1919 .] 
Jenkinson.—Balancing of Locomotives. 
25 
locomotives from the balance point of view. It is interesting to note that 
the English method is better than the American for inside cylinders, but 
not so good for outside. Each country, therefore, adopted the compromise 
which, among those known at the time, was the best suited to its conditions, 
surely more by good luck than good management! 
The high nosing-couple that occurs in four-cylinder engines, which 
are famed for their steady running, compared with that generated on two- 
cylinder engines of similar power with § of reciprocating weight balanced 
(even when the cylinders are outside), is noticeable, and has its bearing 
on the writer’s contention that nosing-couple is negligible on express engines. 
The resisting-power of the adhesion alone to nosing on an engine of the 
size assumed (4-4-0 type) would be in the neighbourhood of 300,000 foot¬ 
pounds, and even if the resistance of the weight of the engine resting on 
the journals is taken a good margin of safety would doubtless result. 
Polar curve of nosing-couple-- and hammerblow-for different angles (5) 
of balance-weights. 
The equations developed in this paper are, of course, only applicable 
to two-cylinder locomotives, but they may be applied to four-cylinder 
engines with cranks at 90° by giving the negative sign to the values of the 
forces and couples deriving from the inside cylinders. Equations for three- 
cylinder and four-cylinder engines with cranks at other angles than 90° 
can be formulated by the same methods of attack, but are not in general 
of such a simple form. 
The portion of the work which is original with the writer consists in 
deriving general formulae based on the angle of the balance-weights for the 
value of the forces or couples causing the three main disturbances, and 
thence recognizing that the English and American methods of balancing 
are only particular cases of the infinite number of solutions that satisfy 
the fundamental requirement of keeping the surging-force down to any 
predetermined amount. The minimum nosing and minimum hammerblow 
solutions are two important cases not likely to be arrived at by any other 
methods than those here adopted. 
