of adjected Equation 467 
In 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 2012, and that the fum of the dog. tangent and 
half the log. fecant of 28° 38' is greater than it by 1337: 
therefore 3349 (2012+1337) : 60" :: 2012 : 56". Theexadt 
arc, therefore, of which the fum of the log. tangent , and half 
the log. fecant is equal to 19.7653631 is 28° 37' 36", and the 
log. fecant of it is 10.0566242, which being increafed by 
0.8494850, the log. of v/50 gives 0.9061092, which is the 
logarithm of 8.055810, the value of x fought, and which is 
true to feven places of - figures. 
E X* A M P L E H. 
To find the value of x in an equation of the form 
X — r 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 -gx — .— 10, and may be transformed to 
x x \/ 9 — v 2 = v/ 10 ; and, therefore, by tab. I. the fquare 
root of the fine into, the cofme of an arc, of which the radius 
is 3, is equal to the fquare root of 10. Coiifequentlyj an ate. 
mufh be found, fuch that the fum of the log, cofine and half 
the log. tangent is equal to half the log. of 10. But beeaufe 
the radius of this arc mud be 3, the log. fines and cofines mult 
be increafed by the log. of 3 ; and, therefore, log. cof. +log. of 3 
+ J log, fine + f log. of 3 muft be equal to half the log. of 10; 
or, an arc muft 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 1 f the log. of 3. Hence, having fub- 
tradted if log. of 3 from half the log. of 10, run the eye 
2 * along* 
