01 



quantity of heat that must be supplied to it to augment its volume 

 hy d V and its temperature by d t. The mechanical value of the work 

 done upon it to produce this change is the excess of the mechanical 

 value of the quantity of heat that has to be added above that of the 

 work done by the fluid in expanding, and is therefore 



J (Mdv^l^ dt)'-pdv. 



It was shewn in the author's paper on the Dynamical Theory of 

 Heat, that this expression is the differential of a function of v and ty 

 so that, if this function be denoted by ^, we have, — 



(p (y, f)= A(JM-p) dv + ^ dt} 



This function would, if the constant of integration were properly as- 

 signed, express the absolute quantity of mechanical energy contained 

 in the fluid mass. Failing an absolute determination of the con- 

 stant, we may regard the function (p as expressing the mechanical 

 value of the whole agency required to bring the fluid mass from a 

 specified zero state to the state of occupying the volume v and being 

 at the temperature t. In the present paper some formulae are givfen, 

 by means of which it is shewn that nearly all the physical properties of 

 a fluid may be deduced from a table of the values of <p for all values 

 of V and t ; and experimental methods connected with the experi- 

 mental researches proposed in the author's last paper, are suggested 

 for determining values of ^ for a gaseous fluid mass. 



4. On a Mechanical Theory of Thermo-Electric Currents. 

 By Professor William Thomson. 



It was discovered by Peltier that heat is absorbed at a surface of 

 contact of bismuth and antimony in a compound metallic conductor, 

 when electricity traverses it from the bismuth to the antimony, and 

 that heat is generated when electricity traverses it in the contrary 

 direction. This fact, taken in connection with Joule's law of the 

 electrical generation of heat in a homogeneous metallic conductor, 

 suggests the following assumption, which is the foundation of tho 

 theory at present laid before the Royal Society. 



When electricity passes in a current of unifornx strength y through 

 a, heterogeneous linear conductor, no part of which is permitted to 



H 2 



