250 



REPORTS ON THE STATE OF SCIENCE, ETC. 



Calculation of Mathematical Tables,— Report of Committee 

 (Prof. J. W. Nicholson, Chairman ; Prof. A. Lodge, Vice-Chairman ; 

 Dr. L. J. CoMRiB, Secretary ; Dr. R. A. Fisher, General Editor ; 

 Drs. J. R. AiREY, A. T. Doodson and J. Henderson, Mr. J. 0. 

 Irwin, Profs. A. E. H. Love and E. H. Neville, Drs. A. J. Thompson 

 and J. F. Tocher, Mr. T. Whitwell and Dr. J. Wishart). 



General Activity. — Nine meetings of the Committee have been held, in London. 

 The resignation by Dr. J. R. Airey of the office of Secretary, which he had held for 

 twelve years, was received with much regret. Dr. D. M. Wrinch, who was unable to 

 attend meetings, has resigned. 



The grant of £30 has been expended as follows : — 



Confluent Hypergeometric functions . . . . . . . . . . £10 



Interpolation of Bessel functions J^ and J^ . . . . . . . . 8 



Preparation of copy for proposed volume . . . . . . . . 5 



Calculation of Hermite functions . . . . . . . . . . . . 4 



Clerical and postal expenses . . . . . . . . . . . . 3 



Volume prepared. — A volume containing the following tabular matter, with even 

 dififerences unless otherwise stated, has now been prepared for the printer. 



Circular functions, without differences : — - Pages 



Sine and cosine 0-0 (0-1) 50-0 to 15 decimals 



0-000 (0-001) 1-600 to 11 decimals 

 I^TiTT to 15 decimals, w=l (1) 100 .. 

 Hyperbolic functions, without differences : — • 



Sinh TTX and cosh Tra; 0-00 (0-01) 4-00 to 15 decimals 



„ „ 0-0000 (0-0001) 00100 to 15 decimals 



Sinh a; and cosh a; 0-0 (0-1) 10-0 to 15 decimals .. 



Sine and cosine integrals : — ■ 



0-0 (0-1) 20-0 (0-2) 40-0 to 10 decimals 



Exponential integral, -15-0 (0-1) 15-0 to 11 decimals . . 

 Integral of logarithmic factorial function 0-00 (0-01) 1-00 to 10 decimals 

 Factorial or IT function, 0-00 (0-01) 1-00 to 12 decimals 

 Derivatives of logarithmic factorial function, i.e. di-, tri- and tetragamma 

 0-00 (0-01) 1-00 and 10-0 (0-1) 60-0, all to 12 decimals 



Integrals of probability integral Hh„ (x), without differences: — 

 x=-1-0 (0-1) vanishing, w=0 (1) 11 j 

 a;=-5-0 (0-1) vanishing, n=12 (1) 15 I to 10 decimals 

 a;=-2-5 (0-1) vanishing, w=16 (1) 21 | 



together with differential coefficients of probability function : — 

 a;=-7-0 (0-1) vanishing, w=l (1) 7, for use to 10 decimals 



Total .. 



5 



16 



1 



4 

 1 

 1 



6 

 3 

 1 

 1 



24 



10 



73 



The accompanying introductory matter for the various tables will bring the 

 volume up to about 100 pages. It has been ascertained that the cost of printing 

 tabular matter will be approximately £2 a page, and that the cost of the volume will 

 be about £200. The Committee desires that provision should be made for publication 

 at an early date. 



Elliptic Function Tables. — The following extract is from the Report of the Com- 

 mittee on Mathematical Tables for the year 1873, written by J. W. L. Glaisher : — 



' The Account of the Tabulation of the Elliptic Functions. — In September 

 1872 it was resolved to undertake the systematic tabulation of the Elliptic 

 Functions (inverse to the Elliptic Integrals), or, more strictly, of the Jacobian 

 Theta Functions which form their numerators and denominators. 



The formulae are : — 



The tables when completed will give 0, Oj, 62, 63, and their logarithms to 

 eight decimals for 



x- 



= 1°, 2°, . . . 90°, jfc=sin 1°, sin 2°, . . . sin 90° 



The tables are thus of double entry, and contain eight tabular results for each 

 of 8,100 arguments, viz. 64,800 tabular results. 



