270 REPORTS ON THE STATE OF SCIENCE, ETC. 
Cunningham Bequest.—(a) The work on the table of reduced ideals and 
primitive units in real quadratic fields has been continued by Dr. E. L. 
Ince. It is hoped that the manuscript will be ready for the printer by the 
end of this year. 
(b) The printing by a photographic process of Prof. L. E. Dickson’s 
tables of the minimum decompositions of the numbers 1-300,000 into fifth 
powers has been put in hand. ‘This will constitute the Committee’s 
Volume III. 
(c) The Council has authorised the preparation and publication of 
a volume containing all the prime factors of all numbers up to 100,000. 
The calculations are being done voluntarily, in duplicate, one copy 
by Mrs. E. Gifford, and the other by Miss E. J. Ternouth, of Reading 
University, and Prof. A. Lodge. 
(d) The purchase, for table-making, of a National Accounting machine 
(formerly called the Ellis) has been authorised, and the machine is now on 
order. It contains an eleven-column keyboard, printing mechanism, and 
six adding mechanisms. 
Bessel functions—The sub-committee formed to draw up a report on the 
tables of Bessel functions which have appeared in the Reports of the Com- 
mittee, with a view to the possibility of their publication in one volume, has 
now completed the examination of these tables. Interim reports were made 
during the session, and action was taken for the preparation of the Y func- 
tions. ' The full report and recommendations of the sub-committee will be 
considered during the next session. 
The Committee has calculated, at the request of Dr. R. Stoneley, 
47-figure tables of the functions F1(x), F-34(x), F:(~), F-2(~), for the range 
x = 0:00(0:01)0-50(0-02)2-50(0-05)5-0(0-1)20-0. 
The preparation of printer’s copy of ¥9(x) and 7;(x) to 10 decimals for 
% = 0:000(0-001)16-00(0-01)25:00 has been completed, as has also copy of 
8-figure values of J,(x) and I,(x) for x = 0-000(0-001)5-000. 
The preparation of an 8-figure table of Y,(x) and Y,(«) for «= 
0-00(0-01)16:00 has been begun, and will be carried to completion next 
year. 
Airy integral—The Committee has received a request from Dr. H. 
Jeffreys for the tabulation of the Airy integral and its first derivative. It is 
hoped that this may be done next year. 
Confluent hypergeometric functions —The Committee has received a request 
from Dr. R. Stoneley for certain calculations in connection with these 
functions. The work is being put in hand by Dr. A. J. Thompson. 
Publication —The Committee has expressed to the Council its desire for 
the publication of the following material : 
(1) The Legendre functions described in the last report ; 
(2) The Bessel functions of orders +} and +? described in this report ; 
(3) The Bessel functions ¥)(x), 7:(x), Io(x) and I,(«) described in this 
report. 
Reappointment—The Committee desires to be reappointed, with the 
addition of Dr. J. C. P. Miller, and with a grant for general purposes of £100. 
