130 Cataclysmic Motion [en. vi 



that already discussed ( 123) in which p was supposed to act impulsively, 

 and the motions will agree quantitively if / fidt is supposed given by equation 



(382). From equation (379). it appears that the spheroid will lengthen to 

 beyond the critical eccentricity '947741, and so finally depart from the 

 spheroidal shape, if 



........................... (383). 



This criterion only holds in the special case in which the tidal forces 

 satisfy the condition we have described as " impulsive." This requires that 

 the tidal forces shall come and go before the spheroid is much different from 

 a sphere. From equations (363) and (382) it is clear that at the end of the 

 action of the tidal forces, the velocity a of the end of the major-axis is 

 given by 



a 



= 



a " R<?v ' 



The time during which the tidal forces are appreciable will be of the 

 order of 2R jv, so that if r Q + 8a is the length of the semi- major-axis at the 

 end of the encounter we have, as regards order of magnitude, 



Let us now agree conventionally to define the action of tidal forces as 

 "impulsive" when Ba is less than r , so that 8b and c are of course less than 

 j^rv With this conventional definition it appears that an encounter will be 

 impulsive if 



z .............................. (384). 



We see that all encounters at great distances satisfy the condition of the 

 tidal forces being impulsive. Considering in detail an encounter in which 

 M ' is equal to the sun's mass (2 x 10 33 grammes) and in which the two stars 

 pass with a relative velocity of 40 kms. a second, we find that the action 

 will be impulsive if the distance of closest approach ,R is greater than 

 8 x 10 13 cms., which is about the distance of Jupiter from the sun. Having 

 regard to astronomical scales of length we may say that all encounters of 

 stars having masses comparable with that of the sun are impulsive except 

 the very closest ones. 



131. Nevertheless we cannot advance far in our cosmogonic problem so 

 long as we consider only purely transitory encounters, and we must try to 

 examine the effect resulting from the actual finite duration of tidal forces. 



It is difficult to obtain definite or exact results, but the general nature 

 of the motion can best be seen by thinking of the tidal body as moving too 



