the Divisions of astronomical Instruments . 241 
determined with sufficient exactness for every practical pur- 
pose. 
Of the time necessary for the examination, a pretty correct 
idea may be formed by considering how many measurements 
are required, and allowing about a minute 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 microscope, and a minute 
and a quarter for making the several bisections. Now, 
in dividing the whole circle into arcs of 15 0 each, it will ap- 
pear that forty-four measurements must be performed ; and 
to examine every point in each arc of 15 0 , there will be 161 
required, making in all 3908 measurements ; and consequently 
the time necessary for completing the whole work will be 
5862 minutes, or about 98 hours. 
The time and labour required for this examination are, no 
doubt, very considerable ; but it ought to be recollected, that 
it will render any great degree of precision, in dividing the in- 
strument, totally unnecessary. Whoever indeed employs this 
method of examinination will be virtually the divider of his own 
instrument, 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 dis- 
tance from zero he will determine for himself, and enter in 
his book to be referred to when wanted. We may likewise 
observe that by this examination we shall not only be se- 
cured against the errors of division, but against those which 
arise from bad centering, and from the 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. 
