MEMOIR OF THE LATE PROF. E. HODGKINSON^ F.R.S. 203 



of the beauij makes an angle witli the vertical. This cir- 

 cumstance affects the above formula in two ways : ist^ it 

 alters the amount of the moment about a line in the neutral 

 surface ; and 2nd_, its tendency is to change the position 

 of the neutral line. Therefore^ unless these corrections are 

 approximated to and applied to the formula, it is not safe 

 to infer_, as Mr. Barlow has done, that, by neglecting the 

 resistance to flexure, the ordinary formula only gives nearly 

 half the breaking weight. 



Another source of error is in the law " ut tensio sic vis,^^ 

 as it is well known, from Mr. Hodgkinson^s experiments, 

 that the forces of extension and compression are neither 

 equal nor vary with the extension and compression when 

 the strains are large. I quite agree, as did Mr. Hodgkinson, 

 with Mr. Barlow as to the existence of a resistance to 

 flexure in the transverse strain of beams besides the ordi- 

 nary forces of tension and compression ; but the mode of 

 estimating this resistance to flexure in Mr. Barlow^s second 

 memoir amounts to the assumption that the force of exten- 

 sion varies by a law expressed by ax + 6, where a and b are 

 constants, and x the distance of the particle from the 

 neutral axis. I may add, in conclusion, that Mr. Hodg- 

 kinson has computed the tensile and compressive forces, 

 subject to a law much more general than the one here 

 alluded to, with great clearness and adaptation to include 

 practical cases. 



Mr. Barlow^ s two memoirs, however, are the first on 

 this subject to insist on the existence of a distinct force to 

 resist flexure ; and although I do not see the force of his 

 comparison of the resistance to flexure with the results of 

 the ordinary formula, or the theoretical method by which 

 he estimates its amount, still I can with confidence recom- 

 mend these memoirs to the engineering student as being- 

 worthy of his attentive perusal. 



In concluding this memoir of one of the most distin- 



