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fuppofed to reprefent the fun’s declination, A E his 
right afcenfion, and H E his diftance from the equi- 
noctial point E *) we have (per fpherics) 
fin. A E : i (rad.) : : co-t. E : co-t. AH, 
fin. AH ' 2 *. fin. EH 1 2 : : lin. E ' 2 : i 2 (radl 2 ) 
From whence we get, fin. AE x co-t. AH x fin. AH ’ 2 
= fin. EH ' 2 x co-t. E x fin. E’ 2 . But co-t. AH x 
fin. AH = co-f. AH x i (rad.), and co-t. E x fin. E 
= co-f. E x i (rad.) : therefore fin. AE x co-f. AH 
x fin. AH = fin. Eh ? 2 x co-f. E x fin. E ; and, con- 
r , , fin. AE X co-f. AH x fin. AH , - _ 
iequently, k x ^ ^ = n co-f. E 
x fin E H |Z (==Ef). 
Let, now, the fun’s longitude EH be denoted by 
Z (confidered as a flowing quantity) ; then, lin. Z 12 
being =q- — q co-f. 2 Z, we (hall have k x co-f. E x 
fin. EH * 2 = a- k x co-f. E x 1 — co-f. 2 Z. But the 
angle defcribed about the axe of rotation P p, in the 
time that the fun’s longitude is augmented by the par- 
ty - 
tide z, will be = — x z. Therefore (by the general 
propofition) we have, as 1 : f £ x co-f. E x 1 — co-f. 2 Z 
: : fx z : i k x j- x co-f. E x z — Z co-f. 2 Z, 
the true regrefs of the equino&ial point E, during 
* No error arifes from confidering the triangles EAe and 
A E H, as being formed on the furface of a fphere, tho’ the earth 
itfelf is not accurately fuch. The angle (EAa) reprefenting the 
effect of the folar force, is properly referred to the furface of a 
fphere ; therefore (after the meafure thereof is truly determined) 
the figure AP ap is itfelf taken as a fphere, in order to avoid 
the trouble of introducing a new fcheme. 
that 
