130 Lord Kelvin on Thermodynamics [r.s.e., sess. 
And, eliminating H by (19), we have finally e and m in terms of 
iv as follows : — 
e = w - t d ^ + e{t,gfg^, • • •) ( 23 ) 
m = w — (t — T)^- + m T (t,g^,g^, • ■ •) ( 24 )- 
§ 8. For the particular case ( = T we fall back on the formulas 
of § 4, and we see that there is in that case no distinction between 
motivity and mechanical work done with the apparatus kept con- 
stantly at temperature T. 
§ 9. Our present notation, tv, H, and e, is exactly that which I 
used forty -three years ago in my paper “ On the Thermo-elastic and 
Thermo-magnetic Properties of Matter,” published in the first num- 
ber of the Quarterly Journal of Mathematics ( April 1855), and re- 
published with additions in the Philosophical Magazine for January 
1878, and in Yol. I. of my Mathematical and Physical Papers 
(Art. XLVIII. Part vii.). Equations (6) and (8) of that article, 
found originally without the very convenient aid to thought given 
by the idea of motivity, are now reproduced as equations (19) and 
(23) above. The application to the thermo-elastic properties of 
fluids, of non-crystalline elastic solids, and of crystals, and to 
Thermo-magnetism, and to Pyro-electricity or the Thermo-electricity 
of non-conducting crystals, which that article contains, and my 
paper on “Thermodynamics of Yolta-Contact Electricity,” read 
before the Royal Society of Edinburgh at its recent meeting of 
February 21, may be referred to as sufficiently illustrating the 
system of generalised co-ordinates and thermodynamic formulas of 
the present communication. 
