r 38 1 
to render the following conclufions more fimple than 
they otherwife would have been ; and as the angle 
a B A is, by hypothefis, but final], its cofine will ap- 
proach fo near to the radius, as not to occafion any 
fenfible error in the refult; and the fame may be ob- 
ferved with regard to what is advanced in prop. IV r . 
It remains now to apply, what has been inveftigated 
above, to the eclipfes of Jupiter’s fatellites, and to 
examine whether the prolatenefs of his figure will 
have any fenfible effed upon their durations j and this 
is become the more neceffary, as that celebrated aftro- 
nomer M. de la Lande (who candidly acknowledges, 
that he was excited to turn his thoughts upon this 
fubjed, from a curfory view of this paper, which 
was (hewn him by Dr. Bevis*) does not feem to 
have confidered the quefiion, with that degree of at- 
tention which I think it demands. 
But before this can be done with exadnefs, it w : ll 
be neceffary to have the inclination of Jupiter’s axis, 
with refped to his ecliptic, and the place of his equi- 
noxes determined by obfervation, neither of which 
I believe has yet been done with any degree of cer- 
tainty ; I fhall, therefore, proceed in this inquiry upon 
M. de la Lande’s hypothefis, that Jupiter’s axis is per- 
pendicular to his orbit j and perhaps this fuppofuion is 
not fo far diffant from the truth, as to occafion any 
material error in the conclufion. It may alfo be re- 
marked, that in the general equation given above, 
> 
V and V exprefs the fine and cofine of the ferni- 
L 
angle of the cone of Jupiter’s fhadow, but this angle 
can never exceed 3', and confequently we may very 
* Viet. ConnoilT. dcs Mouy. Celefb 1765, p. 177. 
fafely 
