40 REPoiiT — 1873. 



(multiples of primes); T. YI. (to 102,000); Baelow, 1814, T. Y. (to 

 100,103) ; Hulsse's Yega, 1840, T. Y. (102,000 to 400,313); Minsingeh, 

 1845 [T. II.] (to 1000) ; Btene, 1849 [T. I.] (to 5000) ; Wackeebaeth, 

 1867 (to 1063) ; Paekhuest, 1871, T. XXIII. (to 12,239). 



Art. 9. Sexagesimal and Sexcentenary Tables. 

 Originally all calculations ■were sexagesimal ; and the relics of the sj'stem 

 still exist in the division of the degree into 60 minutes, and the minute into 

 60 seconds. To facilitate interpolation, therefore, in trigonometrical and 

 other tables, several large sexagesimal tables have been constructed, which 

 are described or referred to below. They are, we believe, scarcely used at 

 all now, for several reasons — first, on account of the somewhat cumbrous size 

 of the complete tables, and secondly because for most purposes logistic 

 logarithms (see § 3, art. 18) are found more expeditious and convenient. A 

 third reason is that both Eernotjlli's and Taylor's tables were published by 

 the Commissioners of Longitude, and, like the other publications of the Board, 

 were advertised so little that their existence never became generally known. 



Bernoulli, 1779. A sexcentenary table to 600 seconds, to every second, 

 giving at once the fourth term of any proportion of which the first term is 

 •600" and each of the other two are less than 600". The table is, of course, of 



double entry ; it may perhaps be best described as giving the value of -^~, 



correct to tenths of a second, x and y each containing numbers of seconds 

 less than 600", .r being expressed in seconds alone, and y in minutes and 

 seconds (though the latter can be turned into seconds at sight, as the number 

 of seconds in the necessary integer number of minutes is given at the top of 

 each page). The .r's run down the left-hand column, and the y's along the top 

 line ; and the arrangement is thus : — The portion of .rfroni 1" to 60" and the 

 whole range of y is given ; this occupies 30 pp. ; then the portion for x from 

 60" to 120", and for y from 60" to 600"; and so on. The chief use of the 

 table consists in the fact that in astronomical tables the difi'erences are 

 usually given for every 10', so that the interpolation gives rise to a proportion 

 of the kind described above : in some cases the use of the table would be 

 preferable to that of logistic logarithms. 



Taylor, 1780 [T. I.] (pp. 240). The table exhibits at sight the fourth 

 term of any proportion where the first term is 60 minutes, the second any 

 number of minutes less than 60, and the third any number of minutes and 

 seconds xmder 60 minutes. If the second term consists of minutes and seconds, 

 the table must be entered twice (once for the minutes and once for the seconds). 

 The table can of course also be put to other uses. 



There is also added a table of the equation of second difference, giving the 

 correction to be applied on this account in certain cases. 



[T. II.] (pp. 250, 251). Giving the thirds answering to the decimals in 

 every column of [T. I.] where the result is expressed in minutes, seconds, and 

 decimals of a second. 



[T. III.] (pp. 263-312). A millesimal table of proportional parts adapted to 

 sexagesimal proportions, giving the result of any proportion in which the first 

 term is 60 minutes, the second term any number under 60 miimtes, and the 

 third term any absolute number under 1000. It is in fact the same as the 

 sexagesimal table [T. I.], only that the third term is expressed in seconds, 

 and is given only to 1000 (16' 40"), and the result is also expressed in 

 seconds (in [T. I.] the third terms are given both in minutes and seconds) and 



