ON THE FURTHER TABULATION OP BESSEL, ETC., FUNCTIONS. 67 



Milne's seismograph registered fifty -seven earthquakes during the 

 year under report, besides several small local and other movements. Of 

 these, three were great disturbances — namely, those recorded on 

 November 9 and 13 and December 16. 



The seismograph for recording vertical movements registered twenty- 

 seven disturbances. 



The Japanese (Omori) seismograph recorded forty-five disturbances. 



The Colaba seismographs No. 1 (E.-W.) and No. 2 (N.-S) recorded 

 forty-five and thirty-nine disturbances respectively. 



TJie Further Tabulation of Bessel and other Functions. — Report of the 

 Committee, consisting of Professor M. J. M. Hill {Chairman), 

 Dr. J. W. Nicholson (Secretary), Professor Alfred Lodge, 

 Dr. L. N. G. Filon, and Sir George Greenhill. 



Part I. — Elliptic Functions. 



During the course of the year Sir George Greenhill has brought forward 

 a scheme for the rearrangement of the Elliptic Function Tables on a new 

 basis. 



This scheme would, in the event of its acceptance by the Association, 

 occupy the greater part of the attention of the Committee for some time', 

 and would also involve a grant from the Association towards the ex- 

 pense of computing. 



It seems desirable, therefore, that the report for the present year 

 should be concerned mainly with this question; and a brief outline, 

 with some specimen tables indicating the nature of the proposed work' 

 is accordingly submitted to the Association for its approval or criticism! 



Subjoined is a specimen table for modular angle 0=45° and 0=75°, 

 which may be taken as typical of the proposed work. The notation used 

 is such that, for example, ©(0) is denoted by ©0, and H(K) by HK. 



The argument of the table proceeds by degrees of the quadrant of 

 the quarter period K or F (90°), instead of degrees of <£=am/K, as in 

 Legendre's Table IX. 



The four columns of A, B, C, D give at r°, where r = 90 /, 



u v I ©0 ' A v i ~ HK ' 



B(O = A(90-r) = H ^/) K , 



C( O = D(90-,)=^/lK 



so that the table proceeds from 0° to 45°, and then turns back again 

 upward, as in the ordinary trigonometrical table of a circular functionr 

 The elliptic functions are given then by 



V*'sn/K=> cn/K = 5, dn/K = 



D' ' D' Vk' D' 



instead of the usual form of Jacobi 



F 2 



