2 . HEPORT— 1873. 



appointment of the Committee, certain tables of hyperbolic antilogarithms or 

 exponentials (viz. e^ and e~^) and of hyperbolic sines and cosines had been 

 commenced by Mr. J. W. L. Glaisher ; and these the Committee determined 

 to print and stereotype on their completion. They are now in the press. 

 A mass of ealcnlations has been made for the tabulation of Eessel's functions, 

 for real and imaginary values ; and it is intended to complete these tables, and 

 then to undertake calculations connected with the Elliptic Functions. 



As yet no tables have been reprinted by the Committee ; and it clearly 

 would not be possible to decide which most reqiiired reproduction, uutil the 

 Report was considerably advanced beyond its present stage. 



All the tables printed by the Committee, whether calculated or reprinted, 

 are to be stereotyped ; and it is intended that they shall ultimately form a 

 volume ; but the tables relating to each function will be published and circu- 

 lated separately as calculated, the stereotype-plates remaining in the posses- 

 sion of the Committee for future use. 



The first object of the Committee was rendered necessary by the fact that 

 the mathematical tables that have been formed, are scattered all over the 

 world in the various mathematical and scientific journals, transactions of 

 societies, &c., so that it is extremely difficult to ascertain what tables have 

 been already calculated in any particular branch of science. Another reason is 

 that tables formed for some particular purpose, and published under a title of 

 special application, are often of equal importance in other investigations ; so 

 that great inconvenience is sometimes felt for the want of a table which 

 already exists under another name and having reference to a different subject ; 

 or it may even be recalculated. The difficulty of knowing exactly the work 

 already done in any subject is one which is common to all parts of science ; 

 but the inconvenience resulting from the nature of a work being obscured by 

 its name is to a great extent peculiar to this subject, or at all events is more 

 painfully felt in connexion with it. A familiar instance of a function occurring 



in several distinct subjects is the integral le-^V.r, which is of importance 





in the determination of the probable error in the method of Least Squares, 

 Astronomical Refractions, and the theory of Heat; and good instances of 

 the manner in which the nature of a table can be obscured by its name are 

 afforded by nautical collections, where under such headings as " Table to 

 find the latitude by double altitudes of the sun and the elapsed time," or 

 " Table of logarithmic risings," &c., are given log cosecants, log versed sines, 

 (Src. A catalogue, therefore, in which the tables were carefully described 

 from their contents seemed very desirable ; and this the Committee hope to be 

 able to accomplish by their Reports. 



It is intended to include all numerical tables that can be regarded as 

 belonging to mathematical science, or which are of interest in connexion 

 therewith ; but none will be noticed in which the tabular results or data are 

 derived from observation or experiment, or merely concern special subjects 

 that arc not generally classed under the head of mathematics. Thus the 

 great majority of astronomical tables, including catalogues of stars, tables of 

 refraction, tables depending on the figure of the earth, &c., will be ex- 

 cluded, as the data for the formation of such tables are derived from observa- 

 tion. ^ The same remark applies to all chemical tables, tables of specific gravity, 

 of weights and measures, for the determination of the longitude at sea, mortality 

 tables, &c. Life-assurance and annuity tables, and all commercial tables 

 will also be excluded. With regard to these last, however, although all tables 

 such as ready reckoners and common interest tables will in general be omitted, 



