1823.] Declination of some of thejixed Stars* 265 



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 more- 

 over 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 httle to the northward of it, will in our 

 latitude give an error in polar distance, amounting 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 instru- 

 ments, like that of Dubhn, which turn in azimuth, and with 

 which the observer has to find the place of all the stars by mea- 

 suring the double of their zenith distances, if he does not find 

 the same zenith point with different stars (provided the instru- 

 ment be well divided) he may be sure that flexure takes place ; 

 but he cannot infer the converse, that flexure does not take 

 place, from his obtaining with all the stars the same error in the 

 line of coUimation. For if the flexure be the same on both sides 

 of the zenith, a supposition by no means improbable, the 

 observer will then have no indication of flexure by the usual 

 method of determining the error of collimation by stars of differ- 

 ent altitudes. Let us suppose that, with an instrument liable to 

 flexure, it is required to measure by both methods the meridional 

 distance of any two stars. The angular distance of the direct 

 images will (as we have already seen) be affected by the differ- 

 ence, or by the sum of two flexures, according as the stars are 

 placed on the same, or on opposite sides of the zenith. In 

 viewing the reflected images, the instrument receiving two new 

 positions, will be subject to two nev/ flexures, by the sum or 

 difference of which (as it may happen) the angular distance of 

 the reflected images will be affected. 



The most probable supposition to be made concerning the 

 flexures is, that at equal inclinations with the horizon, above 

 and below it, they will be the same nearly both in direction and 

 degree, and therefore that the two images below the horizon 

 will approach by nearly the same quantity that the direct images 

 receded, or vice versa. With an instrument therefore having 

 such a system of flexures, the double altitude of each star will 

 be correctly ascertaijaed ; but stars of different ^iltitudes will 



