472 Mr. W. Sutherland on the 



of" 2 to be higher in the surface than in the body of water. 

 This will now be discussed in the next section. 



4. Surface-tension and Constitution of Water 

 in Surface-film. 



The relation which I have shown to exist between the 

 surface-tension a of a mixture and those of its ingredients 

 (Phil. Mag. [5] xxxviii., xl.) is approximately 



a i /p=p 1 a 1 i Jp 1 +p 2 *2*/P2, (20) 



and l/p=jPi/pi+P2/p2 if there is no shrinkage, 



.'. {a 2 \—ai)/p 2 +p l {(a l i — af)/p 1 — (a 2 i—ai)/p 2 }=0. (21) 



We have also Eotvos's discovery (Wied. Ann. xxvii.) that, 

 M.V being the volume of a gramme molecule and «(M»)I the 

 molecular surface-tension <r, then da/dt is nearly the same 

 for all normal liquids, and retains a nearly constant value up 

 to near the critical temperature, while for associated liquids 

 of varying degree of association it is not constant. With 

 the dyne as unit of force Ramsay and his pupils have found 

 a mean value 2"121 for Eotvos's constant da/dt. Ramsay's 

 values of a (Mi;)! or a with M = 18 for water (Proc. Roy. 

 Soc. lvi. p. 177) are given in the next table with a value 

 inserted for the critical temperature and below them the 

 values of IWAa/At. 



Table VIII. 



20° 40° 60 c 80° 100° 120° 140° 368° 

 485-3 466-3 446*2 425*3 403-5 380-7 357-0 

 8 95 100 105 109 114 118 157 



These values of Act/ At show no tendency towards becoming 

 stationary at near 0°, but let us take *92 as the order of their 

 magnitude near 0°. This when multiplied by 3f yields 1*91, 

 which is near enough to the 2' 121 of a normal liquid to 

 suggest that the surface-film of water at 0° consists of 

 (H 2 0) 3 . But if this is so we should also multiply by 

 (l/'88)f, where *88 is the density of our ingredient 2, and 

 this brings 1*91 up to 2*08, which is still nearer the result 

 for an average liquid. There is, therefore, fair evidence that 

 the tension in the surface-layer of water at 0° is sufficient to 

 cause practically the whole of the water there to change into 

 trihydrol, whose surface-tension is that of water at 0°, namely, 

 73*32 dynes per centim., and then by Eotvos's relation the 

 surface-tension of trihydrol at any other temperature is given 





0° 

 . 502-9 



tiQAa/At.. 





