THE AUTHOR'S THEORY OF THE TIDES 151 



resides in the fact of rotation, there being in this case, by 

 premiss, no rotation, there could be no deformation at 

 all; hence the two spheres would arrive at their point of 

 impact as perfectly spherical as when they began falling. 



The alternative answer is that of the hypothesis of 

 statical tides, which astronomers make use of without 

 hesitancy whenever it suits their purpose, in spite of its 

 gross logical inconsistency. This view asserts, that the 

 spheres in question would elongate in the direction of the 

 line of descent, so that by the time they reached the point 

 of collision they would somewhat resemble row-boats 

 meeting bow on. 



In order to expose the fallacy of both these views, 

 let us try the time-honored plan of picking up the other 

 end of the skein, and working backwards. Suppose, 

 then, the collision to be a thing of the past and the resul- 

 tant body to have had time to compose itself, as it natur- 

 ally would, into a new sphere in all respects like our two 

 original ones, only, of course, twice their size. Conceive 

 this major sphere to be cleanly severed in half, and the 

 divided parts to be gently removed from each other to 

 their original separating distance. Without doubt, by 

 the time they arrive at those extreme points, the two 

 hemispheres will no longer be such in shape, but will nec- 

 essarily have acquired their aforetime sphericity. The 

 question then arises as to what should be the interme- 

 diate or transitional shapes. 



May it go without argument, that the chain of trans- 

 formations, going and coming, should be the same, only 

 in reverse order ? If this be conceded, then, according to 

 Newton's idea, the hemispheres immediately following 

 their sundering should instantly leap into spheres then 

 and there, without waiting for further removal. On the 

 other hand, according to the Statics, they should, instead, 

 but quite as spasmodically, reassume their boat-like 

 forms, and from then to the end of the outward journey 

 gradually exchange these for the spherical. These, to 

 my thinking, palpable reductios ad absurdum, effectu- 

 ally refute both these classical owfo'-equilibrium hypo- 

 theses. 



