Mr. Troughton on dividing Instruments. *39 
and from the wearing of its centre ; but the graduation, con- 
sidering the time when it was done, I found to be very good. 
Sir George in his Paper upon the Equatorial (Phil. Trans, for 
1793), after some compliments paid to the divider of his in- 
strument, says, “ the late Mr. John Bird seems to have ad- 
“ mitted a probable discrepancy in the divisions of his eight 
“ feet quadrant amounting to 3";’’ and he refers to Bird on 
the construction of the Greenwich quadrant. This quantity 
being three times as great as any errors that I met with, I 
was lately induced to inquire how the matter stood. Bird, in 
the paper referred to, says, “ in dividing this instrument I 
“ never met with an inequality that exceeded one second. I 
“ will suppose that in the 90 arch this error lay towards the 
“ left hand, and in the 96 arch that it lay towards the right, 
“ it will cause a difference between the two arches of two 
<c seconds ; and, if an error of one second be allowed to the 
“ observer in reading off his observation, the whole amount 
“ is no more than three seconds, which is agreeable to what 
“ I have heard, &c.” Sir George’s examination of his own 
Equatorial furnishes me with the means of a direct compari- 
son : In his account of the declination circle, we find an error 
+ 2" ,35, and another — i",5 ; to these add an error of half 
a second in each, for reading off, which Sir George also ad- 
mits, we shall then have a discrepancy of 4", 85 ; but, as the 
errors of reading off are not errors of division, let them be 
discharged from both, and the errors will then stand, for the 
quadrant 2", and for the circle 3", 85. As the radius of the 
former, however, is four times greater than that of the latter, 
it will appear, by this mode of trial, that the Equatorial is 
rather more than twice as accurately divided as the quadrant. 
T 2 
