NOTES ON THE POSSIBILITY OF FISSION OF A 

 CONTRACTING ROTATING FLUID MASS. 



I. INTRODUCTION. 



In the speculations on cosmogony there are two fairly definite hypoth- 

 eses as to the manner in which a single body may give rise to two or more 

 distinct masses without the intervention of external agencies. The first, as 

 outlined by Laplace, is that possibly a rotating fluid may abandon an equa- 

 torial ring, which will subsequently be brought by its self-gravitation into an 

 approximately spherical mass. The second, the fission theory, had its rise 

 in Darwin's researches on tidal evolution, and in his speculations on the 

 origin of the moon. It has found extensive application in attempts at 

 explaining the great abundance of binary stars. 



The hypothesis of Laplace has the support of no observational evidence, 

 unless we regard the rings of Saturn as such, and rests upon no well-elab- 

 orated theory. On the contrary, there are well-known considerations of the 

 moment of momentum of our system which compel us to reject it as being 

 an unsatisfactory hypothesis for the explanation of the development of the 

 planets. But the fission theory of Darwin, even if the origin of the moon is 

 left aside as being doubtful, has strong claims for attention because of its 

 immediate application to explaining the origin of spectroscopic and visual 

 binaries and certain classes of variable stars. Besides, it is in a general way 

 confirmed by the investigations of Maclaurin, Jacobi, Kelvin, Poincare, and 

 Darwin on the figures of equilibrium of rotating homogeneous fluids, and on 

 their stabiUties. In particular, considering a series of homogeneous fluid 

 masses of the same density but of different rates of rotation it is shown that 

 there is a continuous series of figures of stable equilibrium beginning with 

 the sphere for zero rate of rotation; then, with increasing rotation, passing 

 along a line of oblate spheroids until a certain rate of rotation is reached; 

 then, with decreasing rate of rotation but with increasing moment of 

 momentum, branching to a series of ellipsoids with three unequal axes, and 

 continuing until a certain elongation is reached; and finally, at this point, 

 branching to a series of so-called pear-shaped figures. It has been con- 

 jectured that if it were possible to follow the pear-shaped figures sufficiently 

 far, it would be found that they would eventually reach a point where they 

 would separate into two distinct masses. From this line of reasoning it has 

 been regarded as probable that celestial masses, through loss of heat and 

 consequent contraction, do break up in this way often enough to make the 

 process an important one in cosmogony. 



Aside from the unanswered question as to what form the pear-shaped 

 figures finally lead, there are two reasons for being cautious in accepting the 

 conclusions. One is that the celestial masses are by no means homogene- 



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