98 REPORT— 1896. 
Mathematical Functions—Report of the Committee, consisting of 
Lord RayLEIGH (Chairman), Lord KeEtvin, Professor B. PRICE, 
Mr. J. W. L. GuaisHEeR, Professor A. G. GREENHILL, Professor 
W. M. Hicks, Professor P. A. MacManon, Lieut.-Colonel ALLAN 
CuNNINGHAM, and Professor A. LODGE (Secretary), appointed for 
the purpose of calculating Tables of certain Mathematical Functions, 
and, if necessary, of taking steps to carry out the Calculations, and 
to publish the results in an accessible form. 
Tue first report of the Committee was made in 1889, when they pub- 
lished tables of the Bessel Functions, I(x), for integral values of » fron» 
0 to 11, from ~=0 to 6:0, at intervals of 0:2. The original intention had 
been a calculate jails, of J,(x) for various values a n, but in 1889 
extensive tables of J,(w) and J,(x) were published by Dr. Meissel of Kiel, 
and it was therefore considered advisable to work at tables of I,(z), 
which had not previously been calculated, the two classes of functions 
being connected by the equation— 
ia) 0-7 (rr) 
In 1893 the report of the Committee contained a detailed table of 
T(z) from «=0 to 5100, at intervals of 001, to nine decimal places, of 
which the last figure was approximate. A short table of J o(a/ 2) was 
also given, to nine decimal places, from «=0 to 6-0 at intervals of 0:2. 
The present table of I,() is from «=0 to 5-100, at intervals of -001, 
to nine decimal places, the last figure being approximate, being exactly om 
the lines of the 1893 table of L,(2). 
The Committee desire to recommend that tables of the Bessel Functions 
be published by the Association to six decimal places, with a preface 
giving some of their chief properties. 
The Committee have considered a proposition made at the Ipswich 
meeting last year by Colonel Cunningham, viz. that the British Asso- 
ciation “should be asked to undertake the publication of a ‘New Canom 
Arithmeticus’ which he had already nearly computed. Colonel Cunning- 
ham undertook to prepare one copy at his own expense, and asked that 
the British Association should pay the expense (about 25/.) of preparing 
a second copy and of having the two copies compared and checked ; one 
copy to be Colonel Cunningham’s property, one copy to be the property 
of the Association ; the British Association to be asked also to pay the 
whole cost of printing and publication of the work in. a separate 4to. 
volume (which would be of about same size as Jacobi’s ‘Canon Arith- 
meticus’). Colonel Cunningham would undertake to superintend the 
whole work to completion, and to provide a preface descriptive of the 
tables. 
The Committee propose to recommend the Association ultimately to 
undertake the publication of Colonel Cunningham’s ‘ New Canon Arith- 
meticus’ as proposed by the author. They desire to be reappointed with 
a grant of 25/. for the purpose of preparing a second copy of Colonel 
Cunningham’s table and of comparing and checking the two copies. 
