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II. On the Obliquity of the Ecliptic. By William Gal- 

 braith, Esq. M.A. 



To the Editors of the Philosophical Magazine and Annals. 



Gentlemen, 



T^HE subject of the obliquity of the ecliptic has so fre- 

 =r quently engaged the attention of astronomers, that it may 

 at first appear superfluous for me to attempt, in the present 

 short sketch, to throw much light upon this interesting sub- 

 ject. 



Still, however, it appears to me that sufficient attention has 

 not been bestowed, at certain public institutions, on some parts 

 of it, particularly that arising from a small error in the lati- 

 tude, which, as will presently appear, produces a double effect 

 on the difference between the summer and winter obliquity, by 

 this means rendering that small error very sensible. 



Let w be the summer obliquity, «/ the winter, X the lati- 

 tude, z the zenith distance in summer, z' that in winter, and 

 e the error in latitude; then it will readily appear that in 



Summer u> = X + s — z (1) 



Winter co' =z* — (X-f s) = z'— X — s (2) 



Whence w— co' = 2X — (« + «/) + 2s ={2X— (z + z') + 2e}...(3) 



But 2X— (z+z') should be = 0, if the summer and winter 



obliquities are the same, as it is probable they are ; whence 



co — «/ = Aco = 2e (4)* 



Or the difference of the summer and winter obliquity is af- 

 fected by the sum of the errors in the latitude arising from 

 using an erroneous table of refractions, a constant error in 

 the instrument, &c. 



Hence it is clear that an error in this determination will 

 continue so long as the latitude and the obliquity of the eclip- 

 tic continue to be determined by Bradley's Refractions, which, 

 though they possessed great merit at the time of their first ap- 

 pearance, and in a considerable degree still do so, yet are un- 

 doubtedly inferior to those called the French Refractions, as 

 well as to those of Bessel, Brinkley, Ivory, and Young. 



It has been long known that the Greenwich published de- 

 termination of the obliquity in summer, does not accord with 



* Indeed, without any attempt at demonstration, a very little considera- 

 tion will show that the difference between the summer and winter obli- 

 quity is increased by twice the error of the latitude of the place of ob- 

 servation ; since the zenith distance must be subtracted from the latitude 

 in the former case, and the latitude must be subtracted from the zenith 

 distance in the latter. 



that 



