36 REPORT — 1853, 



0°'2 ; the reading which was found after the long-continued boiling being again 

 restored in about a fortnight. He was not yet prepared to say whether any eflfect 

 is produced by the boiling in the way of bringing the freezing-point of a newly- 

 made thermometer to a permanent position, irrespective of the temporary altera- 

 tion caused by a sudden elevation of temperature. 



Strength of Materials. 



On the Elasticity of Stone and Crystalline Bodies. 

 By Professor Eaton Hodgkinson, F.R.S. 



It is generally assumed by writers on the strength of materials, that the elasticity 

 of bodies is perfect so long as the material is not strained beyond a cei'tain degree. 

 But from the experiments I made several years ago, at the instance of the British 

 Association, on the strength of hot and cold blast-iron (vol. vi.), I was led to con- 

 clude that the assumption was very incorrect, as applied to cast iron at least ; and 

 further experiments rendered it probable that it was only an approximation in any. 

 Among the bodies of most value in the arts, cast iron holds an important place ; 

 and I found that bars of that metal, when bent with forces, however small, never 

 regained their first form, after the force was removed ; and this defect of its 

 elasticity took place whether the cast iron was strained by tension, compression, or 

 transverse flexure. I subsequently found that in the first two strains (by tension 

 and compression), the straining force might be well represented by a function 

 composed of the first and second powers of the change of length produced, — thus, 



w=ae— Je^ 

 w=-a'c — h'(?, 

 where w is the weight applied, ethe extension, c the compression, and a, a, b, b' 

 constant quantities. If the elasticity were perfect, the part depending on the second 

 power must be neglected. The necessity of a change in the fundamehtal assump- 

 tions for calculating the strength of materials may be inferred from the fact, that in 

 computing the breaking weig?it by tension, from experiments on <?-aMsverse flexure and 

 fracture, we obtain the strength of cast iron three times as great as from numerous ex- 

 periments I have found it to be. The formulae of Tredgold give this erroneous 

 result, and those of Navier are in accordance with them. 



Stone. — To obtain the elasticity of stone, I had masses of soft stone, obtained 

 from various places, sawn up into broad thin slabs, 7 feet long, and about 1 inch 

 thick. They were rubbed smooth, and rendered perfectly dry in a stove, and were 

 bent transversely in their least direction by forces acting horizontally. The slabs, 

 during the experiments, were placed with their broad side vertical, and had their 

 ends supported, 6 feet 6 inches asunder, by friction rollers, acting horizontally and 

 vertically. It resulted from the experiments (as shown in a former volume of this 

 Association), that the defects of elasticity were nearly as the square of the weight 

 laid on ; or consequently, as the square of the deflexion nearly, as in cast iron. The 

 ribs never regained their first form after the weight was removed, however small 

 that weight had been. From other ribs of stone, obtained from various localities, 

 and broken transversely by weights, acting vertically, and increased to the time of 

 fracture, the ratio of the deflection to the weight applied was found in various 

 experiments to be nearly as below :- 



The ratios represented by the numbers in each vertical column, are those from each 

 separate rib of stone ; and they would have been equal if the elasticity had continued 

 perfect, but they were increasing where the weights were inci'eased in every instance. 

 The change shown by these experiments to be necessary would increase con- 

 siderably the mathematical difficulties of the subject ; and the difficulties would be 

 greater still, if the change of bulk and lateral dimensions in the bodies strained were 



