20] RELATING TO THE MOON'S ORBIT. 139 



Now, since the orbit would be fixed, were it not for the disturbing 

 force, it might be argued in exactly the same manner as is done by Pro- 

 fessor Challis in the passage above referred to, that the eccentricity of the 

 orbit must be a function of the force which causes the orbit to revolve, 

 but this we know to be a false conclusion. 



What would depend on the disturbing force in this case, would be, not 

 the total amount of the fluctuation of distance in different revolutions, but 

 the number of revolutions of the body in which such fluctuation would take 

 place, or the time of revolution of the apse. If the disturbing force were 

 increased, the total fluctuation in the value of the radius-vector in question 

 would be the same as before, but the change from one of the extreme 

 values to the other would occupy a shorter time. 



The objection mentioned by Professor Challis at the top of page 283, 

 is alone quite fatal to the supposition that the eccentricity of the Moon's 

 orbit must have a particular value. Where is the proof that the eccen- 

 tricity would settle down to such a value, as Professor Challis imagines, if 

 it were initially different ? 



In fact, it is easy to shew, by the method of variation of elements, 

 that there would be no such settlement, but that the non-periodic part of 

 the eccentricity would remain constant. 



182 



