lOS MECHANICS. 



inches wide and four inches deep (that is, four inches 

 thick), is exactly twice as strong as another only four 

 inches wide, and with the same depth. It is twice as 

 wide, and consequently twice as strong ; that is, its 

 strength increases just as the width increases, accord- 

 ing to the rule given. But where one stick of timber is 

 twice as deep^ the width heing the same, it is, four times 

 stronger ; if three times as deep, it is nine times strong- 

 er, and so on. Its strength increases as the square of 

 the depth, as already stated. The same rule will show 

 that a board an inch thick and twelve inches wide will 

 be twelve times as strong when edgewise as when lying 

 flat. Hence the increase in strength given to whipple- 

 trees, fence-posts, joists, rafters, and string-pieces to 

 farm-bridges, by making them narrow and deep. 



Again, the strength of a round stick increases as the 

 cube of the diameter increases ; that is, a round piece 

 of wood three inches in diameter is eight times as 

 strong as one an inch and a half in diameter, and twen- 

 ty-seven times as strong as one an inch in diameter. 

 This rule shows that a fork handle an inch and a half 

 in diameter at the middle is as much stronger than 

 one an inch and a quarter in diameter, as seven is 

 greater than four. Now this rule would enable the 

 farmer to ascertain this without breaking half a dozen 

 fork handles in trying the experiment, and it would 

 enable the manufacturer to know, without the labor of 

 trying many experiments, that if he makes a fork han- 

 dle an mch and a half at the middle, tapering a quar- 

 ter of an inch toward the ends, it will enable the work- 

 man to lift with it nearly twice as much hay as with 

 one an inch and a quarter only through its whole length. 



