512 REPOET— 1888. 



These equations are to be found in the articles by Clausius, in 

 ' Wied. Ann.' referred to; and in 'Ann. Chim.' 5, 30, 1883, pp. 358 and 

 433, in which Clausius' articles are translated. 



Another equation is given by Sarrau,' as a modification of Clausius' : 



_ RT _ Ke--" 

 ^' v-a {v+l3y' 



Bamsay and Young's IsocJioric Lines. 



In the ' Philosophical Magazine ' for May and August 1887 is published 

 Part VI. of a series of papers by Ramsay and Young on Evaporation 

 and Dissociation. In this part, from very copious data extending over 

 lai'ge ranges of pressure, temperature, and volume, a relation is deduced 

 from the isotherms for ether, carbon-dioxide, methyl alcohol, and ethyl 

 alcohol, from which the following conclusion is drawn :- — ■' The relation 

 between the pressures and temperatures of a liquid or gas at constant 

 volume is expressed by the equation ^:=Z)T — a, where j? is the pressure 

 in millimetres, T the absolute temperature, and a and h are constants. The 

 values of these constants depend on the nature of the substance and on 

 the volume. It follows from this that if a diagram be constructed to 

 express the relations of pi-essure, temperature, and volume of liquids and 

 gases, where pressure and temperature form the ordinates and abscissce, 

 the lines of equal volume are straight.' These lines are called isochors. 



From very numerous data obtained by themselves for ether, and 

 published in ' Phil. Trans.' 1886, p. 10, the authors found series 

 of values of p and t°, from which it was seen that for each volume 

 t) of a gram of the substance the lines passing through points, in which 

 p and t were taken as ordinates and abscissjB, were, at least approxi- 

 mately, straight. The volumes in the case of ether ranged from 1"9 cc. 

 to 30(3 cc. ; the pressures from 860 mm-, to 52,700 mm. ; and the tempera- 

 tures from 50° to 280° C. For each isochor the value of — ' (or h) was 



found by finding the whole difference of pressure through the largest 

 range of temperature ; and the value of a by taking the mean of the 

 values for different points on each isochor. The isochor constructed by 

 drawing the line 2)=6T — a was found to agree wonderfully well through- 

 out with the points found by experiment ; the equation for each being 

 verified by deducing from the series of isochors thus found the isotherms ; 

 these calculated isothermal lines were found to give results agreeing very 

 closely indeed with actual observation. 



Clausius ^ had drawn attention to the fact that the line of observed 

 vapour- pressures must cut James Thomson's curve in half, so that the 

 volume above the line is equal to that below it. Now the equation 

 j5=&T — a represents the whole series of isochors for ether by putting for 

 b and a their values for each volume ; and the calculated isothermal lines 

 pass close to the observed points on them ; but for values of v corre- 

 sponding to the sinuous part of each isothermal, the value of p can be 

 calculated from the equation ; this part of the curve can be traced by 

 means of the equation, assuming that the relation j9=tT — a applies to 

 the part of the curve on which we have no observations as well as to the 



' a R. ci. 1885, p. 1145. = Phil. Mag. May 1887, p. 4^0. 



• Wied. Ann. 9, 1870, p. 127; Ann. Chim. 5, 30, 1883, p. 381. 



