ON RAILWAY CONSTANTS. 265 



tlie total resistance. It would follow, then, that whether the load were trans- 

 ported at 5 or 50 miles per hour the expenditure of moving power would be 

 the same. But we have already shown that no constant quantity will express 

 the resistance. The resistance, in fact, is not dependent upon weight merely, 

 but on speed also. 



Of the three elements proposed as the basis of any computation, the first, 

 viz. the character of the gradients, is fixed and unalterable. The second and 

 third, viz. the weight and velocity, may be considered variable. When the 

 dimensions of the engine are once fixed upon, the maximum of load is in- 

 deed limited by the tractive power of the engine and the steepest inclination 

 it may have to ascend, and the speed is limited by the capability of the boiler 

 to generate steam at the rate required, and of the density sufficient to over- 

 come the resistance due to the speed. Within such limits the cases actually 

 occurring in practice must be found to range. And according to the pecu- 

 liar circumstances of the traffic, a high or low rate of speed, light or heavy 

 trains will be adopted. Suppose the case of a perfectly level railway, on 

 which a high average rate of speed has to be maintained. Since resistance 

 is found to increase with the speed in an accelerated ratio, and since the 

 boiler requires time for the generation of steam, a very considerable part of 

 the maximum load which the engine could travel with at a slow speed must 

 be thrown off" to enable it to accomplish the higher rate. In other words, 

 the load must be comparatively small ; less, in fact, than the maximum on an 

 ascending gradient of considerable acclivity. It does not often happen that 

 the surface of a tract of country over which a railway is projected to pass is 

 sufiiciently free from inequality and variations of level as to admit a level or 

 nearly level line to be constructed Avithout entailing great expense in the 

 formation of embankments, cuttings, and other works ; and it therefore be- 

 comes a most important and interesting consideration, how far the expenses 

 of moving power would be increased, and the velocity of transport dimi- 

 nished, by substituting a line of railway whose section shall be more con- 

 formable to the general outline of the country ; a line consequently much 

 less costly, but at the same time presenting a series of gradients, the inclina- 

 tions of which should not be so steep as to render necessary any loss of mo- 

 tive power by application of the brakes during a descent. 



As an abstract question of dynamics, the power expended (under the con- 

 dition that the combined resistances of friction and the atmosphere are con- 

 stant whatever the speed) would be the same for a train travelling between 

 two given points on the same level, Avhether the road were level or undula- 

 ting, making due allowance for the difference of distance traversed. On a 

 level railway the speed of travelling Avould be uniform throughout, and the 

 combined resistances alluded to would then, in calm weather, be constant 

 throughout ; but on an undulating railway the speed of the train would 

 vaiy. And the question comes to this : W^ill the increased velocity on the 

 descending gradients compensate for the time lost in the ascents ? Will the 

 average rate of speed over the whole line be different? In either case the 

 load must manifestly be much smaller than the maximum which the engine 

 could draw on the level at a slow speed. The engine will therefore be able 

 to ascend the gradients of the undulating line merely by reducing its velocity, 

 and thus relieving itself from as much of the excess of resistance, which ex- 

 ists in addition to friction, as may be necessary to enable the power again to 

 equilibrate with the load. The inconvenience is only a reduction of speed 

 during the ascents, and of course a loss of time upon the ascending gradient, 

 as compared with the time that would have been occupied in conveying the 

 train over an equal length of level. 



