On (he Slringlh of Beams, 193 



" The Column No. 1 contains the length of the beams in feet 

 (French). 



The column No. 2 contains the deflexion of each beam in 

 inches and lines (French). 



The column No. 3 contains half the weight of each beam 

 added to the weight that broke it, in lbs. (French.) 



The colunm No. 4 contains the weight that ought to hate 



broken each beam, if the strength is as — . 



, The column No. 5 contains the weight that ought to have 

 broken each beam, if the strength had varied in the inverse ratio 

 of the length. 



Your correspondent objects to the conclusion that the de- 

 flexion of beams is as the square of their length, (No. 208, 

 page 144,) because the deflexion is as the scjuare of the length, 

 and as the strain which is as tiie length ; but he does not say 

 why the deflexion is as the square of the length. In beams of 



w 

 the same length, the deflexion is as -grr,; for when beams are of 



the same length, the weights that will break them are directly 

 as BD% and the deflexion at the time of fracture is as the cur- 

 vature, vvhicli is inversely as the depth: therefore, if VV be any 

 other weight, then, 



BD' : -^- : : W : g^- = the deflexion corresponding to 

 the weight W. 



Now let us conceive the depth and breadth constant, and the 

 length variable, and let AB represent the neutral line, or that 



Vol.4G. No.209. &-p/. 1815. N part 



