214 On the Thermal Properties of Normal Pentane. 



data directly instead of indirectly as in the first method, and 

 4here is not any noticeable " wobbling " at large volumes. 

 t)n the other hand, it is difficult to know how much of the 

 deviation between calculation and experiment may be fairly 

 attributed to experimental error, how much to the intrinsic 

 imperfection of the formula, and how much to the special 

 hypothesis employed. Further investigations were therefore 

 undertaken, and the result of these forms the subject of the 

 present communication. 



After several ineffectual attempts, it was found possible to 

 secure good concordance between calculation and experiment 

 for volumes above 3'4 by means of the following hypothesis : — 

 The values of R, of l-r-e, and of g were taken as being the 

 same respectively as those previously found for isopentane. 

 The two constants I and k were given suitable values derived 

 from the experimental data near the critical point. The 

 values actually found were Z = 5, 6*78, 100, k=- 3'57. 



In order to test this hypothesis as thoroughly as possible a 

 diagram was made in which pv was plotted against v~^; the 

 Calculated isothermals were drawn as continuous lines while 

 the experimental results were put in as dots ; this diagram is 

 reproduced on Plate II. An examination of it shows that the 

 agreement between calculation and experiment is satisfactory; 

 indeed the errors do not exceed 1 per cent, They are con- 

 sequently less than those which occur in the tables published 

 by one of us in conjunction with Prof. Ramsay as proving 

 the truth of the linear law (Phil. Mag. xxiii. pp. 438-447). 

 The improvement effected by means of the present hypothesis 

 is so marked, that it is impossible to attribute it wholly or 

 even chiefly to a compensation of errors : we may therefore 

 regard our previous tentative hypothesis, that the value of I is 

 the same for the two pentanes, as distinctly disproved. But 

 we cannot assert, in the present state of the evidence, that our 

 present hypothesis is actually proved ; we can merely note 

 that it introduces errors so small as to be comparable with the 

 intrinsic imperfection of the characteristic equation. 



Finally we may conclude that the difference of pressure 

 between two isomeric substances at the same temperature and 

 volume involves the same power of the density as the first 

 deviation from Boyle's law ; i. e., the second power. 



