MEMOIR OF EATON HODGKINSON". 



200 



lis. 2. 



the estaWishmcnt of sound practical views of tliis subject, it will be necessary 

 to give a brief exposition, by reference to diagrams, of the history of the section 

 of fracture. 



Every beam of material is ^'S-'^' 



supposed to be composed of an 

 iudelinite number of parallel 

 filaments in the direction of 

 its length, and the breaking 

 of the beam necessitates the 

 breaking of each of the fila- 

 ments of which it is composed. 

 Suppose a beam AB, placed 

 on the fulcnun OF, to be l)ro- 

 ken at the sectitmODIEFL by 

 the weights AV and iv, suspend- 

 ed from the points G and H. 



The theory of Galileo assumes the beam to turn about the fulcrum CF, and 

 each of the tilaments (mu) in the section of fi-acture OLD to sustain an equal 

 force. This hypothesis implies the incompressibility and extensibility of tho 

 material. Leibnitz, the great rival of Newton, assumed the beam to turn 

 about the fulci'um CF, as did Galileo, but assumed, what experiment has con- 

 finned, the force of each filament in the section of rupture to vary in proportion 

 to its distance from the fulcrum CF. This theory implied the incompressi- 

 bility and extensibilitj^ of the material. James Bernoulli, to whose labors 

 science is under great and varied obligations, in reviewing the theories of Gali- 

 leo and Leibnitz, felt convinced of their incorrectness, and that of course they 

 could have no favorable response 

 from the voice of nature. He as- 

 sumed, or rather suggested, the 

 beam (fig. 2) to turn about the line 

 Nw, which is now commonly called 

 the neutral line, and the filaments 

 above Nw to be extended, and those 

 below Nn to be compressed. Ho 

 supposed, with Leibnitz, the force 

 of each filament to be proportional 

 to its distance from N«, the neutral 

 line. -4 jg 



This theory clearly indicates the compressibility and extensibility of the 

 material, and so far agrees with all recorded experience. ]3crnoulli never pushed 

 this idea beyond a suggesticm, and it remained unfruitful in consequences till 

 Mr. Hodgkinson, in this paper, followed it up, and fixed, for the first time, the 

 exact position of the neutral line, and made it subservient to the computation of 

 the strength of a beam of given dimensions. We can scarcely exaggerate the 

 importance of this step, as it fonns the connecting link between the correct 

 assumption of Leibnitz and the complete theory of the transverse strength of 

 beam. Without the position of tlie neutral line, the section of fracture appeared 

 dark and uncertain, and we now wonder that the determination of this line had 

 escaped the ])enetration of Professor Barlow and others who had examined the 

 subject. The oj)inions here expressed are founded upon the results obtained by 

 reading the works of the best authors previous to 182:2. 



Dr. Robison, Playfair, Barlow, Dr. 0. Gregory, and Sir J. Leslie are suffi- 

 ciently known in the walks of science to justify the assertion that their works on 

 elementary sulijccts represent the tme state and progress of the knowle<lge of 

 the strength and strain of materials. Playfair's " Outlines of Natural Philoso- 

 14 s 



