35i Analysis of Sc'wnlijic Books and Memoirs. 



ing it from the wall: and therefore the pressure on the fulcrum /must 

 just be as great as the resistance in F, all the horizontal forces being sup- 

 posed collected into those two points. 



" For the first outline of this subject, see the valuable treatise of Dr 

 Robison, referred to above." 



Before entering more particularly on this subject, it maybe proper 

 to state, that we do not conceive Mr Hodgkinson has, by any means, suc- 

 ceeded in proving, by the calculations he has made, the inaccuracy of the 

 theory in question. Mr Barlow obviously assumes, that the operation 

 of breaking consists of two distinct forces, namely, that necessary to pro- 

 duce extension, and that of compression, and that the strength will be 

 greater as either of these are greater ; and it is, therefore, quite consistent 



1 , 2«M2 1 sba? 

 Suppose d = T a then ^^ = ^ X __ 



2 _4_ sba ? 



i\ U — 32 X l(v + 2) 



3 9 slat 



d ~~ ~R" = 32" X l&+2~ 



4 _ 16 sba* 



d = T" — 32 X 7(^+27 



5 _ 25 sbat 

 d ~T a — 3Y X «w + 2) 



6 _ 36 bat 



d = "8" a — 32 X l(v+2) 



7 49 sba? 



d ~ ~8~° ~ 32" X l^+27 



— Jl _ 64 sba°- 



~~H a 32 X Kv+2y 



The last three terms of which must be false, since they all give the strengths great- 

 er than — , which is that of the joist when every fibre is submitted to ten- 



Hv + 2) 



sion, and the preceding five terms (setting aside accidental coincidences) must be 

 erroneous too, since they lead in a regular progression to the last three. 



Now, as Mr Barlow has offered no reasons against the theory in the text (further 

 than that it does not agree with his own, which we have just been examining,) we 

 see no cause why it should be rejected, especially since it seems to us to be every 

 where consistent and just. 



It may not be improper to mention that M. Coulomb, in his paper on this sub- 

 ject (Mcmohcs preseiites A PAcadimic des Sciences, torn, vii.) makes LXW = the 

 forces in F X PF+ the forces in f X P/, and endeavours to show that the forces 

 in F and f, or those of tension and compression are equal : the theory of Mr Bar- 

 low then differs from that of the French philosopher in this last particular, but we 

 conceive that the latter must be right; — the results from it are the same as from 

 that in the text, though it is much less convenient in its use. We particularly re- 

 fer the reader to the above paper of M. Coulomb, as he has given a very minute 

 analysis of the transverse strain : and the reason why this matter has been so 

 long overlooked, seems to be that both M. Coulomb and Dr Robison have content, 

 ed themselves by giving a bare outline of it." 



