135-137] Summary 137 



SUMMARY OF RESULTS 



137. At this stage we leave the problem of the motions of an incom- 

 pressible homogeneous mass of fluid. Before passing on to the jiext problem 

 it may be of value to summarise, in the briefest and broadest manner 

 possible, the results which have been obtained. 



We have had three distinct problems under discussion I. The Tidal 

 Problem, II. The Rotational Problem, and III. The Double-star Problem. 



In the Tidal Problem we have studied the motion of a primary mass as 

 tides are raised in it by the continued approach and ultimate recession of a 

 secondary mass. 



In the Rotational Problem we have studied the motion of a single mass 

 rotating freely in space, the rotation increasing as the mass cools by 

 radiation. 



In the Double-star Problem we have studied the motion of two stars 

 revolving round one another, a secular change being supposed to occur in 

 their distance apart. 



In all three problems we have found that the motion will consist of two 

 parts. The first may be described as " statical " or " secular " ; the second 

 may be described as "dynamical" or "cataclysmic." 



In the Rotational Problem and in the Double-star Problem, there is a 

 quite precise demarcation between the two types of motion. In the Tidal 

 Problem, the two motions may gradually merge into one another, although 

 here also there may be a precisely defined point of transition. 



In all three problems, the statical motion has been found to consist of a 

 slow secular change of shape in which .the body under consideration remains 

 always of a spheroidal or ellipsoidal shape, except that in the tidal and 

 double-star problems (in which two masses are involved) the spheroidal or 

 ellipsoidal shape of the primary may be slightly distorted by tides of third 

 and higher orders raised by the secondary mass. In the Tidal Problem, the 

 motion is through a series of prolate spheroids ; in the Rotational Problem 

 the motion is first through a series of oblate spheroids (Maclaurin's spheroids), 

 and then through a series of ellipsoids (Jacobi's ellipsoids) ; in the Double- 

 star Problem the motion is through a series of ellipsoids. 



In all three problems, dynamical motion supervenes when the prolate 

 spheroid or ellipsoid reaches a certain elongation. The motion results in 

 the formation of a furrow or system of furrows on the elongated mass. In 

 the Tidal Problem the furrowing process does not commence immediately, 

 and there may be any number of furrows formed. In the two other problems, 

 the furrows start to form at once and only one furrow is formed. 



