268 Introduction to the Study of Science 



construction, in order to increase the speed and effect economy 

 in hauling freight and passenger trains. A recently completed 

 cut-off on a section of the Lackawanna Railroad (Fig. 78) is 

 an example of such engineering economy. At a cost of about 

 $12,000,000, a saving of less than four miles in route is effected ; 

 but the new grade is such that two locomotives now haul the 

 load which required five over the old grade; in passenger 

 traffic twenty minutes is saved, and in freight about one hour 

 over the old schedule. 



Tunnels are necessary on many railroads, and they may be 

 used on highways through hilly country or for subway systems 

 in large cities. The subways of Boston and New York City, 

 the tubes under the Hudson and the East rivers of New York, 

 and the mountain tunnels of the Great Northern Railway in 

 Washington may be mentioned as examples. The advantages 

 of tunnels are many. Prepare a list of advantages for class 

 discussion. Compare them with the disadvantages. 



112. Grades. The inclined plane and work. Aside from 

 commercial benefits to be obtained by locating a road through 

 productive country, there is the necessity of avoiding long and 

 steep grades. Every one knows that it takes less force to 

 haul a load on the level than on a grade ; and that it takes less 

 force to lift it up an incline than to lift it vertically, that is, 

 against the direct force of gravity. The steeper the grade, the 

 greater must be the force to haul the load. If the grade is 

 light, the distance to be covered is greater; but the force re- 

 quired at any moment is less. Another way of expressing it 

 is to say that the amount of work done in lifting a load by the 

 aid of an inclined plane to any given height is about the same, 

 perhaps if anything more, than is necessary in lifting it ver- 

 tically ; but it takes less force at any given moment. 



Suppose a box weighing 400 pounds is to be loaded on a wagon 

 that is four feet above the ground on which the box rests. One 

 man cannot lift the box directly; but with aid of a skid or 

 plank 16 feet long he can load it quite easily. The inclined 



