EVOLUTION OF THE SOLAR SYSTEM. 
519 
In discussing the various planetary subsystems I take most of the numerical values 
from the excellent tables of astronomical constants in Professor Ball’s ‘ Astronomy/ * 
and from the table of masses given above. 
Mercury. 
The diameter at distance unity is about 6" - 5 ; the diurnal period is 24 h 0 m 50 s (?) 
The value of the mass seems very uncertain, but I take Encke’s value given above. 
Assuming that the law of internal density is the same as in the earth (see below), 
we have (7='33438ma 3 , and u=2tt very nearly. Whence I find for the rotational 
momentum 
Cn= 
•34 
10 10 ’ 
Venus. 
The diameter at distance unity is about 16"‘9 ; the diurnal period is 23 h 21 m 22 s (?). 
Assuming the same law of internal density as for the earth, I find 
Cn = 
28'6 
10 10 ’ 
Herschel remarks (‘ Outlines of Astronomy,’ § 509) that “both Mercury and Venus 
have been concluded to revolve on their axes in about the same time as the Earth, 
though in the case of Venus, Bianchini and other more recent observers have contended 
the earth. It may be solved approximately by first neglecting -fm(a/a) s , and afterwards nsing the 
approximate value of a/a for determining that quantity. 
The density of the homogeneous planet is found from 
w=w 
where w is the earth’s mean density. 
To apply these considerations to the earth, we take d=142° 30', /=2"057, which give m as the 
ellipticity of the earth’s surface. 
Then with these values (Thomson and Tait’s ‘Nat. Phil.,’ § 824, table, col. vii., they give however - 835) 
i { 1 ~^^} = ' 83595 
a a 
The first approximation gives - = *9143, and the second -=*9133. 
a a 
Hence the radius of the actual earth 6,370,000 meters becomes, in the homogeneous substitute, 
5,817,000 meters. 
Taking 5'67 as the earth’s mean specific gravity, that of the homogeneous planet is 7’44. 
The ellipticity of the homogeneous planet is "00329 or 3 - 5 - 3 , which differs but little from that of the 
real earth, viz.: -^-g-. 
The precessional constant of the homogeneous planet is equal to the ellipticity, and is therefore "00329. 
If this be compared with the precessional constant "00327 of the earth, we see that the homogeneous 
substitute has sensibly the same precession as has the earth. 
If a similar treatment be applied to Jupiter, then (with the numerical values given in a previous paper, 
Ast. Soc. Month. Not., Dec. 1876) the homogeneous planet has a radius equal to "8 of the actual one; its 
density is about half that of the earth, and its ellipticity is 5 ^. 
* ‘ Text Book of Science : Elements of Astronomy.’ Longmans. 1880. 
