128 



LECTURE 



points to be connected. And this brings us to the consideration of the 

 important subject of grade. 



I have stated that the force required to move a load on a level bears 

 but a small proportion to the whole weight ; but that on an inclined 

 plane, the animal drawing the load must lift it vertically through a 

 distance which depends upon the inclination. Careful experiments 

 have shown that in a first-class mountain road the grade should not 

 exceed one in thirteen — that is, a rise of one foot in every thirteen feet 

 of horizontal distance, and that even this grade should be used only 

 on short sections, and should be varied by frequent levels on which 

 teams may rest. Now, if the difference of height between any two 

 points is more than one thirteenth of the horizontal distance, it will 

 evidently be impossible to connect them by a straight road, since it 

 will be too steep. The horizontal distance must be increased while 

 the vertical distance remains the same. In cases where the points are 

 at the extremities of a straight, narrow valley with precipitous sides, 

 as is frequently found in the Alps, considerable difficulty will be en- 

 countered in getting this increased length, and the ingenuity of the 

 engineer will be severely taxed. 



In Fig. 4., we have two points, 

 A and B, ten miles apart, horizon- 

 tally situated in the same straight 

 valley, and B 5,280 feet above A_, 

 A having an elevation of 1,864 

 feet above the sea, and B 7,144 

 feet, a road ten miles long con- 

 necting them would have a grade 

 of one in ten, which is too steep. 

 The length of the line must, there- 

 fore, be increased. This may be 

 done by running up the valley of 

 the stream to the northwest, as 



indicated by the dotted line 



A C B, or by turning the line upon 

 itself in a series of zig-zags on the 

 slope of the hill on the other side., 

 as shown by the continuous line A D B. Both of these expedients are 

 frequently resorted to. Of course, where there is a valley up which the 

 road can be taken according to the first method, it should be taken 

 advantage of, since the sharp turns of the zig-zags are thereby avoided. 

 On the mountain roads of Switzerland, there are many interesting 

 examples of these zig-zags or lacets, (lacings,) as they are called by the 

 French engineers. Frequently, on the steep side of a valley there is 

 no other way of overcoming the ascent, and they must be resorted to. 

 On the Italian side of the'Spliigen Pass, the road winds in this way 

 down the almost vertical side of" the mountain above the little village 

 of Isella, and the carriage descends rapidly, turning the corners at the 

 end of the zig-zags and swinging backwards and forwards over the 

 valley. 



On the St. Gothard Pass also, on the Italian side, above the village 

 of Airolo, the road leaves the main valley and runs in the same way up 



Fig. 4. 



