184 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES, 

 and by (345) and (346) 



e (3 . 



a at 



e 



By this equation we may calculate directly the amount of heat 

 required to raise a given quantity of the gas from one given tem- 

 perature to another at constant volume. The equation shows that 

 the amount of heat will be independent of the volume of the gas. 

 The heat necessary to produce a given change of temperature in 

 the gas at constant pressure, may be found by taking the difference 

 of the values of x> as defined by equation (89), for the initial and final 

 states of the gas. From (89), (350), and (351) we obtain 



" e , 



m z-i 1-2 



r T , a at 



Li+Lzt e 



By differentiation of the two last equations we may obtain directly the 

 specific heats of the gas at constant volume and at constant pressure. 



The fundamental equation of an ideal ternary gas-mixture with a 

 single relation of convertibility between its components is 



i On Oi 



t e 



u. 2 - .2 



4 /oeo\ 

 (ooo) 



where \ and X 2 have the same meaning as on page 168. 



* The Conditions of Internal and External Equilibrium for Solids 

 in contact with Fluids with regard to all possible States of 

 Strain of the Solids. 



In treating of the physical properties of a solid, it is necessary to 

 consider its state of strain. A body is said to be strained when the 

 relative position of its parts is altered, and by its state of strain is 

 meant its state in respect to the relative position of its parts. We 

 have hitherto considered the equilibrium of solids only in the case in 

 which their state of strain is determined by pressures having the 

 same values in all directions about any point. Let us now consider 

 the subject without this limitation. 



If x', 2/', z' are the rectangular co-ordinates of a point of a solid 

 body in any completely determined state of strain, which we shall call 



*[This paper was originally printed in two parts, divided at this point. For dates see 

 heading, p. 55.] 



