338 NEW SERIES for the 
nite product, we get from it 
-=( 1! 
log a= G y) 
ad infinitum. 
—<—____ 
2 
I I ; 
carta we cam oa tata 
4 
2 
+1 
I 
= 
a? 
and. the product of any finite number of factors of this expref- 
fion will always be lefs than log a. 
TuEseE formule, which are analogous to that given by Ev- 
LER for an arch of a circle, (fee Art. 33.), are not inelegant, 
confidered as analytical transformations. It does not feem, 
however, that without fome analytical artifice, they can be ap- 
plied with advantage to the actual calculation of logarithms, 
by reafon of the great labour which would be neceflary to ob- 
tain a refult tolerably accurate. 
66. I sHaLt now conclude this Paper, with fome examples 
of the application of the formule to the computation of the 
length of one-fourth the circumference of a circle whofe radius 
is unity, (which is the extreme and the moft unfavourable 
cafe), and to the computation of a logarithm; as alfo of the 
modulus of the common fyftem of logarithms, which is the re- 
ciprocal of NariEr’s logarithm of Io. 
EXAMPLE 
