568 



This inconsi- 

 derable com- 

 pared with 

 those incident 

 to dividing, 



METHOD OF EXAMINING ASTRONOMICAL INSTRUMENTS. 



of tiiearc, it is evident, that c in the expression deduced above 

 ( X 2pe J will become 2 e, and the expression itself n ~ l \ 



X 4pe. Hence the possible errour w ill be 



2-1 



4 s = 2 i at 



180* 



2 i 



2-1 2 

 x4H = 3sat90°;- 



3-1 



+ ■—— X 4* = 3-33s 



at 60° 



2 3 — 2 

 , -X2H --x4x2e=:4Eat 120°. The great. 



est errour must therefore lie betwixt 90° and 120°, and 

 nearer to the extremity of the latter than the former arc. 

 At 105° it will be 550a; at 111° it will be 5-50 e - 



2 5-2 



5 



1-5 s-f 



X 4 X 2 e = 9-70?; and at 111 10' it will 



be 9-70 



1*04 £ (the excess of the errour at 111° above 



that at 112°) -f 3*33 t — 12-86 e, which will be found to 

 be the greatest errour betwixt 105° and 120°, and of course 

 the greatest in the first semicircle. In the other semicircle, 

 the process being the same, the possible errours must neces- 

 sarily be the same at the same distances from the first point, 

 reckoning the contrary way upon the circle. 



The magnitude of the quantity s will of course vary upon 

 circles of the same radius, according to the excellence of the 

 glass employed, and the accuracy of the examiner's eye. 

 It will seldom, however, exceed one second upon a circle, 

 the radius of which is one foot; and in general it will not 

 amount to so much. I find that I can read off, to a cer,. 

 tainty, within less than three fourths of a second, and hence 

 I conclude, that I could examine the divisions of my circle 

 without being liable to a greater errour than 9*63 seconds, 

 and those of a circle of three feet radius without the risk of 

 a greater errour than 321 seconds. 



To those people who are accustomed to entertain such 

 exalted notions of the accuracy, with which astronomical 

 instruments can with a certainty be divided, this errour, J 

 dare 'say, will appear very considerable; but for my part, 

 I am perfectly satisfied, that it beais but a small proportion 

 to the accumulated errour which may take place, in spite of 

 nhe utmost vigilance of the ai'tist, in, an instrument divided 



i according 



