202 MEMOIR OF THE LATE PROF. E. HODGKINSON^ F.R.S. 



in operation when a beam is broken transversely than those 

 simply and usually designated tensile and compressive. If 

 a beam is broken transversely^ and the existence and posi- 

 tion of the neutral surface are admitted_, then it is not 

 difficult to conceive the existence of a third force between 

 two adjacent laminae unequally extended or compressed. 



This is really what happens, and the existence of which 

 was well known to Mr. Hodgkinson, who thought it to be 

 so small in practical cases that its accumulated action would 

 not produce much effect on the breaking strain of the 

 beam. Be this_, however, as it may, there is some 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, necessarily involves the equality of 

 tensile and compressive forces — a conclusion which is not 

 justified by Mr. Hodgkinson^s experience. In the second 

 place, Mr. Barlow makes it appear that the error in the 

 breaking strain of a beam is nearly one-half, by neglecting 

 the force of adhesion between the adjacent laminae. We 

 hardly think this conclusion is based upon sound premises, 

 although it necessarily follows from the results of a formula 

 which has been obtained by considering only the two 

 forces, viz. tensile and compressive. But it is hardly fair 

 on the part of Mr. Barlow to institute a comparison be- 

 tween the resistance to flexure and the results of a formula 

 (W = fac?/'H-Z) in which i\idit resistance to flexure is neg- 

 lected, without applying the well-known corrections to 

 that formula. When a beam is strained to a considerable 

 extent, the deflection becomes sensible, and of course the 

 reaction at the supports, being perpendicular to the surface 



