MEMOIR OF EATOII IIODGKIXSON. 



229 



GODSTOXE BRIDGE. 



The span is 30 feet, the weight of engine and tender 33 tons, and weight of 

 half bridge 25 tons; the statical deflection was .19 inch. This was increased 

 to .25 by a speed of 49 miles per hoiu". 



The dynamical deflection 



.Statical deflection "" ' ' 



showing an increase of nearly one-third. 



A pair of steel bars, two feet three inches by two inches broad and one-fourth 

 inch deep, gave the following results : 



"Velocity in feet per second. 

 Central deflection in inches . 



15 

 1.02 



14 

 1.32 



29 

 1.45 



34 



1.30 



44 



l.OC 



A bar of wi'ought iron nine feet long, one inch broad, and three inches deep, 

 with a. load of 1,778 pounds, gave the following results : 



Velocity in feet per second . 

 Central deflection in inches. 



.29 



15 



,33 



29 



,50 



36 



,62 



.46 



In the commissioners' report ]\Ir. Hodgkinson has given the results of a variety 

 of experiments on the transverse strength of cast, mixture of cast and wrought, 

 and wrought ij'on. The experiments were made with great care, and every 

 source of error that could be was eliminated, notwithstanding the trouble and 

 expense which such a procedure necessitated. Still there was a great dilliculty, 

 Avhich was always felt by Mr. Hodgkinson, and which occupied, at various times, 

 much of his attention, viz., to connect the breaking-weight of the beam with its 

 deflection in sucli a uianner as to indicate true practical results. For this pur- 

 pose lie entered into a very general theoretical investigation on the transverse 

 flexure of beams, which is given in the second volume of Tredgold '^ On the 

 Strength of Cast Iron ;" but, in order to make the results of this very general 

 investigation practical, he is compelled to assume, first, that the forces of exten- 

 sion and compression are proportional to the extensions and compressions ; 

 second, that the force of extension is equal to the force of compression ; third, 

 the reaction at the points of support is always vertical. It is not surprising, 

 then, that a formula, based upon so many assumptions, should fail to represent 

 correctly the relation between the breaking-weight and the dimensions of the 

 beam; this is exactly what has taken place. 



The discordance here alluded to has arrested the attention of AY. II. Barlow, 

 esq., C. E., F. R. S., and the results of his investigations are given in two very 

 interesting memoirs, printed in the "Transactions of the lloyal Society'' for 

 1855-'57. It would be great presumption on my part to enter into any profound 

 criticism on the mode of procedin-c and results of these memoirs, revised as tlicy 

 have been by Professor Barlow, wlio is justly distinguished by his genius, high 

 attainments, and long life devoted to the interests of science; but still it may 

 not be out of place here to make one or two observations which occurred to me 

 while reading the inerrujirs. I quite agree with Mr. Barlow that there must be 

 other forces in operation when a beam is broken transversely than those simi)ly 

 and usually designated tensile and compressive. If a beam is broken transversely, 

 and the existence and position of the neutral surface are admitted, then it is not 

 dilficult to conceive the existence of a third force between two adjacent lamina; 

 mi(.'(pially extended or compressed. 



This is really what hap[)cns, and the existence of which was well known to 



