MECHANICS. 161 



resist lengthening more than crushing. The con- 

 sequence of this is, that when the centre of gravity 

 and the fulcrum are brought nearer to one ano- 

 ther, the strength of the beam or bar is diminish- 

 ed. When the heart of a solid mass is cut out, as 

 is supposed of the cylinder, the fulcrum, or the 

 axis of the fracture, is perhaps kept nearer to the 

 surface than when the whole is a solid mass. 

 This, at least, seems to be the most probable ac- 

 count that can, at present, be given of a phenomenon 

 not a little paradoxical, and not yet sufficiently ex- 

 amined. 



In similar beams, or solids, of the sme 

 substance, the strength increases as the square of 

 the lengths ; but the weight increases as the cube. 

 There is of course a limit, which, if a beam of a 

 given shape, and of given materials, were to reach, 

 it could only bear its own weight, and would be 

 incapable of farther increase. 



EMERSON'S Mechanics, scholium at the end of section 

 vin. p. 111. 



240. When a beam, instead of projecting from 

 a wall, is supported at both ends, it must break in 

 the middle, and the termination of the fracture 

 will be on the upper side ; and hence, when a rec- 

 tangular beam is supported at both ends, it is able 

 to carry twice as great a load as when it is sup- 

 ported only at one end. 



VOL. I. L When 



