145 SECTION PHYSICS. 



fancy, and his method has been lately followed by C. Neumann. But 

 the methods introduced by Professor J. Willard Gibbs, of Yale College, 

 Connecticut,* seem to me to be more likely than any others to enable 

 us, without any lengthy calculations, to comprehend the relations be- 

 tween the different physical and chemical states of bodies, and it is to 

 these that I now wish to direct your attention. 



In studying the properties of a homogeneous mass of fluid, consisting 

 of 11 component substances, Professor Gibbs takes as his principal func- 

 tion the energy of the fluid, as depending on its volume and entropy 

 together with the masses, m v m z .... m n , of its n components, these 

 11+2 variables being regarded as independent. Each of these vari- 

 ables is such that its value for any material system is the sum of its 

 values for the different parts of the system. 



By differentiating the energy with respect to each of these variables 

 we obtain ?/ + 2 other quantities, each of which has a physical signifi- 

 cance which is related to that of the variable to which it corresponds. 



Thus, by differentiating with respect to the volume, we obtain the 

 pressure of the fluid with its sign reversed ; by differentiating with 

 respect to the entropy, we obtain the temperature on the thermo- 

 dynamic scale ; and by differentiating with respect to the mass of any 

 one of the component substances, we obtain what Professor Gibbs 

 calls the potential of that substance in the mass considered. 



As-this conception of the potential of a substance in a given homo- 

 geneous mass is a new one, and likely to become very important in the 

 theory of chemistry, I shall give Professor Gibbs's definition of it. 



" If to any homogeneous mass we suppose an infinitesimal quantity 

 of any substance added, the mass remaining homogeneous and its 

 entropy and volume remaining unchanged, the increase of the energy 

 of the mass, divided by the mass of the substance added, is the poten- 

 tial of that substance in the mass considered." 



These ;z + 2 new quantities, the pressure, the temperature, and the 

 # potentials of the component substances, form a class differing in 

 kind from the first set of variables. They are not quantities capable 

 of combination by addition, but denote the intensity of certain physical 

 properties of the substance. Thus the pressure is the intensity of the 



* Transactions of the Academy of Sciences of Connecticut, vol. ili. 



* 



