None
2. Insulator <»• Dielectric. — The conductor of each coil shall be insulated by being covered with three alternate layers of Chatter- ton's compound and gutta-percha, beginning with a layer of the said compound, and no more compound shall be used than may be necessary to secure adhesion between the conductor and the layers of gutta-percha. The dielectric on the conductor of each coil shall weigh not less than SOO lbs. per knot, making the total weight of the conductor of each coil when covered with the dielectric not less than 460 lbs, per knot. 3. Inductive Capacity. — The inductive capacity of each coil of such insulated conductor {hereinafter called the core) shall not exceed 0-275 microfarad per knot, and this shall apply equally to the com[iIeted cable. 4. Insertion of Loading Coils. — The loading coils will be inserted so that diagonal cores in the cable will be used to form a loop or pair, each pair of cores to be fitted with loading coils equally spaced at such distances apart and of such inductance and effective resistance as will make (a) The volume of speech transmitted over a pair of wires in the completed and laid cable at least equal to that through one-seventh of the same length of standard cable, not including terminal losses^ ; ' standard cable Ja that having a wito-to-wiie capacity for each pair of wires nf 0-054 microfarad per statute mile, a loop resiatnnceof 88 ohms per etatnte mile, and nn average LDsuIatiun resistance of nut less than 200 megohms per statute mile jvGooi^le LOADED CABLES IN PRACTICE 283 (h) Tlie quality of speech or articulation not inferior to that of the speech throughout the Btandard cable equivalent' of the loaded cable pair. 5. Interference. — The two loaded cable pairs to be free from telephonic induction or interference, the one from the other, and also from external disturbance from a contiguous cable. 6. Laitelling. — Each coil of core before being placed in the temperature tank for testing shall be carefully labelled with the exact length of conductor and the exact weight of copper and dielectric respectively which it contains. 7- Insulation Resistance. — The insulation resistance of. each coil of core, after such coil shalT have been kept in water main- tained at a temperature of 75° F. for not less than twenty-four consecutive hours immediately preceding the test, shall be not less than 400 nor more than 2,000 megohms per knot when tested at that actual temperature, and after electrification during one minute. The electrification between the first and the second minutes to be not less than 3 nor more than 8 per cent., and to progress steadily. The insulation to be taken not less than fourteen days after manufacture. Each coil of core may be subjected, before the ordinary insulation test is taken, to an alternating electromotive force of 5,000 volts and 100 complete periods per second for fifteen minutes. 8, Preservation. — The core shall during the process of manu- facture be carefully protected from sun and heat, and shall not be allowed to remain out of water, 9. Joints. — All joints shall be made by experienced workmen, and the contractor shall give timely notice to the Engineer-in- chiet or other authorised officer of the PoBtmaster-General whenever a joint is about to be made, in order that he may test the same. The contractorshall allow time for a thorough testing of each and every joint in the insulated trough by accumulation, and the leakage from any joint during one minute shall be not more than double that from an equal length of the perfect core. ' By the standanl cable ciiuivalent oi any loo[) is meant the number nf statute milcB of loop in a standard cable through which the fame volume of speech ia obtained as through the loop under teat. ovGoQi^lc 284 PROPAGATION OF ELECTRIC CURRENTS 10, Taping and Servinti. — The cores to be lour in number, and to be atranded with a left-handed lay, and during the proceea of stranding be wormed with best wet fully tanned jute yarn, bo that the whole may be as nearly as possible of a cylindrical form, and shall then be covered (1) with cut cotton tape prepared with ozokerit compound, (2) with pliable brass tape 0*004 inch in thickness and 1 inch in width, and (3) with another serving of cotton tape, similar to the first, the lap in each case being not less than 0*250 inch. The cores, prepared as above specified, shall then be served with best wet fully tanned jute yam, sufficient to receive the sheathing, hereafter specified, and no loose threads shall, in the process of sheathing, be run through the closing machine. The cores so served shall be kept in tanned water at ordinary tempera- ture, and shall not be allowed to remain out of water except so far as may be necessary to feed the closing machine. 11. Sheathing.— The served core to be sheathed with sixteen galvanised iron wires, each wire having a diameter of 280 mils, or within 3 per cent, thereof above or below the same. The breaking weight of each wire to be not less than 3,500 Iba., with a minimum of ten twists in 6 inches. The length of lay to be 18 inches, and to be left-handed. The wire to be of homogeneous iron, well and smoothly galvanised with zinc spelter. The galvanising will be tested by taking samples from any coil or coils, and plunging them into a saturated solution of sulphate of copper at 60^ F,, and allowing them to remain in the solution for one minute, when they will be withdrawn and wiped clean. The galvanising shall admit of this process being four times performed with each sample without there being, as there would be if the coating of zinc were too thin, any sign of a reddish deposit of metallic copper on the wire. If, after the examination of any particular quantity of iron wire, 10 per cent, of such wire does not meet all or any of the foregoing requirements, the whole of such quantity shall be rejected, and no such quantity or any part thereof shall on any account be presented for examination and testing, and this stipulation shall be deemed to be and shall be treated as an essential condition of the contract. Before being used for the sheathing of the cable, i ovGoQi^lc LOADED CABLES IN PRACTICE 285 the wire shall be heated in a kiln or oven, just sufficiently to drive off all moisture, and whilst warm shall be dipped into pure hot gas-tar (freed from naphtha). The iron wire so dipped shall not be used for sheathing the cable until the coating of gas-tar is thoroughly set. No weld or braze in any one wire of the sheatli shall be within six feet of a weld or braze in any other wire. All welds or brazes made during the' manufacture of the cable shall be regalvanised and retarred. 12. Compound and Serving. — The sheathed cores shall be covered with two coatings of compound and two servings of three-ply jute yarn, the said compound being placed between the two servings and over the outer serving of yarn aforesaid, the two servings of yam to be laid on in directions contrary to each other. The compound referred to in this paragraph shall consist of pitch 85 per cent., bitumen 12^ per cent., and resin oil 2^ per cent., and the yarn referred to shall be spun from the best quality of jute, and shall be saturated with gas-tar freed from acid and ammonia, the yarn being thoroughly dried after saturation and before being used, so as to have no superfluous tar adhering. 13. Measurement and Marks. — A correct indicator shall be attached to the closing machine, and a mark to be approved by the Engineer-in-chief shall be made on the cable at the termination of each knot of completed cable, and also over each joint or set of joints. 14. Laying. — If the tender for laying bo accepted, the contrac- tors shall provide the necessary cable-laying ship and all appHances and all apparatus in connection therewith for the laying and testing of the cable during the laying operations. Facilities must be provided for inspection of the work, if con- sidered necessary, by an officer of the Postmaster- General during the progress of the laying operations. The cable to be laid over the course shown by the dotted red line on the accompanying Admiralty chart, or as hereafter agreed upon. On completion of the laying operations the spare cable left on hoard is to be delivered at the Post Office Cable Depot, ovGoQi^lc 286 PROPAGATION OP ELECTRIC CURRENTS Dover, or paid out and buoyed in the sea near Dover, as may be directed by the EDgiDoer-m-chief. 15. The contractorB are required to guarantee that the com- pleted cable Bhall reach and maintain the standard laid down in the epecification, and before final acceptance the cable shall be subject to such tests and esperiments as the Postmaster- General may deem neeessary during the manufacture, laying, and for a period of thirty consecutive days from the completion of the latter. Major O'Meara states (,loe. cit.) that " the investigations that had been made left little doubt concerning the balance of advantages in favour of the ' coil ' loaded type of cable from the electrical standpoint, but as the expenditure involved was very great, and as it was felt that the main difficulty in connection with this type of cable would be in safely laying the cable at the bottom of the sea, it was considered that special precautions were necessary to ensure that the responsi- bility for any defects that might be disclosed after it had been laid should be definitely traced to the responsible party. To afford the necessary protection to the department, it seemed desirable to stipulate in the specification that the manufacturers of the cable should also undertake to lay it, and to hand it over til situ. This course was approved by the Postmaster- General, and the invitations to tender were issued on these lines. The conditions were accepted by Messrs. Siemens Bros. & Co., who were the succeasful tenderers. " It will be recognised that the mechanical problem in connec- tion with this type of cable was more difficult to solve than the electrical problem, as it was necessary that the part of the cable containing the coils should be so designed that it could be paid over the sheaves of the cable-ship without any risk of damage to the coils themselves. However, Major O'Meara said he was glad to say that the manufacturers saeeeeded in solving this problem in a most satisfactory manner. " The cable was under the constant supervision of the Post Office Engineering Department during the period of its manufacture, and electrical tests were carried out from time to time. On January 18th, 1910, after the completion of the cable, measure- ovGoQi^lc LOADED CABLES IN PRACTICE 287 meats to determine its attenuation constant were made at the works of Messrs. Siemens Eros. & Co. at Woolwich. The con- ductors of the cable were joined up so as to provide a metallic circuit ol 41*704 knots, and in order to get rid of terminal effects artificial cable was joined to tha ends of the loaded cable "as shown in Fig. 10. Current was supplied to this circuit by a generator giving 1'585 voile at a frequency of 750 alternations per second. Eeadings were taken on a therma-galvanometer placed successively at A and B, and the attenuation constant was calculated by the formula h = h *"^- "With ten miles of ' standard ' cable (attenuation constant 0'1187 per knot) at each end of the circuit the current values at A were found to be 0'327 milliampere, and at B 0'172 milliam- pere, a therefore being 00154. "With fifteen miles of ' standard ' cable at each end of the circuit the current values at A were found to be 0*212 milliam- pere, at B 0"110 milliampere, from which we similarly obtain a = 0152. " The volume of the speech transmitted over the loaded cable was also compared with that over an artificial " standard " cable, the electrical constants of which are known. The result of these tests indicated that the attenuation constant of the loaded cable was 00147." The table on p. 288, given by Major O'Meara, supplies the details of the primary constants of this cable both with loading coils inserted and without them, and it also shows the attenuation constants before and after loading. Mr. W. DieseUiorst was entrusted by Messrs. Siemens Bros, with tbe actual operation of laying the cable, and Mr. F. Pollard, Submarine Superintendent, Dover, was detailed to watch the interests of the Post Office. ovGoQi^lc 288 PEOPAGATION OF ELECTRIC CUERENTS 3 ^ to- 1 s 6 5 J ,1 j < i i 1 o 1 > 1 ii 0-0230 0-0520 0-0166 iji ill ij 00124 0-0278 0-0091 1 a s 1 1 { i ii o o 2 XX X fil 2 2 2 S 6 Z IM 22-00 2-00 102-00 Ii 1= Si '■a 1 1 1 11 j 1 ? 1 M ill! ' Three layers of 7-88i mils iron wire, 101-5 turns per iiicli . .) Unloaded. Coils of 100 m.h. every, knot .... Steady current i-esist- ance, a-25 ohms Beeietaiice at 750 p.p.s., 6 ohms IJ si 8 s i 1 1 D.qilizMbvG00l^le LOADED CABLES IN PEACTIOE 289 I I -I il i f obvGoogle 290 PBOPAGATION OF ELECTRIC CURRENTS For the full details of the laying of this cable and the manner in which the engineering difficultiea were overcome in the manu- facture and laying by the contractors, MesBrs. Siemens Bros., the reader must consult Major O'Meara's admirable paper on the subject in the Journal of the Institution of Electrical Engineer!. The photograph reproduced in Fig. 11 is taken by permisBiou from Major O'Meara's paper {he. cit.), and represents the passing of a loading coil in the 1910 Anglo-French cable over the sheaves of the eable-ship Faraday during the process of laying the cable. It will be seen that the type of loading coil adopled does not render the cable to any extent cumbersome and uiibandable. The constants of the cable and some numerical values con- nected therewith both for the unloaded cable and for the cable with loads are very approximately as follows : Unloaded Cable Loaded Cable per nautical mile. per nautical mile. ii=14-42 ohms, iJ=20-45 ohms, i=0-002 henry, L=0-1 henry, C=-138 X 10-« farad, C= 138 x 10-» farad, S=2-4 X 10-6 mhos. S=24 x 10-^ mhos. w=750,p=2nw=4,710. Hence for the loaded cable we have \'lP+piL^= ^418+221,841 VW+f<? = 10-6 v'576+ 422,500 ^SO=yg, Lp=m. cpJ^. Therefore for the loaded cable /BS , /245 „,, , "^V ~2~ ^^^^^ ^ V "Ios=016 (approximately) ; Hence x=^=ii.6 nauts, 1=204-5 1=169 71=13, jvGooi^le LOADED CABLES IN PRACTICE 291 The loading coils, being 1 naut apart, are therefore at the rate of eleven or twelve per wave for the standard wave length, corresponding to a frequency of about 800, and the spacing complies with Pupin's law. As regards the practical improvement introduced by the loading coils in the above cable the following quotation from Major O'Meara'a paper (loc. cit.) is interesting and important. He said : "The cable has been under continuous observation since it was laid, and a large number of tests have been carried out. Par- ticulars of some of them are given in an appendix. It has fortunately been possible to obtain independent testimony on the question of the increase in the range, and in the improvement in the quality uf speech transmitted by means of the loaded cable as compared with a similar cable unloaded. Speech tests were made in July last by Messrs. W. R. Cooper, W. Duddell, F,E.S., W. Judd, and J. E. Kingsbury, and the results are interesting. The cable was looped at the French end (Cape Grisnez), and the English ends were connected to two telephone sets, one installed in the cable hut at Abbot's Cliff and the other in the coastguard look-out shelter some 100 feet distant. Graduated artilicial cables were provided so that the listener at the cable-hut could insert various values of the ' standard ' cable into the circuit until his own limit of satisfactory audibility was reached. It was possible to insert the ' standard ' cable values equally at the two ends of the cable (i.e., so as to form a symmetrical circuit in relation to the submarine cable), or unequally, as desired. The results shown in the table below were obtained. Old Csble. New Cab1«. a»iB by CM-, Addod Len^h of Standard Added Leiigtii of Standard W. R. CJooper . . •. W. Duddell . .. W. Jodd .... J, E. Kingsbury 24 miles symmetrical 24 miles symmetrical 26 miles symmetrical 26 miles symmetrical iS miles symmetrical 1 40mileasimmttncal . 50 milLS symmetrical ( 55 miles at one end 40 miles symmetrical 40 miles symmetrical 24 Ih 26 21 1 + 14 D.qilizMb,G00>^le 292 PROPAGATION OF ELECTRIC CURRENTS " The mean gain by the nee of the new cable is therefore seven- teen miles of ' standard ' cable for the standard of audibility accepted as commercial by the four observers named. When the cables were alone in circuit eome of the observers noticed that in the case of the new cable there was a distinct improvement in the quality of the speech as compared with the old cable. " The employment of unloaded 800-lb. copper aerial conductors, such as are in use for the most important long-distance trunk circuits in this country, will render it possible for very satisfactory conversations to take place from call-boxes between centres in England and on the Continent when the added distances from the ends of the cable do not exceed 1,700 miles; that is to say, with land-lines of this description well-maintained conversations between London and Astrakhan on the Caspian Sea would be possible. In his inaugural address to the Institution,^ Sir John Gavey included a table of equivalents of the various types of unloaded conductors. It may be assumed that in practice aerial conductors of the smaller gauges can be improved by loading twofold, and the conductors in cables threefold, so that it is not difficult to determine the centres betwoen which the new Anglo- French telephone cable will provide communication, assuming that a particular type of conductor is employed to complete the circuit." 5. Effect of Leakance on Loaded Cables.— A brief reference has already been made to the influence of leakance in the case of loaded cables upon the value of the attenuation constant in connection with the doubt thrown upon the possibility of effectively loading gutta-percha insulated cables. This question is important, and must be considered a little more at length. It has been dealt with in a paper by Dr.A.E.Kennelly to which reference has already been made, via., " On the Distri- bution of Pressure and Current over Alternating Current Circuits " (see Harvard Engineering Journal, 1905 — 1906), under the heading " Effect of Dielectric Losses on Loading." Dr. Kennelly discusses this matter as follows : ' See Sir John GftTej'e Inaugural Addreas, Jtntrnal of tlie lattittUion of Electrical Engineers, Vol. XXXVI., p. 26, 1905. ovGoQi^lc LOADED CABLES IN PBAGTICE 293 Let tbe conductor impedance ol the cable, viz., the quantity E + jpL, be denoted by Z^ I Of&s a vector. Then, equating tbe 8i7ieB, ve have ^.2=.ij2+pji2 and tan 6,=^. Tbe ratio Lp/R may be called the reactance factor of the conductor at the angular velocity p. Also tbe dielectric admittance of tbe cable, viz., tbe quantity S + jpO, may be denoted as a vector by Yj, j dp , and hence Yi.^=SHp^C^ and tan 6^=^. The ratio of the susceptance Cp to tbe dielectric conductance S at a particular angular velocity p may be called tbe susceptance factor of tbe cable, although cable electricians generally deal more with the quantity -^ as the ratio to be measured. In any case -i- is the tangent of the angle of slope of the vector Yd. Loading a circuit obviously increases the slope of the vector impedance Z^. This is particularly noticed in tbe case of telephone cables, in which when unloaded tbe reactance factor "^ at a frequency of 800 or for p = 5,000 may be of tbe order of 0-03 to 0-05, and the vectorial angle 0^ may be 1° 80' or 2°-0 or so. On tbe other hand, if there is no dielectric loss S is zero, and the slope of the admittance vector is 90", since then its tangent CpjS is infinite. In such cases we may theoretically diminish the attenuation constant without limit by increasing the inductance of the line per unit of length. For the attenuation constant a is the real part of the product of v'R +jpLi and VS-{-jpC. Tbe reader should remember that to square-root a vector we have to square-root its size and reduce the slope to half, whilst to obtain the product of two vectors we have to multiply the siz^ and add the slopes. Hence, leaving out of account sizes, we may say that if L and S are both very small, then the slope of the conductor impedance vector is nearly zero, and that of the dielectric admittance vector is nearly 90°. Hence the vector representing the square root of their product, or the ovGoQi^lc 294 PEOPAGATION OF ELECTRIC CURRENTS propagation constant, has a slope of 45°. If we keep S Btnall, but make L very large, then the slope of both impedance and admittance vectors ie nearly 90°, and the square root of their product, or the propagation constant, has also aslope of nearly 90°. Hence its horizontal step, or real part which is the attenuation constant, will be small. If, however, S is large, the slope of the admittance vector is much less than 90° and that of its square root much less than 45°, and hence even if the slope of the impedance vector is 90° the slope of tfae propagation constant is something considerably less than 90°, and that means that the attennation constant cannot be reduced to zero. In fact, if S is not zero, but has an appreciable value, then it is useless to load the cable beyond the point at which LpjR becomes equal to CpjS. For the attenuation constant = V 2 in other words when -^ = -^> that is when 0^ = Oj,, or when and if we consider R, S, G, and p to be constant and L variable it is very easy to prove in the ordinary way by finding the 'ar' above expression for a S' the cable is distorsionless. If then there is sensible leakance in the dielectric the attenuation constant a cannot be reduced below the value a — Vsii which it has when the cable fulfils the Heaviside conditions, Ljlt = CjS, for being distorsionless. It follows then that in tbe case of loaded cables great care must be taken to keep tbe leakance S very small, or nearly zero. This accounts for part of the difificulty of loading aerial lines. II we write down the already-given formula for the attenuation constant a of a cable, viz., it is easily transformed into If then ■?i^=''5. "0 tave . - ■/su. jvGoOi^le LOADED CABLES IN PRACTICE 296 If S is absolutely zero, then by making pL or L sufficiently large compared with R we can reduce the value ol o indefinitely. But if S has a, finite value, then beyond a certain point, viz., when L = R-^, we do not decrease, bnt actually increase, the value of a. Accordingly, although in perfectly insulated lines we may with advantage increase almost indefinitely the inductance, provided we do not increase the resistance at the same time ; yet in imperfectly insulated lines there is a limit beyond which increase of the inductance iuerenses instead of diminishing the attenuation constant. The table on p, 296, taken from Dr. Kennelly'e paper on " The Distribution of Pressure and Current over Alternating Current Circuits," shows the difference produced in loading a line of abso- lutely zero leakance up to 200 millihenrys per kilometre and the same loading for a line having an insulation resistance of 10,000 ohms per kilometre, or a leakance of 10"'* mhos per kilometre. In the first case the loading produces a remarkable reduction in the attenuation constant, and in the second case it produces very little. It is abundantly clear, therefore, that a loaded cable must be a well-insulated cable if we are to obtain the benefit of the loading in the form of a small attenuation constant. It is this fact, combined with the large dielectric current of gutta-percha-covered cable, which threw doubt originally upon the possibility of effectively loading submarine telephone cables insulated with G.P. But these doubts have been re- moved by the success of the 1910 Anglo-French Channel telephone cable. It is, however, essential to secure good insulation for the loading coils themselves in underground telephone cables. The practice of the National Telephone Company in this matter is to build underground pits at regular intervals of a mile or two, aa the case may be, and place in these cast-iron watertight boxes in which are contained the highly insulated loading coils. The lead-covered paper-insulated cable enclosing many strands or separate pairs of conductors passes through this pit (see ovGoQi^lc 296 PEOPAOATION OF ELECTEIO CnEREKTS III' ">* I? illl SF. ^ a 5> P fe s 3 h i S.&S. ■* ^'/ /A/ / ^\J oodo ciodd ■= b S a o ' oooo oooo oooo oooo D.qitizeabvG00l^lc LOADED CABLES IN PRACTICE 297 Fig. 8), and the coile are connected into the difEerent circuits. In this manner good inaulation is secured for the line and coils. The attenuation constant of the loaded line can always be calculated very approximately by the formula 4(-+¥)v/§- This formula is arrived at in the following i By the binomial theorem we have for the expansion of a binomial (a + ")" the series If n = o, then Henoe if x is small compared with a, so that we can neglect powers of xja, we have Va + x= Va^+ ^-j^ nearly. Accordingly, if E is small compared with pL and S is small compared with pC, we have and v'S^+^26'2 =pC+^ -^. Since, then, 2a^ = VE^+p''LWS^+p^G+SB-p^LG, it follows that when RjpL and SjpC are both small quantities compared with unity we have ^' - 2 C+2 i+ r + SB. ■=ii»^-m- Accordingly the attenuation is greatly affected by the value of SIC No really satisfactory method has yet been found for measuring the value of the leakance S* or the ratio SjC for telephonic frequencies, but it is found that by taking S'/C=80 this formula gives attenuation constants which are in close agreement with ovGoQi^lc 298 PROPAGATION OF ELECTRIC CURRENTS observed valnea for loaded cables. Thus, ia a discussion on a paper by Professor Perry on " Telephone Circuits," Mr. A. W. Martin, of the General Post Office, gave some useful measare- ments confirming this result for loaded cables. Cables of various lengths were loaded with iron-cored inductance coils, each having effective resistances of 5'4 ohma at 750 fre- quency and 15'0 ohms at 2,000 and 3'6 ohms for steady currents, bIbo an inductance of 0*185 henry per coil. These coils were inserted at various intervals in a line of conductor resistance 18 ohms per mile of loop, and capacity 0'065 m.f.d., and induct- ance 0*001 henry per mile of loop. The attenuation constants were then calculated from the above formula, taking SjC = 80, and they were also measured, and the results were as follows : Interval between Lowling Coilf AUenuatioQ Constants for Frequency 750. CoiU per Waieata ot 2,000. Calculated. ObscTTcd. 11 21 3-2 4-3 Untadod 0011 0012 0013 0014 0-042 0013 0-012 0-012 0-014 0-045 5-6 4-0 3-3 2-8 Very good Very good Good Bad In the case of the Anglo-French telephone cable (1910) above described, the observed attenuation constant corresponds to & value of SjC — 99 instead of 80. There is no doubt that the ratio of SjC for any telephone conductor plays a very important part in determining the speech- transmitting efficiency. In the United States one of the principal difficulties in con- nection with the loading of long distance aerial telephone lines has been the leakage over the insulators, and a more efficient type of glass insulator has had to be substituted fot the ordinary type in order to keep down the leakage, which prevents the loading from having its full effect. The reader will find a considerable amount of valuable infor- mation on the properties of loaded lines in the discussion which ovGoQi^lc LOADED CABLES IN PRACTICE 299 took place at the Physical Society of Loadon on a paper by Piofesaor Perry in 1910 (see The Electncian, March 11th, 1910, p. 879), and also a longer and even more important discussion which took place at the Institution of Electrical Engineers on the paper by Major O'Meara on " Submarine Cables for Long Distance Telephone Circuits" (see The Electi-ician, Vol. LXV., p. 609, 1910, and Vol.LXVL, pp. 875, 417, 419, 589, and 615, 1911), in which all the leading experts in telephony and telegraphy in England took part. ovGoQi^lc D.qilizMbvG00l^le APPENDIX. The table below is taken by kind permission from a paper by Dr. A, E, Kennelly, pablished in the Harvard Engineering Journal, May, 1908. The Sines, Cosines, and Tangents have been taken from LigoviEhi'a Tables published in Berlin in ISWJ. Tbe Colangents, Secants, and CosecanCa have been deduced from the preceding quantities. -. 8i.h.n. OMl..li. TMh.v,. Coth. n. Secb. v. Gosech. u. (HW 0- :ooo 0- » 1-00 « 000 0-01 0-02 0-03 0-OIOOi» 0020001 0-030005 1000050 1000200 1-000450 ooinoo O-02OO0 0-02999 100- 50- 33-34 0-9999 0-9098 0-9905 100- 50- 33-333 0-01 0-02 0-03 0-Ot 008 0-040011 0050021 0O60O36 1-000800 l-y0125O 1-001801 0-03998 0-04996 0-05993 25-013 20-016 16-686 0-9092 0-9087 0-0982 24-99 19-902 16-657 0-04 0-05 0-O6 0-07 0-08 0-09 0-070057 0080086 0-030123 1-O024.-.1 1-003202 1-004053 006389 0-07383 0-08976 14-308 12-527 11-141 0-9975 0-9968 0-9959 14-274 12-487 11-097 0-07 0-08 0-09 010 0-1001fi7 1-005004 O03SG7 10-033 0-9950 9-983 OlO O'll 012 013 0-1 10222 0-120288 0-130366 l-00605r> 1-007209 1-008462 0-10956 0-11943 0-12927 9128 8-373 7-735 0-9940 0-9928 0-9916 0-073 8-314 7-6l>9 0-11 0-12 0-13 014 0-15 0-16 0140458 0-150563 0-160C84 1000816 1-011271 1-012827 0-13909 0-14888 0-15865 7-189 6-716 6-303 0-9902 0-9873 7-120 6-642 6-223 0-14 0-15 0-16 0-17 0'18 019 0-170820 0-180974 0-191146 1-014485 1-016244 1-018104 016838 0-17808 0-18775 5-939 5-615 5-325 0-9857 0-9840 0-9822 5-8.i4 6-.^25 0-17 0-18 0-19 jvGooi^le .. Sinh, «. CCHb.lt. Tanh. 11. Coth.K. S«ch. 1>. 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