ON CALCULATION OF MATHEMATICAL TABLES. 273 



A noteworthy remark was made by the driver of Comrie's one bus, who remembered 

 several earthquakes. According to him the most noticeable feature of these earth- 

 quakes is the sound, which, once heard, cannot be mistaken. It definitely travels, 

 at Comrie, from N. or N.W. to E. or S.E. Once he heard an indubitable earthquake 

 sound and could feel no tremor at aU, but two horses he was tending started violently 

 and stopped dead, showing that they felt a tremor. ' They would not have stopped 

 for a noise.' 



Finally, I could find no knowledge of any records, which I thought might possibly 

 have been preserved. 



Calculation of Mathematical Tables,— Report of Committee (Prof. 

 J. W. Nicholson, Chairman ; Dr. J. R. Airey, Secretary ; Dr. D. 

 Weinch-Nicholson, Mr. T. W. Chaundy, Dr. A. T. Doodson, 

 Prof. L. N. G. FiLON, Dr. R. A. Fisher, Profs. E. W. Hobson, 

 Alfred Lodge, A. E. H. Love, and H. M. Macdonald). 



The following tables referred to in the last Report have been completed : — 



(a) Tables of Fresnel's Integrals. S(x) and C{x) to six places of decimals for the 



range of values of x from 0-1 to 20'0 by 0-1 intervals. 



(6) Tables of the Confluent Hypergeometric function M(a, y, x) for some thirty 



values of the argument x from 0-1 to 8-0, the parameter a ranging from 4-4-0 to — 4-0 



and Y having the four values + \ and + |. 



(c) Tables of sinh x and cosh x to fifteen places of decimals, similar to those of 

 sin X and cos x given in previous Reports of the Committee, x from 0-1 to 10-0 by O'l 

 intervals. 



(d) Corrections of Logarithmic and Bessel Function Tables : the corrections of 

 Thoman's and Degen's Tables of Logarithms were communicated by M. F. J. Duarte, 

 Geneva. 



The publication of the tables of zeros of Lommel-Weber and Neumann functions 

 is deferred. 



For next year's Report it is hoped to submit further tables of the Confluent Hyper- 

 geometric and other functions. 



Fresnel's Integrals, S(x) and C(x). 



For small values of the argument x, from 0-1 to 1-5, S(a;) and C{x) were computed 

 from the ascending series, viz. : — 





15.7 



. + 



x" ^ 



13.6! 



From the tables of Bessel Functions of half odd integral order given to twelve places 

 of decimals in the 1925 Report, S(a;) and C(a;) were found for integer values of x from 

 1 to 20 by the relations 



S(a;)= J3(«)+ J,(a;)+JT,{rr)+J,,(a;)-f .... 



C(x) = Ji(a!)+J,(x)-fJ (a;)+J,,(x) -f . . . . 

 355-5 



1926 T 



