Declination of some of the principal Fixed Stars. 183 



in its former and in its present state. The natural tendency 

 of any such defect would be, I think, continually to increase, 

 and to give results every year more and more distant from the 

 truth : but this is contrary to the known history of the Green- 

 wich observations, which I have found gradually for some time 

 past approaching to those results which are obtained at the 

 present day, and which, according to our present hypothesis, 

 are supposed to be nearly perfect. If the catalogue of 1813 

 were really so erroneous, as our present hypothesis would 

 compel us to regard it, then it would appear that Dr. Brink - 

 ley's catalogue for the same period must have been still more 

 erroneous, as may be seen by inspection of the annexed tables. 

 Now admitting for a moment that there were at that time cer- 

 tain imperfections in the Greenwich and Dublin instruments, 

 no person will believe them to have been so imperfect as our 

 present hypothesis would tend to represent them. 



Let us now examine the second hypothesis, which presumes 

 the catalogue of 1 813 to have been perfect, and consider what 

 confidence is due to the Greenwich observations of the present 

 day. This investigation is to be regarded as important, not 

 merely with a view to the discussion of the nature of the dis- 

 cordances in question, but also from the circumstance, that 

 instruments of well-known celebrity are represented as giving 

 very different results ; for which reason I shall be excused for 

 entering into considerable details on this particular question. 

 As the principal reliance I place on the accuracy of the pre- 

 sent catalogue, and on the superiority of the Greenwich circle 

 over all other instruments, with the history of which I am ac- 

 quainted, is derived from the coincidence of the results ob- 

 tained by the two independent methods ; the one of direct 

 measurement of polar distance, the other of observing the an- 

 gular distance of the direct and reflected image of the stars, 

 it becomes of some importance to consider in what way this 

 coincidence is a proof of the accuracy of either. The source 

 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- 

 j)ossible in theory that any instrument can be wholly fiee from 

 this defect. In the Greenwich circle the number of micro- 

 scopes placed )"ound its circumference have an obvious ten- 

 dency to diminisli 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 tlie fiist in- 

 stance, to give an erroneous distance from tiie pole to ihe 

 zenith: in instruments (lint turn in azimuth, of tlie usual con- 

 struction. 



