394 PROCEEDINGS OF THE AMERICAN ACADEMY § lO 



In conclusion, concerning all the results which have 

 been brought forward (which are the best that I have been 

 able to find) I would suggest that until we discover some 

 more accurate method of measuring temperature than we at 

 present possess, it will be useless to hope to obtain in any 

 thermometric measurement of the rates of change of expan- 

 sion more than an approximation to the truth. 



It is therefore absurd to base a theory even upon such 

 precise measurements as those of Dr. Matthiessen. The 

 atoms are undoubtedly compressible, but we shall be 

 unable to obtain a measure of their compressibilit}' in this 

 way, and we have no reason thus far to suppose that the 

 theory of expansion, developed for the lighter liquids, is 

 not applicable, without modification, to solids. 



The result of the investigation suggests that the treat- 

 ment of matter in its different states ma}' difier only in that 

 here, one factor, there, another, can in practice be neg- 

 lected; and that the Laws of Expansion are fundamentally 

 the same for all bodies, whether they be solid or liquid, 

 vapor or gas. 



§ lo. Maxwell has pointed outin his Theory of Heat^ 

 chapter V., page 107, that the- elasticity of a fluid is ex- 

 pressed by the quotient of the slope of a curve by the 

 volume, which is its abscissa, while the ordinate is the 

 pressure. Hence if the volume be unity, the slope and 

 elasticity are equal. The present section is devoted to 

 the analytical investigation of elasticity and its applica- 

 tion to isothermal curves. 



"It has been suggested by Professor James Thomson" 

 (see Maxwell, chapter VI., page 124), "that the isother- 

 mal curves" [of liquids in contact with their vapors] 

 "for temperatures below the critical temperature are only 

 apparently, and not really, discontinuous, and that their 

 true form is somewhat similar in its general features to 

 the curve ABCDEFGHK:' 



