the Divisions of astronomical Instruments* S85 



times, to. bisect iheir respective points in the measurement 

 oF every arc, and taking a mean oi' the different readings^ 

 o^'for the true position oi' the wire at the real bisection of 

 the point. The wire n)ay be niovcd in this manner eight 

 or ten times at each point (it" such a degree of caution 

 should be thought necessary) and the mean taken in little 

 more tlian a minute ; so that the lime of performing the 

 work will not be so much increased as might perhaps have 

 been apprehended ; and when it is con^pleled, wc may rea- 

 sonably presume that the distance of every point from 

 zero (whilst the temj)crature of the circle continues uni- 

 form) will have been determined with sufficient exactness 

 for every practical purpose. 



OF the time necessary for the examination, a pretty cor- 

 rect idea may be formed by considering how many mea- 

 surements are required, and allowing about a n)inuie and a 

 half for each ; i. e. a quarter of a minute for bringing the 

 extreme points of the arc to the micrometer and the mi- 

 croscope, and a minute and a quarter for making the se- 

 veral bisections. Now, in dividing the whole circle into 

 arcs of 15° each, it wilj ai)pear that forty-four measure- 

 ments must be performed; and to examine every point in 

 each arc of 15°, there will be l6l required, making in all 

 3y0S measurements ; and consequently the time necessary 

 for completing the whole work will be 3S62 minutes, or 

 about 98 hours. 



The time and labour required for this examination are^ 

 110 doubt, very considerable; but it ought to be recollected, 

 that it will render any great degree of precision, in dividing 

 the instrument, totally unnecessary. Whoever indeed 

 employs this method of examination, will be virtually the 

 divider of his own ir.strument ; and all that he will ask of 

 the artist, is to make him a point about the end of every 

 five or ten minutes, whose distance from zero he will de- 

 termine for himself, and enter in his book to be referred 

 to when wanted. We may likewise observe, that by this 

 €xaa)ination we shall not only be secured against the errors 

 of division, but against those which arise frt)m bad center- 

 ing, and from ilie imperfect figure of the circle, and which , 

 in general are of too great a magnitude to be neglected. 



It will,. I dare say, have occurred to you, that whenever 

 we are desirous that an observation should be particularly 

 exact, we may guard it against the effects of unequal ex- 

 pansion or contraction in the metal, by means of the ap- 

 paratus which I have described : for wc have onlv to mea- 

 sure the.arc which has been. determined by the observation 



against 



