270 Introduction to the Study of Science 



box vertically four feet is only 16 foot-pounds. If now it takes 

 22.4 foot-pounds to lift the load the given height with the aid 

 of incline and wheels, it evidently takes considerably more 

 work than is performed in lifting the same load vertically. 

 But the work is so distributed as to make possible its per- 

 formance by a relatively small force. 



To what is this extra work due? It is found to be due in 

 part to the resistance or friction encountered by the rolling 

 wheels on the track and on their axles (page 259 ff.). Some of 

 the friction is eliminated by lubricating the axles, but the 

 remainder is enough to account for the additional work. 



Grades and distances. In building roads engineers plan, 

 wherever a change in level is necessary, as in crossing moun- 

 tains, to keep the grade as light as possible in order to save 

 motive force, and to keep the distance as short as possible in 

 order to reduce to a minimum the friction in hauling. High- 

 ways are not kept as strictly within a limited range of grade 

 as are railroads. But heavy grades on highways are usually 

 short. For railroads, a rise of more than two and one half 

 feet in a hundred feet, or more than a two and one half per 

 cent grade, reduces greatly the hauling efficiency of the road. 

 Light grades and long distances are preferable to heavy grades 

 and short distances. 



Exercise. Is the total amount of work done in lifting a given 

 load up a long incline greater or less than that done in lifting it to the 

 same elevation up a short incline? In which case is the greater 

 amount of force required? 



Grades and tractive effort. The motive force of railroads is 

 limited by certain almost unchangeable conditions. Increased 

 motive force in a steam engine necessitates increased size and 

 weight of engine, which two factors are restricted by the nature 

 of the roadbed, the size and strength of the rails, the gauge of 

 the track, the headway clearance of bridges and tunnels, and 

 many other conditions which are practically unchangeable. 



