OF IRON BEAMS. 421 



neutral line wherever it was being a fixed one. 

 But, I conceive, it proves nothing as to the 

 equality of the momenta of the forces on each 

 side of the neutral line, which was necessary 

 for supporting the principle above. Indeed, I 

 believe that principle incapable of proof, and 

 one which could not have got the currency 

 among authors that it is stated by M. Duleau 

 to have, had it not been for the obscurity of 

 the subject. , 



14. It is that principle, in a more generalized 

 form, upon which I animadverted (Manchester 

 Memoirs, vol. 4.) as forming the basis of Mr. 

 Barlow's Theory of the strength of Timber; 

 but it appears from the quotation above that the 

 mistake has not originated with that gentleman. 



15. The theory I have offered above, and which 

 has been given in a more general manner, as 

 applied to timber, in the volume of the Memoirs 

 just referred to, depends on the equality of 

 the forces on each side of the neutral line, or 

 F' =y, equation (1). There cannot I conceive 

 be any doubt of that equality ; it seems suffi- 

 ciently evident from the principle of the lever, 

 as in Art. 5; but the following mechanical 

 contrivance, the account of which is extracted 

 from a paper of mine which was published in 



