degree. But we are not concerned with the coefficient of mutual induction in this case. We are concerned with another integral, viz., 2* faHda and the adjustment for centre is in truth of primary importance. Special attention should therefore be paid to this in designing apparatus for the absolute measurement of resistance by this method. One other point remains to be noticed in this connection, viz., the possible effect of the difference of the temperature of the coil and disc when measured and when in use. On calculating the correction to be applied for this cause I find it negligible. Again, I would say, as I said last year, that the chief value of these observations consists in the proof they afford of the precision with which the absolute measurement of resistance may be made by this method. A well-constructed apparatus of the kind in a national laboratory-say the Laboratory of the Board of Trade-will, I believe, prove to be the best ultimate standard of electrical resistance. APPENDIX III. Comparison of the Standard Coils used by Professor Jones with The tenth-ohm standards of manganin wire whose value in absolute measure was determined by Professor Jones by means of the experiments described in Appendix II. were compared with the standards of the Association in the following manner. A Wheatstone's bridge was formed in which the arms were the tenth-ohm to be tested, two single-ohm coils and a ten-ohm coil; if the coils had these values exactly, there would of course always have been a balance; since, however, the coils were not accurately correct, there was usually a small current through the galvanometer; the balance, however, could be obtained by placing a large resistance as a shunt either to one of the one-ohm coils or to the ten-ohm coil this resistance, which varied from 10,000 to 20,000 ohms, was taken from a good box of coils. The resistance of the ten-ohm and of the two oneohm coils being known, that of the tenth-ohm coil could readily be found. The four coils dipped into four mercury cups cut in an ebonite block; the bottoms of these cups were copper pieces some 3 to 4 mm. thick. Binding screws screwed into these copper pieces and rising above the mercury served to connect the bridge to the galvanometer and the battery. The mercury cups were somewhat large-about 2.5 cm. in diameterand it was found on January 16 that distinct differences could be observed by moving the tenth-ohm coils slightly so as to bring their terminals either close to or as far as possible from the feet of the one-ohm coils which dipped into the same cups. After this date then two sets of measurements were made for each coil at each observation: in the one the terminals of the coils in any cup were put as close together as possible, in the other the terminals of the tenth-ohm coils were placed at some distance from those of the other coil in the same cup. Both sets of values are given in the table as a means of showing the delicacy of the observations and the error arising from this cause. The tenth-ohm coils were weighted so as to press firmly on to the copper bottoms. No variation was produced by shifting the ten-ohm coil in its cup. One or two Leclanché cells were used in the various experiments: the coils were in water-baths and the temperatures read by a standardised Kew thermometer. The standard coils used were - Elliott 264 1+·000312 (t − 15·45). Nalder 3715= 1+000260 (t −14.95). The results of the experiments are given in the following table. In the results of the experiments made after January 15 the two values given correspond to the two positions of the coil in the mercury cup. They are included to show the magnitude of the error, which may be due to the resistance of the copper bottoms of the cup. Tables giving Values of Nalder No. 4274, No. 389 in terms of the Ohm Standards of the Association. Thus, the values of the coils at 15°-2 are respectively for while in each case the resistance introduced by placing the contact pieces of the tenth ohm coils at some distance from those of the other coils is ⚫000004 ohm 1894. K APPENDIX IV. Comparison of certain Ohm-Standards of the Board of Trade. By J. RENNIE. In the accompanying table are given the results of comparisons which were made on May 29 and 30, 1894, at the Cavendish Laboratory, between the three unit coils : : Elliott's No. 261, Elliott's No. 263, belonging to the Electrical Department of the Board of Trade, and the B.A. standards, Flat, F, G, and H. The bridge was of the Carey Foster pattern, constructed for the Department by Nalder Bros. and Co., and the slide wire used was the one marked B, having a value of 000,050,9 ohm per division. A 100-ohm coil, Elliott's No. 291, was placed in parallel with the Board of Trade coil for each comparison, this being effected by a large mercury-in-paraffin bath. Temperatures were measured by a mercury-in-glass thermometer, which had been standardised at Kew. *The chart referred to, for No. 261 and No. 263 coils, is one supplied for these coils by Mr. Glazebrook, and is dated March 1892. The chart referred to in the case of No. 3876 was constructed from comparisons made by Nalder Brothers between it and their 'master coil,' No. 3717. The coils Nos. 263 and 261 were compared on May 29, 1894, before beginning the above-mentioned series of comparisons. They were found exactly equal, when the temperatures were-No. 263, 12°-65 C.; No. 261, 12° 62 C. The chart values at these temperatures are-No. 263, 0·999175; No. 261, 0.999156; showing a difference of 19 x 10-6 ohms. The corresponding differences deduced from the above table are-from Flat, 18 x 10-6 ohms; from F, 8 × 10-6 ohms; from G, 9 × 10-6 ohms. The comparison No. 261—H is omitted, as the difference obtained was obviously much too large, and must have been caused by some undetected interference. It is evident from the eleven results given in the table that the difference between the coils Nos. 263 and 261 as deduced from comparison with H must be something like 10 x 10 ohms. [Note added October 5, 1894.] APPENDIX V. Table showing Values of five Standard Coils B.A. Units belonging to the Indian Government as compared with Dr. Muirhead's Standard at his Laboratory. By E. O. WALKER, C.I.E., M.I.E.E., Late Superintendent in the Government Telegraph Department in India. Standard used, No. 78, marked right at 15°-7 C., taken as correct. This standard, tested April 27, 1893, against a No. 68 Glazebrook, gave a coil ratio of 1.00015 at 16° C., and 1·00018 at 15°4 C standard Apparatus used, one metre bridge of platinum-iridium wire with a supplementary coil at each end of 20,012 millimetres. Suspended coil galvanometer, resistance 15 ohms (Muirhead and Co.'s). Trough, 45 × 7×5 inches; depth of water 23 inches; quantity of water, 6 gallons; battery used, 1 Hellesen's Dry Cell, No. 3; E.M.F., 1·4 volt. The interest attaching to these tests lies especially in the fact that the standard coils have been exposed to the climate of Calcutta for twentyfour years. They were made, I understand, by Dr. A. Muirhead when in Dr. Matthiessen's laboratory, under the supervision of the latter. In reducing the observations from 2002 to the temperatures given, it has been assumed that all the coils have the same temperature coefficient. APPENDIX VI. On the Specific Resistance of Copper and of Silver. As lately several observers have published the results of measurements made on the specific resistance of copper, it may be worth while to collect these results together in tabular form. The resistances of metals may be expressed in terms of equal weight or of equal volume; that is, as the resistance of a wire of the given material such that one metre of it weighs one gramme, or as the resistance between opposite faces of a cube of the material each face of which is one square centimetre. I have pointed out that Matthiessen 1 considered the first as the most satisfactory mode of expressing resistances, and for these results alone did he make all the actual experiments; the results for specific resistances were calculated from these with the help of specific gravity values obtained in many cases from tables, and not determined directly for the wires used. 1 B.A. Report, 1890, p. 129. Only in cases where considerable masses of the material are used can the specific gravity, and from this the cross-section of the wires, be accurately determined. There is, therefore, an evident advantage in expressing results in terms of weight, as then the determination of the cross-section of the wires becomes unnecessary, and there is no reason why an accuracy of one in two or three thousand should not be attained. Again, it is found that different samples of copper have different densities, according to the method by which they have been prepared; in a table which I published on a previous occasion the variation is from 3-86 to 8.95. Mr. Swan2 gives a value as high as 8.9587. From samples of copper of the same quality I have had wires drawn which differed in density; it was always found that the denser the copper the less is its resistance, and the difference affects much more the results expressed as specific resistances than when expressed as the resistance for a gramme per metre. This is another reason for expressing the results in these terms, at least as well as specific resistances, and for actual practical purposes it is a question of weight rather than volume. In the following tables the results are given for a temperature of 18° C. in C.G.S. units : From Table A it will be seen that Messrs. Swan and Rhodin obtained a value rather lower than that which I got for copper, prepared by myself, and which, expressed as the resistance of a wire one metre long weighing one gramme, is identical with the value that Matthiessen obtained; but the resistance of all these specimens is distinctly greater than that of the copper kindly sent me by Messrs. Bolton-which seems to bear out the B.A. Report, 1890, p. 125. Nature, vol. 1. p. 165. • Phil. Mag, vol. xxxvi. p. 287. |