MATHEMATICAL TABLES 257 



Bessel Functions. — The completion of Volume VI, containing the four 

 principal functions of order o and 1, has been unavoidably delayed. It is 

 expected that it will be published before the end of the year. 



Work on the preparation of a second volume, to contain higher integral 

 orders (up to n — 20), has continued. Values of jf n (x), up to x = 25, 

 and of k„(x), i.e. x"K n (x), up to x — 5, have been completed, under the 

 supervision of Dr. Comrie. Various fundamental values of K„(x) and I n (x) 

 have been computed by Dr. Miller and Dr. Bickley, and further work is 

 being supervised by them, and by Dr. Henderson, Dr. Thompson and 

 Mr. Sadler. 



Airy Integral. — In the Report for 1934 it was stated that the calculation 

 of this integral had been begun, and that the tabular values would be in- 

 cluded in the second volume of Bessel functions. In view of requests for 

 earlier publication, it has been decided to complete the calculations as soon 

 as possible; the Council has authorised the separate issue of these tables. 

 The greater part of the work has been done, by Dr. Miller. 



Elliptic Function Tables. — Several manuscript tables of elliptic functions 

 have been presented to the Committee by the executors of the late R. L. 

 Jones. Dr. Bickley, who examined the tables, reported that they were 

 not suitable for publication by the Committee, as values of the complete 

 elliptic integrals K and E to ten decimals at interval o-ooi in ft 2 are available 

 in tables by Hayashi, while the remaining functions were simple combina- 

 tions of K and E, of rather limited application in electrical standards work. 

 The tables were, therefore, deposited with the National Physical Laboratory, 

 which was already in possession of other allied tables computed by Mr. 

 Jones. 



Sheppard Tables. — A number of tables prepared by Dr. W. F. Sheppard 

 have been handed to the Committee, and have been examined by a sub- 

 committee consisting of Prof. Fisher, Dr. Irwin and Dr. Wishart. The 

 main table is one giving the ratio of tail area to ordinate of the normal 

 (Gaussian) curve up to 10 standard deviations by tenths, to 24 decimals, 

 together with Taylor series coefficients up to the sixteenth, for interpolation. 

 It is proposed to publish this and some other allied and derived tables. 



Legendre Functions. — In the Report for 1932 tables of the Legendre 

 functions that had been prepared were described. These consist of 

 7-figure values of P, t (x) and their differences up to n = 9 for x = 

 o-oo(o-oi)i-oo, up to n = 12 for x = i-oo(o-oi)6oo and up to w = 6 

 for x = 6-o(o- 1)1 1 -o. Authority for the separate publication of these 

 tables is being sought. 



Reappointment. — The Committee desires reappointment, with a grant 

 of £200, with which it is hoped to complete the calculations for the next 

 volume of Bessel functions. 



K 2 



