July 19, 1912] 



SCIENCE 



93 



250° 2.598 



256° 2.396 



257°.4 (critical) 



2.353 X 10" 



The fact that Mills's equation gives a con- 

 stant is, then, rather evidence against the 

 hypothesis that the attraction is inversely as 

 the square of the distance, instead of in favor 

 of that hypothesis. The real representation 

 of the gain in molecular potential energy on 

 passing from the liquid to the vapor is more 

 probably, as Sutherland and others have 

 shown, the expression N-M-K/{l/v — l/V), 

 and not Z(l/«i/3_ yi/s). The former ex- 

 pression is in harmony with the conclusion 

 that the attraction is inversely as the fourth 

 power of the distance. 



3. The Radius of Action of the Molecules. — 

 The most recent calculations of the radius of 

 action of molecules make it about 1.2 to 

 2 X 10"^ cm., or about two molecule diam- 

 eters in the liquid state. As means of meas- 

 urement have improved, the radius has 

 shrunk. The distance between the centers of 

 ether molecules in the liquid state at 20° is 

 about 6 X 10'* cm. Einstein and Suther- 

 land have computed that the radius of action 

 is proportional to, and very nearly equal to, 

 the distance apart of the molecular centers. 

 Kleeman has computed it as a little less than 

 a molecular diameter. The only interpreta- 

 tion of Einstein's result is that the molecules 

 attract only their immediate neighbors and 

 hence, as Mills suggested, molecular cohesion 

 does not penetrate matter. This makes it pos- 

 sible for the cohesion to vaiy inversely as the 

 fourth power of the distance; since, if the co- 

 hesion penetrated matter like gravitation and 

 the attraction was inversely as the fourth 

 power, the cohesional mass is so enormously 

 greater than the gravitational mass that the 

 cohesional attractions of two masses would, 

 when the masses were near, greatly surpass 

 their gravitational attractions. 



•4. Computation of the Cohesive Mass, M. — 

 Since the value " h " of Van der Waals's 

 equation is not constant, but varies both with 

 the volume and temperature, it is impossible 

 to compute M'^K from the deviation from con- 

 stancy of the pressure-volume product of a 



gas. M'^K may, however, be computed from 

 the surface tension, as follows: 8 is the ten- 

 sion along a line one cm. in length and the 

 depth of the surface film, or fv^/^. Then 

 ^/t)i/3 is the surface tension per sq. cm. 

 across the surface film, if the latter is one 

 molecule deep, as it probably is at absolute 

 zero, for which temperature the final compu- 

 tation is made. If this act through the space 

 of a molecule, we have Sv-/^, the molecular 

 surface tension energy. According to Eotvos 

 this is equal to 3.015 X 10-"(r„ — T — 6), 

 using absolute units and the volume of one 

 molecule, and assuming that the number of 

 molecules in a c.c. of gas under standard 

 conditions is 2.77X10^". This value, 

 8v-/^, must be a function of the difference in 

 molecular cohesive energy in the liquid and 

 vapor, or M^K/v — M'^K/V — f8v-/^. At 

 low temperatures M^K/V drops out and at 

 absolute zero M'^K/v^ = f8v-/^ = 3.015 X 

 10-i6(r^_6)/. To find "f" 1 had recourse 

 to Thomas Young's formula: 8^rK/3^ 

 rM-K/3v-; r being the radius of action and 

 equal to v^/^ at absolute zero. Maxwell and 

 Lord Eayleigh have a different coefficient 

 from Young's, i. e., 3/20 instead of 1/3. I 

 could not decide which of these was right, but 

 Maxwell's gives a value for the internal pres- 

 sure requiring an impossible value for " h!' 

 if substituted in Van der Waals's equation, 

 so that Young's seems to be right, unless I 

 have made an error somewhere. We have 

 then 8 = M''-K/?,v^/^; and 8v"'/^ = M-K/2,v^. 

 Therefore ilf2Z = 9.045 X lO'^^C^e — 6). If 

 this value for M-K is substituted in Van der 

 Waals's equation using the critical data for 

 pentane, ether, isopentane and benzene, " 6 '\ 

 is found to have very nearly the uniform 

 value in all of Y^/'iSfi. Van der Waals found, 

 by computing " a " from the coefficient of 

 compressibility, that hg was Fj/2.03; so the 

 two results agree very well. The value ob- 

 tained from the surface tension is, therefore, 

 tolerably correct. The value of M-K has been 

 computed for a large number of substances 

 from the critical temperature, pressure and 

 volume, and from the surface tension; and 

 the results are throughout in close agTcement. 



