MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 201 



verse strength of cast, mixture of cast and wrought, and 

 wrought iron. The experiments were made with great care ; 

 and every source of error that could be was eliminated, not- 

 withstanding the trouble and expense which such a pro- 

 cedure necessitated. Still there was a great difficulty, 

 which was always felt by Mr. Hodgkinson, and which occu- 

 pied, at various times, much of his attention, viz. to connect 

 the breaking weight of the beam with its deflection in such 

 a manner as to indicate true practical results. For this 

 purpose he entered into a very general theoretical investi- 

 gation on the transverse flexure of beams, which is given 

 in the 2nd volume of Tredgold ^ On the Strength of Cast 

 Iron' j but, in order to make the results of this very general 

 investigation practical, he is compelled to assume, 1st, that 

 the forces of extension and compression are proportional to 

 the extensions and compressions ; 2nd, that the force of 

 extension is equal to the force of compression ; 3rd, the 

 reaction at the points of support is always vertical. It is 

 not surprising, then, that a formula, based upon so many 

 assumptions, should fail to represent correctly the relation 

 between the breaking weight and the dimensions of the 

 beam ; this is exactly what has taken place. 



The discordance here alluded to has arrested the at- 

 tention of W. H. Barlow, Esq., C.E., F.K.S.j and the 

 results of his investigations are given in two very in- 

 teresting memoirs, printed in the ^Transactions of the 

 Royal Society' for 1855-1857. It would be great pre- 

 sumption on my part to enter into any profound criticism 

 on the mode of procedure and results of these memoirs, 

 revised as they have been by Professor Barlow, who is 

 justly distinguished by his genius, high attainments, and 

 long life devoted to the interests of science ; but still it 

 may not be out of place here to make one or two observa- 

 tions which occurred to me while reading the memoirs. I 

 quite agree with Mr. Barlow, that there must be other forces 



