the remainder will 
 give the resistance x, or the distance of the fault from 
 the station. 
 
^6 Testing for Faults' 
 
 Although this process appears compHcated, it is really 
 very easy, and occupies but little time. For example : 
 suppose the line to be one hundred units long, and the 
 fault at sixty-eight units' distance, and suppose the re- 
 sistance of the fault to be 96 units, as shown in fig. 25 ; — 
 
 Fig. 25. 
 
 JC 6S. 7/33. 
 
 then ^ = X + y = 68-1-32 = 100 
 S * = .X -)- = 68 4- ^ = 02 
 
 y + z 32 + 96 
 
 T = x + z = 68-I-96 = 164 
 
 We shall, however, have obtained these resistances by 
 measurement, and not by calculation. We have there- 
 fore — 
 
 S X S = 92 X 92 = 8464 ■) 
 
 >- 24864 
 
 T X R = 164 X 100 = 16400 
 
 T X S = 164 X 92 = 15088 
 R X S = 100 X 92 = 9200 
 
 V 242E 
 
 576 
 And the square root of 576 is 24,t which, deducted from 
 
 * See page 81. 
 
 t If the student is unacquainted with the proper method of ex- 
 tracting this, he may obtain it by trial and error : thus, 20 X 20, 
 30 X 30, 40 X 40, &c. 
 
Testing for Faults. yj 
 
 S ( = 92), gives 68 as the resistance of x, or the distance 
 of the fault from the station. 
 
 Of course, knowing .this distance x, the others are 
 obtained with ease; for R — 68 gives y, or the distance 
 from the opposite end, and T — 68 gives z, or the resist- 
 ance of the fault itself This test should, where prac- 
 ticable, be taken from both ends of the line. In the 
 above calculations the resistance of the fault is supposed 
 to remain constant during the measurement of the 
 resistances S and T ; but as in practice this is very apt 
 to vary, the average of several measurements should 
 be taken. 
 
78 Shunts and Derived Circuits. 
 
 CHAPTER XXII. 
 On Shunts and derived Circuits. 
 
 Shunts and derived circuits are of such constant 
 occurrence in telegraphy, that it is necessary to under- 
 stand well their properties. They occur in two forms 
 which, although they at first sight appear different, are 
 essentially the same. In fig. 26, a current flowing from 
 
 Fig. 26. 
 
 A towards C and D divides itself between B C and B D, 
 and if these have an equal resistance, one half the 
 current flows by each branch ; if they are unequal in 
 their resistance the rule is equally simple. Suppose 
 
Shunts and Derived Circuits. 79 
 
 the resistances to be respectively 1 9 ohms and i ohm ; 
 then if we suppose the whole current to consist of 
 20 parts (19 + i), then -^ths will flow through the 
 wire which has a resistance of i ohm, and -^^Ha through 
 that which has 19 ohms ; that is to say, the quantities of 
 electricity passing are inversely as the resistances : the num- 
 bers, in fact, only require changing places to represent 
 the quantities passing. 
 
 Fig. 27 shows another form of derived circuit, with a 
 galvanometer included in one of the circuits, in fact, an 
 ordinary shunt ; and here the same rule applies : if the 
 longer circuit, including the galvanometer, has a resist- 
 ance of 99, and the shorter circuit, or shunt, of i, then 
 calling the whole quantity 100 (99 + i), 99 parts of the 
 current will pass through the shunt wire, and i only 
 through the galvanometer. 
 
8o Resistance of Shunts. 
 
 CHAPTER XXIII. 
 
 On th.e multiplying Proportion of Shunts, and their 
 Kesistance. 
 
 The preceding rule gives us at once the means of 
 calculating the influence of shunts on a galvanometer; 
 for if, out of 100 parts, only one goes through the 
 galvanometer, it is evident that the influence on the 
 galvanometer will be only -j-J^ part of what it would be 
 if the whole current had passed through it — in common 
 parlance, the shunt has a multiplying power of loo. The 
 following is a convenient way of committing this to 
 memory : — 
 
 galv. + shunt 
 
 The multiplying power of a shunt = 
 
 QQ + 1 100 
 
 or — = = loo. 
 
 I I 
 
 shunt 
 
 On the Resistance of divided or shunted Circuits. 
 
 We must now deal with the resistance of such a divided 
 circuit (iig. 26 or 27), and here the rule is as follows. 
 
Ttie Resistance of Shunts. 8i 
 
 Calling the resistance of one circuit R, and the other r, the 
 
 R X '' 
 
 joint resistance of any two circuits = , or t/ie resistance 
 
 R + /- 
 
 equals the product divided by the sum. Thus, in fig. 26 we 
 
 have resistance = — • = -i- = -05 : and again, in 
 
 19 + I 20 ^^' ^ ' 
 
 c r. 99 X I 99 
 
 ng. 27, we have res. = ^^ = ^^ = •90, and in 
 
 99 + 1 100 
 
 ■^ r . • , , 10 X 10 
 
 circuit of two resistances, each 10, we have = 
 
 10+10 
 
 100 
 
 = 5 ; and this form of calculation refers equally to 
 
 20 
 
 a divided circuit, as in fig. 26, or to a shunted circuit, as 
 in fig. 27. If we wish to obtain the total resistance 
 of the circuits we must of course add those of the 
 lengths A and B. Sometimes three or more wires 
 branch off from one spot, and in this case the same 
 principles apply. First find the joint resistance of any 
 two of the circuits, and considering this as one resist- 
 ance, combine it with the remaining one, and so on. 
 For example, let the resistances be 30, 60, and 80 : we 
 
 I. £ , 3° X 60 1800 , , 20 X 80 
 
 have first-^^ -— = = 20, and then -— = 
 
 30 + 00 90 20 + 80 
 
 1600 
 
 = 16. 
 
 100 
 
 Another, and often a readier method of obtaining the 
 
 joint resistance of two or many circuits is as follows : 
 
 add together their reciprocals, and the sum will be the re- 
 
 G 
 
82 The Resistance of Derived Circuits. 
 
 ciprocal of tkeir joint resistance.* Thus, in the case above 
 given, the resistance 
 
 = =. = — - — =i6. 
 
 A + sV + w -0333 + '°i67 + -0125 '0625 
 
 The conducting power of any circuits, whether simple or 
 combined, is of course inversely as their resistances ; that 
 is, it varies as the reciprocals of their resistances. Fig. 28 
 
 Fig. 28. 
 
 represents a compounded circuit of which the resistance 
 would be thus calculated. First obtain the joint resist- 
 ance of E and F, and add it to that of D. To this 
 amount add the joint resistance of B and C, and finally 
 that of A. For the sake of practice, the student may also 
 with advantage calculate the resistance of the accom- 
 pan)dng circuit, beginning with D and E, and then 
 including C, and so on. The calculation is extremely 
 easy, and he will soon perceive that he may elongate 
 the figure to any extent in the direction of B, and 
 
 * The reciprocal of any number is obtained by dividing I by the 
 number : thus ^, or '0333, is the reciprocal of 30, &c. 
 
The Resistance of Derived Circuits. 83 
 
 add any number of similar branches (each of which 
 will convey a portion of the current to earth), without in 
 the least degree changing the total resistance as measured 
 from B. 
 
 Fig. 29. 
 
 He will also perceive the analogy which this case 
 bears to that of an ordinary line circuit, where every 
 pole conveys a certain quantity of electricity to the earth 
 by reason of its imperfect insulation. 
 
84 The Electrical Balance. 
 
 CHAPTER XXIV. 
 On Measurement by the Electrical Balance. 
 
 This arrangement — commonly known as the Wheat- 
 stone balance — is of extended use in telegraphy, and 
 usually takes the place of the differential galvanometer ; 
 for very delicate measurements it is indeed a more 
 sensitive and reliable instrument. 
 
 The arrangement is usually drawn in the form shown 
 at fig. 30, in which the galvanometer is supposed to 
 be connected up in the manner described at page 50. 
 
 In all cases it consists of four parts, ABC and D, vtdth 
 a galvanometer connected across at the junctions c andy^ 
 When a battery current is passed through the arrange- 
 ment it divides itself into two circuits, one 'portion flowing 
 through A and C, and the other portion through B and 
 D ; and if all four resistances be equal the current will 
 have no tendency to pass across from c \o f, and the 
 galvanometer will remain at zero ; but if they be of 
 unequal resistance, then the current will flow from cX.of^ 
 or vice versA, and the galvanometer will be deflected. 
 
The Electrical Balance. 
 
 85 
 
 Having then found nvo equal resistances A and B, and 
 inserted some unknown wire at D, we have only to 
 unplug the resistance coil at C until the galvanometer 
 remains at zero, and the resistance unplugged gives an 
 accurate measure of the resistance of D. When the 
 
 Fig. 30. 
 
 iEarth Earth 
 
 needle remains stationary the following relations always 
 exist between the four parts : if A is equal to B, then C 
 must be equal to D j or if A is equal to C, then B must 
 be equal to D. The following is a more general ex- 
 pression of the proportions which must exist : — 
 
 A : B : : C : D> and consequently, 
 
 A : C : : B : D 
 
 To understand clearly the nature of this arrangement, 
 
 the student must remember that, in every case, the circuit 
 
 is divided at some point into two branches, and therefore 
 
 that at this point the two tensions are equal. At some 
 
86 The Electrical Balance. 
 
 other point the two branches are again joined together, as 
 in fig. 30, or else they both go to earth, as in figs. 31 
 and 32, and they are therefore at this point again at equal 
 tension, whatever may be the lengths of the two circuits 
 in the intervening space. Now calling the tension at the 
 point where the branches first diverge 100, and at the 
 point where they meet again (or where they are connected 
 to earth) o, let us divide each circuit into 100 equal 
 spaces, as in fig. 31. 
 
 Fig. 31. 
 
 fM(° '"""(D--, 
 
 If now a wire be joined across from one half circuit to 
 the other, connecting 50 to 50, or 75 to 75, or as shown 
 in the drawing, 25 to 25, or between any other two 
 points of equal tension, no current will flow through 
 it, because the tensions at these points are similar ; but 
 if they are connected between any two points of 
 ««^^«a/ tension, as, for example, from 50 to 25, of course 
 some current will flow through it, and the galvanometer 
 will be deflected. The proportions above given, 
 A : B : : C : D, which obtain when the tensions are 
 equal, are therefore obvious enough : in the instance 
 given it only amounts to our saying, 75 : 75 :: 25 to 25. 
 
The Electrical Balance. 
 
 ^7 
 
 and similarly in all other cases ; and the other proportion, 
 A : C : : B : D, is in effect only to say, 75 : 25 : : 75 : 25. 
 It is very usual in practice to unite A and B in one 
 box, as shown in fig. 32, having two parallel sets of 
 resistances of ten, one hundred, and one thousand ohms, 
 and by employing ten on one side, and one hundred or 
 one thousand on the other, the corresponding resistances 
 
 XEartTi 
 
 on coil C will have to be multiplied or divided by ten or 
 one hundred, in accordance with the proportions above 
 given ; of course, any other two known resistances may 
 be employed at A and B. For example, suppose A to be 
 290 units, B 1500, and C 6420, then — 
 A : B : : C : D ; or, 
 290 : 1500 : ; 6420 = 33207 ohms. 
 
88 The Measurement of Gutta-percha. 
 
 CHAPTER XXV. 
 On the Measurement of Gutta-percha CaWes. 
 
 The measurement of the insulation of gutta-percha wire 
 so often becomes necessary that a few remarks about 
 its testing may be useful ; the method of making the 
 tests has already been given at pages 56 and 57*; its 
 resistance, however, varies so greatly with its temperature, 
 that without taking this into account very little idea can 
 be formed of its degree of insulation. It is always 
 customary to test it when manufactured at a temperature 
 of 75° Fahr. (or 24° Centigrade), and to refer to its insula- 
 tion at this temperature ; its resistance at 32° is, however, 
 more than fourteen times as great as it is at 75°. On 
 the opposite page will be found a table giving its 
 resistance at different temperatures, taking that at 
 75° as = I. 
 
 Supposing then that we have measured the resistance 
 of a length of 50 miles of cable, at a temperature of 
 40, and find it to be 70-4 megohms, the resistance of 
 each mile would be 70*4 x 50 = 3520 megohms. Re- 
 ferring to 40° in the table, we find 876, and if we wish 
 to know its resistance per mile at the standard tempera- 
 ture, or 75", we have the simple proportion — 
 876 : I :: 3520 : 40i'8 megohms. 
 • See also Appendix. 
 
The Measurement of Gutta-percha. 
 
 89 
 
 We have, in fact, only to divide the resistance we obtain 
 by the number in the table corresponding to the tempera- 
 ture of the cable at which we obtained it. 
 
 To find the resistance at any other temperature, we 
 have only a case of simple proportion. Suppose we have 
 tested a cable giving 100 ohms at 45° Fahr., and wish to 
 know its resistance at 60° ; we have the following pro- 
 portion : — 
 
 As the resistance given in the table for 45° (6 '42 5) is 
 to the resistance given at the required temperature 
 (2 '535), so is the actual resistance of our cable to its 
 resistance at the required temperature, or — 
 
 6'425 : 2'535 : : 100 ohms : 39'4S ohm's. 
 
 TABLE of the relative Resistance of Gutta-percha at 
 different Temperatiires. 
 
 Fahr 
 
 Resistance. 
 
 Fahr 
 
 Resistance. 
 
 Fahr 
 
 Resistance. 
 
 Fahr 
 
 Resistance. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 90 
 
 •394 
 
 75 
 
 1000 
 
 60 
 
 2'535 
 
 45 
 
 6-425 
 
 89 
 
 ■430 
 
 74 
 
 I -064 
 
 59 
 
 2-697 
 
 44 
 
 6-835 
 
 88 
 
 •447 
 
 73 
 
 1-132 
 
 58 
 
 2-869 
 
 43 
 
 7-273 
 
 87 
 
 •475 
 
 72 
 
 I -204 
 
 57 
 
 3-053 
 
 42 
 
 7-738 
 
 86 
 
 ■506 
 
 71 
 
 1-282 
 
 56 
 
 3-248 
 
 41 
 
 8-233 
 
 85 
 
 •538 
 
 70 
 
 1-364 
 
 55 
 
 3-456 
 
 40 
 
 8-760 
 
 84 
 
 •572 
 
 69 
 
 1-451 
 
 54 
 
 3-680 
 
 39 
 
 9-132 
 
 83 
 
 •609 
 
 68 
 
 1-543 
 
 53 
 
 3-912 
 
 38 
 
 9-917 
 
 82 
 
 •648 
 
 67 
 
 1-642 
 
 52 
 
 4-162 
 
 37 
 
 10-55 
 
 8i 
 
 •689 
 
 66 
 
 i'747 
 
 51 
 
 4-429 
 
 36 
 
 H-22 
 
 80 
 
 ■733 
 
 65 
 
 I-8J9 
 
 50 
 
 4-712 
 
 35 
 
 11-94 
 
 79 
 
 •780 
 
 64 
 
 1-978 
 
 49 
 
 5-013 
 
 34 
 
 12-71 
 
 78 
 
 ■830 
 
 63 
 
 2-104 
 
 48 
 
 5-334 
 
 33 
 
 13-52 
 
 77 
 
 •883 
 
 62 
 
 2-239 
 
 47 
 
 5-675 
 
 33 
 
 14-38 
 
 76 
 
 ■940 
 
 61 
 
 2-382 
 
 46 
 
 6-038 
 
 
 
91 
 
 APPENDIX. 
 
 PART I.— ELECTRICAL FORMULA. 
 
 OHM'S LAW. 
 
 E 
 Q=R 
 
 where Q = the quantity of the current, or the strength, 
 or the force, or the intensity of the current, as it is 
 variously called. 
 
 E the electromotive force. 
 
 R = the total resistance in circuit ; or, 
 «E 
 
 ^" nR+r 
 where n represents the number of cells. 
 
 E = their electromotive force. 
 
 R = their internal resistance. 
 
 r = the resistances exterior to the battery. 
 
92 
 
 Conduction. 
 
 CONDXrCTING POWER. 
 
 Conduction is the converse of resistance. The re- 
 ciprocal of any resistance represents its conductivity or 
 conduction ; or the conduction is obtained by dividing i 
 by the resistance : thus, -po-o, ^fg. 
 
 w 
 The conducting power of any wire varies as — . 
 
 The joint conducting power of any two or more 
 circuits having resistances = a, b, and c : 
 
 = reciprocal a + reciprocal b, etc., 
 or as the sum of the reciprocals. 
 
 TABLE of the Relative Conductivity of different Metals 
 
 
 at 32° Falir. 
 
 Silver .... 
 
 lOO 
 
 Copper, pure 
 
 99'9 
 
 „ selected commercial 
 
 • 8s to 95 
 
 „ ordinary commercia 
 
 . 40 to 70 
 
 Brass . 
 
 20 
 
 Gold . 
 
 
 78 
 
 Zinc . 
 
 
 29 
 
 Steel . 
 
 
 . about 16 
 
 Iron . 
 
 
 . about 15 
 
 German silver 
 Tin . 
 Lead . 
 
 
 12 to 16 
 12-4 
 8-3 
 
 Platinum 
 
 
 6-9 
 
 Mercury 
 
 
 1-6 
 
Conduction. 
 
 93 
 
 TABLE giving the Kesistance in Ohms of various 
 Metals and Alloys at 32° Fahr. 
 
 (Jenkin : Cantor Lectures.) 
 
 
 Resistance 
 
 Resistance in 
 ohms of a wire 
 
 Percentage 
 
 NAME OF METALS. 
 
 in ohms 
 of a wire 
 
 one foot long 
 and one thou- 
 
 in variation 
 of resistance 
 
 
 one foot long. 
 
 sandth of an inch 
 
 per degree of 
 
 
 weighing 
 one grain. 
 
 (one mil) in 
 diameter. 
 
 temperature 
 Fahr. 
 
 Silver, hard drawn . . 
 
 •2421 
 
 10-787 
 
 -209 
 
 Silver, annealed . 
 
 
 
 •2214 
 
 9 '93 6 
 
 
 Copper, annealed 
 
 
 
 ■2064 
 
 9-718 
 
 •215 
 
 Gold .... 
 
 
 
 •5849' 
 
 12-52 
 
 •202 
 
 Aluminium 
 
 
 
 
 
 •0682 
 
 17-72 
 
 
 Zinc . . 
 
 
 
 
 
 ■5710 
 
 38-22 
 
 •202 
 
 Platinum 
 
 
 
 
 
 
 3-536 
 
 55 '09 
 
 
 Iron . 
 
 
 
 
 
 
 1-242 
 
 59'io 
 
 
 Nickel . 
 
 
 
 
 
 
 1-078 
 
 7578 
 
 
 Tin . . 
 
 
 
 
 
 
 i'3i7 
 
 80-36 
 
 -202 
 
 Lead . 
 
 
 
 
 
 
 3'236 
 
 ii9'39 
 
 •215 
 
 Antimony 
 
 
 
 
 
 
 3'324 
 
 2 1,6 -oo 
 
 -216 
 
 Bismuth 
 
 
 
 
 
 
 5 '054 
 
 719-0 
 
 -196 
 
 Mercury . 
 
 
 
 
 
 
 18-740 
 
 600-0 
 
 •040 
 
 I Silver, 2 Platinum 
 
 L* 
 
 
 4'243 
 
 148-35 
 
 -017 
 
 I Silver, 2 Gold 
 
 
 2-391 
 
 66-10 
 
 •036 
 
 German silver . . 
 
 
 2-652 
 
 127-32 
 
 ■024 
 
 * This alloy is used for making standard resistances. 
 
 MEASTTBEMENT OF CXniE,EN"TS. 
 
 • I. With a Thomson's reflecting galvanometer the 
 strength of the current or the quantity per second is 
 
94 Currents. 
 
 directly proportional to the angle of deflection : shunts may 
 be used so as to bring the deflections within the range of 
 the instrument. 
 
 2. With an ordinary galvanometer the deflection 
 caused by the weaker current may be reproduced by 
 inserting a shunt with the stronger current ; the shunt 
 ratio (page 80) will represent that of the currents ; but it 
 must not be forgotten that the resistance has been varied 
 at the same time. 
 
 3. With a sine galvanometer the. strength of the 
 current is proportional to the sine of ihe angle of de- 
 flection. A table of sines is given at page/iS/. 
 
 4. With a tangent galvanometer the strength is 
 proportioned to the tangent of the angle of deflection. 
 A table of tangents is given at page 157- 
 
 5. The method of vibrations is sometimes a conve- 
 nient one for determining the strength of the current or 
 its quantity. Place the coils of a horizontal galvanometer, 
 with a suspended needle, east and west, so that the 
 needle is at right angles to it : the current will not, 
 therefore, cause any deflection. Then set the needle 
 vibrating, and count the number of vibrations in one 
 minute, or any other period of time (under the influence 
 of the earth's magnetism only), and call this m. Then 
 
Currents. 95 
 
 ascertain the number when the current c is passing, and 
 lastly when the current C is passing. 
 
 Then w' represents the force of the earth's magnetism, 
 
 c^—m^ represents that of the current c, 
 
 C' — m' that of the current C, 
 
 — i ^ = the force of C in terms of c, 
 
 C^ — m' 
 
 and — = the force of C in terms of the earth's 
 
 magnetic force. 
 It is necessary that the galvanometer should have but 
 one needle, and that this should never swing outside the 
 coUs. 
 
 6. By the Voltameter. — In this instrument the 
 quantity of the current is proportional to the quantity 
 of gas formed. 
 
 7. By the heating of a fine wire. — The heat pro- 
 duced in any circuit is proportional to the square of the 
 quantity of current passing. 
 
96 Resistances. 
 
 MEASUREMENT OF RESISTANCES. 
 
 1. By Wheatstone's Bridge. — This method of 
 measurement, and that by the differential galvanometer, 
 are described at page 84, and at page 54 <?/ seq. 
 
 2. By addition to a known circuit. — This method 
 requires the use a Thomson's, or other galvanometer, 
 whose deflections have a known value : if with a gal- 
 vanometer, battery, and resistance coil, whose total re- 
 sistance is R, we get a deflection D, and if after the 
 addition of the unknown resistance x we get another 
 deflection d, then — 
 
 (f : D : : R : R + ^, 
 
 and X = R. 
 
 a 
 
 3. By comparison with another resistance. — It 
 may occur that the operator have no resistance coils and 
 only one known resistance. Let Z be the unknown 
 resistance of the battery and galvanometer, including, if 
 necessary, any other resistances. Let X be the resist- 
 ance we wish to measure, and let R be a known resistance. 
 Also, let D be the deflection with Z, d that with R -)- Z, 
 and d' that with X + Z. We must first obtain the;value 
 of Z, from which we can afterwards obtain that of X. 
 
 Now D : rf : : Z -f R : Z, 
 ,„ ^XR 
 
Resistances. 97 
 
 Again, D : ^' : : Z + X : Z, 
 
 and X = -. . 
 
 a 
 
 (See also No. 10). 
 
 4. By tensions. — Connect one pole of a battery to 
 earth. Insert a resistance coil R between the battery 
 and the resistance ^» to be measured, which must also 
 have its other end connected to earth. Measure the 
 tensions T and t on each side of the resistance coil 
 (see fig. 39, p. 128), then 
 
 T : / : : R + ^ : ic, 
 
 and X = pjT^. 
 
 5. To test ordinary lengths of insulated wire 
 the most sensitive instruments are necessary. Thomson's 
 galvanometers are always used, and the following method 
 is generally employed : — 
 
 Determine the deflection of the instrument with i cell 
 
 through ro megohms (by using a shunt with a multiplying 
 
 power of 1000 and a resistance of 10,000 ohms). Call 
 
 this deflection D. Test the length of core with a very 
 
 large number of cells, N ; let the length in yards be L, 
 
 and let the deflection obtained with N cells (without the 
 
 shunt) be d. 
 
 D X N X L 
 
 Res. per naut. imle = —3 X 10 megohms. 
 
 ^ d X 2029 ° 
 
 6. To test longer lengths of cable a similar method 
 is employed : the deflection D is obtained with about 
 2 cells, with a shunt having a multiplying power S, and 
 
 H 
 
98 Resistances. 
 
 10,000 ohms. The deflection on the cable is obtained 
 
 with, say 200 cells, without shunt, and is called d; the 
 
 length in nautical miles is called L, and the ratio of the 
 
 two batteries B. 
 
 We have, therefore, the original resistance, 10,000 ohms, 
 
 multiplied by the multiplying power . of the shunt S, by 
 
 the number of cells or ratio between the two batteries 
 
 B (= 100), by the length L, and by the original deflection 
 
 D, and we have to divide the product by the deflection 
 
 of the cable itself, d; or, 
 
 T, ., , SxBxLxD 
 
 Res. per mile = 10,000 ohms . 
 
 d 
 
 The ratio of the batteries may be obtained more cor- 
 rectly by the method given at page 109, and the ratio 
 thus obtained should be substituted for the value B, where 
 accuracy is desired. 
 
 7. Calculating Resistance by tlie time of falling to 
 Half-Tension {Jenkin). 
 
 The resistance R of any core may be calculated from 
 the time of falling to any tension by the formula 
 
 T, '4343 Xt 
 
 R = -=r megohms. 
 
 F X log. — 
 c 
 
 Where F is the electrostatic capacity of the cable in 
 
 farads per mile (or any other length), and t the time in 
 
 seconds of falling from any tension C to any lower 
 
 tension c. 
 
Resistance of Batteries. 99 
 
 When the fall is from tension to half-tension this 
 formula becomes as follows : unfortunately these measures 
 are of little practical value as they are greatly influenced 
 by electrification : 
 
 1-443 X t , 
 
 R = = megohms. 
 
 r 
 
 INTERNAL RESISTANCE OF BATTERIES. 
 
 8. By the sine 0* tangent galvanometer. — If a 
 
 battery joined up in circuit with a sine galvanometer 
 give a certain number of degrees deflection, and we 
 add resistance until the (sine of the) deflection becomes 
 half what it was, we are certain that the resistance 
 is doubled, and, therefore, that the resistance added is 
 equal to the original resistance. If we deduct, therefore, 
 the resistance of galvanometer and connections from the 
 resistance added, we obtain the resistance of the battery. 
 
 9. By Sir William Thomson's method. — Join 
 
 up in a circuit the battery, a resistance coil R, and 
 
 a galvanometer G, and note carefully the deflection ; 
 
 then introduce a second wire S between one pole of the 
 
 battery and the other : this will of course weaken the 
 
 influence of the battery current, and the deflection of 
 
 the galvanometer will become lessened : now decrease 
 
 the resistance of the resistance coil R until the deflection 
 
 of the needle becomes as great as before, and call the 
 
 new resistance r : -then — 
 
 R-r 
 Res. of battery = S x — r-?;- 
 
1 00 Resistance of Batteries. 
 
 10. By Clark's method. — For this method a thick 
 wire differential, or a shunted differential galvanometer 
 is required. Connect the battery in circuit through one 
 half the galvanometer only, and note the deflection; 
 then connect it through both halves of the galvanometer, 
 and add resistance until the deflection is reduced to its 
 first amount : the resistance added will then be equal to 
 the internal resistance of the battery (see p. 60). 
 
 11. By a galvanometer whose deflections are 
 proportional. — Let D be the deflection obtained with 
 the battery in current with a galvanometer, and some 
 resistance r ; and d the ffpflection with some larger re- 
 sistance R (the resistance of the galvanometer being 
 included in R and r) ; and let x = the resistance of the 
 battery. 
 
 Then T) : d ■.:'Si-\^ x -.r-^-x, 
 (</ X R) - (D X r) 
 
 and X = 
 
 D ~d 
 
 In using this method any other resistance y may be 
 included with x, and the formula becomes — 
 (^xR)-(Dxr) 
 
 and by deducting x we get the value of y ; or, if y be 
 large in comparison with x, the latter may be neglected. 
 By this method one resistance r may be compared with 
 another, as in No. 3. 
 
 12. Measuring resistances by tension. — If a re- 
 
Derived Circuits. loi 
 
 sistance coil be joined in circuit with a battery, and so 
 adjusted that the tension at the point of junction is just 
 half the full tension of the battery, the resistance of the 
 coil will be equal to that of the battery (see p. 20). 
 
 PARALLEL OR DERIVED CIRCUITS. 
 
 1. The joint resistance of any two parallel or 
 derived circuits having resistance = a and b is equal 
 to their product divided by their sum, or 
 
 a+b 
 
 2. The joint resistance of any three circuits a, b, 
 
 and c, is 
 
 a b c 
 
 R = 
 
 ab + bc + ac 
 
 3. The joint resistance of any number of resist- 
 ances is obtained by adding together their reciprocals ; 
 the result will be the reciprocal of their joint resistance : 
 
 thus — 
 
 1 
 
 R = 
 
 - + - + -■ 
 a^ b^ c 
 
 (The foregoing formulae . refer equally to derived cir- 
 cuits which, after separating, unite again, or to those 
 which branch off in two or more distinct circuits to 
 earth.) 
 
I02 Shunts. 
 
 GALVANOMETERS AND SHUNTS. 
 
 4. The joint resistance of a galvanometer and 
 
 , ^ . , Galv'. X shunt 
 
 shunt IS as above, -r—-^ . 
 
 Galv'. 4. shunt 
 
 5. The multipljdng power of any shunt is equal to 
 
 Galv'. + shunt Galv'. , 
 
 T^ 1 or -; \- I. 
 
 shunt ^ shunt 
 
 6. To prepare any given shunt. — It is sometimes 
 necessary to prepare a shunt having some definite mul- 
 tiplying power, as for instance! o, 100, etc. : if we call the 
 resistance of the galvanometer G, and of the required 
 shunt s, and let n be the multiplying ratio we require, 
 then — 
 
 G 
 
 s = . 
 
 « — I 
 
 For example, if a galvanometer of 990 units required a 
 
 , . . , QQo qqo 
 
 100 shunt, its resistance must be — — = -i^— =10. 
 
 100 — I 99 
 
 MEASURES OF RESISTANCE. 
 I '045 6 Siemen's units = i ohm. 
 To convert Siemen's units into ohms, multiply by 
 •9564 (see also page 43). 
 I Varley's unit =25 ohms. 
 I megohm = i million ohms. 
 I microhm = i millionth part of an ohm (see p. 43). 
 
Electromotive Force. 103 
 
 MEASUREMENT OF ELECTROMOTIVE FORCE, 
 AND TENSION. 
 
 ELECTROMOTIVE FORCE. 
 
 Until the Committee of the British Association issues 
 standards of electromotive force, this measure can only 
 be given in terms of the force of some other battery : its 
 measurement may be obtained on two systems — either by 
 the application of Ohm's law to a battery in action where 
 the resistances are known ; or, by allowing the battery 
 to remain inactive, and measuring the tension : in which 
 cases the tension is the same as the electromotive force, 
 and the resistances in circuit need not be known. The 
 first five of the following methods belong to the former 
 system, and Poggendorff's method is a combination of 
 both. 
 
 To compare the electromotive forces of two 
 batteries. — i. Let their force be E and E' ; join them 
 up successively in circuit with the same galvanometer, 
 and, by varying their resistance, cause them both to give 
 the same deflection ; their forces will then be in direct 
 proportion to the total resistances in circuit in each case, 
 or 
 
 E' = Ex|, 
 
 where R represents the resistance with E (including that 
 of battery, galvanometer, and the variable resistance), and 
 R' with E'. 
 
104 Electromotive Force. 
 
 2. If the external resistances be made very large indeed 
 in comparison with that of the cells themselves, their 
 internal resistance may often in practice be neglected, 
 and only those of the galvanometer and resistance coil 
 taken into account. 
 
 3. Where the electromotive forces differ greatly, 
 it is often necessary to employ a shunt to diminish the 
 deflection of the galvanometer and bring it within range 
 with the more powerful battery : calling their resistances 
 
 gands, their joint resistance will be '^ , which must 
 
 be employed in calculating the total resistance of R : the 
 respective electromotive forces are then 
 
 4. Where shunts are used in obtaining both the 
 deflections, the formula becomes 
 
 E' = E X 
 
 R'X^ + " 
 
 / ■ 
 
 cr J J 
 
 In all these cases — ■ — represents the " multiplying 
 power of the shunt " described at page 80. 
 
 5. When a Thomson's reflecting galvanometer 
 is employed (or any other in which the deflections have 
 
Electromotive Force. 
 
 105 
 
 a known value), it becomes unnecessary to reproduce the 
 same deflection : calling the deflections d and rf , we 
 have — 
 
 R xaT 
 
 E'= Ex 
 
 R' Xd'' 
 
 6. By the direct opposition of cells. — Where a 
 number of cells are joined up in circuit with, but in 
 opposition to, a number of other cells with a galvanometer 
 inserted, and the numbers adjusted so that no current 
 passes, we have an obvious measure of their electromotive 
 force. 
 
 7. By Poggendorff's method. 
 
 Fig. 33- 
 E 
 
 In this method the more powerful battery E is joined 
 up in circuit with a resistance coil r, and the other 
 battery E' and a galvanometer are connected to the same 
 coil, so that both batteries send a current through r in 
 the same direction : by increasing the resistance of r it is 
 easy either to make the current of E overpower that of 
 E', or to obtain such an equilibrium that E shall remain 
 
]o6 
 
 Electromotive Force. 
 
 inactive, and no current pass through the galvanometer 
 in either direction. When this is effected, we have the 
 following ratio : as the total resistance of E and r is to 
 the resistance of r, so is the electromotive force of E to 
 that of E', or 
 
 r . 
 
 E' = Ex 
 
 E + r 
 
 8. By Clark's Potentiometer. — It has been objected 
 to the preceding system that, since one of the batteries is 
 active, and the other not, we do not obtain a true com- 
 parison of the forces : although attaching little import- 
 ance to this objection, the author has for many years past 
 employed an instrument depending on similar principles, 
 to which this consideration does not apply. 
 
 Fig. 34- 
 
 R is a coil of platinum wire of lOo turns, wound on 
 an ebonite cylinder, which revolves on its axis like a 
 Wheatstone's rheostat ; the ends of the coil are connected 
 
Electromotive Force. 107 
 
 to the axles, which work in the blocks A and B ; / n is 
 a battery of several cells also connected to the blocks 
 A and B, which sends a continuous current through R. 
 A rheostat, Rh., is also inserted, by which the total 
 resistance of the circuit can be varied. E is a standard 
 element (or a thermo-electric pile), also connected to the 
 blocks A and B with an intervening galvanometer, which 
 by a proper adjustment of the rheostat is just balanced 
 by the battery p n va. the manner before described, so 
 that no current passes. Thus far the arrangement is 
 similar to that of PoggendorfF, except that E is used as 
 the standard of comparison instead of/ n. E' is the cell 
 whose tension or electromotive force we desire to measure, 
 and this is connected with the block A and galvanometer 
 g, and a moveable wire n, which can be applied to any 
 part of the wire R. 
 
 Assuming the standard battery E to be exactly balanced 
 by/ n, and to have a tension of 100, and calling the 
 tension at A = o, we have between A and B every tension 
 from o to 100 ; and by applying the wire n successively 
 to different parts of the wire R we soon find a point 
 where the tension of E is balanced, no current passing 
 through g. A scale of equal parts measured along R 
 gives the tension of the cell E' by simple inspection. 
 
 By the use of a Thomson's galvanometer, and by fixing 
 a divided scale on the revolving cylinder, it is easy to 
 measure tensions accurately to the ten-thousandth or 
 hundred-thousandth part of a Daniell's cell. When the 
 battery E' which we wish to measure is more powerful 
 
io8 Electromotive Force. 
 
 than the standard battery E, their positions are reversed, 
 
 and E is connected to the galvanometer g, and wire n. 
 
 When this is the case, employing a scale of loo parts, 
 
 and calling n the number of divisions, we have 
 
 ^. ^ loo 
 E' = E X . 
 
 n 
 
 TABLE giving Approximately tlie Electromotive Force 
 
 of different Batteries. 
 
 Grove's. ....... loo 
 
 Bunsen's 98 
 
 Daniell's . . . . . . -'56 
 
 Smee's (when not in action) . . . -57 
 Smee's (when in action) . . about 25 
 
 Copper and zinc in acid (Woollaston's) . . 46 
 Sulphate mercury and graphite (Marie Davy) 76 
 
 Chloride silver 62 
 
 Chloride lead 30 
 
 The foregoing determinations are the mean of a great 
 many observations by the author, and give the electro- 
 motive force of the battery as taken on a sine galvano- 
 meter. When connected on short circuit, the electromotive 
 force of several of the batteries, and especially the Smee's 
 and Woollaston's, will fall off 50 per cent, or more, owing 
 to the formation of hydrogen on the negative plate. 
 Grove's and Daniell's do not so fall off, because the hy- 
 drogen is reduced by the nitric acid in the one case, and 
 by the oxygen in the other. The internal resistance of 
 Grove's cells is very small, usually below i ohm for a 
 
Tension. 109 
 
 pint cell; Daniell's, from 5 to 15 ohms (see page 60) ; 
 Smee's, below i ohm, varying rapidly with the greater or 
 less deposition of hydrogen. 
 
 The electromotive force of batteries is, within certain 
 limits, very variable, depending on a variety of undeter- 
 mined causes (see page 63). It is not much affected by 
 temperature. 
 
 MEASTJBEMENT OP TENSION OR POTENTIAL. 
 
 9. The potentiometer last described is admirably 
 suited for the measurement of potential, and has been 
 used for tensions as high as 200 cells Daniell.* 
 
 10. By the swing of the galvanometer needle.— 
 If a condenser of convenient capacity, or a short length 
 of cable be immersed in water, and connected to a battery, 
 and the charge be suddenly allowed to escape to earth 
 through a galvanometer with a suspended needle, the 
 swing of the needle will be nearly proportional to the 
 quantity of electricity, and therefore proportional to the 
 tension (the tension is more accurately equal to the sine 
 of half the angle of deflection, but for a considerable range 
 this does not differ sensibly from the angle). t By this 
 method and the use of shunts the tension of a whole battery 
 may be obtained in terms of a standard cell. Observe the 
 
 * See Government Report on the Construction of Submarine 
 Cables, 1861, page 295. 
 
 t See p. 63. This method was first employed in England by the 
 author in 1859 ; it appears also to have been used in Germany by 
 Dr. Siemens about the same time. Its employment for the com- 
 parisons of batteries is due to Mr. Laws. 
 
1 10 Tension: 
 
 swing with the standard cell, and then shunt the galvano- 
 meter until the whole battery gives the same swing. Let 
 T' be the tension of the battery, and T that of the single 
 cell ; g and j the resistances of the galvanometer and 
 shunt ; then 
 
 T' = C±i X T. 
 ■s 
 
 1 1. If the are of vibration be not equal, and we 
 
 call that of the battery d', and of the standard cell d, we 
 have 
 
 d s 
 
 or, more correctly, 
 
 ^, ^ Sini^'fe+^) ^ ^ 
 Sin \ d s 
 
 12. By opposing batteries. — For measuring the 
 tensions on a hne, the method described at p. i8 is the 
 most convenient. A secondary battery (fig. lo) is opposed 
 to the main battery, and connected up in the same 
 direction, with a galvanometer in circuit ; the number of 
 cells is varied until no current passes through the galvano- 
 meter, and this gives the tension of the line at that spot. 
 If the balance cannot be obtained exactly, the addition 
 of one more cell making the deflection too great, and its 
 omission making it too small, the value of the fractional 
 part of the cell is obtained by dividing either of the two 
 opposite deflections by their sum. Thus, if with ten cells 
 we get a deflection of three degrees on one side of zero. 
 
Tension. 1 1 1 
 
 and with eleven cells we get nine degrees on the other 
 
 side, our real value is lo -| — cells, Or iot%- cells. 
 
 3 + 9 ^ 
 
 13. By Thomson's slide resistance. — This instru- 
 ment is an arrangement of one hundred equal resistance 
 bobbins, joined up in series, and having a resistance of 
 one hundred ohms each, so that the whole slide has a 
 total resistance of 10,000 ohms : metal blocks are fixed 
 at the junction of each pair of bobbins, and these are 
 arranged in a series, and numbered from one to one 
 hundred, so that a sliding contact traversing the whole 
 series can be made at pleasure with any bobbin in the 
 set. One end of the series is connected to earth, and 
 the other to a battery which sends a constant current 
 through the whole series ; the tensions at the metal blocks 
 therefore fall regularly from the battery to the end con- 
 nected to earth, where it is o. Calling the tension at the 
 battery end, whatever it may be, one hundred, we have 
 every intermediate tension, at each successive block, from 
 one hundred to one. Mr. Varley has, by means of a 
 moveable derived circuit (reaching across two of the 
 bobbins), which itself consists of one hundred coils, 
 having each a resistance of twenty ohms, devised a 
 means of subdividing each degree of tension into one 
 hundred equal parts, so that the whole tension at the end 
 next the battery is divided into 1000 equal parts. The 
 use of this instrument in conjunction with an electrometer 
 will be explained further on. 
 
 14. By Thomson's electrometers. — These are in- 
 
112 Tension. 
 
 struments in which the mechanical attraction and repul- 
 sion of electrified plates is used to indicate their difference 
 of tension. They are made in two very distinct forms : 
 the portable form, which will not indicate a smaller 
 difference of tension than one DanielFs cell; and the 
 reflecting electrometer, which is so beautifully sensitive that 
 a hundredth part, or even a still smaller fraction of a 
 Daniell's cell may be measured by it. The essential 
 feature in each is the use of a moveable plane, which is 
 kept constantly electrified, and is moved by attraction or 
 repulsion. In the reflecting quadrant electrometer this 
 electrified plane or needle is suspended over two pairs of 
 conducting cheeks, which are provided with terminals on 
 the exterior for making connections, and it inclines to 
 one or the other of them according as their electrical 
 charge is similar or opposite to its own. If both cheeks 
 have the same tension the reflected spot of light remains 
 at zero ; but if one fall below the other, the needle is 
 attracted, and the spot moves to one side or the other. 
 
 The resistance slide and the electrometer are generally 
 used in conjunction ; the cable, insulated at its further 
 end, is connected with one pair of cheeks, and a loose 
 wire is connected to the other pair. The cable is first 
 charged from the battery end of the sKde for some 
 minutes, so that it acquires the tension of one hundred on 
 the slide ; it is then connected to the electrometer, the 
 loose wire being shifted to the same tension, so that the 
 electrometer remains at zero. As soon, however, as the 
 cable is disconnected from the slide and battery, its 
 
Tension. 1 1 3 
 
 tension begins to fall, and the loose wire is gradually 
 shifted down the scale, according to the indications of the 
 electrometer ; the time of falling from degree to degree 
 being noted (see p. 117). In long cables, from their 
 great electric capacity, the smallest change in the potential 
 of the earth or of the battery produces so large a flow of 
 electricity into or out of the cable that reliable measures 
 can seldom be, obtained by the galvanometer ; the time 
 of electrification has also a great influence on the result. 
 The tension is not, however, sensibly influenced by these 
 changes, and therefore in very long cables its measure- 
 ment is the only one that can be rehed upon. 
 
 15. By adjusted condensers." — If the electrometer 
 above described were portable and not so costly, its use 
 would become universal ; for the time of falling from 
 tension to half-tension being independent of all calcula- 
 tion, it would give from year to year the truest measure 
 of the condition of any cable. As it is, however, unsuited 
 for use in boats or on the sea-shore, the author has used 
 condensers very successfully as a means of obtaining 
 graduated tensions. If two condensers of known capacity, 
 one (C) charged, and the other (^) empty, be united, 
 and T be the tension of the battery, their joint tension t 
 
 is readily found by the rule 
 
 C 
 
 If C and c be equal, their joint tension will be one-half 
 the original tension. A condenser, therefore, is made in 
 six parts, which, when successively united, give 90, 80, 
 70, 60, and 50 per cent, of the tension of the battery! 
 
 I 
 
114 Tension. 
 
 One of the condensers and the cable are charged for ten 
 minutes from the same battery. The cable is allowed to 
 remain insulated Until its tension is supposed to have 
 fallen to 90 per cent, of its original charge, and is then 
 suddenly connected through a delicate galvanometer to 
 the first pair of condensers. If the time has been correctly 
 judged and the tension be 90, the galvanometer will be 
 unaffected ; if the tension be above or below 90, a 
 minute charge will enter or leave the cable, deflecting 
 the galvanometer to the right or left. Having thus 
 obtained the time of falling to 90, 80, or 70 per cent., it 
 is easy by the rule given at p. 117 to catch the precise 
 moment of falling to 60 and 50. The charging of the 
 condensers, their union, and subsequent connection 
 through the galvanometer with the cable, are all effected 
 by a single movement of a suitable key. The following 
 are the capacities of the several parts of the condenser, 
 which are such that A with B gives 90 per cent. ; A with 
 B and C 80 per cent., and so on : — 
 
 
 
 
 
 
 Electrostatic 
 
 capacity 
 
 
 
 
 
 in farads. 
 
 A 
 
 (half 
 
 the whole 
 
 condenser) . 
 
 
 •OS 
 
 B 
 
 
 . 
 
 ' » 
 
 • '00556 
 
 
 C 
 
 
 
 
 
 •00694 
 
 
 D 
 
 
 
 
 
 •00893 
 
 
 E 
 
 
 
 
 
 •on 90 
 
 
 F 
 
 
 
 
 
 ■01667 
 
 •05 
 
 •100 
 
 16. By Peltier's electrometer. — This is a valuable 
 instrument for laboratory experiments on short lengths 
 
Tension. 1 1 5 
 
 of cable, especially when combined with an electro- 
 phoms and a pair of equal condensers. The deflection 
 with half the battery power is ascertained, and the time 
 of falling to this deflection gives the insulation (see p. 98). 
 
 DEVELOPMENT OF HEAT AND "WORK. 
 
 The quantity of heat developed in any electric circuit 
 
 varies as the quantity of electricity passing in any given 
 
 time and as the fall of tension. If E be the electromotive 
 
 force of a battery, R the total resistance in circuit, and 
 
 ■p 
 Q the quantity of electricity in farads, then Q = — , and 
 
 •C'2 
 
 the total heat developed = -^. 
 
 R 
 
 Let T — / represent the fall of tension or difference of 
 
 potential at any two points in an electric circuit, then 
 
 heat = Q X (T — ^). If resistance R be taken into con- 
 
 T - t 
 sideration, since Q = -^= — , heat = Q^ x R- 
 R 
 
 If we take the difference of potential in volts V (p. 43), 
 
 the quantity in farads F, the resistance in megohms M, 
 
 and let H represent the heat which will raise a gramme 
 
 (15 '44 grains) of water one degree centigrade, then 
 
 V^ X 4i';72i;o 
 H = V X F X 4157250, or If^^-^- 
 
 If W represent the equivalent of work done in grammes 
 raised to the height of one metre, 
 
 V^ X 9808 
 
 W = V X F X 9808, or 
 
 M 
 
1(6 Electrostatic Capacity. 
 
 ELECTBOSTATIC CAPACITY, CHAHGB, AND 
 DISCHARGE. 
 
 The electrostatic or inductive capacity of any 
 cable, or other insulated body, is the charge which it 
 will receive with the unit tension, or the volt. 
 
 The charge in a cable or condenser, or on any 
 
 electrified body, varies directly as the tension ; it also 
 varies inversely as the distance between the inducing 
 surfaces, and is generally considered to exist only on those 
 surfaces, and not within the interior of a conducting 
 body.* 
 
 The ratio of discharge, or the time required for the 
 charge in any cable to fall to any given tension, does not 
 vary with the degree of tension. If seven per cent, of the 
 charge escape from any cable at 75° Fahr., during the first 
 minute (and with gutta-percha this is about the usual quan- 
 tity), seven per cent, of the remaining quantity will escape 
 during the second minute, and so on ad infinitum. By 
 continually subtracting sfeven per cent, from each re- 
 
 * The author considers it probable that the phenomena of re- 
 siduary discharge, or absorption, or electrification, are due to the 
 induction of layers of positive and negative electricity, which have 
 peiletrated partially into the substance of the dielectric from opposite 
 sides, and are continually uniting and neutralizing each other. Each 
 layer while in transitu behaving exactly as if it were on an interior 
 surface of the dielectric, and inducing a similar amount of electricity 
 on the opposite surface of the insulator — or within its substance. 
 
Electrostatic Capacity. 117 
 
 mainder, we may easily ascertain the number of minutes 
 required for falling to half or any other given ten- 
 sion; or, 
 
 Let C be the original charge in the cable, and c the 
 observed charge at the end of the first minute, or at any 
 other time, t. Let / be the amount of charge we 
 wish to remain in the cable ; then the time of falling to 
 
 , C 
 log-/ 
 
 this tension will be ~ X t = nt. 
 
 log.y 
 
 It usually happens that we want to know the time 
 of falling from charge to half-charge, or, what is the 
 same thing, from tension to half-tension. In this case 
 
 log. — = log. — - = '30103, and the formula becomes 
 / 5° 
 
 ■•JOIO-? 
 
 ^ Xt = nt. 
 
 log. - 
 
 The joint tension of two condensers or cables, 
 
 when one is charged by another, is as follows : 
 
 Let C = capacity of the charged condenser, 
 and T = its tension ; 
 and c = capacity of the other condenser, 
 and / = the tension when they are united. 
 
 C . i 
 
 ThenT x „, = J. 
 
 \^ —J- c 
 
1 1 8 Electrostatic Capacity. 
 
 THE JOINT ELECTROSTATIC CAPACITY OF TWO 
 CABLES. 
 
 If a charged cable or condenser be joined to another 
 cable, the charge will divide itself between the two in 
 proportion to their respective capacities, the tension being 
 the same in both. Let C be a standard condenser, 
 charged to tension T, and let x be another condenser or 
 cable, and t their joint tension when combined. 
 
 Then/ : T : : C : C + «, 
 
 and C T = C «■ + a; /. 
 
 l—t 
 The capacity of x will be, x = — -— C. 
 
 To compare the inductive capacity of one cable 
 with another, or with a condenser (Varley). 
 
 Ascertain which takes the greater charge, the cable or 
 the condenser. If it be the cable, connect it to one coil 
 of the differential galvanometer, and shunt that half of 
 the galvanometer by resistance coils : connect the con- 
 denser to the other coil of the galvanometer : by depress- 
 ing the key, take charge or discharge tests, varying the 
 resistance of the shunt until the needle does not move. 
 Let f be the resistance of the shunt. 
 
 g, that of one coil of the galvanometer. 
 
 f, the length of cable represented by the condenser. 
 
 /, the length of the cable. 
 
 Then s : s-\-g- \ : c : I ; 
 
 and / = •^-ii X c. 
 
Electrostatic Capacity. 
 
 119 
 
 By De Sauty*s Method.— This plan is on the same 
 principle as the Wheatstone balance. 
 
 Fig- 35- 
 
 The condensers C and D are attached in the manner 
 
 shown in the figure, and the resistances A and B are so 
 
 adjusted that, when the key is raised or depressed, no 
 
 movement takes place in the needle : when this is 
 
 the case, 
 
 A : B : : C : D ; 
 
 ^n CB 
 and D = — r— . 
 
 The electrostatic capacity of cables may be com- 
 pared by the means of resistance coils and a galva- 
 nometer, without the use of any condenser (Jenkin). 
 Determine by experiment the resistance R of the circuit 
 through which the battery used to charge the cable 
 would produce the unit deflection on the galvanometer 
 used to measure the discharge. (The unit deflection is 
 90° on a sine galvanometer, 45° on a tangent, and one 
 
120 Electrostatic Capacity. 
 
 division on a Thomson's reflecting galvanometer). Next 
 count the number of oscillations wliich the galvanometer 
 needle, when swinging freely, will make per minute, and 
 let t equal the time occupied by half a complete oscilla- 
 tion of the needle, and let a be the angle to which the 
 needle is thrown by the discharge ; then the capacity — 
 
 t sin \ a 
 
 C = 2 
 
 3-1416 R" 
 
 To obtain the relative inductive capacity of short 
 lengths of cable. — Let D be the discharge from the con- 
 denser, and d that from the cable ; L the length in yards, 
 and 2029 the length of a mile; and let C be the con- 
 stant of the condenser (if not exactly i mile), or the 
 equivalent length of cable. 
 
 D X 2029 
 
 Inductive capacity = 
 
 dx'LxC 
 
 The inductive capacity of cables, where D = 
 diameter of the dielectric, and d the diameter of the 
 copper, varies directly as their length, and inversely as 
 
 log. — : if the length be constant,* 
 
 C = — !--, or C = , • 
 
 log.2 log. D- log. ^' 
 
 d 
 
 and if the diameter of the conductor be constant, 
 . C= ' 
 
 log. D- 
 
 * For the capacity in farads, see pp. 147, 151. 
 
speed of Working. 121 
 
 The charge, or inductive capacity of a strand 
 conductor, is about five per cent, less than that of a 
 solid conductor of the same diameter. The diameter of 
 a 7-wire strand is three times that of one of the wires 
 composing it. 
 
 BATE OF SIGNALLING. 
 The speed of working in any cable varies as log. — 
 
 multiplied by the square of the diameter of the conductor, 
 or, what is the same thing, by the weight per mile of 
 copper J it also varies inversely as the square of the 
 length. Let D = diameter of the dielectric, and d that 
 of the copper, 
 
 D D 
 
 d^ X log. —; weight of copper x log-~7 
 Speed = t- or= - 
 
 If the length be constant it varies as d^ X log. -7 ; and if 
 
 the size of the conductor be also constant the speed 
 varies as log. D.* 
 
 If one cable have twice or thrice the diameter or size 
 of another cable, and also twice or thrice its length, the 
 speed of both will be the same. 
 
 The highest speed theoretically attainable is when the 
 diameter of the conductor is to that of the dielectric as 
 I to I '649, or as "6065 to i : when this is the case, the 
 
 * See note b, p. 168. 
 
122 
 
 Speed of Working. 
 
 copper weighs about 5-2 times as much as the gutta- 
 percha, and log. — becomes "2172. 
 
 TABLE of Actual 'Working Speed on Several Cables. 
 
 
 Date of 
 
 Length 
 in Nau- 
 tical 
 Miles. 
 
 Total 
 Resist- 
 
 Log of 
 
 Actual 
 No. of 
 
 Cable and Section. 
 
 Experi- 
 ment. 
 
 ance of 
 Line^ 
 Ohms. 
 
 D 
 d' 
 
 Words 
 
 per 
 Minute. 
 
 Red Sea. 
 
 
 
 
 
 
 Suakin — Aden . . 
 
 i860 
 
 629 
 
 
 .. 
 
 II 
 
 Malta and Alexandria. 
 
 
 
 
 
 
 Malta — Tripoli . , . 
 
 1861 
 
 230 
 
 802 • 
 
 o'48o89 
 
 •25 ■ 
 
 Tripoli — Benghazi . . 
 
 
 507 
 
 1769 
 
 
 •18 
 
 Benghazi — Alexandria . 
 
 
 597 
 
 2084 
 
 
 '15 
 
 Malta — Alexandria . . 
 
 
 1330 
 
 4641 
 
 
 3-2 
 
 Persian Gulf. 
 
 
 
 
 
 
 Fao — Bushire .... 
 
 1864 
 
 155 
 
 1020 
 
 0-53839 
 
 25 
 
 Manora — Gwadur 
 
 
 256 
 
 15 15 
 
 
 20 
 
 Gwadur — Mussendom . 
 
 
 358 
 
 2294 
 
 
 i6-7 
 
 Mussendom — Bushire 
 
 
 329 
 
 2401 
 
 
 i7'5 
 
 Mussendom — Fao . . 
 
 
 547 
 
 3420 
 
 
 12-1 
 
 Mussendom — Manora . 
 
 
 624 
 
 3785 
 
 
 9-64 
 
 Atlantic Cable, 1865 
 
 1867 
 
 1896 
 
 7652 
 
 0-50200 
 
 17 
 
 Do. do. iS66 
 
 
 1857 
 
 7270 
 
 
 17 
 
Detection of Faults. 12' 
 
 THE MEASUREMENT AND DETECTION OF 
 FATTLTS. 
 
 1. To ascertain the position of a fault by direct 
 measurement. 
 
 This method is described at page 69. 
 
 2. By Blavier's formula. See page 75. 
 
 Let R be the resistance of the line when it was perfect, 
 S the resistance of the faulty line when the distant end is 
 to earth, and T the resistance when it is disconnected 
 from earth. 
 
 The distance x of the fault from the station will be 
 
 x = ^- VS^ + TR-TS-RS, 
 or « = S - -v/(R-S)x (T-S); 
 and the resistance of the fault z will be 
 
 = T - S + -v/S' + TR-TS-RS, 
 
 or 2 = T - S + V (R - S) X (T - S). 
 
 3. By Varley's loop test. (See page 73.) 
 
 Let the resistance of the longer half of the loop 
 be jc. 
 
 That of the shorter half, x. 
 
 The total resistance of both, L. 
 
 The resistance added to the shorter half to make it 
 equal to the longer, R. 
 
124 Detection of Faults. 
 
 Then x ->r y = L, 
 y = X +'R, 
 
 and X = . 
 
 2 
 
 If we add together all the resistances in the circuit the 
 fault will be at the midway point. 
 
 4. By Murray's test. 
 
 Fig- 36. 
 
 This test, like the preceding, requires a double line, 
 so that both ends of the line may be in connection with 
 the instrument. J> n is a. battery very carefully insulated 
 from the earth, with its poles connected to the two ex- 
 tremities of a Thomson's slide R r. The two ends of 
 the line are also connected to the slide, and x is the 
 position of the fault ; a constant current therefore flows 
 through the slide from R to r, and also through the line 
 from R through x to r. A galvanometer g, connected 
 to the earth at E, is provided with a loose wire t, which 
 is moved along the slide until some point is found at 
 which no current passes through it, the tension being 
 
Detection of Faults. 
 
 125 
 
 equal to o ; when this point is found, if we call the two 
 
 portions of the slide R^ and tr, and the two portions of 
 
 the line R;c and f r, we have the following ratio between 
 
 their resistances : 
 
 R/ : tr : : R;c : xr. 
 
 Calling the length of the whole line L, and the resistance 
 
 of the slide 10,000, the distance of the fault x from the 
 
 point R will be 
 
 ^ RO< L 
 
 R^ = , 
 
 10,000 
 
 and the distance from r will be 
 
 r^ X L 
 
 r X = . 
 
 10,000 
 
 Of course, where a slide is not available, ordinary resist- 
 ance coils may be used for obtaining the resistances R t 
 and r t. 
 
 5. By Clark's accumulation test. — -This method, 
 which was first practised by the author upon a cable in 
 the London Docks in i860, is peculiarly suited for 
 ascertaining the position of a very minute fault in an 
 otherwise perfect cable during manufacture. 
 Fig. 37. 
 
126 Detection of Faults. 
 
 Both ends of the line are connected to a battery of a 
 considerable number of cells, and the current flows con- 
 tinuously through it ; two equal condensers, C and C, 
 are also connected to the opposite poles of the battery^^ 
 with the usual provisions for measuring their respective 
 charges ; no connection is made with the 'earth anywhere, 
 except through the fault x, and the whole system is 
 allowed to remain quiescent for a considerable time. 
 
 However minute the fault x may be, it will, after some 
 interval of time, reduce the potential of the line at that 
 spot to o ; and whe'n this is the case all the other 
 tensions along the line, including those of the condensers 
 and battery, will adjust themselves according to well- 
 known laws : the tension of the condenser C will be 
 positive, and that of C will be negative ; and if the fault 
 X were exactly in the centre of the line their charges 
 would be equal in amount though opposite in sign ; but 
 if it be in any other point their charges will vary rela- 
 tively in accordance with its position, and if we measure 
 the discharge from the condensers C and C the follow- 
 ing rule will obtain : 
 
 Q, : G : : p X : n X. 
 Calling the length of the line L, the distance of x from 
 the point/ will be 
 
 L X C 
 
 px = 
 and nx = 
 
 C + C" 
 L X C 
 
 C-fC" 
 As one of the condensers gives a positive discharge 
 
Detection of Faults. 127 
 
 and the other a negative, it is necessary to use a 
 reversing key to bring both deflections into the same 
 direction, and it is obvious that the tensions at C and C 
 may be measured by a Thomson's electrometer, instead 
 of by condensers. 
 
 6. Testing by Thomson's slide (seep. m). — "Ehis 
 is in principle the same as Wheatstone's balance, the 
 parts A and C, p. 85, being replaced by the two portions 
 of the slide, whose total resistance is 10,000 units. 
 
 Fig. 38 is a diagram showing the arrangement of the 
 parts. 
 
 A battery with one pole to the earth has the opposite 
 pole connected through the slide A C to earth, so that a 
 constant current passes through it ; it is also connected 
 through a resistance coil B to the line D, which is sup- 
 posed to be connected to earth or to be faulty ; a galva- 
 nometer is connected to B, and carries a loose wire t, 
 which is moved along the slide A C until a point is found 
 where no current passes through it : when this point is 
 
128 
 
 Detection of Faults. 
 
 found we have the same ratios as in the Wheatstone 
 
 balance, viz., 
 
 A : C : : B : D, 
 
 also A : B : : C : D, 
 
 B X C 
 
 and D 
 
 7. Measuring resistances by tension. — This is a 
 very good way of ascertaining the resistance or the posi- 
 tion of a f^ult in a line or cable. Instead of measuring 
 the resistances directly, the tensions are measured at 
 two different points, either by the discharge from a con- 
 denser, or by a Thomson's electrometer and slide, in 
 the manner before described, and from their ratio the 
 distance of the fault is determined. 
 
 Fig. 39- 
 
 n m = : 
 
 Let the line L make full earth at the fault x, or at its 
 further end, as the case may be. Let R be a resistance 
 coil, and T and t the tensions at each end of the coil, 
 and let x be the distance of the fault from R ; then 
 T - /■ : ^ : : R = «, 
 
 A ^X R 
 
 and X = — . 
 
Detection of Faults. 
 
 129 
 
 It is sometimes better to vary the resistance R until the 
 tension t be exactly half that of T. When this is the 
 case we have * = R. 
 
 8. When the fault makes a partial earth only.— 
 
 Figr- 40. 
 
 .T 
 
 Let b and R be a battery and resistance coil connected 
 to a cable or line, xfs. Let / be the position of a 
 fault, X the resistance of the line between the station or 
 ship and the fault, and fs the line beyond the fault, 
 whose length is immaterial and need not be known. It 
 is assumed that we have the means of correctly measuring 
 the tensions at the points T, t, and j in common measure : 
 if the line be perfect and in the act of paying out, this 
 is easily obtained by insulating the end s ; the tension of 
 the line wiU then be everywhere equal to E, or the 
 electromotive force of the battery, and this gives a 
 standard measure both to ship and shore, which should 
 be observed very frequently. If a fault afterwards appear 
 on the line this tension at and beyond the fault will at 
 once fall to some lower degree, as / or s, and these 
 tensions will be equal whatever be the length of the line 
 between /"and s. Having then obtained the tension of 
 
130 Detection of Faults. 
 
 the line at / by measuring that at s, and having also 
 measured the tensions at T and t, we have the following 
 proportions : 
 
 T-^:/-j::R:^. 
 Or, if we include the battery in our measures, calling its 
 resistance b, we have 
 
 Y.-t\t — s::b-\-^:x, 
 from whence we get the distance of the fault ; 
 
 (/ - j) X R 
 T-/ ' 
 
 (t - s) X {b + R) 
 '''=' = E=l ' 
 
 and for the resistance of the line including that of the 
 fault, we have 
 
 ^X R 
 
 ^+/ = 
 
 T - ^' 
 
 from which, by deducting x, we obtain the value of f. 
 During the lajring of the Atlantic cables these tensions 
 were recorded on shore every five minutes by the discharge 
 of a condenser, and their value signalled through the 
 cable to the ship. 
 
 9. Willoughby Smith's system of testing cables 
 during submersion. This excellent system was first em- 
 ployed during the laying of the Atlantic cables in 1866. 
 Either the ship or the shore becomes the controlling 
 station, and fig. 41 gives the arrangement when the 
 ship controls, as was the case on the occasion referred to . 
 
Detection of Faults. 
 
 131 
 
 G is a Thomson's galvanometer connected with the 
 cable, and R is a very high resistance inserted in the 
 circuit. This resistance may be made of gutta-percha, 
 Fig. 41. 
 R 
 
 tn 
 
 selenium, or other imperfectly conducting material, and 
 should have a resistance of 20 or 30 megohms. A 
 battery of 100 cells is permanently connected to the 
 cable on board ship, with an intervening galvanometer 
 S, on which the state of insulation of the cable is con- 
 stantly indicated. There is no battery on shore ; but the 
 galvanometer G, which is a highly sensitive one, main- 
 tains a steady deflection, due to the very feeble current 
 which passes through the resistance R : this deflection is 
 recorded every minute. The ship reverses its current 
 every fifteen minutes, which being observed on G, serves 
 for a continuity test for the shore. The resistance R being 
 so great, and being constant, does not sensibly interfere 
 with the correct measurement of the insulation of the 
 cable on board ship, nor does it sensibly affect the 
 tension of the line at R, which is practically 100, or the 
 
132 Detection of Faults. 
 
 same as it is close to the battery. In the event of a 
 fault occurring anywhere in the line it would be instantly 
 indicated on board on the galvanometer S, and the 
 tension at R would also fall below 100. In order to de- 
 tect accurately the position of the fault, great care is 
 taken on shore to observe accurately the tension at R. 
 This is done every five minutes by measuring the dis- 
 charge from a condenser C ; the key k puts this con- 
 denser into contact with the line for ten seconds and then 
 discharges it suddenly through the galvanometer^, whose 
 deflection indicates the tension, which is at once trans- 
 mitted to the ship. Knowing this tension before and 
 after the occurrence of a fault, the ship can accurately 
 calculate its position by the system described at No. 8. 
 Every hour a check measurement of this tension is also 
 taken by the electrometer and slide. 
 
 The condenser C has a capacity of about ten farads, 
 and since the line has a tension of about one hundred 
 volts, when it is charged from the line every five minutes 
 it abstracts about 1000 farads of electricity fronl the 
 cable, which is at once made good again by the battery. 
 The effect of this is momentarily visible on the ship's 
 galvanometer S, and serves to show them that the con- 
 tinuity of the line is perfect without at all interfering with 
 their insulation test. 
 
 Lastly, another and very important use is made of this 
 condenser, or rather of an independent one having a 
 capacity of about twenty farads, both on ship and shore. 
 Imagine R to represent a condenser, and suppose the 
 
Detection of Faults. 133 
 
 ship by means of a similar one and a battery to send two 
 or more successive impulses into the line ; although the 
 line is already charged to a tension of 100, and although 
 no electricity actually enters or leaves the cable, these 
 impulses will be transmitted like waves through the line, 
 and will produce distinct and sudden deflections on the 
 galvanometer G to the right and left. In this way, by 
 making the left-hand deflections represent dots, and the 
 right-hand dashes, a continual correspondence can be 
 carried on through the line without interference with its 
 insulation test. 
 
 10. When the conductor of a cable is broken.^ — 
 
 Iri testing the core of a cable during its manufacture, it is 
 
 usual to measure and record the capacity of each mile, 
 
 and the part of the line in which it is placed : if then the 
 
 conductor should become broken within the gutta-percha 
 
 during submersion, these records enable the distance to 
 
 be ascertained. If the average capacity p6r mile be n 
 
 farads and the capacity of the broken section be N 
 
 N 
 farads, the distance of the fraction will be — miles. Such 
 
 a case occurred during the laying of the Persian Gulf 
 cable, at a distance of about 80 miles, and the position 
 of the fault was indicated in this manner within a few 
 hundred yards. The discharge from a condenser of 
 known capacity was taken through a galvanometer, and 
 the discharge from the 80 mile section was afterwards 
 taken through the same galvanometer, with a variable 
 
134 Detection of Faults. 
 
 shunt, which was adjusted so as to reproduce the same 
 
 deflection. Let C be the capacity of the condenser 
 
 expressed in miles of the cable; ^ and j the resistances 
 
 of the galvanometer and shunt, and » the distance of the 
 
 fracture, then, 
 
 s : g + s : : c : X, 
 
 g + s 
 
 and 3c = C X ■ 
 
 s 
 
 The methods of Mr. Varley and Mr. De Sauty (pp. ii8, 
 119), are also well adapted for obtaining this measure- 
 ment. 
 
 Testing for faults in short lengths of wire. — 
 
 Minute faults in short lengths of wire are readily found 
 by connecting a powerful battery to one end of the wire 
 and drawing it slowly through a basin of water 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 
 therefore necessary to make some imperfect connection 
 with the basin by a piece of wood or a wet thread, suffi- 
 cient 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 galva- 
 nometer 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 
 
Detection of Faults. 135 
 
 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 deflectiofi will fall. 
 
 Warren's method. — Mr. Warren, electrician to Mr. 
 Hooper, employs a somewhat similar, but superior ar- 
 rangement. The coil of wire is wound on to two sepa- 
 rate drums, both insulated, and an electrometer is con- 
 nected to each. A powerful battery is connected to 
 the wire, and the induction and the leakage through the 
 dielectric cause each of the electrometers to become 
 deflected. Both drums are now discharged 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 the electrometer deflects, 
 the other one remaining 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. 
 
 The accumulation joint test. — The author has 
 introduced a method which is very suitable for measuring 
 the insulation of joints or other very short lengths of 
 core. The battery is connected with the conducting 
 wire, and the length of core to be tested is immersed in 
 an insulated suspended trough. A condenser is con- 
 nected with the water of the trough, so that all the elec- 
 tricity which escapes from the joint or length of wire in a 
 given time (usually one minute) is collected in the con- 
 
136 Detection of Faults, 
 
 denser. At the end of the minute the whole of this 
 charge is suddenly discharged by a key through a galva- 
 nometer, the deflection of which indicates the quantity 
 which has leaked through the joint in the given time. 
 Joints are very generally tested by this plan, the leakage 
 from 12 or 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. 
 
137 
 
 APPENDIX. 
 
 PART II.— COEFFICIENTS AND TABLES. 
 
 IRON. 
 
 The specific gravity of bar iron is about 77. i cubic 
 foot weighs 481-25 lbs. 
 
 The breaking weight of the commonest iron rod is 
 about 20 to 25 tons per square inch section ; the breaking 
 weight of drawn wires is very much greater, increasing 
 as the wire is finer up to 40 and 50 tons per square inch. 
 Hard drawn wires are much stronger than annealed or 
 rolled wire, and the strength varies greatly with quality ; 
 no genera] rule for strength can therefore be given. 
 
 The weights in the table at page 141 are calculated 
 on the assumption that i cubic foot of iron weighs 
 481 '25 lbs. 
 
 The weight of any iron wire per nautical mile is 
 
 ^— -lbs. 
 62-59 
 
138 Iro7i. 
 
 The weight of any iron wire per statute mile is 
 -lbs. 
 
 72-15 
 
 The diameter of any iron wire weighing n lbs. per 
 statute mile = -\/72'i5 X n mils.* 
 
 The diameter of any iron wire weighing n lbs. per 
 nautical mile = \/62'S9 x n mils. 
 
 The conductivity of ordinary galvanized iron 
 wire compared with pure copper, 100, averages about 
 14, or about ^th that of pure copper. 
 
 The resistance per statute mile of a galvanized 
 
 360000 , , . „ , 
 
 iron wire is about - — t-. — ohms at 60" Fahr. 
 
 The resistance of No. 8 iron wire is about 13-5 
 ohms per statute mile, and of No. 4 about 7 '8 ohms. 
 
 The resistance of iron increases about -35 per cent, 
 for each degree Fahr. 
 
 The weight of iron per nautical mile in any sub- 
 
 marine cable is approximately T^~T cwts., where d — 
 
 the diameter of the wire in mils,* and n the number of 
 wires. (See table, p. 140.) 
 
 * The mil is the thousandth part of an inch. A circular mil is a 
 circular area one thousandth of an inch in diameter ; there are there- 
 fore one million circular mils in a circular inch. It is much more 
 
Iron. 
 
 139 
 
 The diameter of any submarine cable is as fol- 
 lows : — Let D = diameter of cable, d that of the wires 
 composing it, n the number of wires ; then — 
 
 T^ J / 180° 
 D = a X (i + cosecant ), 
 
 . dx (n X 3'2) 
 
 or, approxmiately, D = ^ ^^—^. 
 
 3"M 
 See table of diameters. 
 
 TABLE of the External Diameter of Submarine Cables. 
 
 Sizes. 
 B.W.G. 
 
 Diameter 
 in Mils. 
 
 NUMBER OF WIRES. 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 00 
 
 380 
 
 I-49I 
 
 1-607 
 
 1-848 
 
 2-089 
 
 2-328 
 
 ■2-568 
 
 
 
 340 
 
 1-334 
 
 1-440 
 
 1-654 
 
 1-869 
 
 2-084 
 
 2-298 
 
 I 
 
 300 
 
 I-I77 
 
 X-27I 
 
 r-459 
 
 1-649 
 
 1-838 
 
 2-028 
 
 2 
 
 284 
 
 I -114 
 
 1-203 
 
 I-38I 
 
 I 56r 
 
 1-740 
 
 1-919 
 
 3 
 
 259 
 
 I'OI? 
 
 1-097 
 
 T-260 
 
 1-424 
 
 1-587 
 
 1-751 
 
 4 
 
 238 
 
 0-934 
 
 1-008 
 
 T-157 
 
 1-308 
 
 1-458 
 
 1-608 
 
 5 
 
 220 
 
 0-863 
 
 0-932 
 
 T-070 
 
 1-209 
 
 1-348 
 
 1-487 
 
 6 
 
 203 
 
 0-796 
 
 0-860 
 
 0-987 
 
 1-116 
 
 1-243 
 
 1-372 
 
 7 
 
 180 
 
 0-706 
 
 0-762 
 
 0-875 
 
 0-989 
 
 I -103 
 
 T-217 
 
 8 
 
 165 
 
 0-647 
 
 0-699 
 
 o-8o2 
 
 0-907 
 
 i-oio 
 
 1-115 
 
 9 
 
 148 
 
 0-581 
 
 0-627 
 
 0-720 
 
 0-813 
 
 0-907 
 
 I- 000 
 
 10 
 
 134 
 
 0-526 
 
 0-567 
 
 0-653 
 
 0-736 
 
 0-821 
 
 0-906 
 
 II 
 
 120 
 
 0-471 
 
 0-508 
 
 0-584 
 
 0*660 
 
 0-735 
 
 0-8x1. 
 
 12 
 
 109 
 
 0-428 
 
 0-462 
 
 n-530 
 
 0-599 
 
 0-668 
 
 0-737 
 
 13 
 
 95 
 
 0-373 
 
 0-402 
 
 0-462 
 
 0-522 
 
 0-582 
 
 0-642 
 
 14 
 
 83 
 
 0-326 
 
 0-352 
 
 0-403 
 
 0-456 
 
 0-508 
 
 0-561 
 
 15 
 
 72 
 
 0-282 
 
 0-305 
 
 0-350 
 
 0-396 
 
 0-441 . 
 
 0-487 
 
 16 
 
 65 
 
 0-255 
 
 0-275 
 
 0-316 
 
 0-357 
 
 c-398 
 
 0-439 
 
 r 4- cose 
 
 180 
 
 cant 
 
 n 
 
 3-9238 
 
 4-2360 
 
 4-8637 
 
 5-4964 
 
 6-1258 
 
 6-7588 
 
 convenient in every way to speak of whole numbers than of decimals, 
 and the author has therefore adopted the word mil (as recommended 
 by Mr. J. Cocker) to express the thousandth part of an inch. 
 
140 
 
 Iron. 
 
 TABLE of the "Weiglit of Iron per Nautical Mile in. 
 Cables of different Sizes. 
 
 INCLUDING 3 PER CENT. FOR LAY. 
 
 Size of 
 
 Wire. 
 
 B. W. G 
 
 Diameter 
 in Mils. 
 
 
 NUMBER OF WIRES IN 
 
 CABLE. 
 
 9 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 
 
 cwts. 
 
 cwts. 
 
 cwts- 
 
 cwts. 
 
 cwts. 
 
 cwts. 
 
 00 
 
 380 
 
 [90'87 
 
 212-08 
 
 254-49 
 
 296-91 
 
 339-32 
 
 381-74 
 
 O 
 
 340 
 
 152-68 
 
 169-64 
 
 203-57 
 
 237-50 
 
 271-42 
 
 305-35 
 
 I 
 
 300 
 
 Ii8'84 
 
 132-05 
 
 158-45 
 
 184-86 
 
 211-27 
 
 237-68 
 
 2 
 
 284 
 
 io6'5i 
 
 118-35 
 
 142-02 
 
 165-68 
 
 189-25 
 
 213-02 
 
 3 
 
 259 
 
 88-53 
 
 98-36 
 
 118-04 
 
 137-71 
 
 157-38 
 
 177-06 
 
 4 
 
 238 
 
 74-72 
 
 83-02 
 
 99-62 
 
 Il6-22 
 
 132-83 
 
 149-43 
 
 5 
 
 220 
 
 63-96 
 
 71-07 
 
 85-28 
 
 99-50 
 
 113-71 
 
 127-93 
 
 6 
 
 203 
 
 54-32 
 
 60-36 
 
 72-43 
 
 84-50 
 
 96-57 
 
 108-64 
 
 7 
 
 180 
 
 42-73 
 
 47-48 
 
 56-98 
 
 66-48 
 
 75-97 
 
 85-47 
 
 8 
 
 16, 
 
 35-78 
 
 39-76 
 
 ATV 
 
 55-66 
 
 63-61 
 
 71-56 
 
 9 
 
 148 
 
 28-92 
 
 32-14 
 
 38-56 
 
 44-99 
 
 51-42 
 
 57-84 
 
 10 
 
 134 
 
 23-64 
 
 26-26 
 
 31-52 
 
 36-77 
 
 42-02 
 
 47-28 
 
 II 
 
 120 
 
 19-00 
 
 2I-II 
 
 25-34 
 
 29-56 
 
 33-78 
 
 38-01 
 
 12 
 
 109 
 
 15-57 
 
 17-30 
 
 20-76 
 
 24-22 
 
 27-69 
 
 31-15 
 
 13 
 
 95 
 
 11-86 
 
 13-18 
 
 15-82 
 
 18-46 
 
 21-09 
 
 2J-73 
 
 14 
 
 83 
 
 9-08 
 
 10-09 
 
 12-11 
 
 14-13 
 
 16-15 
 
 18-17 
 
 15 
 
 72 
 
 6-77 
 
 7-52 
 
 9-02 
 
 10-53 
 
 12-03 
 
 13-53 
 
 16 
 
 65 
 
 5-47 
 
 6-08 
 
 7-29 
 
 8-51 
 
 9-72 
 
 10-94 
 
Iron. 141 
 
 TABLE of tlie Sizes and "WeigMs of Iron Wire. 
 
 B. W. 
 
 Dlam. 
 
 Per Statute Mile. 
 
 Nautical 
 
 Mile. 
 Weight in 
 
 Breaking 
 Weight 
 
 Gauge. 
 
 in Mils.* 
 
 Weight in 
 
 Weight in 
 
 Resistance 
 
 at 
 20 Tons 
 
 
 
 lbs. 
 
 cwts. 
 
 in ohms. 
 
 
 per sq. ins. 
 
 
 
 
 
 
 
 Cwts. 
 
 I sq. in. 
 
 — 
 
 17645 
 
 157-54 
 
 -340 
 
 181-63 
 
 400 
 
 I circ. m. 
 
 1000 
 
 13858 
 
 123-73 
 
 -433 
 
 142-65 
 
 314-16 
 
 0000 
 
 454 
 
 2854 
 
 25-48 
 
 2-10 
 
 29-38 
 
 64-40 
 
 000 
 
 425 
 
 2502 
 
 22-33 
 
 2-40 
 
 25-75 
 
 56-40 
 
 00 
 
 380 
 
 2001 
 
 17-86 
 
 3 -co 
 
 20-59 
 
 45-36 
 
 
 
 340 
 
 1600 
 
 14-28 
 
 3-74 
 
 16-47 
 
 36-31 
 
 I 
 
 300 
 
 1245 
 
 II-I2 
 
 4-81 
 
 12-82 
 
 28-27 
 
 2 
 
 284 
 
 I117 
 
 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 
 
 17-79 
 
 5 
 
 220 
 
 670 
 
 5-98 
 
 8-96 
 
 6-90 
 
 15-20 
 
 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 
 
 2-71 
 
 19-75 
 
 3-12 
 
 6-88 
 
 10 
 
 134 
 
 249 
 
 2'22 
 
 24-14 
 
 2-55 
 
 5-64 
 
 II 
 
 120 
 
 199 
 
 1-78 
 
 30-10 
 
 2-05 
 
 4-52 
 
 12 
 
 109 
 
 164 
 
 1-46 
 
 36-49 
 
 1-68 
 
 3-73 
 
 13 
 
 95 
 
 124 
 
 I'll 
 
 48-01 
 
 1-28 
 
 2-83 
 
 14 
 
 83 
 
 95 
 
 -85 
 
 62-93 
 
 •98 
 
 2-16 
 
 15 
 
 72 
 
 72 
 
 •64 
 
 83-65 
 
 -73 
 
 1-62 
 
 16 
 
 65 
 
 58 
 
 •52 
 
 102-6 
 
 •59 
 
 1-32 
 
 17 
 
 58 
 
 46-58 
 
 
 .. 
 
 
 
 18 
 
 49 
 
 33-17 
 
 
 
 -■ 
 
 
 19 
 
 42 
 
 24-35 
 
 . , 
 
 
 
 , , 
 
 20 
 
 35 
 
 17-93 
 
 
 
 -. 
 
 
 21 
 
 32 
 
 14-11 
 
 
 
 
 
 22 
 
 28 
 
 10-76 
 
 
 
 
 •• 
 
 See foot-note, p. 138. 
 
142 Copper. 
 
 COPPER. 
 
 The specific gravity of copper wire according to 
 the best authorities is about 8 '8. 
 
 One cubic foot of copper weighs 550 lbs. 
 
 The ordinary breaking weight of copper wire is 
 about 17 tons per square inch, varying, however, greatly 
 according to the size and temper. 
 
 The weight per nautical mile of any copper wire is 
 
 about —lbs., or more correctly (5476), where a is the 
 
 diameter in mils (thousandths of an inch), and 55 is a 
 constant. 
 
 The weight per nautical mile of a copper strand is 
 
 d^ 
 
 about lbs. 
 
 70-4 
 
 The weight per statute mile of any copper wire is 
 
 d^ 
 T— ; — lbs. A mile of No. 16 wire weighs in practice from 
 
 63 to 66 lbs. 
 
 The diameter of any copper wire weighing n lbs 
 per nautical mile is y/ n x S4"76 mils. 
 
 The diameter of any copper wire weighing n lbs. 
 per statute mile is \/n x 63 mils. 
 
Copper. 143 
 
 The diameter of a copper strand weighing n lbs. 
 per nautical mile is about \/n x 70*4 mils. 
 
 The diameter of any copper wire is half the square 
 
 w 
 root of -— , where w is the weight in ounces, and / the 
 
 length, and d the diameter in inches. 
 
 The resistance of a nautical mile of pure copper 
 weighing i lb. is — 
 
 at 32° Fahr. io9f22 ohms 
 
 at 60° Fahr. 1155 '48 „ 
 
 at 75° Fahr. 1192-33 „ (See page 64.) 
 
 The resistance per nautical mile of any pure copper 
 
 . 1 155 '48 
 wire or strand weighmg n lbs. is at 60° Fahr. 
 
 The resistance per nautical mile of any pure copper 
 
 63281 
 wire d mils in diameter is — -17- ohms at 60° Fahr. 
 
 The resistance per nautical mile of any pure copper 
 
 81361 
 is — -y^ ohms at 60 Fahr. 
 
 The resistance per statute mile of any pure copper 
 
 54892 
 wire is .^ ohms, at 60 Fahr. 
 
144 Copper. 
 
 The resistance of a statute mile of pure copper 
 weighing i lb. is 1002-4 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 
 
 I002'4 
 
 weighing n lbs. is ohms at 60° Fahr. 
 
 The resistance of any pure copper wire / inches 
 
 •ooi5r6 X ^* , 
 m length, weighmg n grams = ohms. 
 
 The resistance of copper increases as the tempera- 
 ture rises •21 per cent, for each degree Fahr., or about 
 •38 per cent, for each degree Centigrade. A table of 
 resistances at different temperatures is given below. 
 
 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. (See page 64.) 
 
 The conductivity of any copper wire, / inches in length, 
 •r5i6 X l^ 
 
 weighing w grains = 
 
 w X res. in ohms' 
 
 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. 
 (= 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. 
 
Copper. 
 
 145 
 
 TABLE for Calculating th.e Resistance of Copper at 
 different Temperatures. 
 
 To increase from lower Tem- 
 
 To reduce from higher Tem- 
 
 perature to higher, mul- 
 
 perature to lower, multiply 
 
 tiply the Res. by the num- 
 
 the Res. by the number in 
 
 ber in Column 2. 
 
 Column 4. 
 
 No. of 
 
 Column 2. 
 
 No. of 
 
 Column 4. 
 
 Degrees. 
 
 
 Degrees. 
 
 
 q 
 
 !• 
 
 
 
 I - 
 
 I 
 
 I "0021 
 
 I 
 
 0-9979 
 
 2 
 
 I "0042 
 
 2 
 
 0-9958 
 
 3 
 
 1-0063 
 
 3 
 
 0-9937 
 
 4 
 
 I -0084 
 
 4 
 
 0-9916 
 
 5 
 
 1*0105 
 
 5 
 
 0-9896 
 
 6 
 
 I"OI27 
 
 6 
 
 0-9875 
 
 7 
 
 1-0148 
 
 7 
 
 0-9854 
 
 8 
 
 I -0169 
 
 8 
 
 0-9834 
 
 9 
 
 I -0191 
 
 9 
 
 0-9813 
 
 lO 
 
 I-02I2 
 
 10 
 
 0-9792 
 
 11 
 
 1-0233 
 
 11 
 
 0-9772 
 
 12 
 
 1-0255 
 
 12 
 
 0-9751 
 
 13 
 
 1-0276 
 
 13 
 
 0-9731 
 
 14 
 
 1-0298 
 
 H 
 
 0-9711 
 
 15 
 
 I -0320 
 
 15 
 
 0-9690 
 
 16 
 
 1-0341 
 
 16 
 
 0-9670 
 
 17 
 
 1-0363 
 
 17 
 
 0-9650 
 
 18 
 
 1-0385 
 
 18 
 
 0-9629 
 
 19 
 
 I - 0407 
 
 19 
 
 - 9609 
 
 20 
 
 1-0428 
 
 20 
 
 0-9589 
 
 21 
 
 1-0450 
 
 21 
 
 0-9569 
 
 22 
 
 1-0472 
 
 22 
 
 0-9549 
 
 23 
 
 1-0494 
 
 23 
 
 0-9529 
 
 24 
 
 1-0516 
 
 24 
 
 0-9509 
 
 25 
 
 1-0538 
 
 25 
 
 0-9489 
 
 20 
 
 1-0561 
 
 26 
 
 0-9469 
 
 27 
 
 1-0583 
 
 27 
 
 0-9449 
 
 28 
 
 1-0605 
 
 28 
 
 0-9429 
 
 29 
 
 1-0627 
 
 29 
 
 . 0-9409 
 
 30 
 
 1-0650 
 
 30 
 
 0-9390 
 
146 
 
 Gutta-percha. 
 
 GXJTTA-PERCHA AlTD INDIA-RtTBBER. 
 
 The specific gravity of gutta-percha is about -qSi. 
 I cubic foot weighs 61 -3 2 lbs. 
 I nautical mile by i circular inch weighs 2036 lbs. 
 I statute mile by one circular inch weighs 1765 lbs. 
 
 Unstretched gutta-percha begins to elongate perma- 
 nently at a strain of 6 cwt. per square inch. 
 
 The following are a few of the standard sizes of gutta- 
 percha wire in ordinary use ; — 
 
 No. 
 
 Diameter in 
 
 Weight of Percha 
 
 
 Mils.* 
 
 per statute Mile. 
 
 
 
 lbs. 
 
 
 
 143 
 
 36 
 
 8 
 
 161 
 
 46 
 
 7 
 
 171 
 
 52 
 
 6 
 
 194 
 
 66 
 
 5 
 
 214 
 
 81 
 
 4 
 
 221 
 
 86 
 
 3 
 
 247 
 
 108 
 
 2 
 
 276 
 
 134 
 
 I 
 
 2S9 
 
 147 
 
 
 
 340 
 
 204 
 
 The weight of gutta-percha per nautical rnile 
 is I lb. for each 481 circular mils of sectional area ; or for 
 
 a solid cylinder —r- lbs. 
 
 * See foot-note, page 138, 
 
Gutta-percha. 147 
 
 The weight of gutta-percha per nautical mile 
 
 in any core is — —^ — lbs., where d is the diameter of the 
 copper in mils, and D the diameter of the gutta-percha. 
 
 The weight of gutta-percha per statute mile 
 _ D'— ^^ 
 
 554-5 " 
 
 The exterior diameter of any gutta-percha core 
 
 =a/« X 70-4-f-N X 481, where n is the weight in lbs. 
 per nautical mile of copper strand, and N the weight 
 of percha. With a solid conductor the diam. = 
 
 \/» X 55 + N X 481. 
 
 The electrostatic capacity per nautical mile ofany 
 
 ■18769 
 gutta-percha core is approximately r^ farads. (See 
 
 Log.— 
 page 33.) d 
 
 The electrostatic capacity of gutta-percha cores 
 as compared with india-rubber coies of similar size is 
 about as 120 to 100. 
 
 The resistance per nautical mile of a gutta-percha 
 
 Log.— 
 core of the best quality = megohms at 75° Fahr., 
 
148 Gutta-percha. 
 
 regarding the four left-hand figures of the logarithm as 
 integer numbers, and the rest as decimals. (See page 34.) 
 
 The resistance of gutta-percha under pressure in- 
 creases, according to Siemens, in the following ratio : — - 
 
 Let R be the resistance and / the pressure in lbs. 
 per square inch ; the resistance under pressure = R X 
 (i + -00023 p). 
 
 The resistance of gutta-percha at 75° Fahr., as 
 compared with Hooper's india-rubber compound, averages 
 about as 100 to 1600. 
 
 The specific inductive capacity of gutta-percha is 
 4'2, that of Hooper's material 3'i, pure rubber 2-8 ; that 
 of air being i (Jenkin). 
 
 The resistance of gutta-percha diminishes as the 
 temperature increases ; the rate of increase is about as 
 follows. Let R = resistance at the higher temperature ; 
 r, resistance at the lower temperature ; t, the difference 
 of temperature in degrees Fahr. : then — 
 
 log. of R = log. oif— flog, of "9399 
 and, log. of r = log. of R + ;f log. of '9399. 
 
 A table of resistance of gutta-percha at different 
 temperatures is given in page 149. 
 
Gutta-percha. 
 
 149 
 
 TABLE of the relative Resistance of Gutta-percha at 
 different Temperatures. 
 
 Fahr. 
 
 Resistance. 
 
 Fahr. 
 
 Resistance. 
 
 
 32 
 
 14-38 
 
 
 62 
 
 2-239 
 
 33 
 
 13-52 
 
 63 
 
 2-104 
 
 34 
 
 12-71 
 
 64 
 
 1-978 
 
 35 
 
 11-94 
 
 65 
 
 1-859 
 
 36 
 
 11-22 
 
 6S 
 
 1-747 
 
 37 
 
 10-55 
 
 67 
 
 1-642 
 
 38 
 
 9-917 
 
 68 
 
 1-543 
 
 39 
 
 9-132 
 
 69 
 
 1-451 
 
 40 
 
 8-760 
 
 70 
 
 1-364 
 
 41 
 
 8-233 
 
 71 
 
 1-282 
 
 42 
 
 7-738 
 
 72 
 
 1-204 
 
 43 
 
 7-273 
 
 73 
 
 I-132 
 
 44 
 
 6-835 
 
 74 
 
 I -064 
 
 45 
 
 6-425 
 
 75 
 
 1 00 
 
 46 
 
 6-038 
 
 76 
 
 -940 
 
 ^I 
 
 5-675 
 
 77 
 
 •883 
 
 48 
 
 5-334 
 
 78 
 
 •830 
 
 49 
 
 5-013 
 
 79 
 
 •780 
 
 50 
 
 4-712 
 
 80 
 
 -733 
 
 51 
 
 4-429 
 
 81 
 
 •689 
 
 52 
 
 4-162 
 
 82 
 
 •648 
 
 53 
 
 3-912 
 
 83 
 
 -609 
 
 54 
 
 3-680 
 
 84 
 
 -572 
 
 55 
 
 3-456 
 
 85 
 
 •538 
 
 56 
 
 3-248 
 
 86 
 
 •506 
 
 57 
 
 3-053 
 
 87 
 
 -475 
 
 58 
 
 2-869 
 
 88 
 
 •447 
 
 59 
 
 2-697 
 
 89 
 
 -420 
 
 60 
 
 2-535 
 
 90 
 
 •394 
 
 61 
 
 2-382 
 
 
 
1 5a India-rubber. 
 
 The ratio of resistance for each degree Fahr. is given 
 in the above table, taking that at the standard tempera- 
 ture of 75° Fahr. as i. To reduce any resistance from 
 any temperature to 75°, multiply it by the corresponding 
 number in the table. For reduction to other temper- 
 atures, the case must be treated as one of simple 
 proportion. (See page 89.) 
 
 HOOPER'S MATERIAL. 
 The weight of Hooper's india-rubber compound 
 
 per nautical mile is i lb. for every 401 circular mils of 
 sectional area. 
 
 The weight of Hooper's compound per nautical 
 
 D' d^ 
 
 mile in any cable is about lbs. 
 
 401 
 
 The weight of Hooper's compound per statute 
 
 mile = 
 
 462-3 
 
 The exterior diameter of any core of Hooper's com- 
 pound is ='\/«x 7o'4-fNx4oi, where N is the 
 weight in lbs. per knot of the compound, and n of the 
 copper strand. 
 
 The resistance per nautical mile of any core of 
 
 D 
 
 Hooper's compound is about Log. -^ X i '5 megohms at 
 
Sea-water. i S i 
 
 75 Fahr., regarding the first four figures of the logarithm 
 as whole numbers. 
 
 The electrostatic capacity per nautical mile 
 of any core of Hooper's material is approximately 
 •14854 
 
 Log.-p 
 a 
 
 farads. 
 
 SEA-WATER. 
 The specific gravity of sea-water is ordinarily 
 I "028, 
 
 One cubic foot weighs 64' 2 4 lbs. 
 
 One cubic foot of distilled water weighs 62-5 lbs.. 
 
 The pressure of the ocean is equal to 2-676 lbs. 
 per square inch per fathom, or i ton i cwt. per statute 
 mile. 
 
 The temperature of the 'ocean below a depth 
 of 1200 fathoms is beheved to be everywhere about 
 40° Fahr. 
 
 ENGLISH MEASTJRES OE LENGTH. 
 The nautical mile, or knot, is the same as the 
 geographical mile ; its length is variously given by dif- 
 ferent authorities ; it is -^th of a degree of latitude, but, 
 owing to the configuration of* the earth, this distance 
 varies from 362,750 feet at the equator to 366,300 feet at 
 
152 Measures. 
 
 364540 
 the poles. At the mean latitude of 45° it is — 7 = 
 
 60757 feet; but in the latitude of Greenwich it is about 
 6083 '3 feet. The measure of 6087 feet, or 2029 yards, is, 
 however, in such general use that we prefer to retain it. 
 
 One nautical mile is about 2029 yards, or 6087 feet, 
 or about \'Ca. more than a statute mile. 
 
 One statute mile is 1760 yards, or 5280 feet. 
 
 To convert nautical into statute miles, multiply 
 by 1-153, or, as a rough approximation, add ^^th. 
 
 To convert statute into nautical miles, multiply 
 by '8674, or, as a rough approximation, subtract 4-th. 
 
 To convert square inches into circular inches, 
 
 multiply by 7854. 
 
 FRENCH AND ENGLISH MEASURES. 
 To convert metres into inches, multiply by 39-37. 
 
 To convert metres into feet, multiply by 3-281. 
 
 To convert metres into yards, multiply by i -094. 
 
 Note. — For the purpose of memory, a metre may be 
 considered as three feet, three inches, and a third. 
 
 To convert kilometres into statute miles, multiply 
 by -6214. 
 
Measures. ' 153 
 
 To convert kilometres into nautical miles, mul- 
 tiply by -539. 
 
 To convert millimetres into inches, multiply by 
 ■03937. 
 
 To convert grammes into grains, multiply by 
 iS"44. 
 
 To convert kilogrammes into pounds, multiply 
 by 2-205. 
 
 MEASURES OF TEMPEEATURE. 
 
 The centigrade thermometer has the difference of 
 temperature between freezing and boihng water divided 
 into 100 degrees, these temperatures being respectively 
 called 0° and 100°. They correspond to 32° and 212° 
 on Fahrenheit's thermometer. 180° Fahr. are therefore 
 equal to 100 cent., or the centigrade degrees are larger 
 than Fahrenheit's, in the proportion of 18 to 10, or 
 9 to 5.' 
 
 To convert centigrade temperatures above freezing 
 into Fahrenheit, multiply them by i'8, and add 32 j or, 
 
 multiply by 2, subtract a tenth, and add 32. 
 
 Thus, 20 cent, x 2 = 40, and 40 — 4 + 32 = 68° Fahr. 
 
 The foregoing rule should be committed to memory 
 as it is easily performed mentally. 
 
1 54 Measures. 
 
 The specific gravity of a cable or other body may 
 
 be obtained by ascertaining its weight in air, W, and its 
 
 weight in water, w : then 
 
 W — zw : W : : I : sp. gr., 
 
 W 
 
 and specific gravity = =7;^ . 
 
 W — w 
 
 If a cable weigh n cwts. per mile, and have a specific 
 
 gravity s, its weight in sea-water will be 
 
 n 
 n X "973 cwts. 
 
 STRAIN OF SUSPENDED WIBES. 
 
 The ordinary dip of line wires for a span of 80 yards 
 is about 18 inches in mild weather : this gives with 
 No. 8 wire a strain of 420 lbs. ; its breaking weight being 
 about 1300 lbs.* 
 
 The strain varies directly as the weight of the wire, 
 and inversely as the dip or versine ; it increases as the 
 square of the span if the dip be constant, but to pre- 
 serve a given strain the dip or versine must increase as 
 the square of the span, or 
 
 L*" :/*:: V:w. 
 The strain is greater at the point of suspension than at 
 the lowest point of the span, by a quantity (equal to the 
 weight of a length of wire of the same height as the 
 versine) which may be neglected in practice. Calling 
 
 * Culley : Handbook of Telegraphy, 
 
Measures. 155 
 
 / the length of span in feet, w the weight in cwts. of one 
 
 statute mile, v the versine in inches, and j' the strain 
 
 in lbs. — 
 
 /* X ^ ^ 
 
 Strain = lbs. approximately, 
 
 31-43 X ?» 
 
 and dip = '— inches. 
 
156 
 
 Measures. 
 
 TABLE of the BirmuLgham Wire G-auge. 
 According to Holtzapffel. 
 
 B. W. 
 
 Diam. in 
 
 Sect, area 
 
 B. W. 
 
 Diam. in 
 
 Sect, area 
 
 Gauge. 
 
 ins. 
 
 in sq. ins. 
 
 Gauge. 
 
 ins. 
 
 in sq. ins. 
 
 I circ. in. 
 
 I -ooo 
 
 •7854 
 
 17 
 
 •058 
 
 •00264 
 
 0000 
 
 •454 
 
 ■I 61 88 
 
 18 
 
 •049 
 
 •00188 
 
 000 
 
 •425 
 
 •141 86 
 
 19 
 
 •042 
 
 •00138 
 
 00 
 
 •380 
 
 •11341 
 
 20 
 
 •035 
 
 • 00096 
 
 
 
 ■340 
 
 •09079 
 
 21 
 
 •032 
 
 •00080 
 
 I 
 
 •300 
 
 •07068 
 
 22 
 
 •028 
 
 •00061 
 
 2 
 
 •284 
 
 •06335 
 
 23 
 
 •025 
 
 • 00049 
 
 3 
 
 •259 
 
 •05268 
 
 24 
 
 •022 
 
 •00038 
 
 4 
 
 •238 
 
 •04449 
 
 25 
 
 •020 
 
 • 0003 1 
 
 5 
 
 •220 
 
 •03801 
 
 26 
 
 •018 
 
 •00025 
 
 , 6 
 
 •203 
 
 •03236 
 
 27 
 
 •016 
 
 •00020 
 
 7 
 
 •180 
 
 ■02545 
 
 28 
 
 •014 
 
 •00015 
 
 8 
 
 •165 
 
 •02138 
 
 29 
 
 •013 
 
 •00013 
 
 9 
 
 •148 
 
 •01720 
 
 30 
 
 •012 
 
 •0001 I 
 
 10 
 
 •134 
 
 •01410 
 
 31 
 
 •010 
 
 •000078 
 
 II 
 
 •120 
 
 •01131 
 
 32 
 
 •009 
 
 • 000063 
 
 12 
 
 •109 
 
 •00933 
 
 33 
 
 •008 
 
 •000050 
 
 13 
 
 •095 
 
 •00708 
 
 34 
 
 •007 
 
 •000038 
 
 14 
 
 , -083 
 
 •00541 
 
 35 
 
 •005 
 
 •000019 
 
 15 
 
 ■072 
 
 • 00407 
 
 36 
 
 •004 
 
 •000012 
 
 16 
 
 •065 
 
 •00332 
 
 
 
 
IS7 
 TABLE of ITatural Sines and Tangents. 
 
 De- 
 grees. 
 
 Sine. 
 
 Tang. 
 
 De- 
 grees. 
 
 Sine. 
 
 Tang. 
 
 I 
 
 •017 
 
 •017 
 
 46 
 
 •719 
 
 1-03 
 
 2 
 
 •035 
 
 •035 
 
 47 
 
 •731 
 
 1-07 
 
 3 
 
 ■052 
 
 ■052 . 
 
 48 
 
 •743 
 
 I'll 
 
 4 
 
 •070 
 
 •070 
 
 49 
 
 •755 
 
 I-I5 
 
 5 
 
 •087 
 
 •087 
 
 5° 
 
 •766 
 
 fi9 
 
 6 
 
 •104 
 
 •105 
 
 51 
 
 •777 
 
 1^23 
 
 7 
 
 •122 
 
 •123 
 
 52 
 
 •788 
 
 I^28 
 
 8 
 
 •139 
 
 •140 
 
 53 
 
 •798 
 
 ^•33 
 
 9 
 
 •156 
 
 •158 
 
 54 
 
 •809 
 
 i'37 
 
 lO 
 
 •173 
 
 •176 
 
 55 
 
 •819 
 
 I -43 
 
 II 
 
 •191 
 
 •194 
 
 56 
 
 •829 
 
 f48 
 
 12 
 
 •208 
 
 •212 
 
 57 
 
 •838 
 
 ^•54 
 
 13 
 
 •225 
 
 •231 
 
 58 
 
 ■848 
 
 i^6o 
 
 14 
 
 ^242 
 
 ■249 
 
 59 
 
 •857 
 
 1^66 
 
 15 
 
 •259 
 
 •268 
 
 60 
 
 •866 
 
 1-73 
 
 16 
 
 •275 
 
 •287 
 
 61 
 
 •874 
 
 i-8o 
 
 17 
 
 •292 
 
 ■306 
 
 62 
 
 •883 
 
 i'88 
 
 18 
 
 •309 
 
 •325 
 
 63 
 
 •891 
 
 1-96 
 
 19 
 
 •325 
 
 •344 
 
 64 
 
 •899 
 
 2-05 
 
 20 
 
 •342 
 
 •364 
 
 65 
 
 •906 
 
 2-14 
 
 21 
 
 ■358 
 
 •384 
 
 66 
 
 ■913 
 
 2-24 
 
 22 
 
 •374 
 
 •404 
 
 67 
 
 ■920 
 
 2-35 
 
 23 
 
 •391 
 
 •424 
 
 68 
 
 •927 
 
 2-47 
 
 24 
 
 •407 
 
 •445 
 
 69 
 
 •933 
 
 2^6o 
 
 25 
 
 •422 . 
 
 •466 
 
 70 
 
 •939 
 
 2-75 
 
 26 
 
 •438 
 
 •488 
 
 71 
 
 •945 
 
 2-90 
 
 \27 
 
 ■454 
 
 •509 
 
 72 
 
 •951 
 
 3-08 
 
 28 
 
 •469 
 
 .■532 
 
 73 
 
 •956 
 
 3-27 
 
 29 
 
 ■485 
 
 •554 
 
 74 
 
 •961 
 
 3^49 
 
 30 
 
 •500 
 
 •577 
 
 75 
 
 •966 
 
 3^73 
 
 31 
 
 •515 
 
 •601 
 
 76 
 
 •970 
 
 4^01 
 
 32 
 
 •530 
 
 •625 
 
 77 
 
 •974 
 
 4^33 
 
 33 
 
 •544 
 
 •649 
 
 78 
 
 •978 
 
 4-70 
 
 34 
 
 •559 
 
 .674 ■ 
 
 79 
 
 •981 
 
 5-14 
 
 35 
 
 ,■573 
 
 •700 
 
 80 
 
 ■985 
 
 5-67 
 
 36 
 
 .•588 
 
 ■726 
 
 81 
 
 •987 
 
 6-31 
 
 37 
 
 •602 
 
 •753 
 
 82 
 
 •990 
 
 7-II 
 
 38 
 
 ■•615 
 
 •.781 
 
 83 
 
 •992 
 
 8-14 
 
 39 
 
 •629 
 
 •810 
 
 84 
 
 •994 
 
 9^51 
 
 40 
 
 ■643 
 
 •839 
 
 85 
 
 •996 
 
 11-43 
 
 41 
 
 •656 
 
 •869 
 
 86 
 
 •997 
 
 14-30 
 
 42 
 
 •669 
 
 ■900 
 
 87 
 
 ■998 
 
 19-08 
 
 43 
 
 •682 
 
 •932 
 
 88 
 
 •999 
 
 28-63 
 
 44 
 
 ■694 
 
 •965 
 
 89 
 
 ■999 
 
 57-29 
 
 45 
 
 •707 
 
 1^000 
 
 90 
 
 fooo 
 
 Infinite. 
 
158 
 
 TABLE OF SaiTABES OF DIAMETEBS. 
 
 For finding the value of d^ and '\/d. 
 
 Num. 
 
 Square. 
 
 Num. 
 
 Square. 
 
 Num. 
 
 Square. 
 
 Num. 
 
 Square. 
 
 I 
 
 I 
 
 38 
 
 1444 
 
 75 
 
 5625 
 
 112 
 
 12544 
 
 2 
 
 4 
 
 39 
 
 15 21 
 
 76 
 
 5776 
 
 113 
 
 12769 
 
 3 
 
 9 
 
 40 
 
 1600 
 
 77 
 
 5929 
 
 114 
 
 12996 
 
 4 
 
 16 
 
 41 
 
 1681 
 
 78 
 
 6084 
 
 115 
 
 13225 
 
 5 
 
 25 
 
 42 
 
 1764 
 
 79 
 
 6241 
 
 Ii6 
 
 13456 
 
 6 
 
 36 
 
 43 
 
 1849 
 
 80 
 
 6400 
 
 "7 
 
 13689 
 
 7 
 
 49 
 
 44 
 
 1936 
 
 81 
 
 6561 
 
 118 
 
 13924 
 
 8 
 
 64 
 
 45 
 
 2025 
 
 82 
 
 6724 
 
 119 
 
 14161 
 
 9 
 
 8r 
 
 46 
 
 2I16 
 
 83 
 
 6889 
 
 120 
 
 14400 
 
 10 
 
 100 
 
 47 
 
 2209 
 
 84 
 
 7056 
 
 121 
 
 14641 
 
 II 
 
 121 
 
 48 
 
 2304 
 
 8s 
 
 7225 
 
 122 
 
 14884 
 
 12 
 
 144 
 
 49 
 
 2401 
 
 85 
 
 7396 
 
 123 
 
 I5129 
 
 13 
 
 169 
 
 5° 
 
 2500 
 
 87 
 
 7569 
 
 124 
 
 15376 
 
 14 
 
 196 
 
 51 
 
 2601 
 
 88 
 
 7744 
 
 125 
 
 15625 
 
 15 
 
 225 
 
 52 
 
 2704 
 
 89 
 
 7921 
 
 126 
 
 15876 
 
 16 
 
 256 
 
 53 
 
 2809 
 
 90 
 
 8100 
 
 127 
 
 16129 
 
 17 
 
 289 
 
 54 
 
 2916 
 
 9J 
 
 8281 
 
 128 
 
 16384 
 
 18 
 
 324 
 
 55 
 
 3025 
 
 92 
 
 8464 
 
 129 
 
 1 6 641 
 
 19 
 
 361 
 
 56 
 
 3136 
 
 93 
 
 8649 
 
 130 
 
 16900 
 
 20 
 
 400 
 
 57 
 
 3249 
 
 94 
 
 8836 
 
 131 
 
 17161 
 
 21 
 
 441 
 
 58 
 
 3364 
 
 95 
 
 9025 
 
 132 
 
 17424 
 
 22 
 
 484 
 
 59 
 
 34B1 
 
 96 
 
 9216 
 
 133 
 
 17689 
 
 23 
 
 529 
 
 60 
 
 3600 
 
 97 
 
 9409 
 
 134 
 
 17956 
 
 24 
 
 576 
 
 61 
 
 3 731 
 
 98 
 
 9604 
 
 135 
 
 18235 
 
 25 
 
 625 
 
 62 
 
 3844 
 
 99 
 
 9801 
 
 136 
 
 18496 
 
 26 
 
 676 
 
 63 
 
 3969 
 
 100 
 
 lOOOO 
 
 137 
 
 18769 
 
 ^7 
 
 729 
 
 64 
 
 4096 
 
 lOI 
 
 I020I 
 
 138 
 
 19044 
 
 28 
 
 784 
 
 65 
 
 4225 
 
 102 
 
 10404 
 
 139 
 
 19321 
 
 29 
 
 841 
 
 66 
 
 4356 
 
 103 
 
 .10609 
 
 140 
 
 19600 
 
 30 
 
 900 
 
 67 
 
 4489 
 
 104 
 
 I0816 
 
 141 
 
 19881 
 
 31 
 
 961 
 
 68 
 
 4624 
 
 105 
 
 IIO25 
 
 142 
 
 20164 
 
 32 
 
 1024 
 
 69 
 
 4761 
 
 106 
 
 II236 
 
 143 
 
 20449 
 
 33 
 
 1089 
 
 70 
 
 4900 
 
 107 
 
 II449 
 
 144 
 
 20736 
 
 34 
 
 1156 
 
 71 
 
 5041 
 
 108 
 
 II664 
 
 145 
 
 21025 
 
 35 
 
 1225 
 
 72 
 
 5184 
 
 109 
 
 II881 
 
 146 
 
 21316 
 
 36 
 
 1296 
 
 73 
 
 5329 
 
 no 
 
 I2I00 
 
 147 
 
 21609 
 
 37 
 
 1369 
 
 74 
 
 5476 
 
 III 
 
 I2321 
 
 148 
 
 21904 
 
159 
 
 
 Table of Squares otDiameteis—coHiinued 
 
 
 Num. 
 
 Square. ; 
 
 Num. 
 
 Square. 
 
 Mum. 
 
 Square. 
 
 Num. 
 
 Square. 
 
 149 
 
 22201 
 
 193 
 
 37249 
 
 237 
 
 56169 
 
 281 
 
 78961 
 
 150 
 
 22500 
 
 104 
 
 37636 
 
 238 
 
 56644 
 
 282 
 
 79524 
 
 151 
 
 22801 
 
 195 
 
 38025 : 
 
 239 
 
 57121 
 
 283 
 
 800&9 
 
 152 
 
 23104 
 
 196 
 
 38416 
 
 240 
 
 57600 
 
 284 
 
 80656 
 
 153 
 
 23409 
 
 197 
 
 38809 
 
 241 
 
 58081 
 
 285 
 
 81225 
 
 154 
 
 23716 
 
 198 
 
 39204 ; 
 
 242 
 
 58564 ' 
 
 286 
 
 81796 
 
 155 
 
 24025 
 
 199 
 
 39601 ' 
 
 243 
 
 59049 
 
 287 
 
 82369 
 
 156 
 
 24336 
 
 200 
 
 40000 [ 
 
 244 
 
 59536 
 
 288 
 
 82944 
 
 157 
 
 24649 
 
 201 
 
 40401 
 
 245 
 
 60025 
 
 289 
 
 835^1 
 
 158 
 
 24964 
 
 202 
 
 40804 1 
 
 246 
 
 60516 
 
 290 
 
 84100 
 
 159 
 
 25281 
 
 203 
 
 41209 : 
 
 247 
 
 61009 
 
 291 
 
 84681 
 
 160 
 
 25600 
 
 204 
 
 41616 ' 
 
 248 
 
 61504 
 
 292 
 
 85264 
 
 161 
 
 25921 
 
 205 
 
 42025 ; 
 
 249 
 
 62001 
 
 293 
 
 85849 
 
 162 
 
 26244 
 
 206 
 
 42436 , 
 
 250 
 
 62500 
 
 294 
 
 86436 
 
 163 
 
 26569 
 
 207 
 
 42849 ' 
 
 251 
 
 63001 
 
 295 
 
 87025 
 
 164 
 
 26896 
 
 208 
 
 43264 ', 
 
 252 
 
 63504 
 
 296 
 
 87616 
 
 165 
 
 27225 
 
 209 
 
 43681 , 
 
 253 
 
 64009 ' 
 
 297 
 
 88209 
 
 166 
 
 27556 
 
 210 
 
 44100 
 
 254 
 
 64516 
 
 298 
 
 88804 
 
 167 
 
 27889 
 
 211 
 
 44521 ■ 
 
 255 
 
 65025 
 
 299 
 
 89401. 
 
 168 
 
 28224 
 
 212 
 
 44944 : 
 
 256 
 
 65536 
 
 300 
 
 90000 
 
 169 
 
 28561 
 
 2.13 
 
 45369 ; 
 
 257 
 
 66049 
 
 301 
 
 90601 
 
 170 
 
 28900 
 
 214 
 
 45796 
 
 258 
 
 66564 
 
 302 
 
 91204 
 
 171 
 
 29241 
 
 215 
 
 46225 - 
 
 259 
 
 67081 
 
 303 
 
 91809 
 
 172 
 
 29584 
 
 216 
 
 46656 
 
 260 
 
 67600 
 
 304 
 
 92416 
 
 173 
 
 29929 
 
 217 
 
 47089 
 
 261 
 
 6812I 
 
 305 
 
 93025 
 
 174 
 
 30276 
 
 2.18 
 
 47524 
 
 262 
 
 68644 
 
 306 
 
 93636 
 
 175 
 
 30625 
 
 219 
 
 47961 
 
 263 
 
 69169 
 
 307 
 
 94249 
 
 176 
 
 30976 
 
 220 
 
 48400 
 
 264 
 
 69696 
 
 308 
 
 94864 
 
 177 
 
 31329 
 
 221 
 
 48841 
 
 265 
 
 70225 
 
 309 
 
 95481 
 
 178 
 
 31684 
 
 222 
 
 49284 
 
 266 
 
 70756 
 
 310 
 
 96100 
 
 179 
 
 32041 
 
 223 
 
 49729 
 
 267 
 
 71289 
 
 311 
 
 96721 
 
 i8o 
 
 32400 
 
 224 
 
 50176 
 
 268 
 
 71824 
 
 312 
 
 97344 
 
 i8r 
 
 32761 
 
 225 
 
 50625 
 
 269 
 
 72361 
 
 313 
 
 97969 
 
 182 
 
 33124 
 
 226 
 
 51076 
 
 270 
 
 72900 
 
 314 
 
 98596 
 
 183 
 
 33489 
 
 227 
 
 51529 
 
 271 
 
 73441 
 
 315 
 
 99225 
 
 184 
 
 33855 
 
 228 
 
 51984 
 
 272 
 
 73984 
 
 316 
 
 99856 
 
 185 
 
 34225 
 
 229 
 
 52441 
 
 273 
 
 74529 
 
 317 
 
 100489 
 
 186 
 
 34596 
 
 230 
 
 52900 
 
 274 
 
 75076 
 
 318 
 
 101124 
 
 187 
 
 34969 
 
 231 
 
 53361 
 
 275 
 
 75625 
 
 319 
 
 101761 
 
 188 
 
 35344 
 
 232 
 
 53824 
 
 276 
 
 76176 
 
 320 
 
 102400 
 
 189 
 
 35721 
 
 233 
 
 54289 
 
 277 
 
 76729 
 
 321 
 
 103 041 
 
 190 
 
 36100 
 
 234 
 
 54756 
 
 278 
 
 77284 
 
 322 
 
 103684 
 
 191 
 
 36481 
 
 235 
 
 55225 
 
 279 
 
 77841 
 
 323 
 
 104329 
 
 193 
 
 36864 
 
 236 
 
 55696 
 
 280 
 
 78400 
 
 324 
 
 104976 
 
i6o 
 
 
 Table of Squares of Diameters — continued 
 
 
 Num. 
 
 ["Square. 
 
 Num. 
 
 Square. 
 
 Num. 
 
 ' Square. 
 
 Num. 
 
 Square. 
 
 325 
 
 105625 
 
 369 
 
 136161 
 
 413 
 
 170569 
 
 457 
 
 208849 
 
 326 
 
 106276 
 
 370 
 
 136900 
 
 414 
 
 171396 
 
 458 
 
 209764 
 
 327 
 
 106929 
 
 371 
 
 13 7641 
 
 415 
 
 172225 
 
 459 
 
 2io68r 
 
 328 
 
 107584 
 
 372 
 
 138384 
 
 416 
 
 173056 
 
 460 
 
 211600 
 
 329 
 
 I08241 
 
 373 
 
 I39129 
 
 417 
 
 173889 
 
 461 
 
 212521 
 
 330 
 
 108900 
 
 374 
 
 139876 
 
 418 
 
 174724 
 
 462 
 
 213444 
 
 331 
 
 I09561 
 
 375 
 
 140625 
 
 419 
 
 175561 
 
 463 
 
 214369 
 
 332 
 
 IIO224 
 
 376 
 
 141376 
 
 420 
 
 176400 
 
 464 
 
 215296 
 
 333 
 
 II0889 
 
 377 
 
 142 1 29 
 
 421 
 
 I77241 
 
 465 
 
 216225 
 
 334 
 
 III556 
 
 378 
 
 142884 
 
 422 
 
 178084 
 
 466 
 
 217156 
 
 335 
 
 II2225 
 
 379 
 
 143 641 
 
 423 
 
 178929 
 
 467 
 
 218089 
 
 336 
 
 II2896 
 
 380 
 
 144400 
 
 424 
 
 179776 
 
 468 
 
 219024 
 
 337 
 
 II3569 
 
 381 
 
 145161 
 
 425 
 
 189625 
 
 469 
 
 219961 
 
 338 
 
 II4244 
 
 382 
 
 145924 
 
 426 
 
 181476 
 
 470 
 
 220900 
 
 339 
 
 II4921 
 
 383 
 
 146689 
 
 427 
 
 182329 
 
 471 
 
 22 I 841 
 
 340 
 
 1 15 600 
 
 384 
 
 147456 
 
 428 
 
 183184 
 
 472 
 
 222784 
 
 341 
 
 I16281 
 
 385 
 
 148225 
 
 429 
 
 I 8 4041 
 
 473 
 
 223729 
 
 342 
 
 I16964 
 
 386 
 
 148996 
 
 430 
 
 184900 
 
 474 
 
 224676 
 
 . 343 
 
 I17649 
 
 387 
 
 149769 
 
 431 
 
 185 761 
 
 475 
 
 225625 
 
 344 
 
 I18336 
 
 388 
 
 150544 
 
 432 
 
 186624 
 
 476 
 
 226576 
 
 345 
 
 II9025 
 
 389 
 
 151321 
 
 433 
 
 187489 
 
 477 
 
 227529 
 
 346 
 
 II9716 
 
 390 
 
 152100 
 
 434 
 
 188356 
 
 478 
 
 228484 
 
 347 
 
 120409 
 
 391 
 
 152881 
 
 435 
 
 189225 
 
 479 
 
 229441 
 
 348 
 
 12IIO4 
 
 392 
 
 153664 
 
 436 
 
 190096 
 
 480 
 
 230400 
 
 349 
 
 121801 
 
 393 
 
 154449 
 
 437 
 
 190969 
 
 481 
 
 231361 
 
 350 
 
 122500 
 
 394 
 
 155236 
 
 438 
 
 191844 
 
 482 
 
 232324 
 
 351 
 
 I23201 
 
 39; 
 
 156025 
 
 439 
 
 192721 
 
 483 
 
 233289 
 
 352 
 
 123904 
 
 396 
 
 156816 
 
 440 
 
 193600 
 
 484 
 
 234256 
 
 353 
 
 124609 
 
 397 
 
 157609 
 
 441 
 
 194481 
 
 485 
 
 235225 
 
 354 
 
 125 316 
 
 398 
 
 158404 
 
 442 
 
 195364 
 
 486 
 
 236196 
 
 355 
 
 126025 
 
 399 
 
 15 9201 
 
 443 
 
 196249 
 
 487 
 
 237169 
 
 356 
 
 126736 
 
 400 
 
 160000 
 
 444 
 
 197136 
 
 488 
 
 238144 
 
 35 7 
 
 127449 
 
 401 
 
 160801 
 
 445 
 
 198025 
 
 489 
 
 239121 
 
 358 
 
 128164 
 
 402 
 
 161604 
 
 446 
 
 198916 
 
 490 
 
 240100 
 
 359 
 
 I28881 
 
 403 
 
 162409 
 
 447 
 
 199809 
 
 491 
 
 241081 
 
 360 
 
 129600 
 
 404 
 
 163216 
 
 448 
 
 200704 
 
 492 
 
 242064 
 
 361 
 
 I3032I 
 
 405 
 
 164025 
 
 449 
 
 201601 
 
 493 
 
 243049 
 
 362 
 
 I 3 1044 
 
 406 
 
 164836 
 
 450 
 
 202500 
 
 494 
 
 244036 
 
 363 
 
 131769 
 
 407 
 
 165649 
 
 451 
 
 203401 
 
 495 
 
 245025 
 
 364 
 
 132496 
 
 408 
 
 166464 
 
 452 
 
 204304 
 
 496 
 
 246016 
 
 365 
 
 133225 
 
 409 
 
 167281 
 
 453 
 
 205209 
 
 ■ 497 
 
 247009 
 
 366 
 
 133956 
 
 410 
 
 168100 
 
 454 
 
 206116 
 
 498 
 
 248004 
 
 367 
 
 134689 
 
 411 
 
 . 168921 
 
 455 
 
 207025 
 
 499 
 
 249001 
 
 ?68 
 
 135424 
 
 412 169744 
 
 456 
 
 207936 
 
 500 
 
 250000 
 
I&I 
 
 TABLE OF LOGAKITHMS. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 
 
 I 
 2 
 
 — oo 
 •ooooo 
 
 ■30103 
 
 36 
 37 
 38 
 
 •55630 
 ■56820 
 •57978 
 
 72 
 73 
 74 
 
 •85733 
 •86332 
 •86923 
 
 108 
 109 
 
 IIO 
 
 •03342 
 ■03743 
 •04139 
 
 3 
 
 4 
 5 
 
 •47712 
 
 •60206 
 
 ■69897 
 
 39 
 
 40 
 
 41 
 
 ■59106 
 
 •60206 
 ■61278 
 
 75 
 76 
 77 
 
 •87506 
 ■88081 
 •88649 
 
 III 
 
 112 
 
 "3 
 
 •04532 
 •04922 
 •05308 
 
 6 
 
 7 
 8 
 
 •77815 
 
 ■84510 
 •90309 
 
 42 
 43 
 44 
 
 ■62325 
 •63347 
 •64345 
 
 78 
 79 
 80 
 
 •89209 
 •89763 
 •90309 
 
 114 
 
 "5 
 J16 
 
 ■05690 
 ■06070 
 •06446 
 
 9 
 
 10 
 
 II 
 
 •95424 
 
 •ooooo 
 
 •04139 
 
 45 
 46 
 
 47 
 
 •65321 
 ■66276 
 ■67210 
 
 81 
 82 
 83 
 
 •90849 
 •91381 
 •91908 
 
 117 
 118 
 119 
 
 •06B19 
 ■07188 
 •07555 
 
 12 
 
 13 
 
 14 
 
 •07918 
 
 ■"394 
 ■14613 
 
 48 
 49 
 5° 
 
 •68124 
 ■69020 
 •69897 
 
 84 
 85 
 86 
 
 •92428 
 • 92942 
 •93450 
 
 120 
 121 
 122 
 
 ■07918 
 ■08279 
 •08636 
 
 15 
 i6 
 
 17 
 
 ■17609 
 ■20412 
 •23045 
 
 51 
 52 
 53 
 
 •7°757 
 •71600 
 • 72428 
 
 8*7 
 88 
 
 89 
 
 •93952 
 •94448 
 •94939 
 
 123 
 124 
 125 
 
 •08991 
 •09342 
 ■09691 
 
 i8 
 19 
 
 20 
 
 ■25527 
 •27875 
 ■30103 
 
 54 
 55 
 56 
 
 ■73239 
 •74036 
 
 ■74819 
 
 90 
 
 91 
 92 
 
 •95424 
 •95904 
 •96379 
 
 126 
 127 
 128 
 
 ■10037 
 ■10380 
 •10721 
 
 21 
 
 22 
 
 23 
 
 ■32222 
 • 34242 
 •36173 
 
 57 
 58 
 59 
 
 •75587 
 ■76343 
 • 77085 
 
 93 
 94 
 95 
 
 •96848 
 •97313 
 •97772 
 
 129 
 130 
 131 
 
 •II059 
 ■I1394 
 •11727 
 
 24 
 11 
 
 ■38021 
 •39794 
 •41497 
 
 60 
 61 
 
 62 
 
 •77815 
 
 •78533 
 •79239 
 
 96 
 97 
 98 
 
 ■98227 
 ■98677 
 •99123 
 
 132 
 133 
 
 134 
 
 ■12057 
 ■12385 
 ■12710 
 
 27 
 28 
 29 
 
 •4313& 
 ■44715 
 •46240 
 
 63 
 
 64 
 65 
 
 •79934 
 •80618 
 •81291 
 
 99 
 100 
 
 lOI 
 
 ■99564 
 •ooooo 
 •00432 
 
 135 
 136 
 
 137 
 
 ■13033 
 
 •13354 
 ■13672 
 
 3° 
 31 
 
 32 
 
 •47712 
 
 ■49136 
 •50515 
 
 66 
 67 
 68 
 
 •81954 
 •82607 
 ■83251 
 
 102 
 103 
 104 
 
 •00860 
 •01284 
 •01703 
 
 138 
 
 139 
 
 140 
 
 ■13988 
 ■14301 
 •14613 
 
 33 
 34 
 35 
 
 •51851 
 •53148 
 •54407 
 
 69 
 70 
 71 
 
 ■83885 
 •84510 
 ■85126 
 
 105 
 106 
 107 
 
 •02 1 19 
 •02531 
 •02938 
 
 141 
 142 
 143 
 
 •14922 
 •15229 
 ■15534 
 
 M 
 
1 62 
 
 Table of IiOgaritluns — contintied. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 144 
 145 
 146 
 
 ■15836 
 •16137 
 •16435 
 
 180 
 181 
 182 
 
 •25527 
 ■25768 
 ■26007 
 
 2l6 
 
 217 
 218 
 
 ■33445 
 •33646 
 •33846 
 
 252 
 253 
 254 
 
 ■40140 
 •40312 
 •40483 
 
 147 
 148 
 149 
 
 •16732 
 •17026 
 •17319 
 
 183 
 
 184 
 185 
 
 •26245 
 •26482 
 ■26717 
 
 219 
 
 220 
 
 221 
 
 •34044 
 •34242 
 •34439 
 
 255 
 256 
 
 257 
 
 •40654 
 ■40824 
 ■40993 
 
 150 
 
 151 
 
 152 
 
 •17609 
 ■17898 
 ■18184 
 
 186 
 187 
 188 
 
 ■26951 
 •27184 
 ■27416 
 
 222 
 223 
 224 
 
 •34635 
 •34830 
 •35025 
 
 258 
 259 
 260 
 
 ■41162 
 ■41330 
 •41497 
 
 153 
 154 
 155 
 
 •18469 
 •18752 
 •19033 
 
 189 
 190 
 191 
 
 •27646 
 •27875 
 •28103 
 
 225 
 226 
 227 
 
 ■35218 
 
 •35411 
 •35603 
 
 261 
 262 
 263 
 
 ■41664 
 ■41830 
 •41996 
 
 156 
 
 157 
 158 
 
 ■19312 
 •19590 
 •19866 
 
 192 
 
 193 
 194 
 
 •28330 
 •28556 
 •28780 
 
 228 
 229 
 230 
 
 ■35793 
 •35984 
 ■36173 
 
 264 
 265 
 266 
 
 •42160 
 ■42325 
 ■42488 
 
 159 
 
 160 
 
 i6t 
 
 •20140 
 •20412 
 •20683 
 
 195 
 196 
 197 
 
 •29003 
 ■29226 
 •29447 
 
 231. 
 232 
 
 233 
 
 ■36361 
 
 •36549 
 ■36736 
 
 267 
 268 
 269 
 
 •42651 
 •42813 
 ■42975 
 
 162 
 163 
 164 
 
 ■20952 
 •21219 
 •21484 
 
 198 
 199 
 200 
 
 •29667 
 ■29885 
 ■30103 
 
 234 
 
 235 
 236 
 
 ■36922 
 ■37107 
 •37291 
 
 270 
 271 
 272 
 
 ■43136 
 •43297 
 ■43457 
 
 165 
 166 
 167 
 
 •21748 
 ■22011 
 ■22272 
 
 201 
 202 
 203 
 
 •30320 
 
 •30535 
 •30750 
 
 237 
 238 
 
 239 
 
 ■37475 
 •37658 
 •37840 
 
 273 
 274 
 275 
 
 ■43616 
 ■43775 
 •43933 
 
 168 
 169 
 
 170 
 
 •22531 
 •22789 
 •23045 
 
 204 
 205 
 206 
 
 •30963 
 
 ■31175 
 ■31387 
 
 240 
 241 
 242 
 
 ■38021 
 ■38202 
 •38382 
 
 276 
 
 277 
 278 
 
 •44091 
 ■44248 
 ■44404 
 
 171 
 172 
 
 173 
 
 •23300 
 
 •23553 
 ■23805 
 
 207 
 208 
 209 
 
 ■31597 
 •31806 
 ■32015 
 
 243 
 244 
 245 
 
 •38561 
 •38739 
 •38917 
 
 279 
 280 
 281 
 
 ■44560 
 •44716 
 •44871 
 
 174 
 175 
 176 
 
 •24055 
 
 ■ 24304 
 ■24551 
 
 210 
 211 
 
 212 
 
 .32222 
 •32428 
 ■32634 
 
 246 
 
 247 
 248 
 
 •39094 
 ■39270 
 •39445 
 
 282 
 283 
 284 
 
 •45025 
 •45179 
 •45332 
 
 177 
 178 
 
 179 
 
 ■24797 
 ■25042 
 ■25285 
 
 213 
 
 214 
 215 
 
 ■32838 
 •33041 
 •33244 
 
 249 
 250 
 251 
 
 •39620 
 •39794 
 •39967 
 
 285 
 286 
 287 
 
 •45484 
 ■45637 
 ■45788 
 
i63 
 
 Table of Xiogarithms — continued. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 288 
 289 
 290 
 
 •45939 
 ■46090 
 •46240 
 
 324 
 325 
 326 
 
 •51055 
 •51188 
 •51322 
 
 360 
 361 
 362 
 
 •55630 
 •55751 
 •55871 
 
 396 
 397 
 398 
 
 •59770 
 
 •59879 
 •59988 
 
 291 
 292 
 293 
 
 •46389 
 •46538 
 ■46687 
 
 327 
 
 3J8- 
 
 329 
 
 •5.1455 
 •51587 
 •51720 
 
 363 
 364 
 
 365 
 
 •55991 
 •56110 
 •56229 
 
 399 
 
 400 
 401 
 
 ■60097 
 •60206 
 •60314 
 
 294 
 295 
 296 
 
 •46835 
 •46982 
 ■47129 
 
 330 
 331 
 332 
 
 •51851 
 •51983 
 •52114 
 
 366 
 
 367 
 368 
 
 •56348 
 •56467 
 •56585 
 
 402 
 403 
 404 
 
 •60423 
 •60531 
 •60638 
 
 297 
 298 
 299 
 
 •47276 
 •47422 
 ■47567 
 
 333 
 
 334 
 335 
 
 •52244 
 
 •52375 
 •52504 
 
 369 
 
 370 
 
 371 
 
 •56703 
 •56820 
 •56937 
 
 405 
 406 
 407 
 
 •60746' 
 
 •60853 
 
 •60959 
 
 300 
 301 
 302 
 
 •47712 
 
 •47857 
 •48001 
 
 336 
 
 337 
 338 
 
 •52634 
 •52763 
 •52892 
 
 372 
 373 
 3 74 
 
 •57054 
 •57171 
 •57287 
 
 408 
 
 409 
 410 
 
 •61066 
 •61172 
 •61278 
 
 303 
 304 
 305 
 
 •48144 
 •48287 
 ■48430 
 
 339 
 
 340 
 
 341 
 
 •53020 
 •53148 
 •53275 
 
 375 
 376 
 
 377 
 
 •57403 
 •57519 
 •57634 
 
 411 
 412 
 413 
 
 •61384. 
 
 •61490 
 
 •61595 
 
 306 
 307 
 308 
 
 •48572 
 •48714 
 •48855 
 
 342 
 343 
 344 
 
 •53403 
 •53529 
 •53656 
 
 378 
 379 
 380 
 
 •57749 
 •57864 
 •57978 
 
 414 
 
 415 
 416 
 
 •61700 
 ■61805 
 •61909 
 
 309 
 310 
 3" 
 
 •48996 
 •49136 
 •49276 
 
 345 
 346 
 
 347 
 
 •53782 
 •53908 
 •54033 
 
 381 
 382 
 383 
 
 ■58092 
 •58206 
 •58320 
 
 417 
 418 
 419 
 
 •62014 
 •62118 
 •62221 
 
 312 
 313 
 314 
 
 ■49415 
 •49554 
 •49693 
 
 348 
 349 
 35° 
 
 •54158 
 •54283 
 •54407 
 
 384 
 385 
 386 
 
 •58433 
 •58546 
 •58659 
 
 420 
 421 
 422 
 
 •62325 
 •62428 
 •62531 
 
 ^'1 
 316 
 
 317 
 
 •49831 
 
 •49969 
 •50106 
 
 35^ 
 352 
 353 
 
 •54531 
 •54654 
 •54777 
 
 387 
 388 
 389 
 
 •58771 
 •58883 
 ■58995 
 
 424 
 425 
 
 •62634 
 •62737 
 •62839 
 
 318 
 
 319 
 320 
 
 •50243 
 •50379 
 •50515 
 
 354 
 355 
 356 
 
 • 54900 
 •55023 
 
 •55145 
 
 390 
 391 
 392 
 
 •59106 
 •59218 
 ■59329 
 
 426 
 427 
 428 
 
 •62941 
 •63043 
 •63144 
 
 321 
 322 
 323 
 
 •50651 
 •50786 
 •50920 
 
 35 7 
 358 
 359 
 
 •55267 
 ■55388 
 •55509 
 
 393 
 394 
 395 
 
 •59439 
 •59550 
 •59660 
 
 429 
 430 
 431 
 
 •63246 
 
 •63347 
 •63448 
 
164 
 
 TaMe of Logarithms — contimied. 
 
 Num. 
 
 Log. 
 
 432 
 433 
 43+ 
 
 435 
 436 
 
 43 7 
 
 438 
 439 
 •HC 
 
 441 
 442 
 443 
 
 444 
 445 
 446 
 
 447 
 448 
 449 
 
 45° 
 451 
 452 
 
 453 
 454 
 455 
 456 
 
 45 7 
 458 
 
 459 
 460 
 461 
 
 462 
 463 
 464 
 
 465 
 466 
 467 
 
 •63548 
 ■63649 
 •63749 
 •63849 
 
 •63949 
 
 • 64048 
 
 •64147 
 •64246 
 
 ■64345 
 
 •64444 
 •64542 
 
 • 64640 
 
 •64738 
 •64836 
 ■64933 
 •65031 
 •65128 
 •65225 
 
 •65321 
 •65418 
 •65514 
 
 ■65610 
 •65706 
 •65801 
 
 ■65896 
 ■65992 
 •66087 
 
 ■66181 
 ■66276 
 ■66370 
 
 ■66464 
 •66558 
 ■66652 
 
 •66745 
 
 •66839 
 •66932 
 
 Log. 
 
 Num. 
 
 469 
 470 
 
 471 
 472 
 
 473 
 
 474 
 475 
 476 
 
 477 
 478 
 479 
 480 
 481 
 482 
 
 483 
 484 
 485 
 
 486 
 487 
 488 
 
 489 
 490 
 491 
 
 492 
 493 
 494 
 
 49? 
 49 J 
 
 497 
 
 498 
 499 
 500 
 
 501 
 502 
 503 
 
 •67025 
 •67117 
 •67210 
 
 •67302 
 
 •67394 
 •67486 
 
 •67578 
 •67669 
 •67761 
 
 ■67852 
 
 ■67943 
 ■68034 
 
 •68124 
 •68215 
 •68305 
 
 •68395 
 ■68485 
 •68574 
 
 •68664 
 
 ■68753 
 ■68842 
 
 •68931 
 •69020 
 ■69108 
 
 •69197 
 •69285 
 ■69373 
 ■69461 
 ■69548 
 •69636 
 
 •69723 
 •69810 
 •69897 
 
 •69984 
 
 ■70070 
 ■70157 
 
 504 
 
 505 
 5c6 
 
 507 
 508 
 509 
 
 510 
 
 5" 
 512 
 
 513 
 514 
 515 
 516 
 
 517 
 518 
 
 519 
 
 520 
 521 
 
 522 
 
 523 
 
 524 
 
 525 
 526 
 
 527 
 528 
 529 
 530 
 
 531 
 532 
 533 
 
 534 
 535 
 536 
 
 537 
 538 
 539 
 
 Log. 
 
 Num. 
 
 • 70243 
 •70329 
 
 • 70415 
 •70501 
 •70586 
 •70672 
 
 •70757 
 
 ■ 70842 
 ■70927 
 
 ■71012 
 ■71096 
 ■7118I 
 
 •71265 
 
 • 71349 
 •71433 
 
 ■71517 
 
 ■ 71600 
 ■71684 
 
 •71767 
 •71850 
 •71933 
 ■72016 
 ■72099 
 •72181 
 
 •72263 
 •72346 
 •72428 
 
 ■72509 
 •72591 
 ■72673 
 
 •72754 
 ■72835 
 •72916 
 
 •72997 
 ■73078 
 
 ■73159 
 
 540 
 
 541 
 542 
 
 543 
 544 
 545 
 
 546 
 547 
 548 
 
 549 
 55° 
 55J 
 
 552 
 553 
 554 
 
 555 
 556 
 557 
 
 558 
 559 
 560 
 
 561 
 562 
 563 
 
 564 
 565 
 566 
 
 567 
 568 
 569 
 
 57° 
 571 
 572 
 
 573 
 5 74 
 575 
 
 Log. 
 
 •73239 
 •73320 
 •73400 
 
 • 73480 
 ■73560 
 
 • 73640 
 
 •73719 
 ■73799 
 ■73878 
 
 •73957 
 
 ■ 74036 
 ■74115 
 
 ■ 74194 
 ■74273 
 ■74351 
 
 ■ 74429 
 •74507 
 ■74586 
 
 • 74663 
 
 • 74741 
 •74819 
 
 •74896 
 
 • 74974 
 •75051 
 
 ■75128 
 ■75205 
 ■75282 
 
 •75358 
 •75435 
 ■7551I 
 
 •75587 
 ■75664 
 •75740 
 
 •75815 
 •75891 
 •75967 
 
i6s 
 
 Table of Logarithms — continued. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 576 
 577 
 578 
 
 ■76042 
 •76118 
 •76193 
 
 612 
 613 
 614 
 
 •78675 
 •78746 
 •78817 
 
 648 
 649 
 650 
 
 •81158 
 •81224 
 •81291 
 
 684 
 685 
 686 
 
 •83506 
 •83569 
 •83632 
 
 579 
 580 
 581 
 
 ■76268 
 
 •76343 
 "•76418 
 
 615 
 616 
 617 
 
 •78888 
 ■78958 
 •79029 
 
 651 
 652 
 653 
 
 •81358 
 •81425 
 •81491 
 
 687 
 688 
 689 
 
 •83695 
 
 •83759 
 ■83822 
 
 582 
 583 
 584 
 
 •76492 
 •76567 
 • 76641 
 
 618 
 615 
 620 
 
 •79099 
 •79169 
 •79239 
 
 654 
 
 655 
 656 
 
 •81558 
 •81624 
 •81690 
 
 690 
 691 
 692 
 
 •83885 
 ■83948 
 •8401 I 
 
 585 
 586 
 
 587 
 
 •76716 
 •76790 
 •76864 
 
 621 
 622 
 623 
 
 •79309 
 •79379 
 • 79449 
 
 657 
 658 
 659 
 
 •81757 
 •81823 
 •81889 
 
 693 
 694 
 695 
 
 •84073 
 •84136 
 •84198 
 
 588 
 589 
 590 
 
 •76938 
 • 77012 
 •77085 
 
 624 
 625 
 626 
 
 ■79518 
 •79588 
 ■79657 
 
 660 
 661 
 662 
 
 •81954 
 ■82020 
 •82086 
 
 696 
 697 
 698 
 
 •84261 
 
 •84323 
 •84386 
 
 591 
 592 
 593 
 
 •77759 
 •77232 
 •77305 
 
 627 
 628 
 629 
 
 •79727 
 •79796 
 •79865 
 
 663 
 664 
 665 
 
 •82151 
 •82217 
 ■82282 
 
 699 
 
 700 
 701 
 
 •84448 
 •84510 
 •84572 
 
 594 
 595 
 596 
 
 •77379 
 
 •77452 
 •77525 
 
 630 
 631 
 632 
 
 •79934 
 ■ 80003 
 •80072 
 
 666 
 667 
 668 
 
 •82347 
 •82413 
 •82478 
 
 702 
 703 
 
 704 
 
 •84634 
 •84696 
 •84757 
 
 597 
 598 
 599 
 
 •77597 
 •77670 
 
 •77743 
 
 633 
 
 634 
 
 635 
 
 •80140 
 •80209 
 •80277 
 
 669 
 670 
 671 
 
 •82543 
 •82607 
 •82672 
 
 705 
 706 
 707 
 
 •84819 
 •84880 
 •84942 
 
 600 
 601 
 602 
 
 •77815 
 •77887 
 •77960 
 
 636 
 
 637 
 638 
 
 ■80346 
 • 80414 
 ■80482 
 
 672 
 673 
 674 
 
 •82737 
 •82802 
 •82866 
 
 708 
 709 
 710 
 
 •85003 
 •85065 
 ■85126 
 
 503 
 604 
 605 
 
 •78032 
 •78104 
 •78176 
 
 639 
 640 
 641 
 
 '•80550 
 ■80618 
 •80686 
 
 675 
 676 
 677 
 
 •82930 
 •82995 
 •83059 
 
 711 
 712 
 713 
 
 •85187 
 •85248 
 •85309 
 
 606 
 607 
 608 
 
 •78247 
 •78319 
 •78390 
 
 642 
 643 
 644 
 
 •80754 
 •80821 
 •80889 
 
 678 
 679 
 680 
 
 •83123 
 •83187 
 •83251 
 
 714 
 715 
 716 
 
 •85370 
 •85431 
 •85491 
 
 609 
 610 
 61T 
 
 ■78462 
 
 •78533 
 • 78604 
 
 645 
 646 
 647 
 
 •80956 
 •81023 
 •81090 
 
 681 
 682 
 683 
 
 •83315 
 •83378 
 • 83442 
 
 717 
 718 
 719 
 
 •85552 
 ■85612 
 •85673 
 
1 66 
 
 Table of Logarithms — continued. 
 
 Num. 
 
 Log. 
 
 720 
 721 
 722 
 
 723 
 
 724 
 
 726 
 727 
 728 
 
 729 
 730 
 731 
 
 732 
 733 
 734 
 
 735 
 736 
 737 
 738 
 739 
 740 
 
 741 
 742 
 
 743 
 
 744 
 745 
 746 
 
 747 
 748 
 749 
 750 
 
 751 
 752 
 
 753 
 754 
 755 
 
 85733 
 85794 
 85854 
 
 85914 
 85974 
 86034 
 
 86094 
 
 86153 
 86213 
 
 86273 
 86332 
 86392 
 
 B6451 
 86510 
 86570 
 
 86629 
 86688 
 86747 
 
 86806 
 86864 
 86923 
 
 87040 
 87099 
 
 87157 
 87216 
 87274 
 
 87332 
 87390 
 87448 
 87506 
 87564 
 87622 
 
 87679 
 87737 
 87795 
 
 Num. 
 
 756 
 75 7 
 758 
 
 759 
 760 
 761 
 
 762 
 763 
 764 
 
 765 
 766 
 767 
 
 768 
 769 
 770 
 
 771 
 772 
 773 
 
 774 
 775 
 776 
 
 777 
 778 
 779 
 780 
 781 
 782 
 
 783 
 784 
 785 
 786 
 
 787 
 788 
 
 789 
 790 
 791 
 
 Log. 
 
 87852 
 87910 
 87967 
 
 88024 
 88081 
 88138 
 
 88195 
 88252 
 88309 
 
 88366 
 88423 
 88480 
 
 88536 
 88593 
 
 88705 
 88762 
 88818 
 
 88874 
 88930 
 
 89042 
 89098 
 89154 
 
 89209 
 89265 
 89321 
 
 89376 
 89432 
 89487 
 
 89542 
 
 89597 
 89653 
 
 89708 
 89763 
 89818 
 
 Num. 
 
 792 
 793 
 794 
 
 795 
 796 
 
 797 
 
 798 
 
 799 
 800 
 
 801 
 802 
 803 
 
 804 
 805 
 806 
 
 807 
 
 810 
 811 
 812 
 
 813 
 814 
 815 
 
 816 
 817 
 8j8 
 
 819 
 820 
 821 
 
 822 
 823 
 824 
 
 825 
 826 
 827 
 
 Log. 
 
 •89873 
 •89927 
 82 
 
 •90037 
 ■90091 
 
 ■ 90146 
 
 •90200 
 •90255 
 •90309 
 
 ■90363 
 •90417 
 •90472 
 
 •90526 
 
 ■ 905 80 
 • 90634 
 
 •90687 
 90741 
 •90795 
 
 •90849 
 ■90902 
 •90956 
 
 •91009 
 •91062 
 •91116 
 
 •91169 
 •91222 
 •91275 
 
 •91328 
 •91381 
 ■91434 
 
 •91487 
 •91540 
 
 ■91593 
 •91645 
 •91698 
 •9175I 
 
 Log. 
 
 828 
 829 
 830 
 
 831 
 832 
 833 
 834 
 835 
 836 
 
 837 
 838 
 
 839 
 
 840 
 B41 
 842 
 
 843 
 844 
 845 
 846 
 
 847 
 
 850 
 851 
 
 852 
 853 
 854 
 
 855 
 856 
 
 857 
 
 858 
 
 859 
 860 
 
 861 
 862 
 863 
 
 •91803 
 ■91855 
 •919081 
 
 •91960 
 •92012 
 •92065 
 
 •92117 
 •92169 
 •92221 
 
 •92273 
 ■92324 
 •92376 
 
 ■92428 
 ■92480 
 •92531 
 
 •92583 
 •92634 
 •92686 
 
 •92737 
 •92788 
 
 • 92840 
 
 •92891 
 ■92942 
 •92993 
 
 • 93044 
 •93095 
 •93146 
 
 •93197 
 •93247 
 •93298 
 
 •93349 
 •93399 
 •93450 
 •93500 
 
 •93551 
 •93601 
 
16/ 
 
 Table of liOgaxitTaxas—ctmtimieil. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 Num. 
 
 Log. 
 
 864 
 865 
 866 
 
 •93651 
 •93702 
 •93752 
 
 900 
 901 
 902 
 
 •95424 
 ■95472 
 •95521 
 
 936 
 937 
 938 
 
 •97128 
 
 •97174 
 ■97220 
 
 972 
 973 
 974 
 
 •98767 
 •98811 
 •98856 
 
 867 
 868 
 869 
 
 •93802 
 •93852 
 •93902 
 
 903 
 904 
 905 
 
 ■95569 
 •95617 
 •95665 
 
 939 
 
 940 
 941 
 
 •97267 
 •97313 
 ■97359 
 
 975 
 976 
 
 977 
 
 •98900 
 
 •98945 
 •98989 
 
 870 
 871 
 872 
 
 •93952 
 • 94002 
 •94052 
 
 906 
 907 
 908 
 
 •95713 
 •95761 
 
 •95809 
 
 942 
 943 
 944 
 
 •97405 
 •97451 
 •97497 
 
 978 
 979 
 980 
 
 •99034 
 •99078 
 •99123 
 
 873 
 874 
 875 
 
 •94101 
 •9415 1 
 • 94201 
 
 909 
 910 
 911 
 
 •95856 
 
 •95904 
 •95952 
 
 945 
 946 
 
 947 
 
 ■97543 
 •97589 
 •97635 
 
 981 
 982 
 983 
 
 •99167 
 •99211 
 ■99255 
 
 876 
 
 877 
 878 
 
 ■94250 
 • 94300 
 •94349 
 
 912 
 
 913 
 914 
 
 ■95999 
 • 96047 
 •96095 
 
 948 
 949 
 950 
 
 •97681 
 •97727 
 ■97772 
 
 984 
 985 
 986 
 
 •99300 
 •99344 
 •99388 
 
 879 
 880 
 881 
 
 •94399 
 •94448 
 •94498 
 
 915 
 916 
 
 9^7 
 
 •96142 
 •96190 
 •96237 
 
 951 
 952 
 953 
 
 •97818 
 ■97864 
 •97909 
 
 987 
 988 
 989 
 
 •99432 
 ■99476 
 •99520 
 
 882 
 883 
 884 
 
 •94547 
 •94596 
 •94645 
 
 918 
 919 
 920 
 
 •96284 
 •96332 
 •96379 
 
 954 
 955 
 956 
 
 ■97955 
 • 98000 
 •98046 
 
 990 
 991 
 992 
 
 •99564 
 •99607 
 ■99651 
 
 885 
 886 
 887 
 
 •94694 
 
 •94743 
 •94792 
 
 921 
 922 
 923 
 
 •96426 
 
 ■96473 
 •96520 
 
 957 
 95S 
 959 
 
 •98091 
 •98137 
 •98182 
 
 993 
 994 
 995 
 
 •99695 
 •99739 
 ■99782 
 
 888 
 889 
 890 
 
 •94841 
 •94890 
 ■94939 
 
 924 
 
 925 
 926 
 
 •96567 
 •96614 
 •96661 
 
 960 
 961 
 962 
 
 •98227 
 •98272 
 :983i8 
 
 996 
 997 
 998 
 
 •99826 
 •99870 
 •99913 
 
 891 
 892 
 893 
 
 894 
 895 
 896 
 
 •94988 
 •95036 
 ■95085 
 
 •95134 
 •95182 
 •95231 
 
 927 
 928 
 929 
 
 930 
 
 931 
 932 
 
 •96708 
 
 ■96755 
 •96802 
 
 •96848 
 •96895 
 •96942 
 
 963 
 
 964 
 965 
 
 966 
 967 
 968 
 
 •98363 
 •98408 
 •98453 
 •98498 
 •98543 
 •98588 
 
 999 
 1000 
 
 9399 
 
 •99957 
 • 00000 
 
 '97307 
 
 897 
 898 
 
 899 
 
 •95279 
 •95328 
 •95376 
 
 933 
 
 934 
 935 
 
 •96988 
 •97035 
 •97081 
 
 969 
 970 
 971 
 
 •98632 
 •98677 
 •98722 
 
 
 
1 68 Notes. 
 
 Note a, page vii. — The following speculations on the source of 
 electricity in a battery may serve to stimulate reflection, but the 
 student should remember that they are not in accordance with received 
 views. 
 
 Since electricity is developed when zinc and other metals combine 
 with oxygen, we may seek for its source either in the metal or in the 
 oxygen ; we may, in fact, regard it as a component part of the 
 metal, which is liberated when it combines with oxygen. In this 
 case, since zinc, hydrogen, and the electropositive metals give more 
 electricity, or electricity at a higher tension than the electronegative 
 metals, we are compelled to assume a different combining proportion 
 of electricity for each metal. Let us, on the other hand, suppose 
 the electricity to come from the oxygen ; let gaseous oxygen be 
 assumed to consi-st of two hypothetical substances in combination, 
 viz., oxyn, which is oxygen in a simple or elementary condition, 
 and calon, which is heat in its latent form. Let heat be simply elec- 
 tricity devoid of tension, all electricity as it falls in tension becoming 
 heat, then — 
 
 Gaseous oxygen = oxyn + calon (heat in combination). 
 Water = oxyn + hydrogen (calon, or heat set free). 
 Oxide of zinc = oxyn + zinc (calon set free as electricity). 
 Carbonic acid = oxyn + carbon (calon set free). 
 The difficulty still arises of explaining how the oxygen as it leaves 
 each negative metal in order to combine with a more positive one 
 (as in the Daniell's battery) produces at every new combination a 
 fresh supply of electricity, or, what is the same question, why it gives 
 a higher tension with some metals than vnth others. 
 
 Azone and oxyn may, perhaps, be identical ; hydrogen probably 
 owes its gaseous form to combination with calon, &c. The sun's 
 light acting on carbonic acid in the tissue of plants liberates the 
 carbon, and restores calon to the oxyn, producing gaseous oxygen, 
 and hence our source of power. 
 
 Note b, page I2I. Speed of working; — On the ordinary Morse 
 system of working it is easy to see that the speed must vary as the 
 square of the length, for the cable has to be wholly charged and 
 discharged at each signal, and since with the double length we have 
 twice the quantity of electricity to supply and twice the resistance to 
 supply it through, it takes four times the time. Increase of tension 
 does not in theory alter the speed, for vrith the double tension the 
 cable holds a double charge, and this counterbalances the mcreased 
 
Notes. 169 
 
 velocity : practically it increases the speed to some extent, because 
 the current attains the strength sufficient to work a relay in shorter 
 time with a powerful current than with a weak one, although the 
 speed of both is the same. 
 
 To work through the Atlantic cables at their highest speed it is 
 necessary to use a condenser either at one or at both ends of the 
 cable, connected up in the manner described at pp. 130, 131, fig. 41. 
 In this arrangement it is impossible for any electricity to enter or 
 leave the cable. The condensers have a capacity of about twenty 
 farads, and when employed with ten cells they create by induction 
 an impulse of two hundred farads at the near end of the line. For 
 each signal the key is only depressed momentarily, and immediately 
 raised again, so that the electrical impulse only endures for an 
 instant, and the next moment the wave rushes back again to restore 
 the equilibrium ; but much of the wave is gone past recall, and 
 continues to roll on to the distant end of the cable, where it strikes 
 against the other condenser, and appears beyond it in the form of an 
 induced wave of I '4 farads, passing through the galvanometer and 
 deflecting the spot of light about | inch momentarily to the right 
 or left and instantly back again to zero. If two or more waves are 
 sent successively in the same direction, the later waves meeting the 
 returning wave are much weakened, and only "5 farads pass out 
 momentarily through the galvanometer and back again. These 
 waves to the left are equivalent to dots in the Morse alphabet ; but 
 when waves are sent first positive and then negative, representing 
 the dot and the dash, each returning wave coincides in direction 
 with its predecessor, and the result is an induced wave through the 
 galvanometer of two farads, and a much larger deflection of the spot 
 of light alternately to the right and left. The smallest quantity of 
 electricity that will work a highly-sensitive polarised relay in its best 
 condition is about I '5 farads, so that the wave could not be used to 
 work a relay unless the currents were alternately positive and negative. 
 
 These waves gradually and rapidly diminish in amplitude as they 
 roll through the cable, and could they be rendered visible would 
 doubtless resemble the undulations seen when. a. rope lying on the 
 ground is violently agitated up and down at one end. The gradually- 
 diminishing waves roll along it for a considerable distance : the wave 
 is transmitted, but the rope itself remains stationary ; just as in the 
 cable no electricity enters or leaves it, but a wave of tension rolls 
 onward within it. 
 
170 Notes. 
 
 With given amplitudes of wave there is little doubt that the law 
 holds good in this case as in the case of ordinary working, viz., that 
 the speed varies inversely as the square of the distance ; but it is not 
 so clear that the other law holds good, viz., that the speed varies 
 inversely as the inductive capacity. The cable has been worked by 
 the condensers while constantly charged to a tension of one hundred 
 cells positive (see p. 130), and also to the same tension negative, 
 without any visible effect on the speed or the amplitude of the wave. 
 Yet in the one case it contained 67,000 farads more, and in the 
 other 67,000 farads less electricity than its normal quantity stored up 
 inductively on the surface of the conductor. The wave utilises only 
 a fraction of the inductive capacity of the cable, and without further 
 experiment it would be rash to say that the portion of inductive 
 capacity not called into action acts obstructively on the passage of 
 the wave. It would almost appear at first sight that with a given 
 conductor a heavier wave would be capable of being transmitted 
 when the inductive capacity was large than when small — a wave 
 slower in its progress forward, but larger in its volume, and there- 
 fore giving a more powerful signal. It is to be regretted that so 
 little facility has been given by the proprietors of existing cables for 
 the determination of these and other similarly interesting questions, 
 seeing that they have so direct and important a bearing on the 
 commercial prospects of telegraphy. 
 
INDEX. 
 
 Absolute units of measurement, 43. 
 Accumulation test, 125,135. 
 Atlantic cable testing, 129, 130, 169. 
 
 Batteries, Daniell's, Smee's, &c., 108. 
 
 electromotive force of, 7, 8, 20, 63, 103, 108, 
 
 • internal resistance of, 4, 8, 60, 108. 
 
 tension of, 21, 108. 
 
 ■ in terms of one cell, 109. 
 
 Birmingham wire gauge, 156. 
 
 Blarier's formula for testing faults, 75, 123. 
 
 Cables, broken conductors in, 133. 
 
 diameter of, 139. 
 
 . effect of pressure on insulation, 148. 
 
 effect of temperature on insulation, 88, 148. 
 
 • electrification of, 98, 116. 
 
 electrostatic capacity of, 33, 118, 120. 
 
 speed of, 121, 122, 168. 
 
 testing for faults in, 69, 70, 73, 123, 130. 
 
 ■ testing insulation of, 88, 97, 125, 130, 135. 
 
 wavea.in, 168. 
 
 weight of iron in, 140 ; copper, 142 ; gutta-percha, 14;. 
 
 Charge and discharge, 25, 26, 29, 116. 
 
 time of falling to half-charge, 35, 98, 11 J, 116, 
 
 Condensers, 113, 117, 132. 
 Conduction, electrical, 2, 82, 92. 
 
 of different metals, 92, 93 . 
 
 Conductivity (see Conduction and Copper). 
 
172 Index. 
 
 Conductor, broken, 133. 
 
 Copper, tables and foimulBe for, 142, 
 
 — conductivity of, 64, 67, 92, 144. 
 wires, resistance of, 64, 67, 143. 
 
 resistance of, at different temperatures, 67, 93, 145. 
 
 CuiTents, electrical, 2, 17, 36. 
 measurement of, 36, 93. 
 
 Deflection, angle of, 94, 100, 105, 109. 
 Derived circuits, 61, 78, 80, 101. 
 
 Earth currents, 41. 
 
 tension of, 11, 41. 
 
 plates, 4, 40. 
 
 Electricity, positive and negative, 16, 25, 30. 
 
 source of, 168. 
 
 Electrical balance, 84, 119, 127. 
 Electrification, 98, 116. 
 Electrolysis of water, 44, 95. 
 Electrometer, Thomson's, ill. 
 
 Peltier's, 115. 
 
 Electromotive force, 2, 6, 9, 103, 107. 
 
 ■ of batteries, 7, 8, 20, 63, 103. 
 
 unit of, 43. 
 
 Electrostatic capacity, 31, 33, 116, 147, 151. 
 of cables, 33, 118, 147. 
 
 Fakad, 3, 33, 36, 43. 
 
 Faults, testing for, 69, 70, 73, 123. 
 
 resistance of, 70, 123, 130. 
 
 French and English measures, 152. 
 
 Galvanometee, constant of, 97. 
 double shunt, differential, 47. 
 
 horizontal, 94. 
 
 quantity, i, 53. 
 
 shunts for, 48, 80, 102. 
 
 German silver, 67, 92, 93. 
 
 Gutta-percha, tables and formulse for, 146. 
 
Index. 
 
 Gutta-percha cables, testing of, 88, 97. 
 
 resistance of, 34, 88, 147. 
 
 electrostatic capacity of, 33, 147. 
 
 Heat, generation of, 39, 46, 95, 115. 
 Hooper's core, 148, 150. 
 
 Induction, 25, 28. 
 Inductive capacity, 32, 116. 
 
 of cables, 32, 147, 148. 
 
 Insulation (see Resistance). 
 
 Intensity, 38. 
 
 Iron, tables and formulae for, 137. 
 
 Joint testing, 135. 
 
 Lightning, 10, 38. 
 
 Line wires, resistance of, 5, 48, 83, 138. 
 
 strain of, 154. 
 
 Logarithms, table of, 161. 
 Logarithmic ratio of cables, 32, 34. 
 Loop testing, 70, 123. 
 
 Magnetic storms, 41. 
 
 force, 95. 
 
 Measures, electrical, 43, 102. 
 
 English, French, &c, 153. 
 
 Megohm, 43, 102, 147. 
 
 Metals, conducting power, 92, 95. 
 
 Murray's method of testing, 124. 
 
 Ohm, 43, 102. 
 
 Ohm's law, 3, 6, 8, 91. 
 
 Potential, electrical, 10, 28, 29, log. 
 
 Potentiometer, 106, 109. 
 
 Pressure, of the ocean, iji. 
 
 resistance of cables under, 148. 
 
 QnANTiTT, electrical, 3, 6, 29, 36, 39. 
 
 dependent on tension, 6, 17, 29, 31. 
 
 unit of 43, 102. 
 
 173 
 
174 Index. 
 
 Rate of signalling, I2i, 122, 168. 
 
 Reciprocals, 81, 92. 
 
 Resistance of batteries, 4, 8, 20, 60, 99. 
 
 of cables, 34, 86, 83, 97. 
 
 — — of copper wive, 59, 64, 65, 143, 
 
 ■ at different temperatures, 67, 145. 
 
 of faults, 70, 123, 130. 
 
 of gutta-percha cores, 88, 148. 
 
 at different temperatures, 88, 149. 
 
 of joint or derived circuits, 81, loi, 
 
 . of a line, 5, 48, 83. 
 
 of line wire, 5, 48, 83, 138. 
 
 measurement of, 54, 56, 85, 96, 99, 128, 
 
 residuary charge, 116. 
 
 Sea water, 151, 154. 
 Shunts, 61, 78, 80, 102. 
 
 multiplying power of, 80, t02. 
 
 Sine, galvanometer, 94. 
 Sines and tangents, table of, 157. 
 Smith's system of testing cables, 130. 
 Specific gravity to measure, 154. 
 
 of copper, 142. 
 
 gutta-percha, 146. 
 
 iron, 137. 
 
 ^ sea-water, 151, 154. 
 
 Specific conductivity of copper, 64. 
 Speed of working, 121, 122, 168. 
 Static electricity, 25, 29, 36. 
 Strain of suspended wires, 154. 
 Strand conductors, 121, 142, 143. 
 
 Table of Birmingham wire gauge, 156. 
 
 of conductivity of metals, 92, 93. 
 
 of diameters of submarine cables, 139. 
 
 • ■ of dimensions and tests of various cables, 176. 
 
 of electromotive force of different batteries, 108. 
 
 of logarithms, 161. 
 
 of resistance of copper at different temperatures, 145. 
 
 of gutta-percha at different temperatures, 149. 
 
Index. 175 
 
 Table of resistance of metals and alloys, 93. 
 
 of sines and tangents, 157. 
 
 of sizes of gutta-percha wire, 146. 
 
 of iron wire, 141. 
 
 of squares and square roots, 158. 
 
 of worlcing speed of cables, 122. 
 
 ■ of weight of iron in submarine cables, 140, 
 
 Tangent galvanometer, 94. 
 Temperature, conversion of, 153. 
 
 effect on conductivity of copper, 67, 145, 
 
 of gutta percha, 88, 149. 
 
 of the ocean, 151. 
 
 Tension, electrical, 10, 24, 29, 38, 84, 109. 
 
 of the earth, 11, 41. 
 
 time of fall of, 35, 98, 113, 116. 
 
 to measure, 15, 17, 19, tl, 109. 
 
 joint, of two cables, 117. 
 
 Testing batteries, 53, 60, 63, 99. 
 
 cables, 69, 97, 123, 130. 
 
 earth connections, 4, 40, 
 
 lines, 5, 18, 49. 
 
 faults, 69, 70, 75, 123, 
 
 Thermometers, comparison of, 153. , 
 Thomson's slide resistance, in, 124, 127. 
 electrometers, in. 
 
 Units of electrical measurement, 43, 102. 
 of Siemen's and Varley's, 44, 102. 
 
 ViBEATiONS, method of measurement by, 94, 109. 
 Volt, 32, 43. 
 Voltameter, 44, 95 . 
 
 Water, electrolysis of, 44, 95 . 
 Waves, electrical, 169. 
 Wheatstone's balance, 84, 119, 127. 
 Wire gauges, table of, 156. 
 Work, unit of, 44. 
 
 THE END. 
 
LONDON: 
 
 PRINTED BY WILLIAM CLOWES AND SONS, STAMFORD STREET 
 AND CHARING CROSS. 
 
ELECTRICAL TESTS OF VARIOUS RECENT SUBE 
 
 DESCRIPTION OF CABLE. 
 
 1. Malta and Alexandria Cable, conductor a 7 wire strand, is iron 
 
 Wires 120 mils diam. (Laid 1861.) .. 
 
 2. Persian Gulf Cable, segmental conductor. 12 Iron Wires 192 mils Jiam. 
 Exterior Covering of Asphalt Compound. (Laid in 1864.) 
 
 3 Hooper's Cable for River crossing in India. Conductor a 7 wire strand. 
 12 Iron Wires 200 mils dlam. (1805.).. 
 
 4. Atlantic Cable. conductor a l wire strand. 10 Steel Wires 95 mils diam. 
 
 Each wire covered with taiTed Manilla liemp. (Laid 18G5.) 
 
 5. Persian Gulf Cable. (Additional length.) Solld Conductor. 12 Iron Wires 
 
 similar to No. 2. Exterior Covering of Asphalt Compound. (1806.) 
 
 6. Ceylon Cable. (Hooper's Core). Conductor a 7 wire strand. 12 Iron 
 
 Wires 200 mils diam. Exterior Covering of Asphalt Compound. (Laid 1866.) . . 
 
 7. Core for India. (Hooper's core) similar to No. 6. No Iron covering. 
 
 (1866.) 
 
 S.Atlantic Cable, conductor a 7 wire strand. 10 Steel Wires similar to No. 
 4, each covered with white Manilla hemp. (Laid 1866.) . . 
 
 9. England and Hanover Cable, containing 4 insulated wires. 
 
 Conductors a 7 wire strand. 12 Iron Wires 305 mils diam. Exterior Covering of 
 Asphalt Compound. (Laid 1806.) 
 
 10. Placentia Bay and Sydney Cable, conductor a 7 wire strand. 
 
 12 Iron Wires 148 mils diam. (1807.) 
 
 Length 
 Laid. 
 
 Knots. 
 
 1330 
 
 1148 
 
 46 
 
 1896 
 
 160 
 
 Diameter. 
 
 Copper, 
 d 
 
 Mils. 
 
 153 
 
 110 
 
 110 
 
 147 
 
 110 
 
 35 110 
 
 Core 
 
 Mils. 
 
 463 
 
 380 
 
 380 
 
 467 
 
 380 
 
 Losrarithm 
 of 
 D 
 
 T 
 
 0-48089 
 
 053839 
 
 053839 
 
 0-50200 
 
 Weight per Knot. 
 
 Copper. Dielectric 
 
 fij3. 
 
 400 
 
 225 
 
 180 
 
 300 
 
 0-53839 225 
 
 380 0-53839 
 
 11. Cuba and Florida Cables. 
 
 Havanah to Key West ... | Conductor a 7 wire strand. 12 Iron Wires (125-4 
 
 40 
 
 1852 
 
 224 
 1121^ 
 
 iss-?! 
 
 Key West to Punta Eassa 
 
 148 mils diam. (1867.) 
 
 12. New Zealand Cable — LyallBayto Blaster Point. Containing 
 
 3 insulatad Wires. Conductors a 7 wire strand. 10 Iron Wires 300 mils diam. 
 Exterior Covering of Asphalt Compound. (Laid 1866.) 
 
 13. South Foreland and La Panne Cable, containing 4 
 
 insulated Wires. Conductors a 7 wire copper strand. 10 Iron Wires 331 mils diam. 
 Exterior Covering of Asphalt Compound. (I^aid 1807.) . . 
 
 .119-9 
 
 42 
 
 47 
 
 110 
 
 147 
 
 87 
 
 102 
 
 87 
 
 87 
 
 87 
 
 380 
 
 467 
 
 280 
 
 348 
 
 290 
 
 289 
 
 0-53839 
 
 050200 
 
 0-50764 
 
 053298 
 
 051229 
 
 0-52138 
 
 256 046872 
 
 180 
 
 180 
 
 300 
 
 107 
 
 150 
 
 107 
 
 107 
 
 107 
 
 lbs. 
 
 400 
 
 275 
 
 330 
 
 400 
 
 275 
 
 330 
 
 330 
 
 Iron 
 Wires. 
 
 Tons. 
 
 1-68 
 
 3-06 
 
 3-3 
 
 0-632 
 
 306 
 
 3-3 
 
 Completed . 
 Cable. 
 
 Tons. 
 
 400 0-632 
 
 150 
 
 230 
 
 166 
 
 168 
 
 120 
 
 8003 
 
 215 
 
 21 
 
 7-45 
 
 7-7 
 
 2-13 
 
 373 
 
 3-8 
 
 1-75 
 
 373 
 
 38 
 
 150 
 
 2-5 
 
 25 
 
 91 
 
 97 
 
 Note. The " Mil " is the — th part of an inch The Megohm = one million ohms. The Farad is the standard unit quantity of Electricity as determined hy the Committee ( 
 of Electricity which with the unit Electromotive force passes through a resist;ince of one Meijohm in one second. The unit of Klectromotive force does not differ greatly from t 
 of a solid wire of the same diameter, and has been so allowed for in calculating the relative capacities. The following empirical data may be found sometimes useful for cal 
 circ. mih" of copper strand, 63 circ. mils of Iron, 481 circ. mils of Gntta Percha, or 401 circ. mils of Hooper's material — weigh one pound per Knot. Hence -tt- 
 eimilarly ^ '~^ ' gives the weight of Gutta Percha in any core. jy^ gives the weight of Iron in cwts. per Knot (including lay) fur any Cable of n wires. 
 
 481 
 
CENT SUBMARINE TELEGRAPH CABLES. 
 
 Lght per Knot. 
 
 Approximate Besistance 
 Besistance of Conductor. Besistance of Dielectric. -pTarfTnafafio r!i■nnn^Ur per Knot when laid. 
 
 at 1'4^ CeLt. at ii^ Cent. JfilectrOBtatiC t^apacity. irrespective ot temperature and 
 
 ' pressure. 
 
 ectric; 
 
 bs. 
 400 
 
 275 
 
 j Iron Completed ! Resistance ! p„^j .»- •• 
 
 Wires. ' C^bie. per Knot, i ^' 
 
 \ 1 I'°'"e 
 
 I 1 i Copper=100. 
 
 Tons. 1 Tons. 
 
 1-68 
 
 3^ 
 
 330 3-3 
 
 213 
 
 373 
 
 3-8 
 
 Ohms. 
 
 349 
 
 6-25 
 
 698 
 
 400 , 0-632 . 175 ; 4-27 
 
 275 3-06 I 373 6 01 
 
 330 3 3 i 3^ 7 52 
 
 330 
 
 400 0-632 150 
 
 
 
 1 
 
 150 
 
 S003 
 
 1094 
 
 230 
 
 2-15 
 
 1 
 
 25 
 
 j 
 
 166 
 
 21 
 
 ! 
 
 25 
 
 163 
 
 745 
 
 91 
 
 59 
 
 4iM 
 
 1207 
 
 8958 
 
 1238 
 
 120 77 
 
 97 
 
 12-46 
 
 12 48 
 
 8539 
 
 8479 
 
 949 
 
 9308 
 
 8817 
 
 Resistance 
 per Knot. 
 
 • Me<rolims. 
 
 115 
 
 Relative j Electrostatic Relative Speci- 
 
 190 
 
 8064 
 
 349 
 
 Specific I Capacity 
 Kesi>tances. per Knot. 
 
 PersianGulf=l 
 
 •Farads. 
 
 0679 
 
 fie Inductive 
 •Capacity. 
 
 Persian Gnlf=>l 
 
 1000 
 
 42-420 
 
 1968 
 
 03486 
 
 02719 
 
 0-3535 
 
 87 27 
 
 8526 
 
 94-63 342 
 
 I 
 
 9232 
 
 8873 
 
 9001 
 
 239 
 
 455 
 
 464 
 
 44-870 
 
 1-932 
 
 1-333 
 
 2-421 
 
 2568 
 
 02782 
 
 0-3535 
 
 0-3447 
 
 0-3507 
 
 8943 
 
 89 29 
 
 317 
 
 217 
 
 172 
 
 131 
 
 I 03297 
 
 03700 
 
 1000 
 
 0-812 
 
 0995 
 
 395 2079 0-3312 0950 
 
 I 
 
 8809 7949 41840 02775 i 0829 
 
 0831 
 
 0995 
 
 0-989 
 
 03566 1050 
 
 1C05 
 
 0«62 
 
 0«70 
 
 Resistance of 1 Resistance of 
 Dielectric. 
 
 • Megohms. 
 
 Malta Tripoli 242 
 
 Tripoli I -an 
 
 Benghazi J ^"^ 
 
 Benghazi ? ,_- 
 
 Alexandria J •'^''••• 
 
 Fao-Buihire 495 
 
 Euihire ) ~Qa 
 
 Mussendom ( •'''° 
 
 Mussendom I 340 
 G wader j 
 Gwader 
 _ Kurrachee 
 
 J239 
 
 Conductor. 
 
 Ohms. 
 
 359 
 3 56 
 
 3 54 
 6-46 
 621 
 
 640 
 630 
 
 2945 
 
 7000 
 
 2437 
 
 1010 
 
 4498 
 
 ^Placentia and 
 St. Pierre 
 
 St. Pierre and joei» 
 Sydney *^' 
 
 1268 
 175 
 
 473 
 
 71 
 
 554 
 
 1183 
 
 tennined by the Committee on Sundards of Electrical Eesisiar.ce appointed by the Britiih Association; it is that quantity 
 does not differ greatly from that of a Daniell's celL— The inductive capacity of a strand is assumed as 5 per cent, less than that 
 ind sometimes nsefol for calculating the approximate weight of cores. 54 circular mils in sectional area of copper, 69 
 mod per Knot. Hence 4r P^^ '^ weight per Knot of any solid copper conductor, and ^ of any copper strand, and 
 bleaf awire*. 
 
 4-01 
 
 389 
 
 1171 
 
 832 
 8-34 
 
 1183 
 1237 
 
 12 39 
 
 1183 
 
 I ( 
 
 LATIMER CLARK. 
 
 January, 1868.