162 MEMOIR OF THE LATE PROF. E. HODGKINSON^ F.R.S. 



did this by equating the forces of extension with the forces 

 of compression — a method which is now universally adopted 

 in computing 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 con- 

 flicts and discussions, the triumphant declaration of Prof. 

 Barlow, at the British Association of 1833, established this 

 great principle, which was first conceived by Mr. Hodgkin- 

 son, who, single-handed, had maintained his position against 

 the formidable powers of acknowledged authorities. Prof. 

 Barlow, in his report " on the Present State of our Know- 

 ledge respecting the Strength of Materials,^' printed in the 

 third volume of the Reports of the British Association 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 in 

 my investigation, by my having assumed the momentum 

 of the forces on each side of the neutral axis equal to each 

 other, instead of the forces themselves. This paper did 

 not come to my knowledge till the third edition of my 

 essay was nearly printed off, and the correction could not 

 then be made.^^ The Rev. Dr. Whewell, in his 'Analy- 

 tical Statics,^ refers to this paper, and gives the investi- 

 gation of the neutral line on the same principle as that 

 adopted by Mr. Hodgkinson, who always maintained that 

 " we could see no cause why it should be rejected, espe- 

 cially since it seems to us to be everywhere consistent and 

 just.^^ (See Manchester Phil. Society^s Memoirs, vol. iv. 

 p. 241.) It appears that his fiiend, Dr. Dalton, took great 

 interest in the deductions of this paper, and discussed them 

 freely with him as he proceeded with his experiments, 

 which will ever be regarded as marking an epoch in the 

 subject of the strength of materials. Indeed the theore- 

 tical investigations of this paper, though new and im- 



