of adjedted Equations. 467 
I11. this manner it will be readily found, that the fum of the log. 
tangent and half the log. fecant of 28° 37' is lefs than that 
difference by 20.12, and that the fum of the log. tangent and 
half the log., fecant of 28° 38' is greater than it by 1337: 
therefore 3349 (2012 + 13.37) : 6o v :: 2012 : 0,6". The exact 
arc, therefore, of which the fum of the log. tangent and half 
the log. fecant is equal to 19.7653631 is 28° 36", and the 
log. fecant of it is 10.0566242, which being increafed by 
0.8494850, the log. of s / 50 gives 0,90610.92, which, is the 
logarithm of 8.055810, the value of x fought, and which, is 
true to feven places of figures. , 
EX A M P L E 11. 
To find the value of x in an equation of the form 
xl — r z x = —a . . 
If r be expounded by 3, and a by 10, as they are in the 
example, given at p. 433. .of the Phil. Tranf. vol. LXX. the 
equation will be x 3 ~^x=z —10, and may be transformed to 
\/a; x .v/9 - T = \/io ; . and, therefore, by tab. I. the. fquare 
root of the fine into the cofine of an arc, of which the radius 
is 3, is equal to the fquare root of 10. . Confeq.uently, an arc 
muff be found, fuch that the fum of the log. cofine and half 
the log. tangent is equal to half the log. of 10. But becaufe 
the radius of this arc muff be 3, the leg. fines and cofines muff 
be increafed by the log. of 3 ; and, therefore, log. cof. -flog, of 3 
+.1 log. fine -f f log. of 3 muff be equal to half the log. of 10 ; 
or, an arc muff be found of which, the fum of the tabular.log* , 
cofine and half the log. fine is equal to the difference between 
half the log. of 10 and if the log. of 3. Hence, having fub- 
traded if log. of 3 from, half the log. of. 10, run the eye 
2. 
