366 PROCEEDINGS OF SECTION H. 
one which a simple calculation based on the parallelogram of 
forces shows to be 448 lbs., situated at an angle of 26 des. 
34 min. from the larger one. This axle is now in a state of what 
the writer proposes to call normal balance, and its critical 
speed is infinite; in other words, no matter how fast it rolls 
along the rails, the pressure will be simply that due to the 
weight, and nothing more. 
An outside crank pin, and the proportion of coupling, or con- 
necting rod, carried by it may be balanced by an equal weight 
at equal radius in the adjoining wheel. This is not exactly 
correct, as the weight in the wheel does not revolve in quite 
the same plane as the crank pin and coupling rod. Still, the 
disturbance due to this cause is in most engines not serious. 
To effect this balance with absolute accuracy there must be a 
larger weight in the near wheel opposite to the coupling crank, 
and a small weight on the same side in the distant wheel. 
For example, taking an actual case, the weight of outside crank 
proportion of coupling rod carried by it was 330 Ibs., and to 
balance this with Loe accuracy needed 363 lbs. opposite it 
in the near wheel, and 33 Ibs. on the same side as it in the far 
wheel. Thus in a coupled engine each wheel would carry two 
balance weights to balance the coupling rods and cranks at 
right angles “to each other, one about eleven times as large as 
the other. Of course, these could be combined into one, and 
combined with the other balance weights by the parallelogram 
of forces, as in the preceding case, and, like them, can be re- 
duced in weight proportionately if the size of the wheels per- 
mits their being placed at larger radius. 
Suppose this is done for all the driving and coupled axles 
of an engine, such an engine is in a state of normal balance, its 
critical speed is infinite, and it is absolutely free from any 
vertical action on the road other than that due to its weight. 
But though most unobjectionable from this point of view, 
such an engine might still be subject to undesirable fore and 
aft movements, and if with outside cylinders lateral movements, 
due to inertia of pistons and other reciprocating parts, and the 
problem of dealing with these is much more difficult than the 
preceding one, and can, in fact, be practically solved only in a 
very partial manner by a method of compromise. The diff- 
culty arises from the fact that reciprocating parts must be 
balanced by revolving weights, and that while the horizontal 
resolved part of the centrifugal force of these weights is useful 
for this purpose, the vertical resolved part is us seless, injurious, 
and, if not kept within proper limits, exceedingly dangerous, 
causing the wheels to act as in the case of 365X, already re- 
ferred to. The mode of treatment re ecommended is as fol- 
lows :— 
