ON TABLES OF CERTAIN MATHEMATICAL FUNCTIONS. lib 



Tables of Certain Mathematical Functions:. — Repm-t of the Committee, 

 consisting of Lord Kelvin (Chairman), Lieut.-Colonel Allan 

 Cunningham (Secretary), Professor B. Price, Dr. J. W. L. 

 Glaisher, Professor A. G. Greenhill, Professor W. M. Hicks, 

 Major P. A. Macmahon, and Professor A. Lodge, appointed 

 for calcidating Tables of certain Mathematical Functions, and, if 

 necessary, for tahing steps to carry out the Calculations, and to 

 piddish the residts in an accessible form. 



The new ' Canon Arithmeticus ' is a set of tables showing the solutions 

 of the congruence of 2'' = R (mod. in) for all prime moduli (■m=p) < 1000, 

 and also for all powers of primes as moduli (»n=^j-, p,^ &c.) < 1000. 

 The tables are twofold, one showing the value of R to argument x, the 

 other showing the value of x to argument R. The tables are on the 

 same plan as Jacobi's ' Canon Arithmeticus,' diflfering therefrom only in 

 that the same base 2 is used throughout, whereas Jacobi uses a primitive 

 root of each prime as base ; these primitive roots (e.g. 967) are often very 

 inconvenient for purposes of practical computing. 



The tables are now complete (in MS. 133 foolscap sheets), and ready 

 for printing. All the work has been done by two independent computers : 

 the work of each has been checked witli that of the other ; all discrepancies 

 found have been examined anew and set right. 



Fxperiments for improving the Construction of Practical Standards for 

 Electrical Measurements. — Report of the Committee, consisting of 

 Professor G. Caeey Foster (Chairman), Mr. R. T. Glazebrook 

 (Secretary), Lord Kelvin, Professors W. E. Ayrton, J. Perry, 

 W. G. Adams, and Oliver J. Lodge, Lord Rayleigh, Dr. A. 

 MuiRHEAD, Mr. W. H. Preece, Professors J. D. Everett and A. 

 Schuster, Dr. J. A. Fleming, Professors G. F. FitzGerald 

 and J. J. ThOxMSON, Mr. W. N. Shaw, Dr. J. T. Bottomley, Rev. 

 T. C. FiTZPATRicK, Professor J. Viriamu Jones, Dr. G. John- 

 stone Stoney, Professor S. P. Thompson, Mr. J. Rennie, Mr. E. 

 H. Griffiths, Professor A. W. Rucker, and Professor A. G. 

 Webster. 



AITENDIX rAGB 



I. Comparison of the Standard Coils used by Professors J. Viriamu Jones and 

 W. E. AyHon in tlieir determination of the absolute resistance of Mercury 

 Kith the Standards of the Association. 5y R. T. Glazbbeook, F.R.S. . 147 

 II. On the Determination of the Temperature Coefficients of two \0-ohm 

 Standard Resistance Coils {Nos. 3873 and 3874) used in the 1897 deter- 

 mination of the ohm. By M. Solomon 151 



in. An- Ampere Balance. By Professor W. E. Ayrton and Professor J. V. 



Jones 157 



The work of testing resistance coils has proceeded as usual during the 

 year. 



The following is a list of the coils tested and of the values found in 

 continuance of the list published in the Report for 1896 : — 



1898. L 



