MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 159 



pressibility and extensibility of the material. James 

 Bernouilli, to whose labours science is under great and 

 varied obligations, in reviewing the theories of Galileo and 

 Leibnitz, felt convinced of their incorrectness, and that, of 

 course, they could have no favourable response from the 

 voice of nature. He assumed, or rather suggested, the 

 beam (fig. 2) to turn about the line l^n, which is now com- 



monly called the neutral line, and the filaments above N?z 

 to be extended, and those below 'Nn to be compressed. He 

 supposed, with Leibnitz, the force of each filament to be 

 proportional to its distance from 'Nn, the neutral hne. 



This theory clearly indicates the compressibility and ex- 

 tensibility of the material, and so far agrees with all re- 

 corded experience. Bernouilli never pushed this idea 

 beyond a suggestion, and it remained unfruitful in con- 

 sequences 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 forms 

 the connecting link between the correct assumption of 

 Leibnitz and the complete theory of the transverse strength 

 of beams. Without the position of the neutral line, the 

 section of fracture appeared dark and uncertain, and we 

 now wonder that the determination of this line had escaped 



