786 Proceedings of the Royal Society 
of numbers were computed only for numbers below 100,000, and to 
fourteen places of decimals. Dr Sang, in the tables first communi- 
cated to this Society in 1872, extended the tables as far as the 
number 200,000, and his logarithms were computed to fifteen places 
of decimals. In his later work, communicated to the Society in 1884, 
the tables are brought down to the number 370,000, and, by adding 
to each of the logarithms already computed the log. of 2 or 3, the 
tables can be completed to 1,110,000. 
In order that his results should be entirely independent of the 
work of previous computers, Dr Sang began by computing the 
logarithms of all the prime numbers from zero to 2000 (and even- 
tually from zero to 10,000) to twenty-eight places of decimals, by 
a method not known in Ylacq’s time, founded on the series for the 
i 1 +x 
expression log. . 
1 — x 
From the logarithms thus obtained, and their multiples and pro- 
ducts, the intermediate quantities were derived (as he explains in his 
paper in the 26th volume of the Transactions , 1872), by means of a 
system of interpolation, which was ascertained to give accurate results 
to the fifteenth figure. 
The recalculation of the tables of logarithms of the trigono- 
metrical functions was performed with equal care, and by strictly 
accurate methods. These were also communicated to this Society 
by papers read in the years 1877 and 1878, and printed in the 
Proceedings. Further tables, adapted to the decimal division of 
the circle, were communicated in 1884. 
Dr Sang’s logarithms of numbers, as is well known, are published 
in the form of seven-place tables. It is to be regretted that the 
fifteen-place tables have not been printed and published. It is 
certainly desirable that such a work should be accessible in a printed 
form in our public libraries. Pending the realisation of this pro- 
ject, it may be hoped that the MS. volumes (which the Fellows had 
an opportunity of seeing two years ago) may in some way be made 
available to science. 
Even more valuable in its immediate results would be the 
publication of the million table carried to seven or eight places of 
decimals. This could be accomplished in two volumes of the 
ordinary size, and ought to be undertaken at the public expense. I 
