52 ON DIVIDING ASTRONOMICAL INSTRUMENTS. 



By the same way of reasoning the errour in the position of 

 the point taken between d and SziX 2f. 



In trisecting the errour of each point zz e X H; and in 

 bisecting the errour zz i ; and in quadrisecting the errour of 

 the middle point zz 'it. 



It appears therefore, that in trisecting, the greatest errour 

 we are liable to does not exceed that of bisection in a greater 

 proportion than that of 4 to 3 ; but in quinquesecting the 

 errour of the two middle points is 2| times greater than in 

 bisecting. It must be considered, however, that in the me- 

 thod of coutinued bisection, the two opposite points must be 

 found by quadrisection ; and the errour 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 be- 

 gin with quinquesection, this method of dividing is not 

 greatly inferior, in point of accuracy, to that by continued 

 bisection. 

 2d method of Second method. This differs from the foregoing, in plac- 

 dividingby j n g dots or scratches in the true points of quinquesection 

 on, and trisection, before we begin to subdivide. For this pur- 



pose, we must have a microscope placed as in page 40, fourth 

 par., at the same distance from the centre of motion as the 

 point is ; and this microscope must be furnished with a 

 movable wire and micrometer, as in page 51 ; and then 

 having first made the fixed wire of this microscope corres- 

 pond exactly with the point, we must draw the scratches b 

 and /3, d and S, &c, as before, and bring the fixed wire to 

 the true point of quinquesection between b and £, in the 

 manner directed in page 226, aud with the point strike the 

 scratch or dot ; and if we please we may, for farther security, 

 as soon as this is done, examine, by means of the movable 

 wire, whether this intermediate scratch or dot is well placed. 

 Advantage of The advantage of this method is, that when this is done, 

 this me»hod. we ma y subdivide and cut the true divisions-, by making the 

 wire of the microscope bisect the intermediate scratches, in- 

 stead of being obliged to use the more troublesome opera- 

 tion of placing it in the proper proportion of distance be- 

 tween the two extremes. 

 Its disadvan- This method certainly requires less attention than the for- 

 tage. merj a nd the whole seems to be attended with considerably 



less 



