248 Mr. William Sutherland on the 



proportional to the quotient of critical temperature by critical 

 pressure, a relation which Dewar has proved experimentally 

 (Phil. Mag. xviii. 1884) for 21 volatile bodies, for which he 

 has determined and collected the data. These with other 

 data since published enable us to determine values of I for 

 certain bodies for which the other methods are not available. 



As there are many more critical temperatures determined 

 up to the present than critical pressures, and as we have seen 

 that an error in the critical temperature is of less relative 

 importance than an error in the critical pressure, we can 

 make ourselves independent of critical pressures with ad- 

 vantage, by employing the approximation that has already 

 been useful to us, that k is proportional to the volume of the 

 liquid at the boiling-point or # = 2 , 83v 1 . Then 



Ml = 409MRT c A;/120 = 800T cVl 



approximately, with the megadyne as unit of force. This is 

 a more accurate form of the relation M/ = 1190T 6 V][ given 

 above, in which we assumed the approximation T 5 = 2T c /3. 



8. Fifth or Capillary Method of finding the Internal Virial 

 Constant, with digressions on the Brownian movement in 

 liquids and on molecular distances. — So far we have been 

 proceeding on a purely inductive path, with two deductive 

 guides in Clausius's equation of the virial and in the law of 

 the inverse fourth power, which requires that the internal 

 virial should vary inversely as the volume. But now, in 

 passing on to our fifth and most useful method of finding I 

 from surface-tension, we must employ a deductive relation 

 between I and surface-tension, furnished by the law of the 

 inverse fourth power. In a previous paper (Phil. Mag. July 

 1887) it was shown that if the law of force between two 

 molecules of mass m, at distance r apart is 3A?n 2 /?* 4 , then the 

 internal virial for the molecules in unit mass is birAp log L/a, 

 p being density, and L a finite length of the order of magni- 

 tude of the linear dimensions of the vessels used in physical 

 measurements, a being the mean distance apart of the mole- 

 cules. The ratio L/a remains the same for a given mass 

 whatever volume it occupies, but I also assumed that L/a is 

 so large a number that log L/a would hardly be affected by 

 such large variations as might occur in the value of L when 

 the behaviour of a kilogramme of a substance was compared 

 with that of a milligramme. To remove the haziness of this 

 assumption, I will now make a more accurate evaluation of 

 the internal virial. 



By definition it is i . i . 2,S3Am 2 /r 3 , and we will evaluate it 



