$ 6 o Mr. Hell i ns’s improved Solution of 
10. An expression of this kind, when c is the only va- 
riable quantity, consisting of several figures, and r and s are 
likewise long numbers, will be much better adapted to the use 
'f) * — ! — £ (? 
of logarithms, when put in this form, — x F - l_ s f ' cc ; 
because the 
multiplications of r and s into cc, or additions of their loga- 
rithms and taking out two numbers, are by this means ex- 
changed for the addition of the constant logarithm of — : the 
quotients ~ and once found, being constant numbers. Thus, 
the numerical value of even S ~ 2C --~ , where r and s are single 
o — ^ C C 
figures, is more easily obtained by ~ x than by the 
former expression. 
11. But it will appear upon trial, that the arithmetical value 
of any three terms p'-\- q'cc -f-r'r 4 , in which p\ q', and r, are 
constant quantities, and cc consists of five or six places of 
figures, may, in general, be more easily obtained by logarithms 
than the arithmetical value of — x '• c ; • And, since the dif- 
S , o Z2 v 0 
ference of the values of these two expressions is inconsiderable 
in the present case, I shall make no further use of the frac- 
tional expression ; but observe, that the logarithm of q'c c, in 
the other expression, being found, the logarithm of re* will be 
had, by adding to it the logarithm of cc ; for q'cc x cc = r'c\ 
And, since the logarithms of the numbers which stand in the 
places of q f and A may be taken out and reserved for use, and 
the logarithms of cc and a, once found, will serve for all the terms 
in which these quantities occur, it will appear by an example, 
that neither many logarithms, nor many numbers correspond- 
