Heretofore, longitudinal motions in trains have usually been studied by assuming that the train can be replaced by a bar whose mass and elasticity are uniformly distributed. By means of a long-neglected branch of mathematics known as “difference equations,” it is easy to solve motion problems for trains of concentrated masses connected by springs.

Motion curves are given for a train of five uniform cars, also for one of five nonuniform cars, following a bump at one end. A motion curve is given for the uniform train when constant forces are applied in succession to the cars. The methods shown make it possible to find the effect of any ordinary force system in far less time than by older procedures.

The velocity of waves of force in a train is discussed. It is shown that the elastic-bar assumption gives large errors for this speed. A better approximation is suggested.

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