PROCEEDINGS OF SECTION H. 365 
the driving wheels bounded along the rails, which were bent 
and broken in the most extraordinary way, as by blows of a 
gigantic hammer, the points of impact being situated at dis- 
tances apart exactly equal to the circumference of the wheels. 
As the critical speed at which the wheels should begin to lft 
off the rails was only 48 miles per hour, while the actual speed, 
according to the finding of a board of inquiry, was 75, the 
wonder is, not that a long stretch of heavy railway was utterly 
disorganised, but that the engine and train escaped total 
destruction. 
These, then, are the actions which we seek to minimise by in- 
serting balance weights in the wheels. 
The mechanism of the locomotive may be divided into parts 
of two kinds. First, those that revolve about a centre; 
second, those that reciprocate, or travel backward and forward. 
Cranks and coupling rods belong to the first class; pistons, 
piston rods, and cross heads to the second. The connecting rod 
is an intermediate case, and may be dealt with by reearding 
part as revolving and part as reciprocating. To divide the 
connecting into its two parts accurately would involve difficult 
mathematics, but it is a sufficiently good approximation to re- 
gard half its length (not half its weight) as one, and half as the 
other. 
Eccentrics, eccentric rods, and valve gearing being compara- 
tively light, and having but a short stroke, especially when 
linked up, as is usual at high speeds, have no perceptible dis- 
turbing action, and so may be ignored. 
Now, revolving masses may be accurately balanced by other 
revolving masses placed opposite to them, and of the same 
moment. By this is meant that a weight of 1 lb. at 1 ft. 
radius may be counteracted by ; 4 Ib. at 2 ft., or 2 lbs. at 4 ft. 
All that is really necessary is that the product of mass oa 
radius be kept the same. 
Mr = Mr' 
If it is net convenient to place the balance weight exactly 
opposite the part to be balanced, to take an actual case, we 
desire to balance an inside crank and big end, weighing 600 
lbs., by weights in the wheels, we must proportion those 
weights inversely to the distance of the crank from the wheels, 
and as in an ordinary inside-cylinder engine the centre of the 
crank is almost exactly twice as far from one wheel as it is 
from the other, we should put 400 lbs. in the near, and 200 
Ibs. in the far wheel at the same radius as the crank. As there 
are two cranks at right angles, each requiring balancing, we 
should thus have two balance weights in each wheel at right 
angles to each other. But there is no objection, from a dynami- 
cal point of view to replacing these two balance weights by 
