160 MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 



the penetration of Professor Barlow and others who had 

 examined the subject. The opinions here expressed are 

 founded upon the results obtained by reading the works of 

 the best authors previous to 1822. 



Dr. Robison^ Playfair, Barlow, Dr. O. Gregory, and Sir 

 J. Leslie are sufficiently known in the walks of science, to 

 justify the assertion that their works on elementary subjects 

 represent the true state and progress of the knowledge of 

 the strength and strain of materials. Playfair^s ^ Outlines 

 of Natural Philosophy/ a work of great merit, and well 

 adapted for the time in which it appeared, contains only 

 the following paragraph on the subject of the neutral 

 line : — 



" But it is also said that a tube of metal has been found 

 to support a greater transverse strain than a solid cylinder 

 of the same diameter; or that a cylinder, when bored in 

 the direction of the axis, and a considerable part taken 

 away, was stronger than before.^' " This must undoubt- 

 edly arise from a change taking place in the position of 

 the falcrum or hinge round which the fracture is made. 

 In the case of a cylinder, and indeed of all solids, the 

 fulcrum is not the mere outward edge, but a point in the 

 interior, on the one side of which the fibres are elongated, 

 and on the other crushed together. The point, then, 

 which serves as the fulcrum will be found within the solid, 

 at a greater or less distance, as the parts resist lengthen- 

 ing more than crushing. The consequence of this is_, that 

 when the centre of gravity and the fulcrum are brought 

 nearer to one another, the strength of the beam or bar is 

 diminished. When the heart of a solid mass is cut out, as 

 is supposed of the cylinder, the fulcrum, or the axis of the 

 fracture, is perhaps kept nearer to the surface than when 

 the whole is a solid mass. This, at least, seems to be the 

 most probable account that can at present be given of a 

 phenomenon not a little paradoxical, and not yet suffi- 



