174 
MT^. J. TT. JEAXS ON THE VIBRATTONS AND 
nearly equal (t.p., equal, except for a multiplying factor of, say, 14 or 1^) to the 
values of the same quantities before the process of ejection commenced. 
All this may he summed up, with sufficient accuracy for the present investigation, 
in the statement that when the ejection of a satellite is taking place the value of 
must he nearly equal to rf). 
CoiicITested hij the Soleir Si/sfenh 
§20. I'o a certain extent the solar system su|)plles material for testing this 
conclusion. Let p,-,. « denote the present mean density and radius of any memher of 
tlie system which is known to have thrown off a satellite, and let be the mean 
value of X, whetlier this denotes a pressure or an elastic constant, then we may 
write 
o n /\ 
At the tune at whicli the satellite was ejected the same ec[uation ought to hold 
with 6 nearly ecpial to unity. Unfortunately we liave no knowledge as to tlie 
changes wliich will have taken place in p^, a, X,, since the ejection of the last satellite. 
XVe shall, for a rough approximation, neglect these changes altogether, take ^ = 1, 
</) = 2, and examine to vdiat extent the equation 
py«VXo = 2 
(62) 
Imlds for the solar system as it now stands. 
It will lie rememliered that there are three sources of error in this equation:_ 
(i.) We are neglecting tlie effect of rotation in bringing about the ejection of a 
satellite. 
(li.) We are neglecting the changes which have taken place since the ejection of 
the last satellite. 
(m.) We are using an arbitrarily chosen value for </., and applying this to every 
])lanet, wlnle we know, from the difference in the physical constitutions of the planets, 
that the value of <j) must be difterent for each. 
These three sources of error would each be serious if we were attempting to get 
accurate results, but as our calculations are necessarily only of the roughest kind, v-e 
may be content to neglect them. 
§ 27. In the accompanying table the masses and radii of the sun, and of those 
planets wh.cli possess satellites, are given in the first two columns; the value of 
nass/(iadius) is given in the third. The units are so chosen that the earth is 
measured by unity in each of these columns. Venus is included for the sake of 
comparison, although the existence of a satellite is extremely doubtful. 
