Mr Hodgkinson on the Strength of' Materials . 175 



ly, that his remarks do not apply to the theory in question. The iron, 

 in my experiments on compression, may be taken as an example of this 

 extreme case. 



In regard to the suggestions of the writer, in the same page of the Re- 

 view, respecting the possibility of a change in the law of mechanical ac- 

 tion, in consequence of an alteration in the situation of the neutral line, I 

 would refer him to the last experiment with the instrument above, from 

 which it appears, that if the forces, on each side of that which before was 

 the neutral spring, were made unequal, that spring was no longer the neu- 

 tral spring, but some other, on each side of which there was an equality 

 in the forces. 



The last observation of the reviewer which will require to be noticed 

 here, is that in which he objects to my conclusion, " that the mean index 

 (.97) of my experiments on extension approaches so nearly to unity, the 

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

 law ;" and the reason assigned, which is certainly not a very strong one, 

 is, that the result of one of the most anomalous of ray experiments differs 

 widely from that law : — In answer to this, and to his remarks immediately 

 following, I would beg to refer him to my note, page 265, in the memoir 

 above, and to page 280, example third, from which last it appears, that, 

 in the fracture of a joist, the error from the assumption of perfect elas- 

 ticity, was not ji-g- part of the breaking weight. If we had taken the 

 elasticities at \ or § of the breaking weight, which is as far as it is prudent 

 to strain materials in architecture, the deviation from perfect elasticity 

 must have caused a much less error. 



Mr Barlow arrived at his conclusions respecting the situation of the 

 centres of tension and compression, from the application of his theory to 

 experiments. It may not then be uninteresting to take one of the experi- 

 ments he used, and, applying the theory I advocate to it, see what the 

 result will be : — As the easiest, we will take his first experiment (page 156) 

 from which it appears that a beam, 21 inches long, and two inches square, 

 fixed at one end in a wall, required a weight of 558 lbs. to produce the 

 fracture ; the neutral line being at about § of the depth of the beam, and 

 the force of direct cohesion on a square inch of the wood equal to 13000 

 lbs. The formula for the strength of a beam, (see my Essay, pages 244. 

 and 245, Memoir above,) give 



W eig „, = I f 5XM c ti o„ tension X <*+,•), {%£%&£ .'"W 



When .», from the above experiment, is equal 13000 lbs., section of ten- 

 sion == j inch, g-\-g' = 1 inch, />+// = f inch, a — f inch, g = § inch, 

 L = 21 inches, W = 558 lbs., and calling C = I ; and supposing W to 

 be unknown, all the rest being given, wc have : — 

 In the first formula, 



w = 13000XjXl =jH 

 24 X 1 



