Royal Society of Edinburgh. 529 



One of the outer bandages was of a reddish colour, which dye 

 I found to be vegetable, but could not individualize it ; my son 

 Mr. Thornton J. Herapath analysed it for tin and alumina, but 

 could not find any. 



The face and internal surfaces of the orbits had been painted 

 white, which pigment I ascertained to be finely powdered chalk. 

 I am, Gentlemen, 



Yours respectfully, 

 Mansion House, Old Park, WlLLIAM HERAPATH. 



Bristol, June 10, 1852. 



LXXIV. Proceedings of Learned Societies. 



ROYAL SOCIETY OF EDINBURGH. 



Dec. 15, /"VN the Quantities of Mechanical Energy contained in 

 1852. ^-^ a Fluid Mass, in different states, as to Temperature 

 and Density. By Professor William Thomson. 



Let p be the pressure of a fluid mass when its volume and tempe- 

 rature are v and t respectively, and let Mdv -\- Ndt be the quantity of 

 heat that must be supplied to it to augment its volume by dv and its 

 temperature by dt. 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+J$dt)—pdv. 

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

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

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

 $(v, t) =f { JM — p')dv + Ndt} . 

 This function would, if the constant of integration were properly 

 assigned, express the absolute quantity of mechanical energy contained 

 in the fluid mass. Failing an absolute determination of the constant, 

 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 given, by 

 means of which it is shown that nearly all the physical properties of 

 a fluid may be deduced from a table of the values of <j> 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 (p for a gaseous fluid mass. 



On a Mechanical Theory of Thermo-Electric Currents. 



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 



Phil. Mag. S. 4. No. 21. Suppl. Vol. 3. 2 M 



