STABILITY OF A GBAVITATlNO PLANET. 
iVo 
Observed. 
Calculated upon the hyjjotliesis 
of the present paper 
fo = 2). 
(1) 
Mass. 
(2) 
Iladius. 
fo) 
Mass 
(I) 
Coefficient Aq. 
Unit = 10^^ absolute 
= 10'^ grammes weight per 
sq. centim. 
(Radius)- 
Run. 
315,000 
109 
2G 
2700 
Venus .... 
0-8 
1-0 
0-9 
3-2 
Ivirth .... 
1-0 
1-0 
1-0 
4-0 
Rlars .... 
0-1 
0-5 
0-4 
•6 
Jupiter .... 
300-0 
11-0 
2-5 
25-0 
Siituni .... 
90-0 
9-0 
1-1 
5-0 
Uranus .... 
14-0 
4-0 
0-9 
3-2 
Neptune . . . 
16-0 
4-4 
0-8 
2-6 
If our IiyjDotheses give a fair account of the facts the iiumljers in tliis tliird C(.)luuiu 
u'ill Ije proportional to Assuming for ^ the uniform value </> = 2, v^e can 
calculate the actual values of and these are given in the fourtli column. 
§ 28. Knowing nothing about the variation in Xq, we shall he content as a 
preliminary hypothesis to suppose it to liave the same value for each planet. 
Combining this with the hypotheses already formulated, we notice that \/Ao^ ought to 
have the same value for each planet, as therefore ought also the function 
mass/(radius)^, which is tabulated in column (3). 
It will he seen at once that there is a certain amount of uniformity about ll)c 
numbers in this column, but it requires some consideration to determine how mncL 
significance is to be attached to this uniformity. 
Now, apart from any hypothesis as to how the solar system originated or reached 
its present configuration—Lc., regarding the solar system as a fortuitous collectio]i ol 
bodies of varying sizes—should expect the mean density to be greatest in the 
greatest planets. We should, therefore, expect the quantity (mass)/(radius)'" to be 
more variable than the I'adius. In other words, we shoidd, d priori, expect less 
uniformity in the third column than in the second. Judged by this criterion, tlie 
uniformity of the numbeis in the third column would he very significant. Further, 
the variation in these numbers is of the kind we should expect. For Instance, it is 
known that the density of Jupiter is very much greater iieai* tlie centre than near the 
surface; we should accordingly expect a large value of (/>, and therefore a large entry 
in the third column. The same argument would apply to tlie Sun, but the physical 
constitution of the Sun is probably so difierent from that of the planets that there 
could be no surprise at the Sun figuring as an exceptional case. Another excejitiou 
is that of Mars. Part of the discrejiancy might, perluqis, be attributed to the 
