238 REPORTS ON THE STATE OF SCIENCE, ETC. 
Cunningham Bequest—(a) The first volume printed under this Bequest, 
namely the Committee’s Volume III, containing Prof. L. E. Dickson’s 
Minimum Decompositions into Fifth Powers, was published in September 1933. 
(b) Volume IV, prepared by Dr. E. L. Ince and entitled Cycles of Reduced 
Ideals in Quadratic Fields, was published in August. 
(c) Volume V, containing the prime factors of all numbers from 1 to 
100,000, is now in the press, and should be available before the end of 1934. 
Since the publication of the last Report, it was learned that Prof. J. 
Peters, of Berlin, had completed in 1930 the manuscript of a table similar 
in all respects to the table that the Committee had undertaken. Prof. 
Peters: kindly offered to place his manuscript at the disposal of the 
Committee ; this offer was gratefully accepted. The table has thus been 
computed in triplicate. 
(d) The 6-register National machine was delivered in August 1933, and 
has proved to be the most powerful aid to table-making yet known. 
(e) The Brunsviga-Dupla, purchased in 1930, has been exchanged for a 
Brunsviga 20, of capacity 12 x II x 20. 
Bessel functions —The publication of these tables, in two volumes, is now 
assured. A grant of £50 was made by the Royal Society, and a. sum of {100 
was voted by the Council. Arrangements have been made with the 
Cambridge University Press for the subsidised publication of Volume VI, 
containing the four principal functions of order o and 1, namely 
(1) F(x) and F,(x) to 10 decimals for 
x = 0-000(0-001)16-000(0-01)25-00. 
(2) Y,(x) and Y,(x) to 8 decimals for x = 0-00(0-01)25-00. 
(3) My, No, My and N, to 8 decimals for 
x = 25-00(0-1)50-0(1)100(10)1000 
for use with the equations 
Fo(x) = My sin x + Ny cos x 
F(x) = N, sin x — VM, cos x 
Y,(x) = No sin x — M) cos x 
Y,(x) = —M, sin x — N, cos x 
(4) p(x) and I,(x) to 8 decimals for x = 0-000(0-001)5-000. 
(5) K,(x) and K,(x) to 8 decimals for x = 0-.00(0-01)5-00. 
(6) e*I,(x), e-*I,(x), e*Ko(x) and e*K,(x) to 8 decimals for 
Xx = 5-00(0-01)10-00(0-1)20-0. 
(7) Auxiliary functions for the interpolation of Y,(x), Yi(x), Ko(x) and 
K,(x) when «x is small, i.e. less than 0-50. 
The copy for this volume, which will contain about 300 pages, is practi- 
cally complete, and composition will be put in hand shortly. 
The second volume, for which much calculation remains to be done, will 
contain functions of fractional order and of order higher than 1, zeros of 
various functions, the Airy integral, the Kelvin functions ber, bei, ker, kei, 
and other allied functions. 
The issue of Nature for 1934 March 17 contained a historical account of 
the Committee’s activity since 1888 in the calculation of Bessel functions, 
and of the financial difficulties that have impeded publication. The 
article, after referring to the possibility of the Committee’s work merely 
resting in manuscript in a fire-proof safe, concludes ‘It ought to be sufficient, 
by directing attention to this possibility, to ensure that funds will be pro- 
vided to . . . make available the result of so many years of voluntary work 
on behalf of mathematical students and others.’ 
