VOL. LXV.] PHILOSOPHICAL TRANSACTIONS. 717 



the observatory, the difference of the latitude of the 2 stations may be found 

 as well from the observations made in one position of the instrument, as the 

 other. If the instrument had suffered no change by being carried over the hill, 

 that is if the line of collimation was not altered by it, the results should come 

 out equally true from the observations taken in both positions of the instrument. 

 On the contrary, if the line of collimation should, by any means, have suffered 

 any alteration between the observations made at the 2 stations, this would cause 

 the difference of latitude to appear too small, by the observations made in one 

 position of the instrument, by the quantity of the alteration, and as much too 

 great, in the other position of the instrument. But still the mean between the 

 2 results, deduced from the observations taken in the 2 different positions of the 

 instrument, would give the true difference of latitude ; and that equally, whether 

 the line of collimation had suffered any change or not. Therefore this will be 

 the best method of comparing the observations together, and I shall take a mean 

 of all the results, deduced from the observations taken in each position of the 

 instrument separately, and then a mean of those means for the true difference 

 of latitude. By single observations of 10 stars; viz. |3, a, and ri Cassiopeae, and 

 I, ti, |3, 39, 45, 465 and 53 Draconis, made on both sides of the hill, with the 

 plane of the sector facing the west, after making the proper allowance for pre- 

 cession, aberration, and deviation, and semi-annual solar nutation of the earth's 

 axis (see my tables annexed to my Observations made at the Royal Observatory,) 

 the apparent difference of latitude between the 2 stations of the observatory, 

 comes out 54". 1, 54".7, 54".0, 55".4, 55*.0, 55".0, 52",2, 54".0, 54'.3, 53*.l, 

 respectively ; the mean of all which is 54*.2 ; the greatest difference of any one 

 result from the mean being only 2". In like manner, by single observations of 

 as many stars ; viz. (3 and aCassiopeae ; t Ursae majoris ; (3, 39, 46, O, 49, and 

 53, Draconis; and 23 Cygni ; made on both sides of the hill, with the plane of 

 the sector facing the east ; after making all the allowances as before, the appa- 

 rent difference of latitude comes out 54".5, 52".3, 56*.8, 53'''.5, 54".5, 57".2, 

 56". 1, 55*.3, 54". 1, 55*.l, respectively; the mean of all which is 55"; the 

 greatest difference of any one result from the mean being 2". The two means 

 54".2 and 55'''.0 differ only 0''.8, which should argue only an alteration of 0'''.4 

 in the line of collimation ; but this is too small a quantity to be depended on ; 

 and therefore it is most probable, that the state of the instrument remained un- 

 varied. However, whether it did or not, the mean of the 2 means, or 54".6, 

 is to be esteemed the apparent difference of latitude between the 2 stations of 

 the observatory, and, when compared with the difference of latitude which 

 should result from the trigonometrical measures, will give the sum of the 2 con- 

 trary attractions of the hill. It must be owned, that this point will be settled 

 with rather more certainty, when all the observations made with the sector, 



