ON CALCULATION OF MATHEMATICAL TABLES. 251 



For the performance of the calculation of and 6^ (6, being deduced 

 from 0) 8,500 forms were printed and bound up into 15 books (550 in each, with 

 a few over). Each book, therefore, contains forms for the calculation of six 

 nineties, viz. from /i;=sin a° (say), x=0°, to A;=sin (a°-f 5°), a;=90°. Similar 

 forms for the calculation of 0i and 02 were printed and bound up into 15 other 

 books. 



The work has been in active progress since the beginning of October 1872, 

 and eight computers have been engaged from that time to the present, under 

 the superintendence of Mr. James Glaisher, F.R.S., and the Reporter. 



It is intended that the tables, which will be completed, it is hoped, by February 

 1874, shall form a separate work, and that they shall be preceded by an intro- 

 duction, in which all the members of the Committee will take part — an account 

 of the application of the functions in mathematics generally being undertaken 

 by Professor Cayley, of their application in the theory of numbers by Professor 

 H. J. S. Smith, and of their use in physics by Sir W. Thomson and Professor 

 Stokes, while the account of the method of calculation, &c., will be written by 

 the Reporter. 



The magnitude of the numerical work performed has not often been exceeded 

 since the original calculation of logarithms by Briggs and Vlacq, 1617-1628 ; 

 and it is believed that the value of the tables will be great. 



After the circular and logarithmic functions there are no transcendants more 

 widely used in analysis than the Elliptic Functions ; and the tables will not 

 only render the subjects in which they occur more complete, but will also, to a 

 great extent, render available for practical purposes a vast and fertile region of 

 analysis. Apart from their interest and utility in a mathematical point of view, 

 one of the most valuable uses of numerical tables is that they connect mathematics 

 and physics, and enable the extension of the former to bear fruit practically in 

 aiding the advance of the latter.' 



The only subsequent references to these tables are to be found in the Reports 

 of the Association in the Recommendations of the General Committee, in which 

 sums totalling £809 were granted, of which apparently £259 was for computing and 

 £550 for printing, and in the Treasurer's Reports, from which it appears that the 

 grants were actually drawn. The tables were never published ; the reason for this 

 was never made public, although verbal statements have been handed down to the 

 efiEect that the tables contained systematic errors. 



The fact that the grants for printing were actually drawn may be taken as proof 

 that the tables were set in type. Contemporary confirmation is afforded by a review 

 of Cayley's Elementary Treatise on Elliptic Functions, by C. W. Merrifield in Nature, 

 Vol. XV, p. 252 (Jan. 18, 1877). ' The arithmetical work is quite rightly omitted. 

 That will find a much better place in the hand-book or introduction which will 

 doubtless accompany or follow the great tables of elliptic functions now being printed 

 for the British Association.' 



The existence of the manuscript volumes was brought to the notice of the Com- 

 mittee by Prof. G. N. Watson after the death of Dr. J. W. L. Glaisher in December, 

 1928. An appfication to the Trustees of Dr. Glaisher's estate resulted in the 30 

 volumes being handed to the Committee. 



The tables have been examined by Drs. R. A. Fisher and J. R. Airey. It appears 

 that no systematic error can be detected, although owing to the method of com- 

 putation the 10th decimal is subject to somewhat large errors. The tables could 

 be used for the publication of an 8-figure table, and the Committee sets the publication 

 of such a table in the forefront of its future programme. 



Cunningham Bequest. — -By the will of Lieut. -Col. A. J. C. Cunningham, R.E., who 

 died on February 8, 1928, one-twelfth of the residue of his estate was left to the 

 British Association, Mathematical Subsection, ' for preparing new mathematical 

 tables in the theory of numbers.' The amount of the bequest is about £3,000. 



The Committee is faced with a question of considerable difficulty in interpreting 

 the terms of the bequest. In order that their future recommendations as to publica- 

 tion of tables may be framed in the most suitable form it is highly desirable that they 

 should have a plain and explicit ruling from an independent authority on the inter- 

 pretation of the phrase ' new mathematical tables in the theory of numbers,' in its 

 relation to its context in the will. Great diversity of opinions is evidently possible as 

 to the connotation of an}' term denoting a branch of mathematics, the conventional 



