The ordinary Sommerfeld-Wilson quantum condition Spdq=nh, when applied to this model, gives a negative value for the ionizing potential, and therefore the model is untenable unless the quantum conditions are modified. Langmuir suggested that the maximum angular momentum

h , 2π

of a single electron should be set equal to and deduced

as the value of the ionizing potential 25.62 volts, in close agreement with the experimental value of 25-4+25 volts obtained by Franck and Knipping.

.

Langmuir does not discuss the question of the spectrum of helium; but if his hypothesis is correct, it would appear that the spectrum should be obtained by setting the maximum angular momentum of an electron equal to an integral multiple of In this model it is clear that the maximum

h

angular momentum of the electron which vibrates in the path ACB is attained at the middle point C. If OC is ro and the angular velocity at C is do, we obtain as our quantum condition,

nh 2π

where mo is the mass of an electron, and n is an integer. Now, Langmuir proves that if - W is the total energy

the system,

of

and from (2), on putting N=2 for helium,

Hence the frequency of the spectrum should be given by

where R is the Rydberg constant and m and n are integers. The formula (7) cannot accord with the ordinary series in the spectrum of helium; but this fact would not preclude the temporary existence of helium atoms of the structure considered in sufficient numbers to show perhaps a weak spectrum. Thus a test of the formula numerically is desirable in order to determine whether it can lead to any lines associated with helium but not belonging to the ordinary series.

The values of m and n in the table were selected with a view to obtaining wave-lengths in the visible spectrum. The first line and the last two show that such lengths can only be given by m=4 or 5.

m=·

The spectrum does not show a correspondence with any known spectrum; and the only conclusion that can be made is that the hypothesis about the quantum condition used in Langmuir's investigation is not correct, though it does lead to a suitable value of the ionizing-potential.

CXII. Adsorption from the Gas Phase at a Liquid-Gas Interface.-Part I. By THOMAS IREDALE *.

T was proposed to measure the adsorption at a liquid-gas interface of a substance which is present, not in solution. in the liquid phase but as a constituent of the gas phase only. The idea is not new (Gibbs, Scientific Papers, vol. i. p. 235; Cantor, Annalen der Physik, vol. lvi. p. 492, 1895; Langmuir, Journ. Amer. Chem. Soc. vol. xxxix. p. 1848, 1917), but has never been given any quantitative expression. From measurements of the surface-energy changes of a liquid under varied pressures of an adsorbed vapour, the amount of the adsorption might be calculated from the Gibbs equation (l.c.), г=-Pap'

do

but the actual measurement of the adsorption itself is of much greater difficulty. Very few such measurements are to be found in the literature, the more notable ones being those of Donnan (Proc. Roy. Soc. A, vol. lxxxv. p. 558, 1911) and Lewis (Phil. Mag. 1908, p. 499, and 1909, p. 466; Zeit. Phys. Chem. vol. lxxiii. p. 129, 1910), which were concerned with the adsorption at liquid-gas and liquid-liquid interfaces respectively of substances in solution in the liquid phase. There exist, however, very considerable discrepancies between the experimental values for the adsorption and those calculated with the aid of the Gibbs equation. One reason for this is probably the fact that the substances employed were either electrolytes or organic substances of high molecular weight which tended to form colloidal solutions, and one could not be sure that the gas laws were obeyed with sufficient accuracy, and there was also the difficulty of a probable irreversible gelatinization of the colloid at the interface. The adsorption of a gas or vapour is free from such defects as these, though in the latter case the interesting phenomenon of incipient condensation must not be overlooked.

The first part of this investigation is concerned with a suitable method of measuring the surface tension of a liquid under the prescribed conditions-i. e., a continuously varying vapour phase.

The Drop-weight Method of measuring Surface Tension.

In view of the recent developments of the technique of this method (Harkins and co-workers, Journ. Amer. Chem. Soc. vol. xxxviii. p. 839, 1916; vol. xli. p. 499, 1919; vol. xlii. p. 2534, 1920), it was decided to employ it in the preliminary investigations, and, if necessary, to use some *Communicated by Prof. F. G. Donnan, F.R.S.

other method later as a check on the results. A careful examination, however, of the recent work in this field has convinced the writer that the drop-weight method, though quite satisfactory practically if the procedure of any particular worker be followed rigidly, does not yet rest on a really rational basis. It would seem that as far back as 1881 (Worthington, Proc. Roy. Soc. vol. xxxii. p. 362, 1881) and later (Guye and Perrot, Archives des Sc. Phys. vol. xi. p. 225, 1901; vol. xv, p. 132, 1903) more was known about the actual conditions of drop formation and detachment than the modern experimenter is aware of, and that in the curious mathematical developments of the original formula much has been assumed but very little explained.

The only reasonable formula for a cylindrical drop hanging from a tube under the influence of gravity is the one quoted by Worthington and Lord Rayleigh (Phil. Mag. (5) vol. xlviii. p. 321, 1899), namely w=πT, where w is the weight of the drop, r the radius of the tube, and T the surface tension. This is an equilibrium condition, and a slight increase in w should result in a detachment of the drop. This, however, never happens, for, by reason of its rapidly changing shape, the drop takes up new positions of equilibrium, and finally detaches at a stage quite beyond our control (Lohnstein, Ann. Physik, vol. xx. pp. 237, 606, 1906). The above formula has therefore to be modified by a correction factor, which varies according to the shape of the drop. This is the method that Harkins has adopted in his more recent measurements, but for some reason or other he prefers to use the formula w=2πrT; and although this gives correct results in the end, as his method is purely a comparative one, it must be admitted that the whole procedure is far from satisfactory. His definition of an ideal drop, as one conforming to that formula, seems without meaning, and can only be used as a convenient standard for want of a better understanding of the real facts of the case.

There was another formula developed in Worthington's day (Worthington, l. c.) which rests on a sounder theoretical basis, and seems to the author to explain in a much more logical manner the more accurate results of the modern experimenter. The fact that it did not come into general use is due to that very reason-that no experimental data in those days were sufficiently accurate to test its validity. Harkins (l. c.), for instance, has shown how unsatisfactory were Rayleigh's results, due to the use of thin-walled tubes. The formula is a comparative one, and rested on the assumption at the time, and is certainly in agreement with the Phil. Mag. S. 6. Vol. 45. No. 269. May 1923. 4 A

interesting fact at the present day, that different liquids may form drops of similar shape from tubes of different diameters.

If T1, T2 be the surface tensions, p1, p2 the densities of two liquids, and K the ratio between two similar linear dimensions of the drops-e. g., the ratio of the radii of the tubes from which they hang, or of the principal radii of curvature,then the equation of symmetry becomes

A satisfactory proof of this equation has already been given by Worthington, and it will not be necessary to repeat it here; but it will be seen that it affords a most convenient method of calculating the surface tension of any liquid of known surface tension and density. For if, by choosing a suitable radius of tube in both cases, the drops of the two liquids can be made to assume similar shapes, then the value of K, the ratio of the two radii, can be ascertained; and that is all that is required now for the solution of the equation. It is yet to be explained, however, in what way it is possible to ascertain the exact shape of the drop and its variation with the size of the tube employed. Now it is a remarkable fact that the shape of a drop is completely decided by the ratio of the radius of the tube to the radius of the detached portion of liquid considered as a sphere, and although this is purely an experimental fact, there are some theoretical reasons for assuming that this must be the case. If the equation of symmetry is to have any significance at all, it must hold right down to the moment of detachment of the drops; and as the rupture undoubtedly occurs at the point of maximum concavity, the same fraction of the hanging drop will detach in the two cases; and, moreover, the radii of the spheres which the detached element of fluid immediately forms will bear the same ratio to the radii of the two tubes. Consequently, if we have a small and a large drop, of different liquids but of the same shape, and we imagine them projected on to a screen, both to the same size, then we could not distinguish between the mode of detachment in the two cases, and the projections of the falling spheres would have the same radius.

We have assumed that the rupture occurs at the point of maximum concavity, as it is here that any upward force due to the surface tension is least; and though the cohesive forces of the liquid are now the deciding factors in the detachment,

* Guye and Perrot, Arch. des Sc. Phys. vol. xiii. p. 178 (1903).