declination of some of the fixed stars. 47 
of error the most to be dreaded in every instrument whatever, 
quadrant or circle, is that which will be caused by the flexure 
of the materials of which the instrument is made. It is im- 
possible in theory that any instrument can be wholly free 
from this defect. In the Greenwich circle the number of 
microscopes placed round its crcumference have an obvious 
tendency to diminish this error, though they cannot annihilate 
it ; but they have no tendency whatever to diminish the error 
arising from the flexure of the telescope attached to the circle. 
The effect of flexure in any circle will be, in the first instance, 
to give an erroneous distance from the pole to the zenith : in 
instruments that turn in azimuth, of the usual construction, 
the error thus occasioned will be applied to every star under 
the form of co-latitude, and a star south of the zenith, will be 
moreover affected by the probably opposite flexure due to 
that point of the instrument on which the star is observed. 
This in stars near the equator, or a little to the northward of 
it, will in our latitude give an error in polar distance, amount- 
ing to about double the error committed in determining the 
co-latitude. On the contrary, the polar distances of stars 
north of the zenith, being affected only by the difference of 
two flexures, will be more accurately determined as they 
approach nearer to the pole, where the errors will wholly 
vanish. Now, though in the usual mode of employing the 
Greenwich circle, viz. in measuring directly polar distance, 
the co-latitude does not become an object of enquiry, yet any 
flexure of the circle will produce a system of errors of the 
same nature as those above pointed out. In instruments, 
like that of Dublin, which turn in azimuth, and with which 
the observer has to find the place of all the stars by measur- 
