174 Analysis of Scientific Books and Memoirs. 



would exert equal forces to the weights w, w', &c. themselves; and, 

 therefore, LM may he considered as the line of the fracture of a beam, 

 whereof ELM is a vertical section, the central spring on which the tri- 

 angle turned being its neutral line, and the springs and weights on each 

 side of it representing the forces of tension and compression ; which, 

 from the experiments above, have no particular relation to their distances 

 from the neutral line, as assumed by Mr Barlow, but must, under all 

 the circumstances, be equal. 



I have now considered, at perhaps too great a length, the principal 

 question in the review ; and as the result has been, in my opinion, une- 

 quivocally to show the erroneousness of the theory in dispute, it may be 

 the less necessary to dwell upon the other remarks of the writer. I shall, 

 however, briefly notice each of them. 



The first thing that particularly arrested my attention, (and it indeed 

 created some surprise) was, to find the writer representing this subject, 

 viz. the research for a correct theory of the lateral strength of materials, 

 " as one rather of curious philosophical inquiry than of actual import- 

 ance," and the reason assigned is, that we can compare the strengths of 

 similar beams without it. In the same manner, we might assert that if 

 we had a globe, or a barrel, of which, by filling or otherwise, we had ob- 

 tained the content, it would be easy to find the content of another globe 

 or barrel, similar to the former, though larger or smaller. But if we knew 

 the content of a cube, or a globe, and wanted that of a barrel, it is evi- 

 dent that it would be indispensably necessary to have some more general 

 rule by which the contents of dissimilar bodies could be compared toge- 

 ther : The same observation must apply to the strength of materials. In 

 timber, indeed, the want of such a rule may be little felt, its beams being 

 generally rectangular ; but iron may be cast into various forms, and it 

 would be considered both expensive and inconvenient if it were always 

 necessary to cast two beams, in order to break one of them, before we 

 could be able to judge of the strength of the other. The opinion of the 

 reviewer, too, in this matter, seems (judging from the labour that philo- 

 sophers have bestowed upon it,) to be at variance with that of almost 

 every writer on the subject, from Galileo to Mr Barlow. I shall, there- 

 fore, leave this, and proceed to his other remarks. I had shown, in the 

 above mentioned Memoir, that, in incompressible bodies, Mr Barlow's 

 theory gave the strength of a beam double what it ought to do ; this, the 

 writer of the Review admits, but makes a charge of an opposite nature 

 against the theory I advocate. It shall be given in his own words — " It 

 is singular Mr Hodgkinson did not perceive, that precisely the same want 

 of generality applies also to his theory, by taking the opposite imaginary 

 case, viz. of the material being infinitely inextensible ; for, in this case, 

 the area of tension being zero, the breaking weight would be zero, or 

 taking any small area of tension, then the strength would be infinite, 

 both inconsistent results." In reply to this, I would ask that ingenious 

 writer, whether I might not, with greater propriety, express my surprise 

 at his not having seen that a body might be inextensible, comparatively 

 with its compressibility, without being infinitely strong, and consequent- 



