of Vapours to Mariotte and Gay-Lussac's Law. 303 



temperature. It is only necessary, by means of a comparison of 

 the pv's which stand in Tables II. and III. immediately over 

 and under the last corresponding horizontal lines with the mean 

 volumes of PV given in Tables II. a and III. a } to make sure of 

 the correct position of the horizontal lines, and to inspect the 

 values of the volumes v between which the horizontal lines lie. 

 In the case of chloroform, at the temperatures examined, may be 

 remarked first a decrease and then an increase of V„ while in 

 the case of bisulphide of carbon there is a continual increase from 

 the lowest temperature (8°'5). In the case of alcohol, nothing- 

 analogous can be seen at the temperatures examined. For 

 the clearer exhibition of these relations, a graphic construc- 

 tion of V, may be contrived. It is usual in the plane coordinate 

 system to take the absolute temperatures as the abscissse x, and 

 as the ordinates y to take simultaneously the corresponding- 

 values of the specific volumes (marked v^ of perfectly saturated 

 vapour, and also those of the volumes Y 1 referred to the vapour- 

 unit of weight (1 kilog.). Of the two curves so constructed, 

 that of v 1 must always drop as the abscissse increase, and run 

 asymptotically into coincidence with a line parallel to the axis of 

 abscissse. The volume characterized by this parallel is the least 

 at which the unit weight of vapour can exist without assuming 

 the fluid form. For the three vapours which have been dis- 

 cussed, the curve of V 2 coincides with the curve of v 1 at the 

 abscissa =« + 9*5, and afterwards, with increasing values, as- 

 sumes a course more removed from the axis of abscissse than the 

 curve of v l ; indeed it appears from all the foregoing observa- 

 tions, that the difference Y 1 — v x constantly increases. Therefrom 

 results the necessity of a minimum of the curve Y lt provided 

 there be an initial descent. For chloroform this minimum is 

 actually proved from the observations. For bisulphide of carbon 

 the same lies close to the neighbourhood of a temperature of 10°, 

 and then the observed constant increase of Y 1 along with the 

 temperature commences. For alcohol, the temperature at which 

 the minimum exists, according to this, would lie higher than 

 70°. At higher temperatures there would probably be found 

 a constant but small increase of V 1 ; at least such appears to 

 be the most natural supposition, after the proof of a minimum 

 of the curve Vj. 



Since any volume of the unit of weight of vapour corresponds 

 to any temperature of the superheated condition when it falls be- 

 tween curves Y 1 and v l in the representation by coordinates, and, 

 on the other hand, corresponds to the gaseous condition when it 

 has both curves between it and the axis of abscissse, the preceding 

 considerations lead to the following result. We can draw a pa- 

 rallel (M N, fig. 2) to the axis of abscissse from any point of the 



