364* METHOD OF EXAMINING ASTRONOMICAL IMSTRUMENTS. 



Method off?* motion of their respective wires. This being done, 

 aniiiiinsj the di- . r , ... - M , 



visions by it wc mn$ t observe, from the positions of the wires, how 



much the interval betwixt them has increased or decreased 



in the measurement of the new arc: and this increase or 



decrease must be noted down with a -j- or — accordingly. 



In the same manner we must proceed through the remaining 



two arcs of 90°, observing and noting down the diiference 



betwixt each and the original arc. 



The point of zero must now be brought again to the mi- 

 crometer, and bisected by the movable wire, and the micro- 

 scope be made to slide back along the arc, till by moving the 

 wire a little we can bisect the point of 60°, and when this is 

 done, the microscope must be clamped. We must then 

 measure the arc of 60* against every succeeding arc of 60" 

 in the circle, precisely in the same way that we measured 

 the first arc of 90° against the other three. The arc of 45° 

 ' is next to be measured against av^ry succeeding arc of 45°, 

 and this will complete all that is necessary to be done in the 

 early part of the morning before the heat of the sun can 

 have affected the temperature of the instrument. The rest 

 may be performed at our leisure. 



You will immediately perceive the object of this kind of 

 measurement. It enables us to determine, with any degree 

 of accuracy that may be required, the proportion which the 

 first and every succeeding arc of the circle, contained be- 

 twixt the micrometer and the microscope, bears to the 

 whole circle, and of course the absolute length of the 

 arcs themselves. Let a denote the real length of the 

 first of these, and ± «', ± H*i ± #"'j &c., the difference 

 betwixt the first and second, the first and the third, fee., 

 respectively : let A represent any other arc, the length 

 of which is known, and which is a multiple of a, as 

 marked upon the instrument, and let this multiple be 

 expressed by n. Then will a -f (a -f- of) -f- (a -f- a") 



■}- {a+ j'j^&t: p (a -f ffi* *" 1 ) = A, and a = 



A-g'-ff'-fl-a"' -' ~ j . Hcncc | t |8 evi(Icnt? that? if 



n 

 there is no errour committed in the measurement of any of 

 these arcs, we shall have the value of a, and consequently 

 of a + af) a+a'', a-\-a"\ &c, and of any arc, com- 

 prehending 



