These consist of the head and tail resistances and the side resistance. The head and tail resistances are nearly constant for all trains of given velocity, varying but slightly with the varying cross-section of engines and cars. The side resistance varies with the length of the train and the character of the cars, whether box-cars or flats. Vestibul-ing the cars of passenger-trains has had a considerable effect in reducing the side resistances by preventing much of the eddying of air-currents between the cars, although this is one of the least of the advantages of vestibuling. Atmospheric resistance is generally assumed to vary as the square of the velocity, and, although this may be nearly true, it has been experimentally demonstrated to be at least inaccurate. The head resistance is frequently assumed to vary as the area of the cross-section, but this has been definitely demonstrated to be very far from true. A freight-train, composed partly of flat-cars and partly of box-cars, will encounter considerably more atmospheric resistance than a train consisting exclusively of either type of car, other things being equal. On account of the extreme variation in the making-up of freight-trains no accurate figures regarding atmospheric resistance would be of much value, and this probably explains why more effort has not been made to obtain accurate determinations of this form of resistance. In the comparatively few experiments which have been made, the head resistance has been assumed to vary as the cross-sectional area and also as the square of the velocity. The results obtained by different experimenters have been so discordant as to be of little value. The discrepancies are due to the fact that both of the assumptions regarding the variation of the atmospheric resistances are inaccurate.

(B) Oscillatory And Concussive

These resistances are considered to vary as the square of the velocity. Probably this is nearly, if not quite, correct, on the general principle that such resistances consist of a series of impacts. The laws of mechanics tell us that the force of impact varies as the square of the velocity. These impacts are due to irregularities in the track and to the effect of the yielding of the rails and ties in a ballast which is not homogeneous in character nor absolutely uniform in its elasticity. Even though it were possible to make a precise determination of the amount of this resistance in any particular case, the value obtained would only be true for that particular piece of track and for the particular degree of excellence or defect which the track then possessed. The general improvement in track maintenance during late years has had a large influence in increasing the possible train-load by decreasing the train resistance. The expenditure of money to improve track will give a road thus improved an advantage over a competing road with a poorer track by reducing train resistance and thus reducing the cost of handling traffic. Although it is almost impossible to determine accurately the effect of a given expenditure in track improvement in reducing track resistance, it is significant to note that the resistances per ton which were measured by experimenters even 25 years ago were far higher than those obtained on the improved tracks of the present day.