Geology. 193 



assume that they approximately offset each other, we may reach 

 some conclusion respecting the possibility of the fission of the 

 actual celestial bodies by discussing the corresponding homo- 

 geneous incompressible body. This is the assumption adopted 

 here, but, because of its uncertainty, in the applications to the 

 solar system, where it turns out fission is impossible, all approxi- 

 mations are made so as to favor fission, and it is assumed that in 

 the actual bodies fission ma}^ be immanent long before it is 

 possible in the homogeneous ones. These safeguards and simpli- 

 fications are possible and easy because it is a negative result 

 which is reached " (p. 158). 



" For the applications we assume that an actual celestial body 

 will not be in danger of fission until the corresponding homo- 

 geneous incompressible body arrives at the state where the 

 Jaeobian ellipsoids branch. The densit}^ at this stage is less 

 than one-fourth that at which the pear-shaped figures branch, 

 and actual fission in the homogeneous bodies is certainly beyond 

 this form, if indeed fission into only two bodies is ever possible. 

 With this very conservative assumption we proceed to some cal- 

 culations. 



" (1) We find that the sun can not arrive at this critical stage 

 until its mean density shall have exceeded 307 XlO 11 on the water 

 standard. This corresponds to an equatorial diameter of the sun 

 of about 22 miles. 



u (2) We find that the sun can not become so oblate as Saturn 

 is now until its mean density shall have exceeded 148X10 10 on 

 the water standard. This corresponds to an equatorial diameter 

 of the sun of about 75 miles. 



"Since even the latter density is impossibly great, we conclude 

 that the sun will never become so oblate as Saturn is now, and 

 that it will always be more stable than Saturn is now. 



" (3) We find that Saturn can not arrive at the critical stage at 

 which the Jaeobian ellipsoids branch until its mean density shall 

 have become 21 times that of water. This corresponds to a polar 

 diameter of 16,500 miles and an equatorial diameter of 28,400 

 miles. We conclude because of the great density demanded that 

 Saturn will never suffer fission. 



" (4) We assume that the earth and moon were once one mass 

 and get their original moment of momentum from its present 

 value. In computing it, however, we make certain approxima- 

 tions so as to get it too large and thus favor the conclusion of 

 fission, then we add to it the maximum amount the sun's tides 

 can have taken from the earth, and finally we add 25 per cent for 

 fear there may be some unknown sensible factors omitted. Then 

 we find that this hypothetical earth-moon mass could not get even 

 to the critical point where the Jaeobian ellipsoids branch until 

 its mean density became 215 times that of water, or about 40 

 times the present mean density of the earth and moon. It would 

 not become even so oblate as Saturn is now until its density had 

 become 10*4 times that of water. Therefore we conclude that 



