172 REPORT— 1873. 



and their logarithms, which are likely to be wanted in connexion with tho 

 tables, will be added. K and K' (complete elliptic integrals) were, as is well 

 known, tabulated by Legendre, and published by him in 1826. 



For the performance of the calculation of and G3 (63 being deduced from 

 9) 8500 forms were printed and bound up into 15 books (550 in each, with a 

 few over). Each book, therefore, contains forms for the calculation of six 

 nineties, viz. from ^•=sin a° (say), x = 0°, to ^ = sin (a°+5°), x = 90°. Similar 

 forms for the calculation of 0^ and 0^ were priated and bound up into 15 

 other books. 



The work has been in active progress since the beginning of October 1872 ; 

 and eight computers have been engaged from that time to the present, under 

 the superintendence of Mr. James Glaisher, F.R.S., aud the Reporter. About 

 three quarters of the work is now performed — having been calculated com- 

 pletely, and its accuracy verified by differences, and 03 being nearly finished 

 also, while very considerable progress has been made with 0^ and 0. . 



It is intended that the tables, which wiU be completed, it is hoped, by 

 February 1874, shall form a separate work, and that they shaU be preceded 

 by an introduction, in which aU the members of the Committee wiU take part, 

 — an account of the application of the functions in mathematics generally 

 being undertaken by Professor Cayley, of their application in the theory of 

 numbers by Professor H. J. S. Smith, and of their use in physics by Sir W. 

 Thomson and Professor Stokes, while the account of the method of calcula- 

 tion &c. will be written by the Reporter. 



The magnitude of the numerical work performed has not often been ex- 

 ceeded since the original calculation of logarithms by Briggs and Vlacq, 

 1617-1628 ; and it is believed that the value of the tables wUl be great. 



After the circular and logarithmic functions there are no transcendants 

 more widely used in analysis than the Elliptic Functions ; and the tables will 

 not only render the subjects in which they occur more complete, but wiU also, 

 to a great extent, render available for practical purposes a vast and fertile 

 region of analysis. Apart from their interest and utility in a mathematical 

 point of view, one of the most valuable uses of numerical tables is that they 

 connect mathematics and physics, and enable the extension of the former to 

 bear fruit practically in aiding the advance of the latter. 



Art. 17. Note on the Centesimal Division of the Degree. — In the note 

 on p. 64 we have expressed an opinion that Briggs and his followers, by 

 dividing centesimally the old nonagesimal degree, showed a truer appreciation 

 of how far improvement was practicable, or indeed desirable, than did the 

 French mathematicians who divided the quadrant centesimally. On reading 

 Stevinus's ' La Disme,' the celebrated tract in which the invention of decimal 

 fractions was first announced, we found that the centesimal division of the 

 degree was there suggested. The following extract from ' La Disme ' is 

 taken from pp. 156 and 157 of ' La Pratique d'Arithmetique de Simon Stevin 

 de Bruges ' (Leyden, 1585), near the end of which ' La Disme ' appears in 

 French. The first publication of the tract, as far as we can find, was in 

 Dutch, under the title " De Thiende .... Beschreven door Simon Stevin van 

 Brugghe " (Leyden, 1585). 



" Article V. Des Computations Astronomiques. — Aians les anciens Astro- 

 nomes parti le circle en 360 degrez, ils voioient que les computations Astro- 

 nomiques d'iceUes, auec leurs partitions, estoient trop labourieuses, pourtant 

 ils ont parti chasque degre en certaines parties, & les mesmes autrefois en 

 autant, &c., a fin de pouuoir par ainsi tousiours operer par uombres entiers, en 

 choissisans la soixantiesme progression, parce que 60 est nombre mesurable 



