70 ON MAGNITUDE [ch. 



of the salt, Ostwald has shewn that we may have particles so minute 

 that they fail to serve as a nucleus for crystalUsation — which is as 

 much as to say that they are too small to have the form and pro- 

 perties of a "crystal." And again, in his thin oil-films, Lord 

 Rayleigh noted the striking change of physical properties which 

 ensues when the film becomes attenuated to one, or something less 

 than one, close-packed layer of molecules, and when, in short, it no 

 longer has the properties of matter in mass. 



These attenuated films are now known to be "monomolecular," the 

 long-chain molecules of the fatty acids standing close-packed, like the cells 

 of a honeycomb, and the film being just as thick as the molecules are long. 

 A recent determination makes the several molecules of oleic, palmitic and 

 stearic acids measure 10-4, 14-1 and 15- 1 cm. in length, and in breadth 7-4, 

 6-0 and 5-5 cm., all by 10~^: in good agreement with Lord Rayleigh and 

 Devaux's lowest estimates (F. J. Hill, Phil. Mag. 1929, pp. 940-946). But 

 it has since been shewn that in aliphatic substances the long-chain molecules 

 are not erect, but inclined to the plane of the film ; that the zig-zag constitution 

 of the molecules permits them to interlock, so giving the film increased 

 stability ; and that the interlock may be by means of a first or second zig-zag, 

 the measured area of the film corresponding precisely to these two dimorphic 

 arrangements. (Cf. C. G. Lyons and E. K. Rideal, Proc. R.S. (A), cxxvin, 

 pp. 468-473, 1930.) The film may be lifted on to a polished surface of metal, 

 or even on a sheet of paper, and one monomolecular layer so added to another; 

 even the complex protein molecule can be unfolded to form a film one amino- 

 acid molecule thick. The whole subject of monomolecular layers, the nature 

 of the film, whether condensed, expanded or gaseous, its astonishing sensitive- 

 ness to the least impurities, apd the manner of spreading of the one liquid 

 over the other, has become of great interest and importance through the work 

 of Irving Langmuir, Devaux, N. K. Adam and others, and throws new light 

 on the whole subject of molecular magnitudes*. 



The surface-tension of a drop (as Laplace" conceived it) is the 

 cumulative effect, the statistical average, of countless molecular 

 attractions, but we are now entering on dimensions where the 

 molecules are fewf. The free surface-energy of a body begins to 

 vary with the radius, when that radius is of an order comparable 

 to inter-molecular distances; and the whole expression for such 

 energy tends to vanish away when the radius of the drop or particle 

 is less than O-Olfx, or lOm^it. The quahties and properties of our 



* Cf. (int. al.) Adam, Physics and Chemistry of Surfaces, 1930; Irving Langmuir, 

 Proc. R.S. (A), CLXX, 1939. 



t See a very interesting paper by Fred Vies, Introduction a la physique bac- 

 terienne, Revue Sclent. 11 juin 1921. Cf. also N. Rashevsky, Zur Theorie d. 

 spontanen Teilung von mikroskopischen Tropfen, Ztschr.f. Physik, xlvi, p. 578, 1928. 



