the second term of the right-hand side characterizes the process of removal of decomposition products, and \(\alpha_2\) must vary with the conditions of blood replenishment. The coefficient \(\alpha_2\) enters into the equation relating the illumination intensity \(I\) to the time \(t\) for the threshold of irritation.

\[ I=\frac{B}{C\alpha_1 k\left(1-\frac{B}{2c}\right)\cdot t} +\frac{B\alpha_2}{2C\alpha_1 k\left(1-\frac{B}{2c}\right)} . \]

For constant \(t\), the coefficient \(\alpha_2\) is linearly related to \(I\). From an increase in \(I\) we may judge an increase in \(\alpha_2\).

The measurements made did indeed give this increase.

The second article placed in the title concerns deviations from the law established by Lazarev and given in the first article,

\[ I.t=a+bt \]

The observations of Broca and Sulzer showed that, upon illumination of the eye, the sensation of brightness at first grows with increasing \(t\), and then falls. Lazarev makes the hypothesis that, in the decomposition of pigment, substances are first obtained which cause the formation of irritating endings of substance \(B\); in turn, the substances \(B\) pass into substances \(D\), which do not cause irritation. It turns out that the integral of the differential equation set up under this assumption is

\[ I=A\left(e^{-\omega t}-e^{-\omega_1 t}\right) \]

and expresses quite satisfactorily the results of the experimental investigation.

It is interesting to note that the same relation between irritation and the time of the irritation threshold was discovered by V. Henri when ultraviolet rays acted on a small animal of the crustacean species Cyclops.

Б. В. Ильин.

Osmotic Pressure and Density Fluctuations in Concentrated Emulsions.

(Jean Perrin et René Constantin, Comptes Rendus t. 158, p. 1341, 1914).

The above-mentioned works concern the dependence of the osmotic pressure of emulsions on the concentration of granules. Perrin draws an analogy between an undiluted emulsion and a liquid whose molecules are correspondingly enlarged. This analogy allows him to apply the Van der Waals equation. In a vertical layer of emulsion the osmotic pressure is

\[ P=P_0+\Pi\frac{\omega}{s}, \]

where \(P_0\) is the pressure for the height \(H=0\). On the other hand, according to the Van der Waals equation:

\[ P=\frac{RT}{V}+\frac{bRT-a}{V^2}, \]

where \(R\) is the gas constant, \(T\) the absolute temperature, \(V\) the volume of the emulsion containing \(N\) granules. Two equations of state give:

\[ P=P_0+H\frac{\omega}{s}=\frac{RT}{N}\cdot n+\frac{bRT-a}{N^2}\cdot n^2, \]

where \(n\) is the number of granules per unit volume, for a given level \(H\). This relation gives the dependence of \(P\) on \(n\) (concentration).

If, however, one writes two such equations for the numbers \(n\) and \(n_0\) and subtracts them from one another, one obtains:

\[ \frac{\omega}{s}\cdot\frac{H}{n-n_0}=\frac{RT}{N}+\frac{bRT-a}{N^2}\left(n+n_0\right). \]

Plotting along the \(X\)-axis \(\left(n+n_0\right)\), and along the \(Y\)-axis \(\dfrac{H}{n-n_0}\), one obtains a straight line, whose ordinate at the origin of coordinates gives \(\dot N\). Thus, we have a new method for obtaining Avogadro’s constant. The value obtained is \(60.10^{22}\). Once the dependence of the osmotic pressure on the concentration \(\dfrac{dP}{dn}\) (Perrin calls this the osmotic compressibility of the emulsion—la compressibilité osmotique de l’emulsion) has been established, one can test the validity of the relation given by Smoluchowski for fluctuations of density.

\[ \delta=\frac{n-n_0}{n_0}=\frac{1}{\sqrt{-\pi\,\frac{N\eta v_0\,dP}{2RT\,dv_0}}}\quad \text{(I),} \]

where \(v_0\) is the specific volume, \(P\) the osmotic pressure, and \(N\) Avogadro’s number. The relation for \(\delta\) may also be given in another form:

\[ \delta=\frac{n-n_0}{n_0}=\frac{2n_0^{\,n_0}\cdot l^{-n_0}}{n_0!}\sqrt{\frac{\beta}{\beta_0}}\quad \text{(II),} \]

where \(\beta\) is the observed coefficient of compression, and \(\beta_0\) the coefficient of compression under the assumption that Clapeyron’s equation is applicable (the case of an ideal gas). This dependence was verified experimentally for colloidal solutions by Svedberg (Zeitschr. f. phys. Chem. 73, 547, 1910), and for emulsions by Il’in (Zeitschr. f. phys. Chem. LXXXIII B., 5 Heft). But since both solutions and emulsions were taken only weakly concentrated, \(\dfrac{\beta}{\beta_0}\) proved to be equal to unity. René Constantin takes considerably higher concentrations (up to \(\dfrac{1}{15}\)), and as a consequence Clapeyron’s equation is already inapplicable. The values for \(\delta\), calculated by formula (I), give complete agreement with experiment.

The possibility of applying to emulsions not only the Boyle–Mariotte–Gay-Lussac equation (Clapeyron), but also the Van der Waals equation, which gives a significantly more detailed model of molecular phenomena, compels one to arrive at certain interesting conclusions.

There is no doubt that the phenomenon of Brownian motion, and the conditions of the motion of granules in emulsions, in reality do not correspond to the molecular-kinetic model. The possibility of applying to emulsions (to solutions) the kinetic theory of gases (liquids) is based solely on the statistical character of the phenomenon. It seems to me that this circumstance should be emphasized not only with respect to emulsions, but also with respect to “gases.” Very often far more real significance is attached to the molecular-kinetic model than is in accordance with reality. It is always necessary to remember that the real kinetic theory of gases is only a model, a working hypothesis, and that the experimental confirmation of the laws of kinetic theory proves nothing more. Indeed, in Brownian motion, which manifestly does not correspond to the molecular-kinetic model, not only Clapeyron’s equation is confirmed, but even Van der Waals’s equation! And it is clear why. If among the quantities \(x, y, z, \ldots\) there exists the relation:

\[ f(x, y, z, \ldots)=0 \quad \text{(I),} \]

then this still does not mean that \(x, y, z, \ldots\) are the real coordinates of the phenomenon. \(X, y, z, \ldots\) may be arbitrary functions of real coordinates \(u, v, t, \ldots\)

\[ \begin{aligned} x&=\mu(u, v, t, \ldots)\\ y&=\psi(u, v, t, \ldots) \quad \text{(II)}\\ z&=\chi(u, v, t, \ldots) \end{aligned} \]

If relation (II) and the relation

\[ f[\mu(u, v, t, \ldots), \psi(u, v, t, \ldots), \chi(u, v, t, \ldots)]=0 \quad \text{(III)} \]

exist, then equation I also holds.

B. V. Ilyin.

Laws of Excitation by Ultra-Violet Rays.

(Viktor Henri, Archives des sciences physiques No. 1 and 2, 1913).

The article placed in the title is a brief monograph summarizing a whole series of works by the author and his students. This monograph once again shows how many valuable and often unexpected results have been yielded in recent years by the application of physico-chemical methods to the study of problems of biology and physiology. First of all, it should be noted that the boundaries between physics and chemistry have been definitively erased. If earlier it was possible to divide phenomena into physical and chemical, the former being defined as those in which the composition of the substance does not change, then now such phenomena as radioactivity, photochemical reactions, the photoelectric effect, capillarity phenomena, and a whole series of processes of so-called physical chemistry undermine the precision and categorical nature of these