418 PHILOSOPHICAL TRANSACTIONS. [anNO 17/8. 



for both together. It is here done separately, in order thence to discover also 

 the ratio of their effects. 



And first for the southern observatory o. Secondly, for tlie northern observatory p. 



Affirmatives. Negatives. Affirmatives. Negatives. 



1.. 24.795 N.w.-)., 3.. 2374S.W.-I., 1 1. . 25.078 s.w. I ., 9. - O.Oiy n.w. I ^ 



2..19.792N. E. J • 4... 0.:375s.E. J^ 12. . ■20.26'l s. e. J ^'- 10. . O.O9O n. e./ ^ 



7.. 24.806 s. w.l^ 5.. 13.534 N.w. J „ 13. . 25.637 n.w. "I 15. . 2.774 s. w. ) i 



8.. 29.213 s. E. /^''P- 6.. 12.356 N.E./^^P- 14..26.l6l n.e./^^P- i6..5.61()s. e.\^ 

 y8.606 = sum of affirm. 28.639 sum. 97.137 = sum of affirm. 8.493. 



28.639 = sum of negat. 8.493 = sum of negat. 



69.ij67 = effective sum of the sines for o. 88.644 = effective sum of the sines for p. 



69-967 = the same for o. 

 158.61 1 = the sum of the sines for bothobs. 



From these numbers it appears, that the effect of the attraction at the 

 northern observatory, is to that at the southern one, nearly as 70 is to 89, or 

 as 7 to 9 nearly. This difference is to be attributed chiefly to the efl^ect of the 

 hills on the south of the southern observatory, which were considerably greater 

 and nearer to it than those on the back of the northern observatory. For 

 though the southern observatory was placed 273 feet above the level of the 

 northern one, which removed it considerably more above the centre of gravity of 

 the hill than the latter, it was at the same time placed considerably nearer than 

 the other to the middle in a horizontal direction ; so that probably the one dif- 

 ference nearly balanced the other ; and accordingly we find that the sum of the 

 affirmative altitudes for o is 44.587, and of those for p 45.339, which differ by 

 only a 45th part nearly. 



. It only remains now to multiply the sum of the sines by the common breadth 

 of the rings, and by the common difference of the sines of the angles made by 

 the meridian and the several radii. It has already been observed, that the former 

 is 666^, and the latter -yV ; therefore -J^- X 666^ = ^^^ = ^-^ is their product: 

 consequently, 158.611 X 4-2-2- = 8811^ nearly, is the sum of the two opposite 

 attractions made by the hill, &c. at the two observatories. 



In order now to compare this attraction with that of the whole earth, this 

 body may be considered as a sphere, and the observatories as placed at its sur- 

 face ; since the very small differences of these suppositions from the truth, are 

 of no consequence at all in this comparison. Now the attraction of a sphere, 

 on a body at its surface, is known to be = ^cd, where dis=. the diameter of the 

 sphere, and c ^ 3,14l6 =: the circumference of the circle of which the diame- 

 ter is 1. But cd is = the circumference of the circle to the diameter d; and 

 therefore the attraction of a sphere will be expressed by barely •?- of its circumfer- 

 ence ; which is a theorem well adapted to the present computation. The length 

 of a degree in the mean latitude of 45°, is 57028 French toises (see p. 327 Phil. 

 Trans. 17 68 :) and the same result nearly is obtained by taking a mean among 



