of Edinburgh , Session 1876-77- 
343 
2. On the Construction of the Canon of Sines, for the Decimal 
Division of the Quadrant. Edward Sang, Esq. 
The convenience of having only one system of numeration is 
so well recognised, that there is no need for any discussion. 
Already the numerical nomenclatures of all nations having any 
culture have been converted to one, namely, the decimal system, 
and traces of the ancient use of dozens, scores, fifteens, or sixties, 
can be found in only a very few of them. Although we count our 
hours in sixty minutes, we do not date the present as the year 
thirty-one sixties and seventeen . Yet, in the matters of measure, 
weight, and value, the old and irksome divisions continue to be 
used ; nay, even in those departments of science which most need 
laborious calculation, we continue to employ the ancient scale of 
division. 
It is, indeed, remarkable that, while men of business are striving 
for uniformity in the modes of counting and of measuring, trigo- 
nometers and astronomers should remain unconcerned as to the 
subdivision of arcs and of time. We are rapidly approaching the 
anomalous position of using the decimal division of the earth’s 
quadrant as the source of our standards of weights and measures, 
and of yet rejecting that division in our notation of angles. 
The want of trigonometrical tables suitable to the new division 
is the real cause of this backwardness; the construction of these 
tables is essentially the first step to the universal employment of 
the decimal system. This has been long and well recognised. In 
the end of the last century, Borda computed the decimal canon ; 
this computation was superseded by that which the French G-overn- 
ment caused to be made under the superintendence of Prony ; 
but neither of these has been put to press. The only centesimal 
table available to the trigonometer is that given for each minute 
of the quadrant, in Callet’s “Tables Portatives;” it was collated 
with the manuscripts of Borda and of Prony, but is presented in 
a most inconvenient form. 
The eminent astronomer, Laplace, adopted the decimal divi- 
sion of arcs, of distance and of time, in his “ M6canique Celeste,” 
published in the last year of the century. The force of this illus- 
trious example might long since have gained universal accept- 
2 z 
VOL. IX. 
