The N.Z. Journal of Science and Technology. 
22 
[Jan, 
with cranks at right angles. The surging-force is equal to that caused by 
a mass left unbalanced at each crank, given by— 
U = M -|- R — B (cos 8 -fr sin 8) 
or B (cos 8 -f- sin 8) = M + &R ... (4) 
where U = mass left unbalanced at each crank, in pounds; k = fraction 
of the reciprocating mass balanced. 
We will assume throughout that the maximum allowable speed of the 
locomotive is such that V — d. This agrees very closely with general 
practice, and seems a very fair assumption. In which case— 
Maximum value of surging-force = 4-535 fU. 
If the engine is not to be bodily vibrated the surging-force must not 
W 
exceed - ’ where W = weight of engine in pounds, and 6 = the usual or 
average factor of adhesion. 
Thus we arrive at— 
U must not exceed 
W 
27f 
It was probably reasoning along these lines that led G. R. Henderson 
to suggest* * * § in a paper to the Engineers* Association of Virginia in 1896 
W 
that might be left unbalanced per side. Later the Master Mechanics' 
360 
Institute resolved*}" that 
W 
400 
might be so left. 
Obviously, however, any 
such rule should include the factor r, if engines of different strokes 
are to be dealt with. In England the rather absurd empirical rule is 
generally adopted that k in equation (4) should be f, which means that 
U does not exceed J of the reciprocating weight. In any case, the writer 
is convinced that U should be kept as small as possible consistent with 
the hammerblow being kept within allowable limits. There is no doubt 
that there is a marked saving in fuel and repairs gained by so doing, and 
from D. K. Clark and the “ Canute ”J onwards all locomotive history tends 
to prove this. The surging is most objectionable from the point of view 
of the driver, who likes a smooth-riding engine ; and for some not easily 
explainable reason its deleterious effect on locomotive economy is very 
pronounced. There is certainly a tendency among locomotive - designers 
to be too easily satisfied upon this point, so long as the mystic value 
of f for k is not reduced. 
The statement of Sharp* that the surging-force “ is less objectionable 
than the vertical or horizontal couples ; it merely produces a cyclic varia¬ 
tion of pull on the drawbar,” is misleading, since the “ cyclic variation ” 
at high speeds is generally about four times the total pull! 
The nosing-couple causes transverse swaying of the engine to and fro 
across the track, and both Sharp§ and Dalby|| speak respectfully of the 
“ derailing-danger ” caused thereby; but modern experience discounts 
their statements. Four-cylinder engines running without balance-weights 
are now ordinary practice in England and on the Continent, and such 
engines are renowned for their steadiness ; yet the nosing-couple is very 
much larger than in the ordinary two-cylinder engine with balance-weights. 
The New Zealand balanced compounds have the large low-pressure cylinders 
* G. R. Henderson, Locomotive Operation, 2nd ed., p. 43, 1907. 
t Trans. Master Mechanics ’ Inst, of America, 1896, p. 160 ; 1897, p. 120. 
j Zerah Colburn, Locomotive Engineering, p. 253, 1871. 
§ Archibald Sharp, Balancing of Engines, p. 178. 
|| W. E. Dalby, The Balancing of Engines, p. 85. 
