OF IRON BEAMS. 415 



thenJ^Xefx =: Sf and by mechanics y*Xa:c/a; 



= ffs,fXa^dx = gps, Wkemse/Vdi/ = s'.fYydy 



= jl^'i f^y^dy = SP'^' W® hdivt therefore, 

 from equation (4), 



gs = ng's\ (6) 



Cor. If « = 1, gs z=. g^s\ 



Hence it appears that the neutral line divides 

 the surface of fracture so, that the parts mul- 

 tiplied by the distances of their centers of 

 gravity from that Hne are in a given ratio ;* and 

 when equal extensions and compressions are 

 produced by equal forces, these products are 

 equal. The experiments on cast and malleable 

 iron, further on, give w = 1, answering to this 

 latter case, but the mean from my experiments 

 on timber, before the elasticity was destroyed, 



gave w = -J- ; see paper on the Strength of 

 Materials, Manchester Memoirs, vol. 4, pages 

 273 and 4. 



9. If we put in equation (5) the values from 

 article 8, we obtain 



W x' G/ = -i- (gps + ng'p's') = '^(p + p'), 



since ng's' = gs. 



• Mr. Barlow, Essay on Strength of Timber, has arrived at the 

 same conclusion; but it is to be regretted, tliat able Philosopher 

 has mistaken the consequences resulting from it. 



