1047 
Astronomy. — “On the figure of the planet Jupiter.” By Prof. 
W. DE SITTER. 
The potential function of a body possessing axial symmetry is *) 
= 1 Nd B; 3 
Sune a -{- = GE Pi (swt ORT. 
EN je C 
Bi OE} be) dm. 
m fa) 
S 
where 
In these formulas the axis of symmetry is chosen as axis of §, 
The coordinates of the element of mass dm are §, 4,5; 9? =§ + 
+ 7° + 6’, and the integrals must be extended over the whole body. 
Further d is the planetocentric latitude, and P; are the zonal har- 
monies of order 2. If the origin of coordinates is taken in the centre 
of gravity, we have 
Be). 
If the plane of §, 4 is a plane of symmetry, then also 
Be bss = Oar aes, EL 
I adopt from the theory of the four large satellites 
rr, = — 0.01462. 
The motion of the perijove of satellite V then gives 
15 
24 000058. 
bt 
By anaiogy we can conclude 
B, 
pe = — 0.00002. 
The effect of the term in B, can thus never amount to more 
than a few units in the fifth decimal place, even at the surface of 
the planet. Since the values of B, and B, are uncertain to a larger 
amount than this, we neglect 4, altogether. 
If now the body rotates about the axis of & with the velocity w, 
we must, at the surface, have 
| Ti Soh EEE NT: 
VP, = fm E + en P, (sind) + en) P, (sin | + $ wr? cos? d= const. 
If we put 
jm 
where b is the equatorial semidiameter, and 
1) TisseranD, Méc. cél. Il p. 319—822. 
