ON CALCULATION OF MATHEMAIICAL TABLES. 305 



Calculation of Mathematical Tables. — Report of Committee 

 (Prof. J. W. Nicholson, Chairman; Dr. J. R. Airey, Secretary; 

 Dr. D. Wrinch-Nicholson, Mr. T. W. Chaundy, Dr. A. T. Doodson, 

 Prof. L. N. G. FiLON, Drs. R. A. Fishkr and J. Henderson ; 

 Profs. E. W. HoBSON, Alfred Lodge, A. E. H. Love and 

 H. M. Macdonald). 



During the past year most of the tables referred to in the Report for the Leeds meeting 

 have been completed and now appear in the present Report ; tables of the Zonal 



Harmonics P„ (cos 6) and 'i-^ '- to ten places of decimals for various values of n 



00 



and will be ready for publication next year. Professor A. Lodge has computed 

 tables of P„ (cos 6) to seven places of decimals for = 0° to 90° by 5° intervals and 

 n=0 to 20. {Phil. Trans. 203, A. 1904.) 



Tables of functions are set out in this Report as follows : 



(a) Sines and cosines of angles in circular measure to fifteen places of decimals for 

 0=20-0 to 40-0 radians by 0-2 intervals. 



(6) Hyperbolic sines and cosines, sinh nx and cosh nx, for a;=0'00 to 4-00 by 

 O'Ol intervals to fifteen places. 



(c) Sine and Cosine integrals. Si {x) and Ci (x) x ranging from 20-0 to 40-0 by 0-2 

 intervals to ten places. 



(<i) Bessel Function Derivatives -g- . Jv (x) where v=+f ■ +3,a;fromO-0 to 20-0 



ov 



by 0"1 intervals to six places. 



|-co _^<2 



(e) Probability Integral I e . dt and other functions of higher order derived by 

 Jz 

 repeated integration, for both positive and negative values of the argument, x from 

 0-0 to +7-0 and various values of the order, to ten places. Dr. Fisher has called 

 attention to the importance of these functions and also suggested the desirability of 

 mcluding tables in the Report of the Committee. 



For next year's Report, in addition to the tables of Zonal Harmonics of high 

 order with the first derivatives, it is proposed to publish further tables of the 

 Confluent Hypergeometric function M (a . y . a;), Bessel functions of fractional order, 

 extended tables of the Bessel functions Vr (z) and Vm (x) and their first ten zeros 

 [Report, 1916, pp. 52, 57, 62 ; Table VII computed by Mr. H. G. Savidge], and 

 Elliptic functions with both real and imaginary arguments. Professor A. Lodge 

 has computed tables of the series 



^ " 7r+ij"^V2~7r+2J"^V3~n+"3/ + • ■ • ■ 



and has kindly offered these to the Committee for publication. The entries are to 

 seven places for n=0 to n. = 50- at intervals of O-I and to ten places, with first and 

 second differences, for w = 50 to n=5l at intervals of 0-01. 



The publication of Mathematical Tables in book form has been under consideration 

 during the past year or two, and some progress has been made in the preparation and 

 arrangement of the tables which have appeared in past Reports of the Committee : 

 tables from other sources may be included, e.g- Meissel's tables of Bessel functions 

 of zero and unit order, Jq (x) and Ji (x), etc. It is recommended that the format of all 

 the tables in the volume should be uniform. As the Committee's activities have 

 extended over a period of more than thirty years, the lack of uniformity in the 

 printing and arrangement of the tables is easily understood. 



Sines and Cosines (0 in radians). 



Tables of these ratios have already appeared in Reports of the Committee, viz. : 

 Sin and Cos 0, from 0-000 to 1-600 by 0-001 intervals with subsidiary tables 

 to ten places, and from 0-0 to 100 by intervals of 0-1 to fifteen places (1916 Report), 

 Sin and Cos 0, from 1 to 100 radians to fifteen places (1923 Report), from 

 100 to 20-0 radians by 0-1 intervals and from 20-0 to 50-0 radians by 0*5 intervals to 

 fifteen places (1924 Report). 



1928 X 



