Prof. Thomson on the Dynamical Theory of Heat. Ill 



the data required for the calculation of // as being supplied in a 

 complete and satisfactory manner. 



34. There remains only the third of the data, or the volume 

 of a given weight of saturated steam, for which accurate experi- 

 ments through an extensive range are wanting ; and no experi- 

 mental researches bearing on the subject having been made since 

 the time when my former paper was written, I see no reason for 

 supposing that the values of /a which I then gave are not the 

 most probable that can be obtained in the present state of science ; 

 and, on the understanding stated in § 33 of that paper, that 

 accurate experimental determinations of the densities of saturated 

 steam at different temperatures may indicate considerable errors 

 in the densities which have been assumed according to the 

 " gaseous laws," and may consequently render considerable alte- 

 rations in my results necessary, I shall still continue to use 

 Table I. of that paper, which shows the values of /x for the tem- 

 peratures i, li, 2| . . . 230i, or, the mean values of yu. for each 

 of the 230 successive Centigrade degrees of the air-thermometer 

 above the freezing-point, as the basis of numerical applications 

 of the theory. It may be added, that any experimental researches 

 sufficiently trustworthy in point of accuracy, yet to be made, 

 either on air or any other substance, which may lead to values 

 of /i differing from those, must be admitted as proving a discre- 

 pancy between the true densities of saturated steam, and those 

 which have been assumed*. 



35. Table II. of my former paper, which shows the values of 



/ 



fidt iov t=\, t = 2, t = Z, . . . ^ — 231, renders the calculation 



of the mechanical effect derivable from a given quantity of heat 

 by means of a perfect engine, with any given range included 

 between the limits and 231, extremely easy ; since the quan- 

 tity to be divided by J f in the index of the exponential in the 



* I cannot see that any hyjiothesis, such as that adopted by Clausius 

 fundamentally in his investigations on this subject, and leading, as he shows 

 to determinations of the densities of saturated steam at different tempera- 

 tures, which indicate enormous deviations fi-om the gaseous laws of varia- 

 tion with temperature and ])ressure, is more probable, or is probably nearer 

 the truth, than that the density of saturated steam does follow these laws 

 as it is usually assumed to do. In the present state of science it would 

 perhaps be wrong to say that either hypothesis is more jjrobable than the 

 other [or that the rigorous truth of either hypothesis is j)robable at all]. 



t It ought to be remarked, that as the unit of force inijdied in the de- 

 terminations of IX is the weight of a ])ouud of matter at Paris, and tlie unit 

 of force in terms of which J is expressed is the weight of a pound at Man- 

 chester, these numbers ought in strictness to be modified so as to express 

 tlic values in terms of a common unit of force ; but us the force of gravity 

 at Paris differs by less than ij;'^^ of its own value from the force of gravity 

 at Manchester, this correction will be mudi less than the probable errors 

 from other sources, and may therefore be neglected. 



