DISASTROUS EFFECTS OF COLLISION ON RAILWAYS. 315 



Since -= ™ is the vertical distance of the centre of gravity of 



M + M below that of M ; it follows that in the second case, as in 

 the first, the impulse must pass through the centre of gravity of the 

 whole carriage M + M', in order that no rotatory motion may be 

 impressed. 



In the third case, if, for greater practical convenience, we wish to 

 determine the distance (q t suppose) of the point of quiescence below 

 the centre of gravity of the whole carriage, denoting by ft, the height 

 of the centre of gravity of the whole carriage above the level of the 

 axle, we have 



Mb Mb 



ft =ft - 



M+ M'~ M+ M 

 k' 



±d ' I 1 + v) ° 



M 



q ~ q M+ M'~ ~ TTT FT M+ M 



Reducing and substituting for b its value in ft,, we find 



b ' M' m 



v l£_~ M + M'' r* 



r 2 



If, with Tredgold, we suppose M' = l£ 



M '' 1? * b ' M' h'* . . 



°, vt = ng-nar, • ^ b < ver y nearl y- 



M + M + M ' 



r 



r ' = 12/ 



, tons, 



and M + M' 



M 1 

 and at a rough estimate take - = ^, we find q = .006^ Very nearly. 



Thus, if b,= 12 inches, q,= .072 inches; 



if b, = 18 inches, q t = .108; 



if ft, - 2 feet, q, = .144. 



Hence we see, that the weight of the wheels and axles, and the 

 roughness or smoothness of the rail, make no difference perceptible in 

 practice ; and that in order to ensure the absence of rotatory motion in a 



