562 
THE JUMP OF THE DRIVING-WHEEL OF A LOCOMOTIVE ENGINE. 
In order that there may be a jump, this expression must be negative. 
or 
or 
9 
>W-1-Wi or 
(58.) 
(59.) 
The Driving-Wheel of a Locomotive Engine. 
The attention of engineers was some years since directed to the effects which 
might result from the false balancing of a wheel by accidents on railways, which 
appeared to be occasioned by a tendency to jump in the driving-wheels of the 
engines. The cranked axle in all cases destroys the balance of the driving-wheel 
unless a counterpoise be applied ; at that time there was no counterpoise, and the 
axle was so cranked as to displace the centre of gravity more than it does now. 
Mr. George Heaton, of Birmingham, appears to have been principally instrumental 
in causing the danger of this false balancing of the driving-wheels to be understood. 
By means of an ingenious apparatus*, which enabled him to roll a falsely-balanced 
wheel round the circumference of a table with any given velocity, and to make any 
required displacement of the centre of gravity, he showed the tendency to jump, 
produced even by a very small displacement, to be so great, as to leave no doubt on 
the minds of practical men as to the danger of such displacement in the case of 
locomotive engines, and a counterbalance is now, I believe, always applied. To 
determine what is the degree of accuracy required in such a counterpoise, I have 
calculated from the preceding formulae that displacement of the centre of gravity 
of a driving-wheel of a locomotive engine, which is necessary to cause it to jump 
at the high velocities not unfrequently attained at some parts of the journey of an 
express train ; from such information as I have been able to obtain as to the 
dimensions of such wheels, and their weights, and those of the engines'}'. The 
weight of a pair of driving-wheels, six feet in diameter, with a cranked axle, varies, 
I am told, from 2^ to 3 tons ; and that of an engine on the London and Bir- 
mingham Railway, when filled with water, from 20 to 25 tons. If n represent the 
number of miles per hour at which the engine is travelling, it may be shown by a 
simple calculation, that the angular velocity, in feet, of a six-feet wheel is represented by 
22n 1 
or by gW very nearly. In this case we have, therefore, — since W represents the 
* This apparatus is exhibited by Professor Co-wpek in his lectures on machinery at King’s College. It has 
also been placed by Col. IVIohin among the apparatus of the Conservatoir des Arts et Metiers at Paris. 
t 1 have not included in this calculation the inertia of the crank rods, of the slide gearing, or of the piston and 
piston rods. The effect of these is to increase the tendency to jump produced by the displacement of the centre 
of gravity of the wheel ; and the like effect is due to the thrust upon the piston rod. The discussion of these 
subjects does not belong to my present paper. 
