dividing astronomical Instruments. 227 
the operation ; then the error in the position of /3 = s, and the 
point b errs 45 in the same direction, and therefore the point 
assumed as the true point of quinquesection, will be at the 
distance of ^-from ( 3 , and the error in the position of this 
point = s x 1^-. 
By the same way of reasoning, the error in the position of 
the point taken between d and £ = e x 2~. 
In trisecting the error of each point — s x if; and in bisect- 
ing, the error = s ; and in quadrisecting, the error of the middle 
point = 2 6. 
It appears therefore that in trisecting, the greatest error 
we are liable to does not exceed that of bisection in a greater 
proportion than that of 4 to 3 ; but in quinquesecting the error 
of the two middle points is 2j times greater than in bisecting. 
It must be considered, however, that in the method of conti- 
nued bisection, the two opposite points must be found by qua- 
drisection ; and the error of quinquesection exceeds that of 
quadrisection in no greater proportion than that of six to five ; 
so that we may fairly say, that if we begin with quinquesec- 
tion, this method of dividing is not greatly inferior, in point of 
accuracy, to that by continued bisection. 
Second Method. 
This differs from the foregoing, in placing dots or scratches 
in the true points of quinquesection and trisection, before we 
begin to subdivide. For this purpose, we must have a micro- 
scope placed as in page 224, first par. at the same distance from 
the center of motion as the point is ; and this microscope must 
be furnished with a moveable wire and micrometer, as in page 
