228 



REPORT 1893. 



plete, together with tables of J„(^)j to six decimal places. It will be 

 noticed that the march of Ii(a;) in the present table is such that interpo- 

 lation by first differences only will give accnrate results to six decimal 

 places. It is proposed to preface the book of tables with a short account 

 of the History, Theory, and Applications of the Bessel Functions, drawn 

 up by Professor A. Gr. Greenhill. 



The Committee are adding to the present Report a short table of 

 3o{x\/i). If desired, a table of J„(.«\/i) from x^O to 6'0 at intervals of 0-2, 

 for integral values of n from to 11, could be published next year. 



The Committee have expended the grant of 15Z., and desire reappoint- 

 ment, with a further grant of 15/. 



The Secretary has some copies of the 1889 Report, and will have some 

 of the present Report, which he will be pleased to forward to anyone wish- 

 ing to make use of the tables before their republication in book form. 

 His address is, Englefield Green, Surrey. 



The Committee wish to point out an error in the 1889 Report. The 

 differential equation of which I„ is one solution has a wrong sign before 

 its third term ; it should be 



x^ --^■\-x-—{x^-\-n^)u=\j. 

 ax^ ax 



The work of calculation has been much hindered by faults in the 

 Edmondson's calculating machine which was bought by the Committee. 

 It has been returned to the maker several times, and has never been 

 entirely satisfactory. Latterly the greater part of the work has been 

 done on Professor McLeod's machine, which he is always kindly ready to 

 lend. 



