90 THE ROYAL SOCIETY OF CANADA 



produced the curves down to the axis of zero surface tension. For 

 each liquid the intersection occurs not far below the critical tem- 

 perature, but it will be seen that the curves are far from straight 

 and that the well-known linear equaton Tg = k {dc — di — 6) where di 

 is about five or six degrees, is only an approximation holding for a small 

 range of temperature below the critical temperature. 



Again it seems to me that surface energy should be used and 

 not surface tension. It is well-known that when a film contracts 

 isothermally it does mechanical work given by TX (decrease of area) 

 and also gives out heat to the surroundings. The formula connect- 

 ing T, the surface tension, with S, the surface energy, is the well- 

 known free energy equation 



dT 



where d is the temperature. The temperature coefficient of T is 

 not constant. This alone would make Taylor's extrapolated value 

 of T at 0°A rather wide of the mark. 



dT 



For water at 273°A, — is about .147 in C.G.S. units so that 5 



dd 



at 273°A = 75.6-f40.1 = 115.7 ergs per sq. cm. 



Putting in Taylor's equation the values of the physical con- 

 stants of water at 273°A we get 



/564X4.18X10'V 18X1- 



N 116 / 367r 



= 1.34 X lO^'' 

 Supposing we take the physical constants at 373°A; 

 5373 = 58.8 + 373 X.185 = 127.8 ergs per sq. cm. 



/498X4.18X107V 18 X. 962 

 . . n ={ j X 



V 128 / 367r 



= 5.89 X 10-^ 



The variation shows that although the value of n will be of the right 

 order the calculation is useless for getting an accurate value of 

 Avogadro's number. The formula does not include all the facts, 

 the assumptions are too approximate^ and the data are not suffi- 



'For example, our knowledge of the value of T for spheres of just over mole- 

 cular size is very vague and it is the shrinkage of surface in the early stages which 

 apparently liberates the most energy (loc. cit. p. 885). Also the vapour pressure 

 relations of small drops, involving among other things the change of latent heat 

 of vaporisation with change of curvature, would have to be considered. 



