462 THE POPULAR SCIENCE MONTHLY. 



a very short time the plank would begin to "bend and buckle in the 

 center. In order to increase the strength of this primitive bridge, 

 we could place another plank beside it, making the bridge twenty- 

 four inches wide, and, if the passing load were made to bear upon 

 the entire width of this bridge, of course the bridge would bear 

 just twice as much as one plank; but, in order to double the 

 strength of the bridge, we have also doubled the amount of 

 material necessary in its construction, and therefore have not in 

 any way increased the economy. 



This system might be carried on to infinity, and almost any 

 amount of required strength be obtained by placing a sufficient 

 number of planks one beside the other. But, returning again to 

 the two planks, instead of placing them one beside the other, sup- 

 pose we place one plank on top of the other, and nail them to- 

 gether firmly, so that they shall act as one plank (Fig. 2). We 



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Fig. 2 



then have a bridge eighteen feet long, twelve inches wide, and six 

 inches deep. In this bridge we have exactly the same amount of 

 material we had when the two planks were placed side by side, 

 but we have four times as strong a bridge instead of only twice ; 

 that is, we have doubled the amount of material, but we have 

 multiplied the strength by four. 



If one plank would hold up one hundred pounds on the center, 

 then the two planks placed side by side would hold up two hun- 

 dred pounds ; while, placing the planks one on top of the other, 

 and nailing them firmly together, they would hold up four hun- 

 dred pounds. In this way we see that, in order to increase the 

 strength of the bridge or beam faster than we increase the amount 

 of material, the increased amount of material should go into the 

 depth of the beam and not into the width of it. This is one of 

 the first principles in the resistance of material, that the strength 

 of a beam varies directly as the width that is, if we make the 

 beam twice as wide, it will hold twice as much ; and that the 

 strength varies as the square of the depth that is, if we make 

 it twice as deep, it will hold up four times as much. If we make 

 it three times as deep, it will hold up nine times as much of a 

 load. So that you can readily understand that, in order to in- 

 crease the strength of the bridge or beam without increasing the 

 material in the same proportion, the increased amount of material 

 should be put into the depth and not into the width. 



We now have a bridge twelve inches wide and six inches deep, 

 which will hold up four times as much as our original bridge, 

 twelve inches wide and three inches deep, and the amount of 

 material is simply doubled. To advance one step beyond this, 



