BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF flenrg W. Sage 1891 A. mm /?/ ' „«...„. Jnlverelty Liorary arV18671 A guide tor the electric testing of tele 3 1924 031 242 070 olin.anx The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031242070 ELECTEIC TESTING .TELEGRAPH CABLES. A GUIDE ELECTEIC TESTING TELEGEAPH CABLES. BY COLONEL V. HOSKI.ER, EOTAL DANISH ENGINEERS. THIRD EDITION. B. & F. N. SPON, 125, STRAND, LONDON. NEW YORK: 12, CORTLANDT STREET. 1889. PREFACE TO FIEST EDITION. Having had the control of the manufacture of about 3500 nautical miles of Telegraph Cables, made mostly with Hooper's Core, but also with Core of ordinary Gutta-percha and of Willoughby Smith's Gutta-percha, I have had fre- quent . opportunities of ascertaining the correctness of the data given in this book. I do not expect an Electrician will discover anything new in these pages, but if he should find this Guide a useful one to put in the hands of young men who have to learn practical testing, I shall feel satisfied in having published it. V. H. London, 1873. PREFACE TO THIRD EDITION. The Congress of Electricians in 1881 have made some alterations necessary, and some few methods of testing have been added, in the hope of making this Guide more useful. V. H. Copenhagen, 1889. CONTENTS. PAGE 1. Electric Tests 1 2. Standard Degree of Temperature 1 3. Immersion in Water 1 4. Arrangements before Testing 2 5. Apparatus 3 6. The Use of a Shunt '. 3 7. Electric Units 4 8. The Order of the Tests 6 A.— THE CONDUCTIVITY OF THE COPPER. 9. Explanation of the Method 6 10. Practical Execution of the Test 10 11. Calculation of the Conductivity 10 12. The Eesistance of the Galvanometer 12 13. The Resistance of the Battery 13 14. The Resistance offered by the Earth-plate 15 15. Examples 15 B — THE CHARGE OF THE CABLE. 16. Practical Execution of the Test 18 17. Constant c of the Condenser 19 18. Calculation of the Charge 20 19. Examples 22 C — THE INSULATION OF THE CABLE. 20. Pratical Execution of the Test 24 21. Ohm's Law 25 22. Constant n of the Battery 25 23.. Constant <£ of the Galvanometer 26 24. Calculation of the Insulation 27 25. Insulation Test by Loss of Charge 30 viii CONTENTS. FAGE 26. Insulation Test by the Electrometer 32 27. Strong Batteries with Changing Currents 34 28. Examples 34 3> — THE INSULATION OP A JOINT. 29. Practical Execution 38 30. Standard for Joints 40 E—THE POSITION AND MAGNITUDE OP A FAULT. 31. Signs of Faults 41 32. Tests from both Ends of the Cable 43 33. Tests from one End of the Cable 48 TESTING DURING THE LAYING OF A CABLE. 34. Electrical Arrangement on Ship and on Shore 53 35. Instructions for Testing on Ship and on Shore 54 FORMULAE. 36. Formulae for the Charge of Cores 57 37. „ for the Insulation of Cores 58 38. „ for the Speed in Cables 60 39. „ for the Weights of Conductor and Insulator 63 40. „ for the Diameters of Cores 64 41. „ for the Diameters of Cables 65 TABLES. Table 1. Temperature Coefficients for Copper 66 Table 2. Temperature Coefficients for Hooper's India-rubber .. .. 67 Table 3. Temperature Coefficients for ordinary Gutta-percha .. .. 68 Table 4. Temperature Coefficients for Willoughby Smith's Gutta- percha 69 Table 5. Conversion of Yards into Knots 70 Table 6. Natural Sines 71 Table 7. Natural Tangents 72 Table 8. Common Logarithms 73 ELECTRIC TESTING TELEGKAPH CABLES. 1. ELECTEIC TESTS. The Electric Testing employed during the manufacture of cables, or cores, ascertains : A. The Conductivity of the Copper. B. The Charge of the Cable. C. The Insulation of the Cable. D. The Insulation of a Joint. E. The Position and Magnitude of a Fault. 2. STANDAED DEGEEE OF TEMPEEATUEE. As the temperature has an essential influence on the con- ductivity of the copper and the insulation of the cable, all test-results ought to be reduced by calculation to a standard degree of temperature. For this purpose 75° Fahrenheit = c. 24° Centigrade has been chosen. 3. IMMEESION IN WATEE. The air not being so good an electric conductor as water, and the amount of the charge depending on how the B 2 ELECTRIC TESTING OF TELEGRAPH CABLES. electricity in the copper conductor influences the water outside the dielectric, the cable has during the determina- tion of its charge and its insulation to be immersed in water, the water to be in electric connection with the earth through an iron tank. 4. ABBANGEMENTS BEFOEE TESTING. "When a cable has to be tested, it ought to be discharged, by connecting it to earth for some hours before the test. A good earth connection may be obtained by using, in factories, gas or water pipes ; on board cable ships, the iron hull of the ship ; and with a submerged cable its iron wire sheathing. During cable laying it is well to have one battery for the speaking instruments, and two testing batteries, as a single battery would become polarised. If Leclanche^s cells be used, they should be filled with sawdust saturated with sal- ammoniac solution, and some water added every morning. The cells should be well insulated in a wooden tray, mounted on glass or earthenware supports. All apparatus should be insulated by being placed on india-rubber or ebonite sheets, which should be well rubbed every morning, that humidity or dust may not destroy the insulation. Ebonite should be washed with boiling water, rinsed well in distilled water, and dried, to remove the film of acid produced, or its surface varnished with shellac. It is advisable not to use leading wires, but, where pos- sible, to take the ends of the cable, from which the sheath- ing has been removed, direct into the testing room. THE USE OF A SHUNT. 3 When a cable end has to be insulated, the core must be uncovered for 18 inches, free from all hemp, iron wires, and if india-rubber core, free from all felt, and the conductor bared for one inch. One inch of the core near the conductor, and half an inch of the conductor near the core is then paraffined, and, during the insulation test, the end is left hanging in the air. 5. APPAEATUS. For electric tests the following apparatus are principally- used : — Batteries (B) up to 500 elements. Thomson's Beflecting Galvanometer (G) with Shunt (Sh). Condenser (Cd). Beversing Battery Keys (BK). Short-circuit Keys (SK). Charge and Discharge Keys (DK). Commutators (Cm). Wheatstone's Bridge (WB) with Shunt (Sh). Besistance-coil (B). 6. THE USE OP A SHUNT. A shunt is generally used with a galvanometer, and in such a way that only a part of the electric current passes through the galvanometer, while the "rest passes through the shunt. A properly proportioned shunt must be used in order that the deflection of the galvanometer needle may not be too large. The resistance of the shunt diminishes as b 2 4 ELECTRIC TESTING OF TELEGEAPH CABLES. the length of the cable or the sensitiveness of the galvano- meter increases. s *4~ o The multiplying power or value v of the shunt is = , s where s is the resistance of the shunt, and g the resistance of the galvanometer. Should, for instance, s be = 1, and g = 99, v will be = 1 + " = 100 ; then only one hundredth part of the whole current will pass through the galvanometer, and the current will be 100 times greater than is indicated by the deflection of the galvanometer needle. When it is desired to give the shunt a certain power, its resistance s can be found from the previous equation, as s f is = — - — . v — 1 When a circuit includes a galvanometer of resistance g, and a shunt of resistance s, the total resistance of galvano- O X s meter and shunt is y - , and if it is required to maintain 9 + s ^ the resistance g of the circuit constant, then a resistance o s cp q — — — = '-- must be added. In calculating insulation 9+s g+s B it is not necessary to account for the resistances g and s. 7. ELECTEIC UNITS. The Congress of Electricians in Paris 1881, fixed the following electric units, based upon the fundamental units : 1 Centimetre, 1 Gramme, and 1 Second ; or as it is called for brevity, the C. G. S. system. ELECTKIC UNITS. 5 The Unit of Resistance (E) is : 1 Ohm (w), also called the Legal Ohm, or the Congress Ohm. It is = 10 9 C. G. S. units, and' is the resistance of a prism of mercury, 1 • 06 metre long, and 1 square millimetre in section, at 0° C. The old Ohm, also called the British Association Unit, = 1 B. A. XL, was the resistance of a prism of mercury, 1 ' 0493 metre long, and 1 square millimetre in section, at 0°C. 1 Siemens Unit = 1 S. U. is the resistance of a prism of mercury, 1 metre long, and 1 square millimetre in section, at 0° C. IB. A. U. = 1-0493 S. U. 1 S. U. = 0-9536 B. A U. = 0*943 legal Ohm. (Professor Weber found 1 S. U. = 0-955 B. A. U., or IB. A. U. = 1-047 S.U.). 1 Megohm (O) = 1 Million Ohms. The Unit of Electromotive Force (E) is : 1 Volt = 10 s C. G. S. Units, and is about equal to the electromotive force of a Daniell's cell. The Unit of Current Strength (C) is : 1 Ampere = 10r* C. G. S. Units = 1 Volt . ^ lOiim 1 Milliampere = y^g^ Ampere. The Unit of Quantity (Q) is : 1 Coulomb = 10 _1 C. G. S. Units = 1 Ampere per second. The Unit of Capacity or Charge (K) is : 1 Farad = 10~ 9 C. G. S. Units = 1 po° 1 * >mb , or, to quote 1 Volt ^ the words of Sir William Thomson, when explaining the 6 ELECTEIC TESTING OF TELEGRAPH CABLES. practical units, "1 Farad is the capacity of a condenser, which holds one Coulomb, when the difference of potential of its two plates is one Volt." 1 Microfarad = 1 millionth part of a Farad. 8. THE OEDEE OF THE TESTS. The Tests are best taken in the following order : Resistance of the Galvanometer. Conductivity of the Copper. Charge of the Leading wires. „ of the Cable after 1 minute's Insulation. „ „ by instantaneous Discharge. Constant c of the Condenser. Constant n of the Battery. Constant of the Galvanometer. Insulation of the Leading wires. Insulation of the Cable. A.— THE CONDUCTIVITY OF THE COPPER. 9. EXPLANATION OF THE METHOD. In this electric test of the cable, the positive current from the copper, C, Fig. 1, in the battery (B) is generally put to earth (E). The negative current from the zinc (Z) is put' through a wire (W) to the Wheatstone bridge (WB) and divides at a THE CONDUCTIVITY OF THE COPPER. 7 into two parts ; one passes through a c and the cable (Ca) to earth, and the other through a b and the resistance-coil (E) to earth. The connection to earth can be omitted, and C directly connected to d. By removing the plug e, the current through be passes through the galvanometer (G) with shunt (Sh). There will be no current through b c, and no deflection of the galvano- meter needle, if the two currents a b d and acd are of the same potential at b and at c. This occurs when the resistance in a b : the resistance in a c = the resistance in R : the resistance in Ca ab E ac or, — = 7=- : or, Ca = —z- E = E . a c Ca ab From ac = ab, Ca = E. The proportion between the resistance a c and a b can be varied from to , and 10 1000 this proportion is termed the ratio of balance. The resistance E is now to be varied until the spot of light from ,the galvanometer covers the zero on the scale ; it will perhaps be found that the spot of light moves to the left in diminishing E, that is by inserting a plug into the resistance-coil. The plugs in the resistance-coil must be carefully kept clean. As a paid-out cable is more or less affected by earth- currents, it is necessary to test it alternately with the zinc and copper-poles. If the earth-current be weak, and the difference between the zinc and the copper-readings small, the arithmetic mean of the tests will give the resistance of the cable; but when the earth-current is strong, it is 8 ELECTRIC TESTING OF TELEGRAPH CABLES. advisable to increase the strength of the testing battery, and to calculate the resistance by the formula «/r. K, where r is the resistance obtained when the cable is connected with the zinc-pole, and K that with the copper-pole. Earth-currents are always present, varying both in direc- tion and strength, sometimes slowly and sometimes rapidly, and appear to have daily two maxima of positive and two of negative currents. lines running east and west are more affected by earth-currents than those running north and outh ; and Aurora Borealis, thunderstorms, and earthquakes are generally preceded, accompanied, or followed by cur- rents of great strength, entirely overcoming the working currents. A second metJiod for finding the copper-resistance has been recommended. Having arranged the connections for copper-resistance as in Fig. 2, and connected one end of the cable to n of the Wheatstone bridge, the other cable end being put to earth at the distant station, the key SK is depressed, and the deflection from the earth-current through the galvanometer and a proper shunt noted ; /of the reversing key (BK) is next depressed, to put the battery in action through the cable and resistance-coil. To give the earth- current the least possible time to alter, the plugs of the resistance-coil are now adjusted as quickly as possible, until the spot of light covers that division on the scale where the deflection from the earth-current was observed, i. e. the so-called "false zero." If necessary, the position of the deflection of the earth-current may again be observed and another reading of the resistance in the bridge taken • but when the earth-current is steady, one reading either with THE CONDUCTIVITY OF THE COPPER. 9 the zinc or with the copper-pole will be sufficient, and give as satisfactory a result as a long series of readings alternately with zinc and copper-currents in the usual manner. Sir William Thomson recommends a third method, stating that during the tests for copper-resistance of the Direct United States Cable, differences of potential between the Irish and Nova Scotian earths were found varying rapidly in amount from 5 to 18 cells, but always in the same direction. The ordinary bridge method would have given no result at all in so disturbed a condition of the cable, but the method by simple deflection was used. A time of comparative tranquillity was chosen, a reading taken, and the galvano- meter then as quickly as possible short-circuited, the battery reversed, the galvanometer circuit re-opened, and a fresh reading taken. Half the space travelled by the spot of light from the first reading to the second is taken as being the deflection that would be produced by the battery applied in either direction were there no earth-current. This was done seven times, and. the half range found to be 232 - 3. Immediately after it was found that the same battery applied in two directions through the galvanometer and 7300 Siemens' units gave 232 divisions on one side of zero, and 233 on the other — mean 232 "5. Then the copper- resistance to be inferred from the observations is 000.5 jr^jr-s X 7300 = 7306 Siemens' units. 10 ELECTEIC TESTING OF TELEGKAPH CABLES. 10. PBACTICAL EXECUTION OP THE TEST. For the ordinary test the apparatus indicated in Fig. 2 is used. The copper-pole (C) of the battery (B) is, by lifting g, con- nected, through i and I in the key BK, to the screw to in the resistance-coil (B) ; the zinc-pole (Z) is connected, by depres- sing /, through h and k in the key BK, to the screw z in the Wheatstone bridge. The battery consists of 4 to 10 cells. The two ends n and o of the balance branches are directly connected with the bridge d e of the galvanometer. The ratio of balance is generally for the testing of the core and r ^ i j- • iooo c ., , , 1000 , of the leading wires = , oi the cable = , and of the galvanometer = 8 1000 One end of the cable is connected to to, the other to n. When / is depressed the current traverses the cable and the resistance B, which is varied until there is no deflection of the galvanometer. The resistance of the cable is now calculated by the ratio of balance and the indicated resistance (B). The resistance of the leading wires is found in the same way as the resistance of the cable, by removing the cable, and connecting only the leading wires between to and n. 11. CALCULATION OP THE CONDUCTIVITY. The resistance of the cable and leading wires being = B', and the resistance of the leading wires = L, the resistance Bj of the cable only will be = B' — L. THE CONDUCTIVITY OF THE COPPER. 11 The Ohm, is used as the unit of resistance. The length of the cable being = I knots, or nautical miles, the resistance per knot will be : T" As the resistance of the copper increases '21 per cent., or •0021 for every degree Fahrenheit increase of temperature, when the test is made at a temperature t, the resistance at 75° F. will practically be : E 2 (l + -0021(75°- <)) I Supposing the resistance H 2 to have been found at 85°, the resistance at 75° will be : E 2 (1 - (-0021 x 10)) = -979 E 2 , see Table I. As a wire of pure copper with the length of 1 knot and the weight of 1 lb. has at 75° F. a resistance of 1192 ■ 33 Ohms, a wire with the weight of P lbs. per knot will have a resistance of Ohms. The core of the China- Japan Cable, with a weight of 300 lbs. copper per knot, would therefore have a 1192 "33 resistance = = 3 • 9744 Ohms, if it were of pure 300 ^ copper. The conductivity of the copper conductor of this cable, expressed in a percentage of the conductivity of pure copper, or the specific condioctwity of the conductor, is therefore : 3-9744 x 100 x I x = E 2 (l+ -0021(75-0) 12 ELECTEIC TESTING OF TELEGRAPH CABLES. Generally, several cables are tested at the same time, and the calculation is then facilitated by the use of logarithms, which are best taken in the following order : log. x = - log. B 2 - log. (1 + • 0021 (75-4) ) + lo S- l + log. 3 -9744 + log. 100. 12. THE RESISTANCE OF THE GALVANOMETEB, The resistance of the galvanometer, used to ascertain the charge and the insulation of the cable, has to be found in the same way as the resistance of the cable, by placing the galvanometer instead of the cable between m and n, Fig. 2. The ratio of balance will be = 1000 If only one galvanometer is to be had, its resistance can be found thus: — The resistance of the galvanometer at a certain degree F. being always exactly given by its manu- facturer, its resistance at the temperature during testing, read from a thermometer fixed to the galvanometer, is easily calculated by the preceding rule. A Table for the resist- ances between 40° and 75° F. ought to be calculated for each galvanometer, and its correctness ascertained by comparison with the resistances obtained by measurement with a second galvanometer. If the resistance of the galvanometer at 60° F. is 10600 Ohms, its resistance at 65° F. will be : 10600(1+ -0021 x 5) = 10711 Ohms. A second method of finding the resistance E of the galvanometer, when only one galvanometer is at hand, THE CONDUCTIVITY OF THE COPPEK. 13 consists in inserting between c and d of the Wheatstone bridge, Fig. 1, the shunt Sh, finding its resistances r. If Sh = 55^ , r may be = 11-00 and E is = 10989 999 ■ 1_ 99 1 9 = 110-70 = 10959 = 1214-00 = 10926 The mean of these three resistances E gives the true resist- ance E = 10958. 13. THE EESISTANCE OP THE BATTERY. To find the resistance of a battery, connect its copper-pole C, Fig. 2, to earth, and its zinc-pole with the button e of the galvanometer. Connect the two buttons, e and d, of the galvanometer by a copper wire of small resistance, and put d to earth. By depressing /, the current passes to earth through the shunted galvanometer, the resistance of which is so small that it may be neglected, and a certain deflection u is found on the scale. Then put between the zinc-pole and the galvanometer a resistance E so great that the deflection is only = - ; E will be = the resistance of the battery. With a Daniell's battery of 140 cells, and a galvanometer with a resistance of 10,700 Ohms, a copper wire with a re- sistance of • 2 Ohm was used, and a deflection of 120° obtained. By placing in the circuit a resistance of 3500 Ohms, the deflection of 60° occurred ; the resistance of the battery was therefore 3500 Ohms, or 25 Ohms per cell. 14 ELECTRIC TESTING OF TELEGRAPH CABLES. If a battery, such as Leclanche"s, becomes polarised when working on short circuit, its resistance may be determined by a second method, by putting between the zinc-pole and the galvanometer, not shunted, which has a resistance g, a re- sistance r, giving a deflection u' ; this resistance is increased to E, giving a deflection - ; the resistance x of the battery is then found by : u' x + E + a t, „ = \ ; y ; or, x = E - 2 r - g. J«' x + r-\-g If g is so small compared to R that it may be neglected, then x = E - 2 r. If the deflection is halved by increasing the resistance from 4000 to 10,000 Ohms, the resistance of the battery is 2000 Ohms. The resistance of the battery may be determined by a third method, by first using a resistance r, and the galvanometer shunted with a resistance s, giving a deflection v! ; by re- moving the shunt and inserting a resistance E the same deflection vl is obtained; E is = the electromotive force. We find: E * Es E s(r + g) s + r + g x(s + r +g)-{-s(r-{-g) x+B.+g X+ s+r+g E-r x = s- 9+r- If g + r is made = s, then : x = E — r. THE CONDUCTIVITY OF THE COPPEE. 15 14. THE RESISTANCE OFFERED BY THE EARTH PLATE. To detect that an earth-plate offers resistance, one cell is connected by its copper-pole to earth, and by its zinc-pole through the galvanometer to another earth ; , a certain de- flection is then found on the galvanometer scale. The two wires, one from the copper-pole and the other from the galvanometer, are then connected together, instead of being both put to earth, and the deflection will be the same as before, if the earth-plates are in good order. Should the latter deflection be greater than the former, the earth con- nection is faulty; and as this often arises from the earth being dry, this fault may often be prevented by keeping the earth around the plate drenched with water. 15. EXAMPLES. Example 1. Length of the core . . = 5 knots. Temperature .' = 70° F. Number of elements in the battery = 4. Eatio of balance = — — . During testing, the following columns in a. journal are daily to be filled up. Columns 1 and 2 are given ; cols. 3, 4, and 9 are read from the resistance-box ; and cols. 5 to 8 are to be calculated. 16 ELECTRIC TESTING OF TELEGRAPH CABLES. Length of Core in Knots. Tem- pera- ture. Measured Resist- ance of Leading Wires. Measured Resistance of Core and Leading Wires. True Re- sistance of Core. Resist- ance at 75° F. Resist- ance per Knot at 75° F. Specific Conduc- tivity. Resist- ance of Gal- vano- meter. 1 2 3 4 5 6 7 8 9 5-000 70° 130 2244 21-14 21-36 4-272 93-03 5850 The true resistance of the core is the resistance of the core and leading wires, minus the resistance of the leading wires, divided by the ratio of balance, or : 2244 - 130 1000 To" = 21-14 Ohms. As the test has been taken at a temperature of 70° F. the resistance at 75° F. will be : 21-14(1 + -0021 X 5) = 21-36 Ohms. And as the length of the core is 5 knots, the resistance per knot, at 75°, is : ?^= 4-272 Ohms. The resistance of a pure copper conductor with a weight of 300 lbs. per knot being 3 • 9744 Ohms, the specific con- ductivity of the copper conductor will be : 3-9744 x 100 4-272 = 93-03 The conductivity is calculated by using logarithms as follows : THE CONDUCTIVITY OF THE COPPER. 17 log. OP THE GALVANOMETEE. The sensitiveness of the galvanometer, evaluated by the constant <£, is determined as follows : only 1 cell is used as a battery (Fig. 6) ; one end of a resistance-coil of 10,000 ohms THE INSULATION OF THE CABLE. 27 is connected to the cell; its other end being connected to earth, through the key SK and the galvanometer. A shunt with resistance s' and multiplying power v' is used. When a deflection has thus been obtained, we find according to Ohm's Law :. v' of the galvanometer may be determined by using the whole battery of, say, 200 cells ; the resistance of the battery, say, 25 Ohms per cell, has then to be added to the resistance of the coil. The use of such a high resistance facilitates the test, as it is not necessary to determine the constant of the battery, that is, the electro-motive force of the battery compared with the electro-motive force of one cell. 24. CALCULATION OP THE INSULATION. The current is first led only into the leading wires, which are not yet connected to the cable. After | minute the plug of the galvanometer is removed, and after another J minute the deflection u', is read. If the deflection after 1 minute from cable and leading wires is U, then the deflection from the cable only will be : U - «' = U'. If a shunt s with a multiplying power v has been used, the deflection U' has to be multiplied by v, and v U' is a 28 ELECTEIC TESTING OF TELEGRAPH CABLES. measure for the insulation. The resistance s of the shunt will be in inverse proportion to the length of the cable. The shunt as well as the galvanometer has always to be well insulated. It should be observed that the deflection is taken on the same side of zero of the scale, and, if possible, at nearly the same point of the scale, as the deflection U' from the cable. When these two deflections are compared, we obtain : 1 n ^ 10000 * x ' or the resistance x of the insulation is _ nxv' X X 10000 "" «U' If the galvanometer is feebly sensitive, the constant can be determined from the whole battery, that is to say, from n elements, and should a shunt be used with the multiplying power v 2 : n v 2 x 10000 "** = loooo' 0I x = — vU* This equation being independent of n, it is in this case unnecessary to know the strength of the battery. As the insulation is in inverse proportion to the length of the cable, which can be put = I knots, the insulation per knot will be _ n x v' X X 10000 X I vJJ' The resistance of the insulation diminishes as the tempera- ture increases, and if the resistance x I is measured at, for instance, t degress below or above 75° F., the resistance THE INSULATION OF THE CABLE. 29 X I ' calculated at 75° F. -will, with Hooper's core, be , or xl x 1' 026' (see Table II.). This number, with which it has been necessary to divide or multiply the result, so as to reduce from one temperature to another, is termed the temperature coefficient. When therefore the insulation has been measured at t degrees below 75°, the insulation per knot at 75° will be nxv' X (t>10000xl DXU'x 1-026' ' The resistance at 75° F. for gutta-percha will be found by using in the formula, instead of l - 026* as with Hooper's core, 1"076* with ordinary gutta-percha (see Table III.), and 1'080* with Willoughby Smith's gutta-percha (see Table IV.). If the constant of the galvanometer is taken with the whole battery, a shunt v' = 100, and a resistance of 10,000 Ohms, then the insulation at the observed temperature will v vl "When the temperature cannot be correctly measured by a thermometer, as when the cable is in a tank, sometimes full of water, sometimes without, or when it is paid out into the sea, the temperature of the cable may be calculated by its copper resistance, when this resistance at 75° F. is known. If the resistance of a cable per knot at 75° F. is known to be 4' 25 Ohms, and the measured resistance is 4*00, then the temperature of the cable is found as follows : 4-25 = 4-00 (1 + -0021 (75-f) ) be = — , megohms. 30 ELECTKIC TESTING OF TELEGRAPH CABLES. or 4-25-4-00 which gives = -0021(75-*°;, 4-00 ^ J _ _ 4-25-4-00 -0021 x 4-00 * = 45°. If it should be required to determine the insulation after 2 minutes' electrification, the deflection is read after 2 minutes, and the calculation made as previously described. If the calculation be made by logarithms, the following formula is used : log. x = log. n + log. v' + log. 4> + log. 10000 - * log. 1-026 — log. v — log. U' + log. I. 25. INSULATION TEST BY LOSS OF CHAEGE. • The spot of light reflected on to the scale of the galvano- meter is often very unsteady during the insulation test. This may be caused by the battery being strongly polarized, or by the connection to earth being faulty, or by adjoining machines making the test-table shake, or by cables being coiled into tanks near to the cable under test, or in a laid cable by earth-currents. This unsteady deflection occurs particularly with india-rubber cables. For india-rubber cables it may be advisable to confirm the insulation test by determining the loss of charge. If a cable, charged from a battery of 10 to 20 cells for 1 minute, insulated for 1 minute (= *) and discharged, gives the deflection u' ; and the same cable, charged for 1 minute and then instantly discharged, gives a deflection u, then the charge will fall to half charge in t' minutes, and THE INSULATION OF THE CABLE. 31 log. ~ 0-30103 /'= '- 5 t = ■ /. log.- log. , Vl U The insulation resistance per knot in megohms may then be expressed by 1-443 * 60 x f = '4343 x 60 x i ° Clog.- • v, where C is the charge in microfarads per knot, and t is ex- pressed in minutes. The resistance found in this way will generally be higher than that taken directly after 1 minute's insulation, and agrees better with the resistance of the 2 minute, and which depends on the absorption of electricity by the dielectric, or the electrification of the cable until it is fully charged. Example. — If the deflection falls in 1 minute from 100 to 98-5, , _ 0-30103 0-30103 _ ~, 100 ~ 0-00655 ~ b " S '98-5 The insulation resistance at the existing temperature is = TFlR = ^^ megohms. Another method is, when cables of high insulation resistance have to be compared, to charge the cable through the shunted galvanometer for 10 seconds, reading the imme- diate deflection u ; then to insulate the cable for 1 minute and recharge it through the galvanometer without shunt, reading the immediate deflection u', which indicates the 32 ELECTRIC TESTING OF TELEGRAPH CABLES. quantity of electricity required to refill the cable to its original charge. The shunt may be given such a resistance that the deflection u . with a good cable is equal to v!. Different cables may then be easily compared with this one. 26. INSULATION TEST BY THE ELECTEOMETEE. The insulation of a cable may be found by means of an electrometer, and this instrument enables us to notice the continuous fall of charge in a cable. A very thin, flat aluminium needle is suspended between two plates, charged with electricity. If the needle has a negative charge, it will be repelled from the one plate, which is negative re- lative to the other plate, and the motion of the needle will be indicated by the motion of the spot of light, reflected by a mirror attached to the needle ; the deflection will be sensibly proportional to the difference of charge in the two plates. One pole of the battery is to earth, its other pole is per- manently connected with one plate of the electrometer, and by a short contact of 15 seconds with the other plate, which is in connection with the cable. The two plates are there- fore, when the short contact is first broken, at the same potential or electro-motive force ; but the potential of the plate connected with the cable will fall, in consequence of the leakage through the dielectric of the cable, while the potential of the other plate will remain unchanged, and the spot of light will move from its first undeflected position. As the deflection ought only to increase in a certain pro- portion, the condition of the cable may be ascertained by observing the deflection every fifth or tenth minute. THE INSULATION OF THE CABLE. 33 The insulation I of a cable, in megohms per knot, is calcu- lated by the following formula : j = -4343 t Olog.1 where C is the charge in microfarads, u the first observed deflection on the electrometer scale, and u x the deflection after any time t, expressed in seconds. Example. — If the deflection after l m 45 s is 395, and after 2 m 15 s is 391 • 5, and the charge is = -44, then : -4343 x 30 1 = — fqf = 7660 megohms. •44 x log. 391-5 The electrometer can be used in every test, when a con- denser is ordinarily employed, by substituting the electro- meter for the condenser and the galvanometer. The electrometer is supposed to have, compared with the galvanometer, some advantages, when used for testing short coils of high dielectric resistance, or cables ' in course of sheathing, while machinery is in motion, or for testing several cables at the same time, especially when tests of long electrification are taken, or for testing a paid-out cable affected by earth-currents. But if the electrometer is damp, its indications are incorrect, and as, in spite of every pre- caution, it is difficult to keep it from effects of moisture, the insulation test of a cable should not depend only on measure- ment with an electrometer. D 34 ELECTKIC TESTING OF TELEGRAPH CABLES. 27. STEONG BATTEEIES WITH CHANGING CUEEENTS. It is desirable at the daily testing of an india-rubber core to have, for half an hour before testing, a battery of 500 cells with reversing currents connected to the core. The insula- tion test is then to be taken by connecting the core, first, for 5 minutes to the zinc-pole of the battery, reversing the current for 2 minutes, leaving the core to earth until it is quite discharged, and then connecting it for 5 minutes to the copper-pole, noting the deflection at every minute; the deflections obtained from both currents ought to fall in the same proportion. With a standard Hooper's core, the deflection at the fifth minute is half the deflection at the second minute. The same operation is performed at the final test of a cable, only the deflections are in this case noted for 15 minutes, instead of 5 minutes. 28. EXAMPLES. Example 1. Length of india-rubber core . . = 5 knots. Temperature = 70° F. Number of elements (generally 250) here = 100. Eesistance of galvanometer . . = 5850. Deflection from the leading wires = 3. Shunt with core = ; v = oo". Shunt with galvanometer . . = 10 Ohms ; v' = 586. Shunt with battery = 100 Ohms; %=59'5. The following eight columns are to be filled up in a journal ; 1, 3, and 5 are given, 4 and 6 are read, and the others are calculated. THE INSULATION OF THE CABLE. 35 Shunt with Battery. Constant n of Battery. Shunt with Gal- vano- meter. Constant of Galvano- meter. Shunt with Core. Deflection after l m . Total In- sulation at 75°. Insula- tion per Knot at 75°. 1 S 3 4 6 6 7 8 100 93-40 10 260° 139° 900 4500 If the deflection is with 1 cell = 280° and with 100 cells and 59-5 x 440 a shunt of 100 = 440°, then n is = 280 93-40. The coefficient of temperature, or 1-026 5 , is found in Table II. = 1-137. Total insulation at 75° = »X«'X<£x 10000 93-40x586x260x10000 U' X 1-026' 139x1-137 = 900 megohms. Total Insulation per knot at 75° = 900 x 5 knots = 4500 megohms. If the calculation be made by logarithms : log. x = log. n + log. v' + log. + log. 10000 - log. 1-137 - log. U' + log. 5. log. 93 • 40 = 1 • 9703469 log. 1 • 137 = • 0557605 log. 586-0=2- 7678976 log. 139 = 2 ■ 1430148 log. 260 = 2-4149733 log. 10000 = 4 ■ 0000000 2 ■ 1987753 11-1532178 2-1987753 log. 900 = 8-9544425 log. 5 =0-6989700 log. 4500= 9-6534125 D2 36 ELECTRIC TESTING OF TELEGRAPH CABLES. Example 2. Length of india-rubber cable . . = Temperature = Number of cells = Eesistance of galvanometer . . = Shunt with cable = Shunt with galvanometer . . = Shunt with battery = 100 knots. 70° F 100. 5955 Ohms. 3000; v = 2-985. 50; v' = 120-1. 80; «b =.75-44 Shunt with Battery. Constant n of Battery. Shunt with Gal- vano- meter. Constant

of Galvano- meter. Shunt with Cable. Deflection after l m . Total In- sulation at 75°. Insula- tion per Knot at 75° 1 2 3 4 5 6 7 8 42 252-42 70 148° 1500 390° 6 450 X = 252-42 x 151-86 x 148 x 10000 x 75 804x390x3-013 " ~ = 45 ° meg ° hmS ' Example 4. Length of gutta-percha core = 2 knots. Temperature = 75° F. Number of cells = 200. Eesistance of galvanometer . . = 5620. Shunt with core = 3000; v = 2-8733. Shunt with galvanometer . , = 20 ; v' = 282. Shunt with battery .. .. = 33; ® a =171'30. Shunt with Battery. Constant n of Battery. Shunt with Gal- vano- meter. Constant (/>of Galvano- meter. Shunt with Core. Deflection after l m . Total In- sulation at 75°. Insula- tion per Knot at 75°. 1 2 3 4 6 6 7 8. 33 171-30 20 188° 3000 252° 125 - 250 171-30. 282.188 . 10000 .2 252 .2-8733 = 250 megohms. 38 ELECTEIC TESTING OF TELEGEAPH CABLES. D.— THE INSULATION OF A JOINT. 29. PEAOTIOAL EXECUTION. For this test, in addition to the apparatus described, a well-insulated trough is used, 3 feet long, and full of water {Fig. 7). The joint, when it has become quite cool, and has been soaking in water for 3 hours, is, with a copper-plate P connected to an insulated copper-wire, lowered into the trough. The core on each side of the joint is then carefully dried. The battery is of the same strength as at the insulation test, or 500 cells. It is necessary first to test the insulation of the trough and leading wires by loss of charge. By connecting P to u, and depressing q for 15 seconds, the plate P is charged from Z through the key BK and the wire x. The plate is in- stantaneously discharged by releasing q and depressing r, the discharge passing through 6, the galvanometer, and c to earth. The trough is again charged, kept insulated for 1 minute and discharged. If the loss of charge, when the leading wires are short, is more than 2 — 3 per cent, the trough is badly insulated, and its insulation must be improved A test should be taken to prove that all connections are in order. The joint J is connected to k, and when / is de- pressed, the current from Z passes through BK to the joint, which is then charged ; an induced current in the water of the trough is produced, which current is taken up by the THE INSULATION OF A JOINT. 39 plate P. After J minute, r is depressed, and the plate P discharged through the galvanometer to earth. The plate P is connected to s, the condenser to u, and q is depressed ; the joint is connected to k, and / is depressed for 1 minute, during which time the condenser becomes charged with the quantity of electricity that passes through the dielectric. At the end of 1 minute, q is released and r depressed. The charge of the condenser passes then through b, the galvanometer, and c to earth, and the amount of the charge is determined by the deflection of the galvanometer. If the joint is then instantly discharged to earth by releasing/, an induced current in opposite direction to the first will be produced in the trough, and will, when P is connected to b, give the same deflection on the scale of the galvanometer as the first current, if all is in order. The insulation of a joint may often be easily determined by another method, by connecting the battery to the insu- lated trough. The leakage from the charged trough through the joint into the cable can be measured by noting the de- flection on the galvanometer at the discharge of the cable, after the joint has been immersed for 5 minutes. When a defective joint, which often is the result of a flaw, is met with, Warren advises to use a third method : First, well clean it with water or naphtha, unless there is fear that the naphtha will conceal the defect. Connect it to an electrometer, and charge the entire joint by grasping it with the hand ; then let the outer surface be freed. The operator then tests the piece of core on one side of the joint, taking care not to touch the insulator junction, by gradually wetting with a camel's-hair pencil which is in communication with 40 ELECTEIC TESTING OF TELEGKAPH CABLES. the earth. The other side is dealt with in the same way. If the electrometer shows no fall of tension, the fault is in some part of the joint ; the junctions are next tested separately by passing the pencil carefully around them. Dry carefully the parts found defective, and proceed in the same way to test the joint itself; this is best done from the middle, going carefully round the core towards one of the ends or junctions. A galvanometer will serve equally well for this test, unless the loss from the joint is very small. 30. STANDAED FOE JOINTS. No more electricity should pass in a certain time through a joint to the plate P, than would pass in the same time through a faultless core twice as long as the joint, or 6 feet long. The test ought therefore first to be made with 6 feet of faultless core and then with the joint. To simplify the test it may however be agreed that the charge received through the joint, which has been connected to the battery during 1 minute, must not be larger than say # 0005 micro- farad, or xo"o o P ai * °f * ne charge of a condenser, the charge of which is • 5 microfarad. If the full charge of a condenser through a shunt, with a" multiplying power of 2000, gives a deflection u, the charge, which the condenser has received in 1 minute through the joint, ought only to be so great that, when charged, it gives, through a shunt with a multi- plying power of 2, a deflection not greater than u. The condenser must be entirely discharged when used for testing joints, and a special condenser ought to be reserved for this use. POSITION AND MAGNITUDE OF A FAULT. 41 E.— THE POSITION AND MAGNITUDE OF A FAULT. 31. SIGNS OF FAULTS. Larger faults, as a break in the conductor, or a hole in the dielectric, are easily discovered, as there will be obtained a smaller charge or a smaller insulation than in the faultless cable ; small faults are more difficult to ascertain, but that they exist may be assumed : When the copper-resistance at 75° F. is found to be lower in the cable than it was in the core ; When the charge diminishes ; When the loss of charge of the cable after 1 minute's charge and 1 minute's insulation increases,, and is, for instance, at 60° F. with india-rubber more than 3 per cent., and with gutta-percha more than 15 per cent.* of the original charge ; When, at the insulation test, the fall of the deflection from the 1st to the 2nd minute is too small, and is for in- stance, at 60° F. with india-rubber less than 20 per cent., and with gutta-percha less than 4 per cent. If the needle of the galvanometer is very unsteady during the loop test, it is likely that two faults may be found in the cable. If a fault is small, the best plan is to enlarge it by in- creasing the number of cells in the battery to 100 elements in a paid-out cable, and to 1000 elements in a cable in course of * See L. Clark and K. Sabine : ' Electrical Tables and Formulas,' 1871, p. 121. 42 ELECTRIC TESTING OF TELEGRAPH CABLES. manufacture, changing the current, for instance, every 5th minute, until the fault is perfectly broken down. When the zinc-pole is connected with the cable, the con- ductor will be coated with hydrogen and the iron wires with oxygen, and this polarization will create a current in the cable so that the cable disconnected from the battery will give a deflection on the galvanometer-scale, say to the right. If the copper-pole is connected with the cable, the hydrogen on the conductor will be reduced and replaced by oxygen, while the iron wires will be coated with hydrogen, and the cable current will give a deflection in the opposite direction, or to the left. There is a moment when these opposite actions of the hydrogen and the oxygen are apparently balanced, where the end of the wire is unpolarized and pro- bably uncoated, and then only can its correct resistance be determined. The test is then quickly made, alternately with negative and positive currents, the mean of which is taken. As the current, when the copper-pole is connected to the cable, oxidizes the exposed conductor, the insulation of the cable is apparently improved, but at the same time some of the conductor is consumed. To preserve a cable it is therefore better to have the zinc-pole connected to the cable. When the zinc-pole is connected with a broken cable, its copper-resistance ought to diminish as the conductor is de-oxidized ; but if it does not diminish at first this may arise from the formation of hydrogen bubbles on the con- ductor, which increase its resistance, and the current must then be kept on until the resistance decreases and finally remains almost unchanged. It is well in a broken cable to POSITION AND MAGNITUDE OF A FAULT. 43 connect the zinc-pole to the conductor for a certain time, say 12 hours, and then change the current every 5th minute. As the strength of the cable-current may be equal to that of about one Daniell's cell, the larger the number of cells used in testing the less this cable-current will influence the result. Sometimes however it is advisable to use small battery-power, to diminish the polarization and render the measurement steadier. The proper resistance of the fault will often be equal to the resistance of two or three miles of core, so that the real distance to the fault is two or three miles less than that shown by the test. 32. TESTS FKOM BOTH ENDS OP THE CABLE. The test can be taken from both ends of the cable, when in course of manufacture, or when the fault is so small that it is possible to work through the cable, or when there are two telegraph lines between the two stations. This test, termed the loop test, is independent of the resistance in the fault, and should be used whenever possible. The cable in which there is a fault at p, Fig. 8, is con- nected with its ends to m and n in such a way, that the fault is nearer to m, and thus nearer to the resistance-coil E, it being impossible to establish equilibrium unless this con- dition is fulfilled. The earth wire, which is generally connected to the point m of the Wheatstone bridge, is removed, as the current here passes to earth through the fault. The battery should contain as many cells as possible. 44 ELECTRIC TESTING OE TELEGKAPH CABLES. Eatio of balance should be made equal to 1, viz.: 1000: 1000 or 100 : 100. The copper-resistance E in the faultless cable is supposed to be known from earlier tests ; the length of the cable is I. When the fault has shown itself, the resistance of the greater length np is put = y, the resistance of the smaller length mp = z, and the resistance of the fault = q. The resistance E has now to be decreased to E x to cause the needle of the galvanometer to remain at zero. Then: y + z = R and y + q = Ej -j- z + q, or y = E x + z. Consequently : E — Ei The distance x of the fault from m is found from the equation. E I zl - = -, or x = -^. z x E Example. Length of the cable = 120 knots. E = 500 Ohms. Ei = 160 Ohms. Then; y + z = 500, and y = 160 + z. Consequently : 170 x 120 .„ „ , z = 170, and x = — ^ 40-8 knots. 500 POSITION AND MAGNITUDE OF A FAULT. 45 By connecting the points m and I, and removing the earth wire from the key BK the circuit is closed metallically through the cable, and in this way the original copper- resistance E may be determined independent of the fault. The test may be taken from both ends by another method : Insulate at the two ends alternately for 5 minutes, while the copper-resistance is taken at the other end with negative and positive current, alternately, as quickly as possible. The cable is insulated at ra, and the resistance found by testing from the end n is : Ri = y x q i when the cable is insulated at n, the resistance found by testing from the end m is : E, = z + q. As E = y + z, these three equations give : Ej — B 2 = y — z, and R -4- R* — E 2 y = 2 A resistance should be inserted at the end nearest the fault, so that the fault is placed in the centre of the circuit and the same results approximately obtained from both ends. If the earth-current is weak or constant, it may be advisable first to try to determine the position of the fault by a third method, without employing a battery. The cable is insulated at the end m, Fig. 8, and put to earth at n through a galvanometer, properly shunted, the current through the fault at jp in the cable giving a deflection u. A resistance 46 ELECTRIC TESTING OF TELEGRAPH CABLES. E 2 is put in circuit until' the deflection u/ 2 is obtained, then E 2 = y + q, as the resistance of the galvanometer and the shunt may be neglected. In the same way, from the end m is found: E 3 = z + q; which with E 2 = y + q gives : E 2 — E 3 = y — z. We then have : E = y -f- s , an d we find : Ej — E 3 + E = 2 y, or K 2 — R 3 + E A. fourth method of finding the copper-resistance consists in connecting both ends of the cable to earth through the galvanometer at the two end stations, where the deflections u and u' are read. If the length of the cable is = I, and the resistance of the fault be not taken into consideration, then the fault is at a distance = -, X I from the one end, and v, + 11 T x I from the other end. If the resistances E and E t u + u are inserted between the galvanometer and the earth until there are obtained deflections only half those previously observed, then E + Ei gives the resistance of the cable + twice the resistance of the fault. In the potential method for finding faults, Thomson's Quadrant Electrometer is very often used, but an ordinary galvanometer with a condenser may be employed. The ob- servations are taken simultaneously at both ends of the cable. To compare the deflections of the galvanometer at the two end stations, it is advisable to charge with a standard electro- POSITION AND MAGNITUDE OF A FAULT. 47 motive force, such as L. Clark's Standard Cell, a standard condenser, say of 1 / 3 microfarad, and to read the deflection, when the condenser is at both stations discharged through the galvanometer ; if the galvanometer at A gives 300°, while the galvanometer at B gives only 200 degress, then 1° at A has to be put equal to 2 / 3 ° at B. The cable, with a fault at /, Fig. 9a, is at one end con- nected to a battery and resistance-coil B, its other end being Fig. 9o. SIC insulated at the distant station at w. A current from a battery with the key BK is kept flowing through the resistance B and the cable. If there is only one fault, the potential of the line will fall gradually towards the fault, and be the same at the other end of the cable as at the fault. Consequently, if the potentials at V and v are measured, and the electrician at the other end measures the potential at u, that is, the same as at the fault /, sufficient data are obtained to determine the position of the fault. The arm q of the key DK, Fig. 96, is depressed, and making contact at s, charges the condenser to the potential, of the point V ; after 15 seconds the condenser is discharged through the shunted galvanometer by releasing q and de- pressing r. This deflection having been noted, the potential 48 ELECTRIC TESTING OF TELEGRAPH CABLES. at the point v is next'ascertained in the same manner as that at V. Meanwhile the potential at u has been determined by similar operations, the end u having been connected to a condenser simultaneously, or as near as possible simul- taneously, with the operations at the other end. We then have : V — v v — u v — u 33. TESTS FKOM ONE END OF THE CABLE. a. By Copper-resistance. "Where there is good connection to earth at the fault, and the cable is broken, the copper-resistance in the length np, Fig. 8, is measured. Should this resistance be = r, whilst the resistance in the whole cable, which has a length I, is previously found, when the cable is perfect = E, then the 7* X I length n p is = -^— . It The copper-resistance may also be found by leading the current from two or more cells through the galvanometer with a shunt of small resistance, say 100 feet of leading wire, into the cable. Alternately positive and negative currents are employed, and the mean reading is taken. Instead of the cable, a resistance is then put in circuit, until the same deflection is obtained, and this resistance is the copper- resistance of the cable. The following applies to a broken cable : Mr. Kennelly has proved experimentally that, when the strength of the testing current does not exceed 25 milli- Position and magnitude oe a fault. 49 amperes, the resistance of the exposed copper wire varies inversely as the square root of the current. By measuring the copper resistance with two different, but known, battery powers alternately with positive and negative currents, or by balancing the resistance to the " false zero " (see page 8), we obtain one value (E) say with c cells, and' another value (Ei) say with c x cells, both representing the resistance of the cable up to the break plus the resistance of the break itself. In accordance with Kennelly's law, as quoted above, we arrive at the following expression for the true resistance r of the cable up to the break (i.e. with the resistance of the latter eliminated), viz : E v c — E, v c, T := — Vc — V^ For example, when E = 1500", E x = 1600", c = 25 and c-i — 9, then the true resistance r, up to the break, is deter- mined by: 1500^25-1600^9 V25 - V9 = 1350". Sir Henry Mance eliminates the polarization current and the earth current by applying one current only instead of reversing the battery, and by varying the ratio of balance, so that two readings are obtained, one with the ratio 1000 : 1000, and another with 100 : 100. The Wheatstone bridge is to be manipulated in the following manner : — Two readings are taken with the same current, as rapidly as possible after each other, the testing battery not to be disconnected or reversed during the two observations. Let the reading E 50 ELECTRIC TESTING OF TELEGEAPH CABLES. obtained with the — proportion coils be = E 1; and the reading obtained with the — — proportion coils be = E 2 ; let the resistance of one of the smaller proportion coils of 100 be = P 1; and the resistance of one of the larger proportion coils of 1000 be = P 2 ; then the true resistance of the cable tested up to and through the break is : Bi P2 — Eg • Pi P2 + R2 , — Pi — Ei Tn this formula, which is derived from Kirchhoff s laws, no notice is taken of the internal resistance of the battery. If the resistance of the battery be called / the formula reads as follows : r = Bi(2^ + Pj-B,. * 2+2 Ej-E + 23 Both sides of the equation multiplied by Ei — E -j- 2 z give: . « 2 + 2 (E 2 - E) 2 = - E 2 - Ej R 2 + E E t + E E 2 2 = E - E 2 + VE^-E 1 E 2 + EE 1 -EE 2 y = E - z = E 2 - VEI-E 1 E 2 + EE l -EE 2 V = E 3 - V(E -EsKE^Es). The resistance in np being thus determined, the position of the fault is found as before. e 2 52 ELECTRIC TESTING OF TELEGEAPH CABLES. Example. Length of the cable = 120 knots. E = 500 Ohms. T H = 400 Ohms. Ks = 379 Ohms. Then let there be found : z = 160, and y = 340. Thus the length np is = 340 x 12 ° = 81-6 knots. 8 r 500 c. Test by Charge. If the fault is caused by a break in the copper wire, whilst the dielectric is quite sound, or when it is possible, in a broken cable, to seal the exposed copper wire to a com- parative state of insulation, the position of the fault is found by charging the cable from one end, determining the amount of the charge, and dividing tlds by the known charge per knot. When an earth or polarization current is flowing, it will, according to its direction, either increase or decrease the apparent discharge from the cable. To eliminate this effect, the throw of the galvanometer needle, caused by this current, should be observed, and the deflection due to the discharge only calculated by the following formula, viz. : x= VU(TJ- «); where U is the deflection (the throw of the needle) of the discharge and the polarization current, and u the deflection due to the polarization current only. The above formula is based upon Mr. Hockin's investi- gations, and is found of great value in practice. TESTING DURING LAYING. 53 TESTING DURING THE LAYING OF A CABLE. 34. ELECTEICAL AERANGEMENT ON SHIP AND ON SHOEE. 1. When on ship (Fig. 10) / is depressed, the current passes from h through k, b and the testing screw T of the commutator into the cable connected to the screw C, and insulated in a commutator at its other end on shore. By opening the short-circuit key SK, the current passes through the shunted galvanometer, and a deflection is obtained. Eegular fall of the deflection indicates good condition of the cable; with decrease of insulation the deflection will increase. By disconnecting T from, and connecting S to, the cable, the ship is put in circuit for speaking. 2. On shore (Fig. 11) the cable is connected to a com- mutator, and a clock causes, every tenth minute, the arm p q to touch for some few seconds the button r, charging the condenser and at the same time giving a throw on the ship galvanometer ; when the arm p q again touches the button t, the condenser is discharged through the shore galvanometer. Instead of a commutator, an ordinary charge and discharge key may be used, worked by hand. If the insulation is decreasing the discharge becomes smaller, and in the event of loss of continuity, or a total loss of insulation, neither charge of the condenser nor discharge will be obtained. 54 ELECTRIC TESTING OF TELEGRAPH CABLES. The ends of the cable must always be kept, dry and paraffined. If the cable is permanently connected through a veiy high resistance E 2 and a galvanometer Gr 2 to earth, ship is able to signal at any time to shore by either reversal or reduced tension, and shore obtains by this arrangement a permanent insulation and continuity test. For this re- sistance a bar of selenium, or a plumbago line on glass may be used, and a suitable shunt may be used to make the de- flection on the galvanometer scale about 200 divisions. 3. Both ship and shore must be provided with a complete set of testing apparatus, always kept ready for testing at any moment. 85. INSTKTJCTIONS FOE TESTING ON SHIP AND ON SHOEE. 1. On ship, the cable being connected to galvanometer for insulation test, the deflection is read every minute and noted down. The resistance of the battery and the constant of the galvanometer being determined, the insulation readings for every 10 minutes are reduced in the ordinary way to megohms per knot. 2. Ship must note the time when the continuity-throws from shore occur, which will be about every tenth minute. 3. Ship will reverse the current every hour, when the discharge-throws on shore will also be reversed. 4 Ship will reverse the current 10 minutes before noon, and shore will acknowledge this by pressing in the stud s three times and bringing the arm j? q in contact with r, TESTING DURING LAYING. 55 giving three kicks on the ship galvanometer. Ship then releases T and depresses S, and shore having on its commu- tator released T' and depressed S', all will be in readiness for speaking. Ship then gives shore the time by sending dots, stopping at exactly twelve o'clock Greenwich time. Ship sends any necessary information, as distance run and miles paid out, as quickly as possible, always finishing by "in- sulate," which shore station will immediately obey, both stations releasing S and S' and depressing T and I", and being again ready for the insulation-test. 5. Ship not to send any communications except those ordered by the chief electricians and engineers. 6. On shore, the condenser in every tenth minute, com- mencing at the full hour, connected through the arm p q and the button r of the commutator for 10 seconds to the cable, the charge abstracted from the cable producing a throw on the deflection-scale on board; the condenser is instantly afterwards discharged through the shunted galvanometer G' by the falling back of the arm p q to the button t. To render this reading accurate, it is important to make it as high as possible. Shore must multiply these readings by the value of the shunt, and enter the true value of each reading. 7. At reversals at the full hour, except at noon, shore will not alter any connections, but simply note time and amount of throw on the galvanometer G-' ; but if reversals are not at the hour, shore will depress the stud s three times and join up for speaking, ready to receive messages from ship. 8. Shore to make no communication whatever, or ask any questions, except in reply to demands from ship. All infor- mation demanded to be given with as few words as possible. 56 ELECTRIC TESTING OF TELEGRAPH CABLES. 9. Shore to keep a diary, in which the names of the electrician in charge and the clerk on duty are entered, so that the responsible party for any time can be found. In the diary all observations must be recorded in full, and timed. 10. The testing-room on shore must be kept strictly private, and no one admitted except on business. 11. Should any loss of insulation or any fault occur, and ship, having carefully examined all connections, has found that the extra loss of current is due to the cable, the current is reversed, as a signal to shore to join up for receiving messages, and if speaking is possible ship may, for instance, direct shore to remove end of cable from the commutator, carefully retrim and insulate it, that ship may take insulation- test. Should the fault make speaking impossible, ship and shore will proceed as follows : — Shore having joined up for speaking until the next full 10 minutes, insulates for 10 minutes, puts to earth for 10 minutes, and continues to insulate and put to earth alter- nately every 10 minutes until the next full hour. Shore then again joins up 10 minutes for speaking, and commences again to insulate and put to earth alternately every 10 minutes until the next full hour, and so on until signal is received from ship. If a fault in the instruments makes speaking impossible, at every full hour ship and shore join up for speaking for 10 minutes, but always insulate again until the next full hour. 12. From the day communication with the ship ceases, shore will have daily to take two series of tests, each of twelve readings for copper-resistance, six with zinc to cable, FORMULA. 57 and six with copper to cable, alternately. One series of these tests to be taken at 9 A.M., and the other at 6 P.M. 13. Records of the tests made and results obtained are to be carefully kept, both on ship and shore. 14. 'The chief electrician has to ascertain before starting that all instruments are in good order and all connections properly made, as well on shore as on board ship. 15. The above regulations can only be modified by order from the ship. The strictest fulfilment is of the utmost urgency, and no excuse whatever for any neglect will be accepted. FOBMUL.E. 36. FOEMUL.E FOE THE CHAEGE OF COBES. The charge C per knot of a core is determined by the following equation : E.Z C = c TV Elog. » a where c is a constant, E the electro-motive force of the battery, I the length in knots of the core, E the resistance per knot of the insulator, D the diameter of the core, and d the diameter of the conductor. If for Hooper's core, the following numbers are given : C = -45, E = 4000, D = -318", d = ■ 145", and if E is = 1, and 1=1, then c is = 614. 58 ELECTRIC TESTING OF TELEGRAPH CABLES. The charge C per knot is then _ 614 _ -153 5 4000 log. ? log. - d d microfarads. The charge C per knot with ordinary gutta-percha core is •1877 l0g -f microfarads. The chairge C per knot with Willoughby Smith's gutta- percha core is found to be •15163 i D l0S -d microfarads. Example. — "When d = -145" and J) = "318, the capacity is : With Hooper's core = "45 With ordinary gutta-percha core .. .. = *55 With Willoughby Smith's gutta-percha core = -44 37. FOEMTJLiE FOB THE INSULATION OF COEES. The insulation per knot at 75° F. is : With Hooper's core .. .. =1*3 X log. — megohms. With ordinary gutta-percha core = -077 x log. — „ a With Willoughby Smith's core = -035 x log. — FORMULA. 59 where D is the diameter of the core, and d the diameter of the conductor, and -where the first four figures of the loga- rithm are regarded as a whole number. The insulation per knot at 75° F. of a core with a strand conductor, calculated by weights, and not by diameters, is : / W For Hooper's core .. .. =1-3 X log.^ / 1 + 5 ■ 7 - For ordinary gutta-percha 1 = , Q „„ , /, , g. g W core ) °'\/ ~ w For Willoughby Smith's) = . 035 / „ W gutta-percha^core .. ) ~ ° \/ ' w where W is the weight of the dielectric and w the weight of the conductor, and where the first four figures of the loga- rithm are regarded as a whole number. Example. — When d = '113 and D = "291, the insulation is: With. Hooper's core = 5340 megohms. With ordinary gutta-percha core = 316 „ With Willoughby Smith's gutta-percha core = 144 „ When u = 180 lbs. and W = 180 lbs., then the insulation is : With Hooper's core = 5340 megohms. With ordinary gutta-percha core = 345 „ With Willoughby Smith's gutta-percha core = 157 „ 60 ELECTRIC TESTING OF TELEGRAPH CABLES. 38. FOEMUL.a: FOE THE SPEED IN CABLES. The speed of working a cable is proportionate to : S _1 PxG'° T PxCx r where S is the specific conductivity of the copper, I the length of the cable, C the charge of the cable per knot, and r the resistance of the copper per knot. When the holes in the machine, in which the copper wires are drawn, are worn out, the diameter of the wires, and consequently their conductivity will increase, and the speed of the cable would also increase, if the charge did not generally increase at the same time, by which the speed will be again diminished. When it is fixed that the specific conductivity S shall be not less than 90 per cent., and the charge C not more than • 44 microfarad, then the speed through 1 knot of cable will 90 be proportionate to tjj = 205 ; and the charge may increase to "45 and -46 microfarad, without the speed being altered, if the conductivity of the copper at the same time increases to 93-25 and 94-30, because ^rf- = ^- = 205. ' '45 -46 As the charge of the core is inversely proportionate to i0 §- -j t and the resistance of the copper is inversely pro- portionate to d 2 , where D is the diameter of the core in mils, (or thousandths of an inch), and d the diameter of the conductor in mils., the working speed can also be expressed by : d 2 (log. D -log. ' = d . 180 1 — sin. . 180 sin. — n Example. — For a cable with 12 wires, No. 8, each with a diameter of -165": D "=' 165 "x 1 -^S li =- 4w - 66 ELECTRIC TESTING OF TELEGRAPH CABLES. TABLE I. TEMPERATURE COEFFICIENTS FOR CALCULATING THE RESISTANCE OF COPPER AT 75° F. Temperature lower than 75°. Coefficient. Logarithm of Coefficient. Temperature higher than Coe 75°. fficient. Logarithm of Coefficient. 1-0000 •0000000 1 0000 •0000000 1 1-0021 •0009111 1 9979 •9990870-1 2 1-0042 •0018202 2 9958 •9981721-1 3 1-0063 ■0027275 3 9937 •9972553-1 4 1-0084 •0036328 4 9916 ■9963365-1 5 1-0105 •0045363 5 9896 •9954597-1 6 1-0127 •0054808 6 9875 •9945371-1 7 1-0148 •0063805 7 9854 •9936126-1 8 1-0169 •0072782 8 9834 •9927302-1 9 10191 ■0082168 9 9813 •9918018-1 10 1-0212 •0091108 10 9792 •9908714-1 11 1-0233 •0100030 11 9772 •9899835-1 12 1-0255 ■0109357 12 9751 •9890492-1 13 1-0276 •0118241 13 9731 ■9881575-1 14 1-0298 •0127529 14 9711 ■9872640-1 15 1-0320 •0136797 15 9690 •9863238-1 16 1-0341 •0145625 16 9670 •9854265-1 17 1-0363 •0154855 17 9650 ■9845273-1 18 1-0385 •0164065 18 9629 •9835812-1 19 1-0407 •0173256 19 9609 •9826782-1 20 1-0428 •0182010 20 9589 •9817733-1 21 1-0450 •0191163 21 9569 ■9808666-1 22 1-0472 •0200296 22 9549 •9799579-1 23 1-0494 •0209411 23 9529 •9790473-1 24 1-0516 ■0218506 24 9509 •9781348-1 25 1-0538 •0227582 25 9489 •9772204-1 26 10561 •0237050 26 9469 ■9763041-1 27 1-0583 •0246088 27 9449 ■9753858-1 28 1-0605 •0255107 28 9429 •9744656-1 29 1-0627 ■0264107 29 9409 •9735435-1 30 1-0650 •0273496 30 9390 •9726056-1 31 1-0671 •0282051 31 9369 •9716932-1 32 1-0692 •0290590 32 9348 ■9707187-1 33 1-0713 •0299111 33 9327 •9697420-1 34 1-0734 •0307616 34 9306 •9687630-1 35 1-0755 ■0316104 35 9285 •9677819-1 36 1-0777 •0324979 36 •9264 19667985-1 37 1-0798 •0333433 37 ■9243 ■9658130-1 38 10819 •0341871 , 38 ■9222 •9648251-1 39 1-0841 ■0350693 39 •9201 ■9638350-1 40 1-0862 ■0359098 40 •9180 •9628427-1 ELECTRIC TESTING OF TELEGRAPH CABLES. 67 TABLE II. TEMPERATURE COEFFICIENTS FOR CALCULATING THE DI- ELECTRIC RESISTANCE OF HOOPER'S INDIA-RUBBER AT 75° F. Difference in Tem- perature, *. 1-026*. t Log. 1-026. Difference in Tem- perature, *. 1026*. iLog. 1-026 1-000 •00000 21 1-715 •23415 1 1-026 ■01115 22 1-759 •24530 2 1-053 •02230 23 1-805 •25645 3 1-080 •03345 24 1-852 ■26760 4 1-108 ■04460 25 1-900 •27875 5 1-137 •05575 26 1-949 •28990 6 1-167 •06690 27 2-000 •30105 7 1-197 •07805 28 2-052 •31220 8 1-228 •08920 29 2-105 •32335 9 1-260 •10035 30 2-160 •33450 10 1-293 •11150 31 2-216 •34565 11 1-326 •12265 32 2-274 •35680 12 1-361 •13380 33 2-333 •36795 13 1-396 •14495 34 2-394 •37910 14 1-443 ■15610 35 ' 2-456 •39025 15 1-470 •16725 36 2-520 •40140 16 1-508 •17840 37 2-586 •41255 17 1-547 ■18955 38 2-653 •42370 18 1-587 •20070 39 2-722 •43485 19 1-629 •21185 40 2-793 •44600 20 1-671 •22300 68 ELECTRIC TESTING OF TELEGEAPH CABLES. TABLE III. TEMPERATURE COEFFICIENTS FOR CALULATING THE DI- ELECTRIC RESISTANCE OF ORDINARY GUTTA-PERCHA AT 75° F. Tempera- ture Fahr. Resistance. Log . Resistance. Tempera- _, . ture Fahr. Kesl jtance. Log. lesistance. 32° 23-622 1 373317 67° 1 801 255514 33 21 947 1 341375 68 1 673 223496 34 20 391 1 309439 69 1 555 191730 35 18 945 1 277495 70 1 444 159567 36 17 602 1 245562 71 1 342 127753 37 16 354 1 213624 72 1 247 095867 38 15 195 1 181701 73 1 158 063709 39 14 117 1 149742 74 1 076 031812 40 13 116 1 117801 75 1 000 000000 41 12 186 1 085861 76 9418 973959 42 11 322 1 053923 77 > 8870 947924 43 10 520 1 022016 78 8354 921895 44 9 774 990072 79 7867 895809 45 9 081 958134 80 7410 869818 46 8 437 926188 81 6978 843731 47 7 839 8942H1 82 6572 817698 48 7 283 862310 83 6190 791691 49 6 767 830396 84 5829 765594 50 6 287 798444 85 5490 739572 51 5 841 766487 86 5171 713575 52 5 427 734560 87 4870 687529 53 5 042 702603 88 4586 661434 54 4 685 670710 89 4319 635383 55 4 353 638789 90 4068 609381 56 4 044 606811 91 3831 583312 57 3 757 574841 92 3608 557267 58 3 491 542950 93 3398 531223 59 3 244 511081 94 3200 505150 60 3 013 478999 95 3014 479143 61 2 800 447158 96 2839 453165 62 2 601 415140 97 2674 427161 63 2 417 383277 98 2518 401056 64 2 245 351216 99 2371 374932 65 2 086 319314 100 2233 348889 66 1-938 287354 ELECTRIC TESTING OF TELEGRAPH CABLES. 69 TABLE IV. TEMPERATURE COEFFICIENTS FOR CALCULATING THE DI. ELECTRIC RESISTANCE OF WILLOUGHBY SMITH'S GUTTA-PERCHA AT 75° F. Tempera- ture Fahr. Resistance. Log. Resistance. Tempera- ture Fahr. Resistance. Log. Resistance. 32° 27-913 1-445807 67° 1-858 •269046 33 25-834 1-412192 68 1-719 •235276 34 23-910 1-378580 69 1-591 •201670 35 22-128 1-344942 70 1-473 •168203 36 20-480 1-311330 71 1-363 •134496 37 18-954 1-277701 72 1-261 • 100715 38 17-542 1-244079 73 1-167 •067071 39 16-235 1-210452 74 1-080 •033424 40 15-025 1 ■ 176815 75 1-000 •000000 41 13-906 1-143202 76 ■9375 ■971971 42 12-870 1-109579 77 •8789 ■943940 43 11-911 1-075948 78 •8240 •915927 44 11-024 1-042339 79 •7725 ■887899 45 10-203 1-008728 80 •7242 •859859 46 9-442 ■975064 81 •6789 •831806 47 8-739 ■941462 82 ■6365 •803798 48 8-088 •907841 83 ■5967 •775756 49 7-485 •874192 84 ■5594 •747723 50 6-928 •840608 - 85 •5245 •719746 51 6-412 •806994 86 •4917 •881700 52 , 5-934 •773348 87 •4609 •663607 53 5-492 •739731 88 •4321 •635584 54 5-083 •706120 89 ■4051 ■607562 55 4-704 •672467 90 •3798 ■579555 56 4-354 ■638888 91 •3561 •551572 57 4-029 ■605197 92 •3338 •523486 58 3-729 ■571592 93 •3130 •495544 59 3-451 •537945 94 •2934 •467460 60 3-194 •504335 95 ■2751 ■439491 61 2-956 ■470704 96 ■2579 •411451 62 2-736 ■437116 97 •2417 •383277 63 2-532 ■403464 98 ■2266 •355260 64 2-343 ■369772 99 •2125 ■327359 65 2-169 ■336260 100 •1992 •299289 66 -2-007 ■302547 70 ELECTRIC TESTING OF TELEGRAPH CABLES. TABLE V. CONVERSION OF YARDS INTO KNOTS. Yards. Knots. Yards. Knots. Yards. Knots. Yards. Knots. 1 000493 31 015278 61 •030064 91 •044850 2 000986 32 015771 62 ■030557 92 ■045343 3 001479 32 016264 63 •031050 93 ■045836 4 001971 34 016757 64 •031542 94 •046329 5 002464 35 017250 65 •032035 95 •046822 6 002957 36 017743 66 •032528 96 •047315 7 003450 37 018326 67 •033021 97 •047808 8 003943 38 018728 68 •033514 98 •048301 9 004436 39 019221 69 ■034007 99 ■048794 10 004929 40 019714 70 ■034500 100 •049287 11 005421 41 020207 71 ■034993 200 •098571 12 005914 42 . 020700 72 ■035485 300 •147856 13 006407 43 021193 73 ■035978 400 •197141 14 006900 44 021686 74 •036471 500 ■246427 15 007393 45 022178 75 •036964 600 •295712 16 007886 46 022671 76 •037457 700 •344998 17 008379 47 023164 77 •037949 800 •394283 18* 008871 48 023657 78 •038433 900 •443568 19 009364 49 024150 79 •038935 1000 ■492854 20 009857 50 024643 80 •039428 1100 ■542139 21 010350 51 025136 81 ■039921 1200 •591424 22 010843 52 025628 82 •040414 1300 •640710 23 011336 53 026121 83 •040907 1400 ■689995 24 011828 54 026614 84 •041400 1500 •739280 25 012321 55 027107 85 •041892 1600 •788566 26 012814 56 027600 86 •042385 1700 ■837851 27 013307 57 028093 87 •042878 1800 •887137 28 013800 58 028586 88 •043371 1900 ■936422 29 014293 59 029078 89 •043864 2000 •985707 30 014786 60 029571 90 •044357 2029 1-000000 ELECTRIC TESTING OF TELEGEAPH CABLES. 71 TABLE VI. NATURAL SINES. Degrees. Sines. Degrees. Sines. Degrees. Sines. 1 •017 31 ■515 61 •874 2 ■035 32 ■530 62 •883 3 ■052 33 ■545 63 •891 4 •070 34 ■559 64 •899 5 •087 35 •574 65 •906 6 •105 36 ■588 66 ■914 7 •122 37 •602 67 •920 8 •139 38 •616 68 •927 9 •156 39 ■629 69 ■934 10 •174 40 ■643 70 •940 11 •191 41 ■656 71 ■946 12 •208 42 ■669 72 ■951 13 •225 43 ■682 73 ■956 14 •242 '. 44 •695 74 •961 15 •259 45 ■707 75 •966 16 •276 46 •719 76 ■970 17 •292 47 •731 77 •974 18 •309 48 ■743 78 •978 19 •326 49 ■755 79 •982 20 •342 50 •766 80 •985 21 •358 51 • -777 81 ■988 22 •375 52 •788 82 ■990 23 ■391 53 ■799 83 •993 24 •407 54 ■809 84 •995 25 •423 55 •819 85 •996 26 •438 56 •829 86 •997 27 •454 57 •839 87 •998 28 •469 58 •848 88 •999 29 •485 59 ■857 89 ■999 30 ■500 60 •866 90 1-000 72 ELECTRIC TESTING OF TELEGRAPH CABLES. TABLE VII. NATURAL TANGENTS. Degrees. Ti n gents. Degrees. Tangents. Degrees. Tangents. 1 017 31 ■601 61 1-804 2 •035 32 •625 62 1-881 3 •052 33 •649 63 1-963 4 ■070 34 ■674 64 2-050 5 087 35 •700 65 2-145 6 105 36 •727 66 2-246 7 123 37 •753 67 2-356 8 141 38 •781 68 2-475 9 158 39 •810 69 2-605 10 176 40 •839 70 2-747 11 194 41 •869 71 2-904 12 212 42 •900 72 3-078 13 231 43 •933 73 3-271 14 249 44 •966 74 3-487 15 268 45 1-000 75 3-732 16 287 46 1-036 76 4-011 17 306 47 1-072 77 4-331 18 325 48 1-111 78 4-705 19 344 49 1-150 79 5-145 20 364 50 1-192 80 5-671 21 384 51 1-235 81 6-314 22 404 52 1-280 82 7-115 23 424 53 1-327 83 8-144 24 445 54 1-376 84 9-514 25 466 55 1-428 85 11-430 26 488 56 1-483 86 14-301 27 510 57 1-540 87 19-081 28 532 58 1-600 88 28-636 29 554 59 1-660 89 57-290 30 577 60 1-732 90 00 ELECTKIC TESTING OE TELEGRAPH CABLES. TABLE VIII. liOGAKITHM OF NUMBERS FEOM TO 100. No. O 1 3 3 4 5 6 7 8 9 Prop. 00000 30003 47712 60206 69897 77815 84510 90309 95424 10 00000 00432 00860 01284 01703 02119 02530 02938 03342 03743 415 11 04139 04532 04922 05307 05690 06070 06446 06819 07188 07555 379 12 07918 08279 08637 08990 09342 09691 10037 10380 10721 11059 314 13 11394 11727 12057 12385 12710 13033 13354 13672 13988 14301 323 14 14613 14922 15229 15533 15836 16137 16435 16732 17026 17319 298 15 17609 17898 18184 18469 18752 19033 19312 19590 19866 20140 281 16 20412 20683 20952 21219 21484 21748 22011 22272 22531 22789 264 17 23045 23300 23553 23805 24055 24304 24551 24797 25042 25285 249 18 25527 25768 26007 26245 26482 26717 26951 27184 27416 27646 234 19 27875 28103 28330 28556 28780 29003 29226 29447 29667 29885 222 20 30103 30320 30535 30749 30963 31175 31386 31597 31806 32015 212 21 32222 32428 32633 32838 33041 33244 33445 33646 33846 34044 202 22 34242 34439 34635 34830 35025 35218 35411 35603 35793 35984 193 23 36173 36361 36549 36736 36922 37107 37291 37475 37658 37840 185 24 38021 38202 38382 38561 38739 38916 39094 39270 39445 39619 17? 25 39794 39967 40140 40312 40483 40654 40824 40993 41162 41330 170 26 41497 41664 41830 41996 42160 42325 42488 42651 42813 42975 164 27 43136 43297 43457 43616 43775 43933 44091 44248 44404 44560 158 28 44716 44871 45025 45179 45332 45484 45637 45788 45939 46090 153 29 46240 46389 46538 46687 46835 46982 47129 47276 47422 47567 148 30 47712 47857 48001 48144 48287 48430 48572 48714 48855 48996 143 31 49136 49276 49415 49554 49693 49831 49969 50106 50243 50379 138 32 50515 50651 50786 50920 51055 51189 51322 51455 51587 51720 134 33 51851 51983 52114 52244 52375 52504 52634 52763 52892 53020 130 34 53148 53275 53403 53529 53656 53782 53908 54033 £4158 54283 126 35 54407 54531 54654 54777 54900 55022 55145 55267 55388 55509 122 36 55630 55751 55871 55991 56110 56229 56348 56467 56585 56703 119 37 56820 56937 57054 57171 57287 57403 57519 57634 57749 57863 116 38 57978 58093 58206 58320 58433 58546 58659 58771 58888 58995 113 39 59106 59218 59328 59439 59550 59660 59770 59879 59989 60097 110 40 60206 60314 60423 60531 60638 60745 60853 60959 61066 61172 107 41 61278 61384 61490 61595 61700 61805 61909 62014 62118 62221 104 42 62325 62428 62531 62634 62737 62839 62941 63043 63144 63246 102 43 63347 63448 63548 63649 63749 63849 63949 64048 64147 64246 99 44 64345 64444 64542 64640 64738 64836 64933 65031 65128 65225 98 45 65321 65418 65514 65609 65706 65801 65896 65992 66087 66181 96 46 66276 66370 66464 66558 66652 66745 66839 66932 67025 67117 95 47 67210 67302 67394 67486 67578 67669 67761 67852 67943 68034 92 48 68124 68215 98305 68395 68485 68574 68664 68753 68842 68931 90 49 69020 69108 69197 69285 69373 69461 69548 69636 69723 69810 88 50 69897 69984 70070 70157 70243 70329 70415 70501 70586 70672 86 74 ELECTRIC TESTING OP TELEGRAPH CABLES. TABLE VIIL— continued. LOGARITHM OF NUMBERS FBOM TO 100— continued. No. 1 2 3 4 5 6 7 8 9 Prop. 51 70757 70842 70927 71012 71096 71181 71265 71349 71433 71517 84 52 71600 71684 71767 71850 71933 72016 72099 72181 72263 72346 82 53 72428 72509 72i91 72673 72754 72835 72916 72997 73078 73159 81 54 73239 73320 73399 73480 73560 73639 73719 73799 73878 73957 80 55 74036 74115 74194 74273 74351 74429 74507 74586 74663 74741 78 56 74819 74896 74974 75051 75128 75205 75282 75358 75435 75511 77 57 75587 75664 75740 75815 75891 75967 76042 76118 76193 70268 75 58 76343 76418 76492 76567 76641 76716 76790 76864 76938 77012 74 59 77085 77159 77232 77305 77379 77452 77525 77597 77670 77743 73 0:) 77815 77887 77960 78032 78104 78176 78247 78319 78390 78462 72 61 78533 78604 78675 78746 78817 78888 78958 79029 79099 79169 71 62 79239 79309 79379 79449 79518 79588 79057 79727 79796 79865 70 63 79934 80(103 80072 80140 80209 80277 80340 80414 80482 80550 69 64 80618 80686 80754 80821 80889 80956 81023 81090 81158 81224 68 65 812:»1 81358 81425 81491 81558 81624 81690 81757 81823 81889 67 C6 81954 82020 82086 82151 82217 82282 82347 82413 82478 82543 66 67 82607 82672 82737 82802 82866 82930 82995 83059 83123 83187 64 68 83251 83315 83378 83442 83506 83569 83632 83696 83759 83822 63 69 83885 83948 84011 84073 84136 84198 84261 84323 84386 84448 63 70 84510 84572 84634 84696 84757 84819 84880 84942 85003 85065 62 71 85126 85187 85248 85309 85370 85431 85491 85552 85612 85673 61 72 85733 85794 85854 85914 85974 86034 86094 86153 86213 86273 60 73 86332 86392 86451 86510 86570 86629 86688 86747 86806 86864 59 74 86923 86982 87040 87099 87157 87216 87274 87332 87390 87448 58 75 87506 87564 87622 87680 87737 87795 87852 87910 87967 88024 57 76 88081 88138 88196 88252 88309 88366 88423 88480 88536 88593 57 77 88649 88705 88762 88818 88874 88930 88986 89042 89098 89154 56 78 89209 8926.1 : 89321 89376 89432 89487 89542 89597 89653 89708 55 79 89763 89818 8.)873 89927 89982 90037 90091 90146 90200 90255 54 80 90309 90363 90417 90172 9J526 90580 90634 90687 90741 90795 54 81 90848 90902 90956 91009 91062 91116 91169 91222 91275 91328 53 82 91381 91434 91487 91540 91593 91645 91698 91751 91803 91855 53 83 91908 91960 92012 92065 92117 92169 92221 92273 92324 92376 52 84 92428 92480 92.031 92583 i 92634 92686 92737 92789 92840 92891 51 85 92942 92993 93044 93095 93146 93197 93247 93298 93349 93399 51 86 93450 93r,00 93551 93601 93051 93702 93752 93802 93852 93902 50 87 93952 94002 94052 94101 94151 94201 94250 94300 94349 94398 49 88 94418 91498 94547 94596 91045 91694 94743 94792 94841 94890 49 89 94939 94988 95036 95085 95134 95182 95231 95279 95328 95376 48 90 95424 95472 95521 95569 95617 95665 95713 95761 95809 95856 48 ELECTRIC TESTING OF TELEGRAPH CABLES. 75 TABLE VIII.— continued. LOGARITHM OF NUMBERS PROM TO 100— continued. No. 1 2 3 4 5 6 7 8 9 Prop. 91 95904 95952 95999 96047 96095 96142 96190 96237 96284 96332 48 92 96379 96426 96473 96520 96567 96614 96661 96708 96755 96802 47 93 96848 96895 96942 96988 97035 97081 97128 97174 97220 97267 47 94 97313 97359 97405 97451 97497 97543 97589 97635 97681 97727 46 95 97772 97818 97864 97909 97955 98000 98046 98091 98137 98182 46 9fi 98227 98272 98318 98363 98408 98453 98498 98453 98588 98632 45 97 98677 98722 98767 98811 98856 98900 98945 98989 99034 99078 45 98 99123 99167 99211 99255 99300 99344 99388 99432 99476 99520 44 99 99564 99607 99651 99695 99739 99782 99826 99870 99913 99957 44 Indices of Logarithms : — Log. 4030 =3-60530 „ 403 =2-60530 40-3=1-60530 Log. 4-03 = -60530 „ -403 =T-60530 „ -0403 =¥-60530 „ -00403=3-60530 LONDON! PRINTED BY WILUAH CLOWES AND SONS, LIMITED, STAMFORD STREET AND CHARING CROS5. IVlIEATSTOME'S BBIDGE TO! Pig. 2. COPPER KESISTAWCE TEST. Fig.3 E CHAH.GE TEST. Fig. 3b. Fig. 4. IKSUXlATIOBT test. lug.. 5. CONSTANT OF THE BATTERY; Tig 6. CowsTJorx or the Gajlvaetomjeter. "Fig. 7. JOIJSTT TJIST, Fig. 8. TEST FOB. "FAULT. Fig. 9b. Battery Tig. 10. OS SHIP. OB SHOBlE. Fig.1I.