Chemistry and Physics. 397 



striking and important analogy between the volume-energy equa- 

 tion of a gas and the surface-energy equation of a liquid has 

 recently been investigated by Ramsay. The former equation 

 has the well-known form py = RT, in which v is the volume of 

 the gas, p the pressure upon it in atmospheres, T the absolute 

 temperature, and R a constant, which when the unit of volume is 

 the volume in liters occupied by the molecular mass in grams, be- 

 comes 0*0819. The equation representing the surface-energy of 

 a liquid is ys = k(r — d) ; in which y is the surface tension, s the 

 surface, h a constant analogous to R and r the temperature 

 measured downward from the critical temperature. Since the 

 origin of the line representing the variation of surface energy 

 with temperature is not at the critical temperature but about 6° 

 below it, a constant d is subtracted from r. By a series of ex- 

 periments with ethyl oxide, methyl formate, ethyl acetate, ben- 

 zene, chlorbenzene aud carbon tetrachloride, the author has shown 

 that the molecular surface energy of liquids which do not dis- 

 sociate, varies directly with (r—d) within very wide limits of 

 temperature. In comparing different liquids with each other it is 

 necessary to select surfaces on which equal numbers of molecules 

 lie. And since the molecular volume of a liquid is that volume 

 in cubic centimeters which is occupied by the molecular mass 

 taken in grams, it is evident that the cube root of the molecular 

 volume gives the relative number of molecules along a line one 

 centimeter long and that the square of this value represents the 

 relative number of molecules distributed on unit surface; i. e., on 



2. 



one square centimeter. Hence the expression (My) 3 may be 

 termed the "molecular surface" of a liquid. This quantity mul- 



tiplied by y the surface tension, gives y(\\v) 3 , the molecular sur- 

 face energy; i. e., the energy which must be expended in produc- 

 ing a surface on which a definite number of molecules is distributed, 

 this number being the same for all liquids. Since the rate of 

 change of the surface energy with temperature is a linear func- 

 tion of the temperature, the first differential coefficient d'E/dt or 



2 



d \_y{M.v)^\l dt has the constant value 2-121. 



In connection with Emily Aston, Ramsay has now applied 

 these considerations to the determination of the molecular formu- 

 las of liquids. From the equation (yCMv)^—y'(M.v'f)/(t'—t) = 



2.121 or K, we have M — K(t'-t)/(yiA-r'v'^); from which 

 knowing the molecular surface energy at two or more temper- 

 atures, the molecular masses can be calculated. The liquids used 

 were such as promised to show a higher molecular mass.than that 

 expressed by their ordinary formulas ; such as phenol, bromine, 

 nitric and sulphuric acids and phosphorus. The value y was ob- 

 tained from the rise of the liquid in a capillary tube, by the ordi- 

 nary equation y=%r/igd, in which r is the radius of the tube, h the 

 height of the column, g the gravitation constant and d the density 



