ABSTRACT BY THE AUTHOR 363 



constant volume, a denotes the constant value of pv+mt, E and H 

 depend upon the zeros of energy and entropy. The two last equations 

 may be abbreviated by the use of different constants. The properties 

 of fundamental equations mentioned above may easily be verified 

 in each case by differentiation. 



The law of Dalton respecting a mixture of different gases affords 

 a point of departure for the discussion of such mixtures and the 

 establishment of their fundamental equations. It is found convenient 

 to give the law the following form : 



The pressure in a mixture of different gases is equal to the sum of 

 the pressures of the different gases as existing each by itself at tJie 

 same temperature and with the same value of its potential. 



A mixture of ideal gases which satisfies this law is called an 

 ideal gas-mixture. Its fundamental equation in p, t, fi lt fJL 2 , etc. is 

 evidently of the form 



(20) 



where 2^ denotes summation with respect to the different components 

 of the mixture. From this may be deduced other fundamental 

 equations for ideal gas-mixtures. That in \/r, t, v, m^ m 2 , etc. is 



(21) 



Phases of dissipated energy of ideal gas-mixtures. When the 

 proximate components of a gas-mixture are so related that some of 

 them can be formed out of others, although not necessarily in the 

 gas-mixture itself at the temperatures considered, there are certain 

 phases of the gas-mixture which deserve especial attention. These 

 are the phases of dissipated energy, i.e., those phases in which the 

 energy of the mass has the least value consistent with its entropy 

 and volume. An atmosphere of such a phase could not furnish a 

 source of mechanical power to any machine or chemical engine 

 working within it, as other phases of the same matter might do. 

 Nor can such phases be affected by any catalytic agent. A perfect 

 catalytic agent would reduce any other phase of the gas-mixture 

 to a phase of dissipated energy. The condition which will make the 

 energy a minimum is that the potentials for the proximate com- 

 ponents shall satisfy an equation similar to that which expresses the 

 relation between the units of weight of these components. For 

 example, if the components were hydrogen, oxygen and water, since 

 one gram of hydrogen with eight grams of oxygen are chemically 

 equivalent to nine grams of water, the potentials for these substances 

 in a phase of dissipated energy must satisfy the relation 



