128 Cataclysmic Motion [CH. vi 



but the alteration is so slight as to be of no importance within the limits of 

 accuracy which are required for cosmogonic discussions. 



128. A more important matter is that we have in effect supposed the 

 tide-generating mass to move forward and then backward along a line (Ox) 

 through the primary, which has in consequence always been an axis of sym- 

 metry. In nature the tide-generating mass will not in general approach 

 the primary along a line through its centre; indeed if it did a material 

 collision would occur, and the course of events before this collision took place 

 would be relatively unimportant. 



We must examine what happens when the tide-generating mass passes 

 by the primary in an orbit which does not involve a material collision. Let 

 us examine the motion in three cases, in which the tide- generating body 

 moves (i) exceedingly slowly, (ii) exceedingly fast, (iii) at an intermediate 

 rate. 



129. When the motion is exceedingly slow an equilibrium theory, such 

 as has already been developed, will give approximately accurate results if the 

 major-axis of the primary is supposed always to point to the secondary. 

 A slow rotation will of course be set up in the primary and this will slightly 

 alter its shape, but in a search for the general characteristics of the motion, 

 such as we are now engaged in, small effects of this kind are not worth 

 delaying over. 



130. When the motion of the tide-generating mass is exceedingly rapid, 

 we may treat the tidal forces as " impulsive " as has already been done in 

 123. A tide-generating potential fl acting for an interval dt will set up in 

 the primary a system of impulsive velocities which may be derived from a 

 velocit} 7 potential ldt. Thus if the tidal forces act only for a short interval 

 from to r, they will set up impulsive velocities which will be derivable 

 from a velocity potential <I> given by 



-0= fldt. 



To examine the general effect of the motion of the tide-generating mass, 

 it will be sufficient to consider the simplest case. We shall accordingly 

 suppose the tide to be raised by a point or sphere of mass M' . 



Let v denote the velocity of the secondary mass at any instant. Then in 

 any interval dt, the secondary moves over a distance of path da = vdt The 

 contribution to <I> is 



but may also be expressed as 



M' 



