Elasticity of Stone and Crystalline Bodies. 109 



where w is the weight applied, e the extension, c the com- 

 pression, and a, a', b, b' constant quantities. If the elasti- 

 city were perfect, the part depending on the second power 

 must be neglected. The necessity of a change in the funda- 

 mental assumption for calculating the strength of materials 

 may be inferred from the fact, that in computing the break- 

 ing weight by tension, from experiments on transverse flex- 

 ure and fracture, we obtain the strength of cast-iron three 

 times as great as from numerous experiments 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 horizon- 

 tally. 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, 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 broke transversely by weights, acting vertically, and in- 

 creased to the time of fracture, the ratio of the deflexion to 

 the weights applied were found in various experiments to be 

 nearly as below : — 



•02 



•01 



♦02 



•018 



•02 



•027 



•035 



•012 



•022 



•023 



0-22 



•032 



•05 



•0125 



•033 



•024 



•024 



•035 



•07 



•014 



•036 



•027 



•025 



•038 



•09 



•015 







•026 





•11 



•016 











The ratio represented by the numbers in each vertical co- 

 lumn, are those in 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 increased in 



