Mr Hodgkinson on the Strength of Materials. 357 



In the second, 



, „ Log. 60 1-7781512 



90 : 20 : : 270 : (53)" = 60. .\ * = T^J 3 = i7t242759 = 1 ' 03 - 



.98 + 1.03 + .91 _ ,. 



" And taking the mean, we have g — ••>' — ulu " 



mate mean value of v- A number which so nearly approaches to unity, 

 the index of perfect elasticity, that it seems unnecessary to assume any 

 other law." 



We cannot here subscribe to the author's decision ; for admitting »= lj 

 we should have 20 : 28 : : 105 : 147, (taking his own example,) whereas the 

 experimental number is 241, instead of 147, which is too great a differ- 

 ence to allow us to use this law in any physical inquiry. The fact un- 

 questionably is, that woody fibres differ very essentially from bodies per- 

 fectly elastic ; their extension, for a certain time, is nearly or exactly pro- 

 portional to the existing force ; but beyond a certain point, they diminish 

 in their resistance as they are more extended, and in the particular exam- 

 ple in question, a part of the fibres still retained their entire elastic force, 

 while the outward ones were considerably reduced in their resisting power, 

 and consequently the deduction made by considering them all as in one 

 state is fallacious. The same remark applies to the experiments on the 

 law of compression. With respect to the chapter employed in deducing 

 the neutral line, it is so involved in the question on which we have al- 

 ready entered at some length, that we must pass it over in this place; ob- 

 serving only, that the relations deduced with respect to the area of tension 

 and compression, differ considerably from what is shown to be the actual 

 case in Willow, by Duhamel, and in Fir, by Mr Barlow, by direct experi- 

 ment. The former of these experimenters cut his bars three quarters 

 through, filling up the cut by a wedge, without diminishing the strength, 

 and the latter cut his fir beams 5-8ths through, with but a very slight 

 diminution. The discrepancy, however, is, we conceive, sufficiently ac- 

 counted for by the author ; viz. that his computations relate to beams 

 moderately strained, and the others to the breaking strains. The author 

 having thus first investigated the question on general principles, as ex- 

 plained in the leading part of this paper, and then deduced successively 

 the laws of tension and compression ; and, lastly, the position of the neu- 

 tral line or axis, proceeds to the solution of several examples somewhat 

 parallel with those given by Mr Barlow in his Essay, with a view of con- 

 necting the direct resistance of materials with their resistance to a transverse 

 strain, and, admitting his previous deductions, with great ingenuity and 

 precision ; but the accuracy of the whole is involved in the doubtful posi- 

 tion which we have endeavoured to examine in the early part of this arti- 

 cle.^ Fortunately, however, this doubt affects only what may be consider- 

 ed the curious side of the question, the useful part being in a great mea- 

 sure independent of it ; for in all practical determinations, engineers, ar- 

 chitects, and others concerned in such inquiries, naturally make their cal- 

 culations from experiments of a similar kind to the case in hand; as, for 

 example, where the question is a tie, they look to experiments on direct 



