196 Mr. Mallet on the Physical Conditions 



contraction due to a given difference of temperature), in accordance with the 

 well-known fact, that the dilatation in bulk of solids is (quam prow.) three times 

 the lineal expansion. 



This singular result, which, it should be mentioned, however, is not fully 

 confirmed by the experimental facts of Wertheim (Ann. Ch. Ph. t. xxiii. p. 52), 

 would seem to indicate a radical difference, in the nature of the molecular forces, 

 which resist change of form by mechanical force, and those which are developed 

 in the change of volume by heat, and therefore that we should at present take 

 with some reserve the conclusion commonly asserted by physical writers on heat, 

 that " The mechanical force brought into operation by change of temperature 

 in the expansion or contraction of a bar of metal through a given fraction of its 



length, -Y, is precisely equal to the mechanical force required to extend or to 



compress the bar by the same fraction." We shall return to this subject here- 

 after, in considering the construction of wrought-iron guns built up in rings. 



For all cases of a practical character in construction, the change of volume 

 in relation to the lineal elasticity is small, and may be neglected ; we are, there- 

 fore, concerned at present only with lineal elasticity, as a resistance to force 

 applied in one or in two rectangular axes, and may also pass by the elasticity 

 of torsion, which Mr. Eankine, in common with some other physicists, in an 

 able paper (Institut. for 1850), makes a third and separate class. 



117. Continuing our last notation : the prismatic bar, whose length is L and 

 cross section A, is extended or compressed in length by a force P, and suf- 

 fers an extension or compression I, which is proportional to its length, so 



that -jr- is a constant = i for unit of length. 



The elastic resistance which balances this force e, on the unit of surface, 

 is measured by e x ^4, or by 



— = P ^ or P = ^Ai — ei, A being = 1. (13) 



Assuming that elasticity remained perfect, and such that the bar would bear to 

 be extended or compressed by a range equal to its own length, we have in the 

 equation 



I 



