8 Dz. Kirkwood on certain Harmonies of the Solar System. 
only about 17 minutes. But with Bond’s estimate of the thick- 
ness of the ring, this value of the mass would indicate a density 
more than three times that of Saturn—a greater density than 
has been found for any planet, primary or secondary, exterior 
state of the case, to adopt, without alteration, the received value 
of Saturn’s period of axial revolution, viz: 10h. 29m. 17s. 
we use the masses of Jupiter, Saturn and Uranus, adopted in 
the American Nautical Almanac, we find the diameter of Saturn’s 
sphere of attraction = 85478. Hence the constant of rotation 
C =—, = 985°161; log C= 2°998507. 
The diameters of ihe Uli a attraction for the other planets 
are then found from the form 
log bat dog n/ —log C). 
The results, bstciea: are as follows :— 
Diameter of the sphere of attraction of Mercury, 0°1992 
é ee e 
nus, 0°3801 
“ 4%: Mf - Earth, 05340 
iy “ce “ tc ars, 0 7731 
i si ” 2 Jupiter, 48342 
% ° = . Saturn, 85478 
is int Kabair oe too large, as seems to have been more re- 
cently admitted by Leverrier himself. We will, therefore, pe 
Encke’s value, 53537. The calculation is obvious and need no 
be repeated. We find 
The mass of Mate = sastaet- 
it3 
Remarks, 
1. This value of Mercury’s mass is considerably greater than 
= found by Encke, but is very nearly identical with Leverrier’s 
oS d value. 
Our mass of Mars is somewhat less than Burckhardt’s. Mr.. 
researches on the ae! of the sun have led him to the 
ision that a considerable diminution of that value is actually 
wt of Pipe ag, 1. 
aoe 
