472 Mr. H. W. Chapman on 



From (5) 



^ = (o + It cos 6)6- h sin 66 2 -^ 2 sin 6{h + a cos 0) — o*^a sin 0. 



This also can never become infinite, as will be seen by 

 considering the expressions for yjr, 0, co d . 



*/ p 2 I 7W~2 



For the motion to be physically possible, \ L must 



always < some fixed quantity v, depending on the nature of 



*/TT 2 i Tp 2 



the egg and plane. We have seen that L- L cannot 



R 



become large by the numerator becoming large ; it remains 



to see whether it can become large by the denominator 



becoming small. 



From (7) we have 



ll=hfJb-\-g. 



We must therefore see if hfi +g can be made to become small 

 without I\ 2 + F 2 2 also becoming small. 

 Equation (18) gives 



A2 /A 2 h 2 _/* \ •• h A - (h, 9 „ 9X ghA 2 \ 



-M(X 2 + C^ 2 -An 2 + A 2 K) 



. 3gr// A 2 2 ■ A /M] ~ Z¥ 2 TZk ~ 77~- 



\/^+A + C* + 2C^ + (C-A)^ 



Suppose h positive, and put o> 3 negative and in |large 

 enough to make \ positive. Take /,t = 0. 

 Then we have 



A * (A +1 + 5) ( ; ^)= - ! A ^ 2 - « ^ +c » 2 ) + a v(s£[ - 1 ) 



+ (negative terms). 



_ We can clearly make this as small as we like by choosing 

 co 3 and m properly. 



We have still to see that this is a possible position under 

 the circumstances. 



