[ *8 ] 
Received January 8, 1767. 
1 ^ 
III. A general Investigation of the Nature 
of the Curve , formed by the Shadow of a 
prolate Spheroid , upon a Plane f anding at 
right Angles to the Axis of the Shadow ; in 
a Letter to the Royal Society , by Mr. 
George Witchell, F, R. S, 
Gentlemen, 
, . : - 
. v 
Read Jan. 15,^ Beg leave to lay before the Royal So- 
1167 ' JL ciety the following inveftigation of an 
irregularity in the duration of the eclipfes of Jupiter’s 
fatellites, occafioned by the figure of his body. 
It has been known for a long time, that Jupiter’s 
body was not truly fpherical, but a prolate lpheroid, 
and that in a much greater degree than any of the 
other planets ; but notwithftanding this, it was never 
fufpedted that it would affedt the durations of the 
eclipfes of the fatellite, till Dr. Bevis firft thought of 
it, in the latter end of the fummer 1761. 
The Dodtor, being at that time indilpoled, recom- 
mended the fubjedt to my confideration ; and, in 
confequence of his requeft, I not long after pre- 
fented him with a folution of the problem, being in 
fubftance 
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