230 MEMOIR OF EATON HODGKINSON. 



Mr. Hodgkinson, who tlionglit it to be so small in practical cases tliat its accumu- 

 lated action would not produce much effect on the breaking strain of the beam. 



Be this, however, as it ma}^, there is sonie little difficulty in subscribing to all 

 that Mr. Barlow advances on this important and interesting subject. In the first 

 place there might be an exception taken to Mr. Barlow's method of fixing the 

 position of the neutral line. Does he not fix it by an appeal to his senses rather 

 than by the result of the mathematical analysis of the data he has obtained from 

 experiment'? The position which he fixes upon, viz., the centre of the beam, 

 necessarity involves the equality of tensile and compressive forces, a cfOnclusion 

 which is not justified by Mr. Hodgkinson's experience. In the second place 

 JMr. Barlow makes it appear that the error in tlie breaking strain of a beam is 

 nearly one-half by neglecting the force of adhesion between the adjacent laminse. 

 We hardly think this conclusion is based upon sound premises, although it neces- 

 sarily follows from the results of a formula which has been obtained by consider- 

 ing only the two forces, viz., tensile and compressive. But it is hardl}^ fair on 

 the part of Mr. Barlow to institute a comparison between the resistance to flexure 

 and the results of a formula (W=fac//^-?) in which that resistance to flexure is 

 neglected, without applying the well-known corrections to that formula. When 

 a beam is strahied to a considerable extent the deflection becomes sensible, and of 

 course the reaction at the supports, being perpendicular to the surface of the beam, 

 makes an angle with the vertical. This circumstance affects the above formula 

 in two ways : fii"st, it alters the amount of the moment about a line in the neutral 

 surface ; and, second, its tendency is to change the position of the neutral line. 

 Therefore, unless these corrections are apjn'oximated to and applied to the for- 

 mula, 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 ^^iit tensio sic vis" as it is well knowni, 

 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 exist- 

 ence 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 resist- 

 ance to flexure in Mr. Barlow's second memoir amounts to the assumption that 

 the force of extension varies by a law expressed by ax-\-b, where a and b are 

 constants, and x the distance of the particle from the neutral axis. I may add, 

 in conclusion, that Jlr. Hodgkinson 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 ordi- 

 nary formula, or the theoretical method by which he estimates its amount, still I 

 can with confidence reconnnend these memoirs to the engineering student as 

 being worthy of his attentive perusal. 



In concluding this memoir of one of the most distinguished members of the 

 society, I cannot help feeling that the description herein given of his character 

 and labors falls short of the real position which they occupy in the public mind ; 

 and although I have had much pleasure in reading and collating the discoveries 

 of Mr. Hodgkinson, I regret that the preparation of this memoir has not been 

 placed in abk'r hands. One thing, however, consoles me, and supplies me with 

 an ample reward, which no criticisms on my effort can possibly cancel, and that 

 is, I have been engaged, to the best of my abilit}", in the endeavor to perpetuate 

 the memory of a great and good man, whose singuhir pi'aise it is to have spent 

 his life and his great powers for the good of mankind, with a single aim to truth 

 nnd science, without desiring or gaining pecuniary reward. 



