THE JUMP OF THE DRIVING-WHEEL OF A LOCOMOTIVE ENGINE. 
563 
weight of a single wheel and its portion of the axle, and Wi represents the weight, 
exclusive of the driving-wheels, which must be raised that either side of the 
engine may jump*, that is, half the weight of the engine exclusive of the driving- 
wheels,— W=li to li tons, W, = 8 | to 1 1 | tons, g=32-19084 ; whence I have 
made the following calculations from formula (59.). 
Weight of the 
engine in tons, 
including the 
driving-wheels. 
Weight of a pair 
of wheels with 
Formula (59.) 
reduced, 
128-76(i+^) 
A > \ 
Displacement of the centre of gravity of a six-feet 
driving-wheel, which will cause a jump of the 
wheel on the rail. 
cranked axle, 
in tons. 
Rate of travelling in miles per hour. 
50 . 
60 . 
70 . 
2*5 
1030-08 
-4128 
•2867 . 
•2106 
20 
3 
858-4 
•3434 
•2384 
•1751 
2'5 
1287-6 
•5150 
•3576 
•2628 
25 
3 
1073 
•4292 
•2908 
00 
It appears, by formula (59.), that the displacement of the centre of gravity necessary 
to produce a jump at any given speed, is not dependent on the actual weight of the 
engine or the wheels, but on the ratio of their weights ; and, from the above Table, 
that when the weight of the engine and wheels is 6 f times that of the driving- 
wheels, a displacement of 2f inches in the centre of gravity is enough to create a 
jump when the train is travelling at sixty miles an hour, or of 2 inches when it is 
travelling at seventy miles ; this displacement varying inversely as the square of the 
velocity is less, other things being the same, as the square of the diameter of the 
wheel is less ; for the radius of the wheel being represented by a, the angular velocity 
is represented by *'= 7^5 and substituting this value, formula (59.) becomes 
If the weight W of the wheel be supposed to vary as the square of its diameter and 
be represented by this formula will become 
* It ■will be observed, that the cranks being placed on the axle at right angles to one another, when the 
centre of gravity on the one side is in a favourable position for jumping, it is in an unfavourable position on 
the other side, so that it can only jump on one side at once, and the efforts on the two sides cdternate. 
