NAPIER COMMEMORATIVE LECTURE. a 
These trigonometrical functions were still regarded as 
lines, not ratios. Vlacq took the radius as 10. Owing 
to this, the logarithm. of the sine of 90° is 10, and the 
logarithms of the other sines have the characteristics 9, 8, 
etc. The common explanation of the characteristics, 10, 
9, 8, etc. in the logarithms of the trigonometrical ratios— 
namely, that the number 10 has been added to the logarithm 
of the ratio to make the characteristic positive—is not 
correct. The truth is that the tables of logarithms, which 
we now possess, have been copied, more or less directly, 
from the tables drawn up by Briggs and Vlacq between 
1620 and 1630. The principal change has been that, 
during one period, there has been a fashion for a smaller, 
and, in another period, for a larger number of decimal 
places. Also, of course, such errors in computation as 
had crept into the work of these two pioneers have been 
eliminated. 
Briggs died in 1632. The last years of his life were 
devoted to the calculation of more extensive tables of the 
logarithms of the trigonometrical functions. The work 
of Briggs, like that of Vlacq, has never been superseded. 
The rapidity and industry with which they performed this 
immense piece of computation must always be the admir- 
ation of mathematicians. 
In the accounts of some writers on the History of the 
Discovery of Logarithms—notably in that which Hutton 
prefixed to his mathematical tables—greater credit than 
he could rightly claim has been ascribed to Briggs for the 
improvement in logarithms from the form in which Napier 
first published them. The credit for the change to the 
base 10 must be shared between Napier and Briggs; but, 
as the idea of the change had occurred to Napier as early, 
if not earlier, than to Briggs, those, who would call the 
logarithms to the base 10 “‘Briggsian’’ Logarithms, do 
