258 Mr. William Sutherland on the 



a different scale, we conclude that if we use the value of the 

 surface-tension measured at a constant fraction of the critical 

 temperature, and under a constant fraction of the critical 

 pressure, we ought to get correct relative values of I ; as 

 surface-tension is not appreciably affected by pressure, we 

 can dispense with the condition as to pressure and use mea- 

 surements of a made under a pressure of one atmosphere at a 

 constant fraction of the critical temperature. I have chosen 

 the fraction as two-thirds, because it gives a temperature near 

 to the boiling-point of most liquids. 



Schiff's abundant measurements (Ann. der Cliem. ccxxiii., 

 and, further, Wied. Beibl. ix.) include not only the height to 

 which different liquids rise in a capillary tube at their boiling- 

 points, but also its temperature-coefficient, which is such as 

 to show that the height in every case vanishes near the critical 

 point. 



Let H be the height to which a liquid rises in a tube of 

 radius 1 millim. ; then if H really vanished at the critical 

 temperature and varied linearly w r ith temperature, we should 

 at 2T c /3 have H = T 6 .&/3, where b is the temperature-coefficient. 

 But to use this would be to depend too much on the accuracy 

 of b. 



If H$ is the value at T b the boiling-point, then T C = T 6 + H 6 /Z>, 

 and 



H = H, + (T 4 - 2T c /3) b = EU/3 + T b b/3, 



which depends partly on H 6 , measured by Schiff, and partly 

 on b. Now a = Hp/2 = R/2v ; 



.'. I or cctv?/ml = cE-V%/2m?, 



l=c(JI b /S + T b b/Z)vl/2mh 



If H is measured according to the usual practice as the 

 height in millimetres for a tube of radius 1 millim., that is, if 

 a is measured in grammes weight per metre,, then if I is 

 desired in terms of the megadyne, gramme, and centimetre as 

 units, c/2 = 5930, a mean value. Apart from all hypothesis 

 about molecular force, our last relation between the virial 

 constant and the constants of capillarity will be amply con- 

 firmed by the extensive comparisons soon to be presented in 

 Tables XXIY. and XXV. Meanwhile a few consequences of 

 the relation may be glanced at. 



9. Establishment on Theoretical grounds of Eotvos's relation 

 between surface-tension, volume, and temperature. — Accord- 

 ing to the modified equation of the fourth method of finding 

 Z, M/ = 800T c v 1 ; and according to that of the fifth method, 

 lz=.coLV^Im\. The first of these equations w r ould be more 

 accurate if we replaced v x by v, which in the second means 

 the volume at 2T c /3 ; so M?=800T^ ; and m the actual mass 



