470 THE STRENGTH 



D, throughout the same beam, will be a constant 

 quantity, or nearly so; the strength of the 

 beam therefore at any part will be nearly in 

 proportion to that; of its bottom rib at that 

 part; and as the strain will be less toward the 

 ends, the bottom rib may be reduced there 

 likewise. 



; Suppose the bottom rib to be formed of two 

 equal parabolas, the vertex of one of them 

 A C B being at C ; 



C 



then by the nature of the curve, any ordinate 

 rf e is as A e X B e ; the strength of the bottom 

 rib therefore, and consequently that of the 

 beam at that place will be as this rectangle. 

 It is shewn too by writers on the strength of 

 materials that the rectangle A 6 x Be is the 

 proportion of strength which a beam ought to 

 have to bear equally the same weight every 

 where, or a weight laid uniformly over it; it 

 would appear therefore that the beam above is 

 rightly devised, and these views will be 

 strengthened by the future experiments. 



The length of the parabola AB in the fol- 



