Molecular Constitution of Water. Aid 



by the equation 



« 2 (54/p 2 )l = 73-32(54/-88)l- 2*121*. . . (22) 



With it we calculate the values of a 2 i in the next table, also- 

 tabulating Ramsay's values for a? and obtaining {oc^—ah)lp 2 . 



Table IX. 



t 0° 20° 40° 60° ?0° 100° 120° 140 0, 



a 2 * 8-563 8-395 8-217 8-041 7-858 7'675 7-489 7-296- 



ak 8-563 8-400 8-219 8-017 7*797 7-556 7-301 7-027 



(a^-a i )/p 2 -028 -070 -138 



It appears from this table that up to 40° the surface-film 

 of water consists of pure trihydrol (H 2 0) 3 , but that at 60° 

 and higher temperatures the surface-tension is so much re- 

 duced as to allow some of liquid 1 to form. Now at 40° the 

 surface-tension is 67 - 56 dynes per centim., and in the body- 

 water the amount of 1 per gramme is '716, and the value of 

 dpjdf at 40° is '000.133, and therefore the tension per square 

 centim. required to convert this amount of 1 into trihydrol 

 will be -716/-000133 or 5380 atmos. Therefore the thickness- 

 of the surface-film (defined below) is 



, 67-56/538 xl0 7 = 12-6xl0" 9 centim. 



Now Kelvin's estimate of the order of magnitude of 

 ordinary molecular diameters is 2 X 10 -9 centim., so that our 

 surface-film would be only a few molecules thick. This- 

 agrees with what I have suggested as to the thickness of the 

 surface-film according to the law of the inverse fourth power 

 for molecular attraction. Of course with such a law of force 

 it is impossible that there can be any natural boundary 

 between surface-film and body of fluid, and it is obvious that 

 the tension must be greatest in the first layer of molecules 

 on the surface ; in the tenth layer we can imagine the at- 

 tractions of the eleventh to the eighteenth equilibrating those 

 of the first nine, and the dissymmetry causing tension in our 

 tenth layer is only that due to a mass which begins at nine 

 times the molecular diameter away ; the effect of this must 

 be very small compared to the effect of dissymmetry in the 

 condition of the first layer. The thickness of the surface- 

 film D can be most rationally defined as twice the distance 

 of the centre of tension from the surface, in symbols 



V§fdl=tffldl, 



where / is tension per unit area at depth I from the surface. 



