DISASTROUS EEFECTS OF COLLISION ON RAILWAYS. 305 



kind, a point, at which if a horizontal impulse be communicated, no 

 jumping motion of the kind we are considering can possibly result, 

 but if the impulse be communicated, at a point lower than this, the 

 carriage will lift up its fore wheels, and if higher than this, it will lift up 

 its hind wheels. 



Professor Willis has been so kind as to fit up, at my request, a small 

 model, which affords a most satisfactory experimental proof of the truth 

 of this proposition*, which I previously arrived at by mathematical 

 considerations. 



If we neglect the mass of the pair of wheels and axle about which 

 the rotation is supposed to take place, a simple mathematical calcu- 

 lation suffices to show, that the point of quiescence, or that at which 

 the horizontal impulse must be applied, in order that no rotatory motion 

 of the kind we are considering may be impressed, will be situated in the 

 same horizontal level with the centre of gravity of the carriage. But 

 since in locomotive engines the wheels and axles are of considerable mass, 

 (in Stephenson's locomotive the driving pair of wheels and the axle 

 connecting them weigh about a ton and a quarter,) it was desirable 

 to ascertain how far this circumstance would cause the point of quiescence 

 to deviate from the level of the centre of gravity. 



The problem then becomes more complicated, but the result of the 

 investigation shows, that when the rail is regarded as perfectly smooth, 

 the deviation of the point of quiescence from the centre of gravity of 

 the whole carriage, including the wheels and axle, is nothing, whatever be 

 the mass of the latter. The roughness of the rail may however cause it to 

 deviate slightly below this level, but even in the case of perfect roughness, 

 the deviation is so slight that in practice it may be safely neglected. 



The mathematical details connected with this part of the subject 

 will be given in the sequel ; and I now proceed to mention a second 

 principle, which is essential to the solution I am about to offer, and 

 which, in the absence of sufficient data, I assume rather as a very 

 probable hypothesis, than as a mathematically demonstrated theorem 

 like the former. The principle I assume is this, that if the two 



* The experiment was exhibited at the time the communication was read. 



