460 The Atmospheres of the Planets. (October, 
immense thickness that must generally be 5000 miles, though 
at times nearly 15,000 miles in depth, this explanation 
for the cause of the elongation is scarcely satisfactory, as 
no account is taken of the changes that must occur in the 
progress of the shadow across the disc. But apart from 
this, the supposition of such an immense depth of semi- 
transparent atmosphere is only possible if the surface of 
Jupiter possesses the tremendous temperature of 150,000° C. 
—a degree of heat impossible to realise; and that must render 
Jupiter a rival to the sun in intrinsic brilliancy. Now, the 
ground on which this hypothesis rests, which, considering the 
very small number of observations must be held to be 
extremely slight, may be divided into two: first, the equa- 
torial penumbral fringe, and secondly, the elongation of the 
shadow. With regard to the former, as the true penumbre- 
of the shadows of the satellites is very considerable, being 
in the case of the nearest satellite nearly as broad as the 
dark shadow, whilst in the case of the farthest it is nearly 
four times as broad, and yet is rarely distinctly to be seen, 
any penumbral fringe that may be detected cannot be well dis- 
tinguished from the effects of the true penumbrz ; whilst 
the action of the atmospheres of the planet’s satellites must 
still further complicate the appearance of the shadow. As. 
far, therefore, as any deduction made from the presence of 
a penumbral fringe under these conditions, unless it could 
be shown that the appearances were independent of the true 
and atmospheric penumbre, no legitimate conclusion could 
be drawn. But from the great variability in the size of 
shadows of the satellites on different occasions, it is known 
that the penumbral fringe must be variable. As there must 
be a penumbra entirely round the satellite, the mere inability 
on certain occasions to detect it near the Polar region can- 
not be held to show much. 
It can, however, be easily shown that when Jupiter is in 
quadrature the true form of the shadows of its satellites is 
elliptical without resorting to any hypotheses of an extra- 
ordinarily translucent and deep atmosphere. For taking 
the most unfavourable case of an equatorial transit, and 
putting @ for the Jovian ecliptical longitude of the shadow, 
measured from the point where the sun is in the zenith, and 
considered positive towards the east, then denoting by @, 
the ecliptical longitude of the centre of the earth, the 
length of the shadow of the satellite as seen from the earth 
will be obviously . 
8 
P cos (9Q—0,) d 6 = sin (6” —0,)—sin (0-6). 
