210 MEMOIR OF EATON HODGKINSON. 



pliy," a work of great merit and well adapted for the time in which it appeared, 

 contains only tlie 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 undoubtedly arise from a change taking 

 place in the position of the fulcrum 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 lengthening 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 frac- 

 ture, 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 sufficiently exam- 

 ined." (See Playfair's " Outlines," vol. i, p. 153.) Professor Barlow, in his 

 ''Essay on the Strength and Stress .of Timber," published in 1817, at page 32, 

 shows in an admirable manner the inaccurate views of Dr. Robison respecting 

 the determination of the neutral line, but fails entirely to remedy the defect. 

 Barlow proposes, what is equally ineffective, to fix the position of the neutral 

 line, by supposing the moments of the extended fibres about the neutral axis to 

 be equal to the moments of the compressed fibres about the same line." Sir J. 

 Leslie, in his "Elements of Natural Philosophy," published in 1823, at page 

 234, states that "in the case of a horizontal beam supported at both ends, but 

 depressed by its own weight, the upper surface becomes concave and the under 

 surface convex. The particles of tlie upper surface are therefore mutually con 

 densed ; in a certain intermediate curve the particles are not affected longitud 

 inally, though bent from their rectilineal position. This curve of neutral action 

 may be assumed in the middle of the beam." Dr. 0. Gregory, in his *' Mechan- 

 ics," published in 1826, at page 122, vol. i, states, in reference to the subject of 

 the neutral line, " There is, moreover, the consideration that, when a beam 

 deposited horizontally, or nearly so, is ruptured by a vertical pressure, a horizon- 

 tal stratum, from end to end, is compressed, and the other poriion extended or 

 stretched, the thin lamina between these two being regarded as a neutral axis. 

 This, again, is a curious topic of inquiry." This author gives several theories 

 of the strength of materials from Venturoli, not any one of which contains the 

 correct determination of the neutral line. From these quotations of the best 

 informed writers, are we not justified in the inference that to the late Professor 

 Htxlgkinson belonged the merit of first accurately conceiving the true mechan- 

 ical principle by which the position of the neutral line in the section of fracture 

 could be determined? He did this by equating the forces of extension with the 

 forces of compression — a method which is now universally adopted in comput- 

 ing the strength of beams. This method of fixing the neutral line, like all 

 new methods, advanced to its present position by slow degrees ; but, after many 

 conflicts and discussions, the triumphant declaration of Professor Barlow, at the 

 British Association of 1833, established this great principle, which was first con- 

 ceived by Mr. Hodgkinson, who, single-handed, had maintained his position 

 against the formidable powers of acknowledged authorities. Professor Barlow, 

 in his report " On the Present State of Our Knowledge Eespecting the Strength 

 of Materials," printed in the third volume of the reports of the British Associa- 

 tion for the Advancement of Science, 1833, very justly alludes to this subject, 

 and states as follows : " Mr. Hodgkinson, however, in a very ingenious paper 

 read at the Manchester Philosophical Society in 1822, has pointed out an error 



