MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 169 



is that represented in tlie accompanying figure^ where the 

 material is shown collected in two thin but wide flanges, 

 but united by a narrow rib. That which constitutes the 

 strength of the beam being the resistance of its material 

 to compression on the one side of its neutral axis, and its 

 resistance to extension on the other side, it is evidently a 

 second condition of the strongest form of any given sec- 

 tion, that when the beam is about to break across that 

 section by extension on the one side, it may be about to 

 break by compression on the other. 

 So long, therefore, as the distribution 

 of the material is not such as that the 

 compressed and extended sides would 

 yield together, the strongest form of 

 section is not attained. Hence it is 

 apparent that the strongest form of 

 the section collects the greater quan- 

 tity of the material on the compressed or the extended 

 side of the beam, according as the resistance of the ma- 

 terial to compression or to extension is the less. Where 

 the material of the beam is cast iron, whose resistance to 

 extension is greatly less than its resistance to compression, 

 it is evident that the greater portion of the material must 

 be collected on the extended side. 



^^ Thus it follows, from the preceding condition and this, 

 that the strongest form of section in a cast-iron beam is 

 that by which the material is collected into two unequal 

 flanges joined by a rib, the greater flange being on the 

 extended side, and the proportion of this inequality of the 

 flanges being just such as to make up for the inequality of 

 the resistances of the material to rupture by extension and 

 compression respectively. Mr. Hodgkinson, to whom this 

 suggestion is due, has directed a series of experiments to 

 the determination of that proportion of the flanges by 

 which the strongest form of section is obtained. 



