MEMOIR OF THE LATE PROF. E. HODGKINSON, F.R.S. 163 



portant, form only a small portion of its merits. The 

 experiments recorded in it established the laws, ^^ that the 

 extensions of the fibres of a bent beam were proportional to 

 the forces during the early stages of flexure ; but as the 

 extensions arrived nearer to fracture,, they increased faster 

 than the forces;" and, "that so long as the forces are 

 moderate, and are applied in the direction of the fibres, 

 the compressions will be as the forces ; but when the beam 

 becomes bent, the fibres, being then crushed, offer a feeble 

 resistance to the force." These results were obtained 

 direct from the unerring voice of nature. The first of 

 these laws was announced by Dr. Kobison, as a general 

 law of nature, on the simple authority of a few experi- 

 ments on the slips of gum caoutchouc and the juice of the 

 berries of the White Bryony, of which a single grain will 

 draw to a thread two feet long, and again return to a 

 perfectly round sphere. (See ' Manchester Memoirs,' vol. iv. 

 p. 252.) 



" On the Forms of the Catenary in Suspension Bridges" 

 (read February 8th, 1828, vol. v.). 



The Chain-bridge at Broughton, Manchester, which 

 broke down by a troop of soldiers marching over it, and 

 the celebrated Menai suspension bridge, built by Telford, 

 had stimulated inquiries respecting the best form of such 

 structures. These inquiries, naturally enough, led to a 

 reconsideration of the catenary, a curve the properties of 

 which, under given conditions, were first discovered by 

 James Bemouilli. (See Leslie's *^ Geometry of Curved 

 Lines.') 



In this paper a great degree of generality is given to the 

 catenarian curve. After the known properties of the com- 

 mon catenary are clearly investigated, the formulae are 

 then applied with great ability to determine the form of 

 suspension bridges when the weight of catenarian chain, 

 the weight of the roadway y and the weight of the suspension- 



m2 



