314 Mr POWER, ON THE PREVENTION OF THE 



with which must be combined the conditions, 



r 



, V 



a = — • 

 r 



Substituting these values of §& and a, and equating to zero the 

 coefficients of Ss, $0, we obtain 



= F-(M+M')V + Mba - M'V.^, 



= Fh - Fb + MbV - M{a* + V + #) «. 

 The former of which gives 



F+Mba 



V = 



M+M'(l+^) 



Substituting this in the second, and putting 





q = ; re- > we find 



E. h ~ g 



a " M ' a 3 + If + qb ' 

 Hence in general, 



E- LzS 



a ~ Ma* + h* + qb' 



M' 



where q = when -^ = o, 



sv when the rail is smooth, 



M + M' 



M'(l + ^)b 



— when the rail is perfectly rough. 



M + M (l + £) 



