580 TRANSACTIONS OF THE 



the friction. If, on the other hand, the velocity were to dimin- 

 ish gradually, the power would be inferior to tlie friction ; but if 

 we take the engine at the moment it has acquired a certain uni- 

 form velocity, and if that velocity be maintained without altera- 

 tion, the jpower of the engine thus applied must be exactly eq\ial 

 to the friction it undergoes, or else there would be acceleration 

 or retardation in the motion. Thus knowing the power obtained 

 by the engine, we necessarily know the resistance to the motion, 

 which is the sum of the friction of the train and that of the 

 engine; and, besides, this sum is equal to the power applied ; 

 consequently, the friction of the engine is equal to the power 

 applied, less the friction of the train. 



This would give us the precise friction of tlie engine, if we 

 knew the pressure in the cylinder. But there are cases in which 

 the pressure in the cylinder is equal to the pressure in the boiler. 

 These cases are those in which the engine attains the limit of its 

 power with the pressure at which it is working; or when it draws 

 the largest load it can draw with that pressure. When the engine 

 has arrived at the limit of its power, the pressure in the cylinder 

 cannot be less than in the boiler. The friction of engines is 

 always increased by the load ; it is a principle in statics, and 

 shown by the lever or pulley, that two forces to equilibrate on 

 that machine, the fulcrum, must support the resulting eflbrt of 

 the two forces; friction follows precisely the same rule, being 

 itself in proportion to the pressure. The curves on our railroads 

 offer an additional friction, which is greater according to the 

 degree of their incurvation. 



The cars on a railroad, being oblong, have a tendency to con- 

 tinue their motion in a straight line; consequently if they are 

 compelled to follow a curve, the flange of the wheel no longer 

 passes in a tangent along the rail without touching it, as it does 

 in a direct motion. The rail presents itself crosswise before the 

 wheel, and forces it to deviate from its direction. And the wheel 

 that follows the exterior rail of the curve, has farther to travel 

 than that which follows the interior rail. On passing the curves, 

 the cars are thrown by the centrifugal force of the motion against 

 the outwai'd rail, the result is a lateral friction of the flange of 

 the wheel against the rail, which does not exist in direct motion. 

 The air forms a resistance to a train in motion; when five cars 

 move together, the air resists about 9 lbs. per ton; if each moved 

 separately, the average resistance would be about 11 h lbs. per 

 ton. 



