r 40 ] 
Jiplis in a , b> c, Sec. let a A, ^B, cC, Sec. be taken 
each equal to the given term — , and the points A,B,C, 
See. will be in the required curve. 
It appears from confidering the nature of this 
curve, that it will have two cufps, one at each ex- 
tremity of its Idler axis, which will approach to- 
ward each other, according as the diflance J is aug- 
mented ; therefore, if the diftance of the fedtion of 
the fhadow, from Jupiter’s center, was taken, fuch 
that b — the leffer axis of the curve would 
r — c 
then vanilla, and the cufps meet in the center, and 
thereby form two diflindt fhadows (as reprefented 
in fig. 8) ; in confequence of which, if a fatelles, 
revolved at that diflance, it might fuffer a double 
eclipfe, at the fame conjundtion, which remarkable 
phenomenon may alfo happen, at a lefs diflance 
from Jupiter, in fome circumflances. 
I fhall now flaew how the duration .of an eclipfe 
of a given fatelles may be determined independant 
of the equation of the curve ; and this, perhaps, 
will be the more acceptable, as it will afford a prac- 
tical rule, which may be applied, in every pofition 
of Jupiter’s axis, with very little trouble. This may 
be done by the help of the following propofition. 
PROPOSITION VI. 
If a circle eD/G be deferibed about the conjugate 
axis GD, of a given ellipfis A DBG, and a right 
line E F be drawn, making the given angle Fn D, 
with 
