180 Mr. Mallet on the Physical Conditions 



Were these data known, a formula could be obtained by wliich the total effect 

 may be expressed of the splitting strain, produced by the mechanical effort of 

 the expanded interior, upon the relatively cold and unexpanded exterior of the 

 gun, — a force variable in the direction of the radius, and which is a maximum 

 at the interior surfiice, and zero or a minimum at the exterior one, or at a point 

 somewhat within it. 



10. — Mechanical Equivalent of Expansion by Heat. 



88. The measure of the mechanical equivalent of heat employed in producing 

 dilatation or contraction in a solid, may be expressed in tons by the equation, 



T - t 

 F=- i (3) 



c 

 in which T is the higher, and ; the lower temperature, and c a constant repre- 

 senting the number of thermometrical degrees that the given solid must be heated 

 or cooled to produce an elongation or a contraction equal to that which it 

 would undergo by a tensile strain, or a compressive force of one ton, upon the 

 unit of surface. This equation assumes the body absolutely hard, and its elas- 

 ticity perfect, and hence is not absolutely true for any known substance. All 

 ductile metals, when heated or cooled under the constraint of resisting forces, 

 appear slowly to change their forms, and so accommodate themselves without 

 rupture or disunion to a strain, which, were they perfectly rigid, we shall see 

 presently, must in many practical instances otherwise far surpass the total 

 cohesion of the material. Thus, for example, the wrought-iron tires of railway 

 carriage-wheels are "shrunk" on red hot upon the bodies of the wheels, and 

 either cooled instantly in water, or permitted to cool slowly. In either way 

 it may be shown that the force developed by the contraction from a red heat 

 to the temperature of the atmosphere (60°), must inevitably, and in every case, 

 rupture the metal of the tire band, because the amount of contraction would far 

 exceed the total extension due to rupture of the iron. It does not do so, how- 

 ever, unless in exceptional instances, arising from defective workmanship or 

 material ; and the reason is, that through the ductility of the iron, especially at 

 a high temperature, it yields to the force, and draws out in length slowly, as 

 it cools, until the elastic forces assume a new state of equilibrium, and with the 



