of Edinburgh, Session 1885 - 86 . 
785 
Tables requisite tberefor and, generally, for his recalculation of 
Logarithms both of Numbers and of Trigonometrical Ratios, after 
the following statement by the Hon. Lord Maclaren : — 
The Society is aware that, by the terms of its foundation, the 
Makdougall-Brisbane Prize may he awarded either for contributions 
to the Society’s publications, or for services rendered to science 
outside the work of the Royal Society. 
In awarding this prize to Dr Edward Sang, both requisites are 
fulfilled ; because we make this award in recognition of the valuable, 
original, and responsible work on which Dr Sang has been engaged 
for many years, and which has been from time to time communi- 
cated to the Society, I mean the recalculation of the logarithms of 
numbers and of trigonometrical ratios. The latest of Dr Sang’s con- 
tributions on this subject is the paper read in 1884, entitled “On 
the Need for Decimal Subdivisions in Astronomy and Navigation, 
and on Tables requisite therefor.” 
More than fifty years have elapsed since Dr Sang began to take a 
part in the work of mathematical and physical investigation; and 
from the year 1857 to the present time he has been a constant 
contributor to the Transactions and Proceedings of the Royal Society 
of Edinburgh. His papers cover a wide range of inquiry, embracing 
various branches of pure mathematics, mechanics, and optics, as well 
as the application of these sciences to practical astronomy, chrono- 
metry, and naval architecture. I must, however, in this brief notice 
of the work of Dr Sang, confine myself to the subject immediately 
in hand. 
I begin with one fact, which I state on the authority of the 
Encyclopaedia Britannica, and which I think demonstrates the utility 
and value of the investigations for which this prize is awarded. It 
is this, that until Dr Sang undertook the labour of independent 
computation of the logarithmic tables, all the published tables, 
English and foreign, were derived from one and the same source, 
viz., from the tables which were compiled more than two centuries 
ago, partly by Briggs, and partly by the Dutch mathematician 
Ylacq. If Dr Sang had done nothing more than verify their results 
by independent computation, he would have rendered a valuable 
service to mathematical science. But Ylacq’s tables of the logarithms 
3 F 
VOL. XIII. 
