If the total resistance against which the train is maintained in motion with an instantaneous velocity of V feet per second is R, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.
If now the prism P be interposed as in the figure, the whole beam is not only refracted upward, but also spread out into the spectrum RV, the horizontal breadth of the band of colours being the same as that of the original image S.
Hence if all the energy supplied to the train is utilized at one axle there is the fundamental relation RV (I) Continuing the above arithmetical illustration, if the wheels to the axle of which the torque is applied are 4 ft.
= RV (2) where T 1, T2, T3, &c. are the torques on the axles whose respective angular velocities are wl,w2, W3, &c.
Multiplying through by w we obtain Tw = 2FwD = 2µWwD = RV (4) This is a fundamental energy equation for any form of locomotive in which there is only one driving-axle.