On the Elastic Forces of Vapours in vacuo and in Gases. 269 



formulae (109) (110) of [15.], we ought to have. As regards 

 the signification of the five foregoing principal types, which it 

 has been thought convenient to distinguish among themselves, 

 and to aiTange according to the various ways in which they 

 involve the symbols of the form [eff), it will be found, on review- 

 ing the analysis employed, that they all express ultimately only 

 consequences of that one very simple and useful formula, 



V^V^V'=^"Sa^-iSt"t, (67) 

 which, with a slightly different notation, has been elsewhere 

 shown to be so important in the Calculus of Quaternions *. In 

 fact, the equations (95). ..(98), on which those five separate types 

 have been founded, may all be deduced from (67) and (69), 

 whereof the latter is a consequence of the former. 



Observatory of Trinity College, Dublin, 

 August 14, 1854. 



[To be continued.] 



XXXV. On the Elastic Forces of Vapours in vacuo and in Gases, 

 at different Temperatures ; and on the Tensions of the Vapours 

 furnished hy mixed or superposed Liquids. ByM..\ . Regna ult f- 



ACCORDING to the views which I have adopted regarding 

 the mode of generation of the power in machines moved 

 by elastic fluids, the motive power produced by the expansion of 

 any elastic fluid is always in proportion to the loss of heat under- 

 gone by this fluid in the part of the machine where the power 

 is produced. 



During the last few years, several distinguished geometricians 

 have endeavoured to deduce this principle from abstract consi- 

 derations, founded upon hypotheses of greater or less probability. 

 For my own part, I have long laboured to bring together the 

 experimental data, by means of which the theoretical motive 

 power produced by a given elastic fluid which undergoes a cer- 

 tain change of volume, as v.^ell as the quantity of heat which 

 becomes latent in consequence of this change, might be calcu- 

 lated a priori. Unfortunately these data are very numerous, and 

 most of them can only be determined by extremely delicate and 

 difficult experiments. 



One immediate consequence of the principle which 1 have just 

 enunciated is the following : — 



When elastic fluids of different natures produce an equal amount 

 of power, they must lose equal quantities of heat. 



In oi'der to submit this law, deduced from the general prin- 



* See the author's Lectures on this subject, cited in former notes to this 

 paper. 



t From the Comptes Rendus for August 14, 1854. 



