ON THE BIBLIOGRAPHY OF SPECTROSCOPY. 227 



Bibliography of Spect7'oscopy.— Report of the Committee, consisting 

 of Professor H. McLeod (Ghairman), Professor W. C. Roberts- 

 Austen (>S'ecre/!a*^?/), Mr. H. G-. Mad AX, and Dr. D. H. Nagel. 



The collection and verification of titles of papers on spectroscopy have 

 been continaed during the past year, and it is expected that another 

 instalment will be ready for printing at the next meeting. 



Mathematical Functions. — Report of the Committee, consisting 

 of Lord Rayleigh {Chairman), Lord Kelvin, Professor Cayley, 

 Professor B. Price, Mr. J. W. L. GtLAISHER, Professor A. Gr. 

 GrREENHiLL, Professor W. M. Hicks, 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 for m . 



The first Report of the CoQimittee was in 1889 (at Newcastle-on-Tyne), 

 when they published tables of I„(a;) for integral values of n from to 11, 

 from a!=0 to 60, at intervals of 0-2 ; I,j(a;) being defined by 



^"^"^=^"'''^"^'^^=2^{^ + 2(2^ + 24(2. + 2)(2. + 4)+ ' ' -j' 



The present tables of Ii(ie) are from x=0 to S'lOO, at intervals of "001, 

 and are given to nine decimal places, the last figure being approximate. 

 They have been calculated by means of Taylor's Theorem, the successive 

 derived functions being obtained by use of the formula 



and of the formnlte derivable from this by successive differentiations. 

 The values of these derived functions were checked by double cal- 

 culation of the values of Ii(a;) halfway between those given in the 1889 

 table; thus, for exnmple, Ti(2-3) was calculated as Ii(2'2 + 0"1) and also 

 as Ii(2'4 — O'l). This important check confirmed at the same time the 

 values of Ii(,^;) which were given in the 1889 table, so that certainly the 

 tables now given are free from any systematic error. When the present 

 tables were finished, accidental errors were discovered and corrected by 

 taking out first and second differences, and then, finally, the printed tables 

 were checked by continuous addition of the first diiferences on Edmond- 

 son's calculatiuif machine. It is confidently hoped, therefore, that the 

 tables are free from serious error. 



Tables of lo(.f) have also been calculated, and are in a forward state, 

 but are not quite ready for printing this year. 



It is proposed to have the tables republished in book form when com- 



a 2 



