36G METHOD OF EXAMINING ASTRONOMICAL INSTRUMENTS. 



Mattatd of ex- micrometer and the microscope comprehends an arc of 60°, 



amining the di- , , . , , . 



visions by it. as marked upon the instrument, and this arc is measured 

 against every succeeding arc of 60 Q in the whole circle, we 

 shall have the greatest errour that can be committed in de- 

 ducing the arc of 120° from the addition of the two first 



6-2 

 arcs of 60°, equal to — — x2x2e = 2.66 e. After these 



Temarks, we may proceed to consider how the remaining 

 divisions upon the circle may be examined with the least 

 probable errour, and to ascertain the amount of the greatest 

 to which the process can in any case be liable. 



Let the arc of 30° be now measured against every suc- 

 ceeding arc of 30° in the first, third, fourth, and sixth arcs 

 of 60°; and let the length of each be determined from a sepa- 

 rate comparison with the arc of 60°, in which it is com- 

 prehended, and not from a general comparison with all the 

 four. The arc of 15° must then be measured against 

 every succeeding arc of 15° in the first, third, fourth, 

 sixth, seventh, ninth, tenth, and twelfth arcs of 30^, and 

 the value oi* each deduced from a comparison with the 

 arc of 30, in which it is contained. When this is done, 

 we shall have determined the length of every succeeding 

 arc of 159, G f the first arcs of 30°, 45°, 60°, 75' (= 

 60° + 15°) 90°, 105° (= 90-f- 15°), 120° (= 60 + 60°), 

 135° (= 90° + 45°), 1 50° ( = 120°+ 30°), 165° (= 150« 

 -f- 15°), and 180° in each semicircle. 



We must next measure the arc of 5 Q against every suc- 

 ceeding arc of 5 Q in the whole circle, and deduce the 

 values of the first, and of the sum of the first and second, 

 in each succeeding arc of 15 Q from a comparison with the 

 arc of 15° in which they are contained. We must then 

 proceed to determine the values of the first arc of 3° in each 

 15°, and of its multiples the arcs of 6°, 9°, and 12°. We 

 must also put down the value of the last arc of 3° in each 

 arc of 15°, and then deduce the values of the first and last 

 arcs of l y in each arch of 15°, from a comparison with the 

 arc of 3° in which they are respectively contained. 



We shall now have measured in each arc of 15° the first 

 arcs of l p , 3°, 5°, 6°, 9°, 10°, 12°; and by taking the 

 last arc of one degrec ; which has likewise been determined, 



* from 



