REPORTS 



ON 



THE STATE OE SCIENCE. 



Heport of the Committee, consisting of Professor Cayley, F.R.S., 

 Professor Stokes, F.R.S., Professor Sir W. Thomson, F.R.S., 

 Professor H. J. S. Smith, F.R.S., and J. W. L. Glaisher^ B.A., 

 F.R.A.S. (Reporter), on Mathematical Tables. 



§ 1. General Statement of the Objects of the Committee. 



The purposes for which the Committee was appointed were twofold, viz. 

 (1) to form as complete a catalogue as possible of existing mathematical 

 tables, and (2) to reprint or calculate tables which were necessary for the 

 progress of the mathematical sciences. 



These two objects, although so far connected, that it Avas absolutely 

 essential before any tables were calculated or reprinted to be certain that 

 such tables were not already in existence or easily accessible, were in other 

 respects quite different ; and the Committee have therefore decided to keep 

 them distinct. The reasons in favour of the adoption of this course are ob- 

 viously very strong, as a new table would be out of place in a Report which 

 in other respects was merely a detailed catalogue. A further argument 

 against the publication of the tables in the Reports of the Association, is 

 the great objection to needlessly scattering tables. Tables of a kindred 

 nature collected together, are of far more value than the same could be if 

 dispersed in several volumes of a periodical ; and if the tables of the Com- 

 mittee were published annually as calculated, it would happen not only that 

 they would have to be sought in several volumes, and their utihty in conse- 

 quence considerably impaired, but sometimes even portions of the same table 

 would be separated. The Committee have therefore considered that they 

 would best carry out the second object for which they were appointed, by 

 publishing their tables separately and independently of the Annual Reports 

 of the Association. 



The form cliosen for this publication is a quarto of the same size as that 

 of the Philosophical Transactions, this size being necessary for the uniformity 

 of the tables, as a large page is required in order to contain the values of the 

 function tabulated, together with its first, second, and third differences, which, 

 when given, should range with the former on the same page. Before the 



1873. jj 



