ON CALCULATION OF MATHEMATICAL TABLES. 259 
Calculation of Mathematical Tables.— Report of Committee (Prof. 
J. W. Nicuotson, Chairman; Prof. E. H. Neviuue, Acting Chair- 
man; Prof. A. Loner, Vice-Chairman ; Dr. L. J. Comrin, Secretary ; 
Drs. J. R. Atrey, A. T. Doopson, R. A. FisHer, J. HENDERSON, 
J. O. Inwiay, Prof. A. E. H. Love, Dr. E. 8. Pearson, Mr. F. Rozsrns, 
Drs. A. J. THompson and J. F. Tocuer, Mr. T. WHITWELL and Dr. J. 
WISHART). 
General activity—Seven meetings of the Committee have been held in London. 
Dr. R. A. Fisher resigned as General Editor, and Dr. J. Henderson was appointed 
to edit the volume described in detail in the Committee’s last report. Dr. E. 8. 
Pearson and Mr. F'. Robbins were co-opted by the Committee. 
The grant of £65 has been expended as follows :— 
Calculations connected with Emden’s equation . = ae OU 
Clerical and postal expenses ; : ; : : A wheat 
Volume prepared.—The sum of £200 was voted in November 1930 by the Council 
for the printing of this volume, and arrangements were immediately made for its 
publication. Great care has been taken with typographical details in the endeavour 
to set a standard for the printing of tables of this nature. It is hoped that the 
volume Will be published shortly before the Centenary Meeting, and that it will be 
the first of a series. 
Cunningham Bequest.—In October 1930 the Royal Society was asked by the 
Secretary of the Association to give a ruling for the guidance of the Committee on 
the terms of this bequest. The reply was, in effect, that (a) it would be very difficult 
to state in general terms what tables could be regarded as coming within the terms 
of the bequest, but not difficult to give a ruling in the case of any particular table 
suggested, and (b) the proposed tables of elliptic, Bessel and confluent hypergeometric 
functions were not regarded as falling within the terms of the bequest. 
The Committee has been in touch with various authorities on the theory of 
numbers, in an endeavour to establish a suitable programme of tabulation. Final 
suggestions are not yet available. 
Calculating machines—Two machines, a Brunsviga-Dupla and a Nova- 
Brunsviga IVa, have been purchased from the funds of the Cunningham Bequest. 
These machines are of general utility, and will be used in whatever programme is 
ultimately undertaken with the Cunningham Bequest. Meanwhile they have been 
used in research on interpolation formule, and in the solution of Emden’s equation. 
Emden’s equation.—Tables have been prepared of the solutions of this equation 
together with certain auxiliary quantities derived from the fundamental solutions. 
Prof. Sir Arthur Eddington, at whose request these tables were undertaken, has 
arranged with the International Astronomical Union for a grant of £100 for printing 
expenses. It is anticipated that a volume of about 50 pages will be issued before 
the end of this year. A description of the methods employed will be given in the 
preface to the published tables. 
Interpolation formule.—The Committee has devoted considerable attention to the 
question of the best methods of presenting tables so that values of the functions for 
arguments intermediate between those tabulated can be readily obtained, regard 
being had to two conflicting interests, namely the cost of printing and the convenience 
of the user. The standard practice has been the printing of even order differences as 
far as necessary so that these may be used in conjunction with a formula such as 
Everett’s, the coefficients of which have been tabulated. 
The attention of the Committee was drawn to a method proposed by Jordan 
(Metron, Vol. vii, No. 3, 1928, pp. 47-51) which consists of linearinterpolation between 
the tabular values uw) and w, adjacent to the required interpolate, then between 
M1 and wu, w_» and wg, and so on as far as required. If these linear interpolates 
_ are represented by a, b, c, d, e . . . the final interpolate is 
a— G’(b — a) + G*(c — 3b + 2a) — GY'(d — 5c + 9b — 5a) 
+ Gvii(e — 7d + 20c — 286 + 14a) 
