80 



MECHANICS. 



Sometimes several forces act at once on different parts. 

 For example, the spokes of Avagon-wheels require strength 

 at the hub for stiffening the wheel ; they must be strong 

 in the middle to prevent bending, and large enough at 



Fif^. 94. 



a ^ 



the outer ends, where they are soonest Aveakened by de- 

 cay. Hence there should be nearly a uniform taper, 

 slightly larger at the middle, and with an enlargement at 

 the outer end, as c (fig. 94). 



A very useful rule in practice, in giving strength to 

 structures, is this : The strength of every square beam or 

 stick to support a weight increases exactly as the width 

 increases, and also exactly as the square of the depth in- 

 creases. For example, a stick of timber eight 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, according to the rule given. But where 

 one stick of timber is twice as deep^ the width being the 

 same, it is four thnes stronger ; if three times as deep, it 

 is nine times stronger, 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 inch- 

 es wide will be twelve times as strong when edgewise as 

 when lying flat. Hence the increase in strength given to 

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

 to farm-bridges, by making them narrow and deep. 



