37 2 Dr. Herschel on the 
That we may have a point in our ellipfis from which to 
depart, I fliall have recourfe to two meafures of pofitions. The 
frit was taken O&ober i4d. 16 h. 28' 42'', when the fatellite 
was 66° 3' fouth- following the planet. In fig. 2. let qmv be 
a portion of an ellipfls, conftrudled on the femi-tranfverfe cq , 
and femi-conjugate cv, taken as 44,23 to 34,35 ; ^MF an arch 
of a circle, defcribed with the radius cq abtout the center c ; 
tn the fituation of the fatellite in its elliptical orbit, the 14th 
of October ; A its apparent, and M its real place in the cir- 
cle; Vc the parallel of the planet. Then we fliall have, by 
calculating from the known period, the arch 7M 45 0 r q ' ; and 
FA, by obfervation, 66 3 qj . But from the nature of the ellip- 
fls, as Vc is to vc fo is (the tangent of the angle qcNl to 
the radius cn ) to mn (the tangent of the angle qcA to the fame 
radius). Hence qcA is found 38° 7'; and therefore AcM 
7 0 1 o'. That is, when the angle of pofition was taken, the 
fatellite appeared to be q° 10' lefs advanced in its orbit than 
it fhould have done, owing to its motion in an orbit whole 
plane is inclined to the vifual ray. The meafure therefore 
corre&ed, or rather reduced to the circle, inftead of 66° 3', 
will be 58° 53' fouth- following ; to which, adding the calcu- 
lated arch qA, and from the fum deducting 90°, we have the 
pofition ^cS with the meridian 14 0 io' on the fouth-preceding 
fde. In the fame manner I proceed with the fecond meafure 
taken O&ober 20 d. 16 h. q' 34" ; when the fatellite appeared 
to be 82° 12'' north-preceding the planet. Here the arch yM 
is 25 0 21', AcM 5 0 9' ; and the meafure corrected 77 0 3' north- 
preceding, which gives the inclination of the axis to the me- 
ridian 12 0 24' on the north- following fde. I have no 
reafon to prefer either of the meafures, and therefore take 
a mean of both, which is 13 0 17' from fouth-preceding to 
3 north- 
