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



nouilli, by showing, both theoretically and experimentally, 

 the true method of determining, in the section of fi-acture, 

 the exact position of the neutral line, and of calculating 

 the strength of the beam. 



In order, then, to show more clearly the steps taken by 

 Mr. Hodgkinson in the establishment of sound practical 

 views of this subject, it will be necessary to give a brief ex- 

 position, by reference to diagrams, of the history of the 

 section of fracture. 



Fiff. 1. 



Every beam of material is supposed to be composed of 

 an indefinite number of parallel filaments in the direction 

 of its length, and the breaking of the beam necessitates the 

 breaking of each of the filaments of which it is composed. 

 Suppose a beam, AB, placed on the fulcrum CF, to be 

 broken at the section CDIEFL by the weights W and w, 

 suspended from the points G and H. The theory of Galileo 

 assumes the beam to turn about the fulcrum CF, and each 

 of the filaments [nm) in the section of fracture CLD to 

 sustain an equal force. This hypothesis implies the in- 

 compressibility and inextensibility of the material. Leib- 

 nitz, the great rival of Newton, assumed the beam to turn 

 about the falcrum, CF, as did Galileo, but assumed, what 

 experiment has confirmed, 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 incom- 



