of Bessel's Astronomical Observations. 435 



* = R sin 2" 1-64 Fr ° m WhlCh f ° ll0WS 



r — r = 2 , 2 = 0.0007587 line. 



In examining the deviations of the axis from the horizontal 

 position, the state of the Jevel before and after reversing was 

 always consulted : we have the elevation of the western end 

 above the eastern one expressed in seconds = 



15 b = - -£—. — J, ~ and likewise 



R sin ] 



h' — h = (x + x') R sin l"-082; therefore 

 15 b = (x + x') l"-082 + 815; where the upper figure 

 is to be taken for the eastern, the lower one for the western 

 position of the circle. If the level is observed in one position 

 only, we have 15 b = x. 2'"64 + 0"«576. 



4. Examination of the Invariability of the Instrument "while 

 revolving. 



After the observation of Mr. Pond, who found a considerable 

 change of the old Greenwich transit while revolving, a more 

 accurate investigation of this point seems to be indispensable. 

 It has, however, no small difficulties, if it be required to find 

 out and to take into the account even small constant errors. 

 On the supposition that the deviations from the meridian re- 

 sulting from a change of the instrument itself, depend on the 

 sine and cosine of the single zenith distance, or, which is the 

 same thing, that they take place in a great circle, the deviation 

 of the middle wire from the meridian will be in opposite posi- 

 tions of the axis 



15 (a + «) sin (<p — 8.) + 15 (b -f /S) cos (<p — 8) + 15 c 

 and 15(a'-r-a)sin(p - 8) + 15 (U — /3)cos (p — 8) + 15 c' 

 •where a, b, c, a', b', c' denote the fifteenth parts of the devia- 

 tions in azimuth, in the horizontality of the axis, and of the 

 error of collimation, and « and /S the deviations peculiar to 

 the instrument, all expressed in seconds. The first formula I 

 suppose to be for the eastern position of the circle, the other 

 for its western position. 



From these formulae it is apparent that by astronomical ob- 

 servations in contrary positions only, the quantity 2 /3 cos (p — 8) 

 + (c — c') can be determined ; but not «, which is altogether 

 joined with the azimuth, and has no influence on the re- 

 sults obtained by the transit : it only causes that a vertical 

 plane which is described by the line of collimation is not per- 

 pendicularly intersected by the horizontal axis ; and there is 

 3 I 2 no 



