the sun is in the general direction of the constellation Carina. The approximate galactic longitude of this center (which is to be taken as the center of the local cluster rather than that of the galactic system) is indicated in figure 1 by the short line across the galactic equator. A greater frequency of stars is to be noted in this direction, especially of the fainter objects plotted in figures 2 and 3.

We recall that Strömberg's researches, through showing that stars of types F, G, and K appear to have motions related to the same center as that determined for the B-type stars, may be taken as strongly supporting the hypothesis of a local cluster which involves all types of stars. The observed decrease of stellar density with distance from the sun, for all the principal spectral classes, is also almost conclusive evidence that the phenomena of the local cluster are not confined to the B stars alone. It appears highly probable, therefore, that the inclination and extent now under investigation refer to the cluster as a whole, and not only to these blue giant stars which, because of their uniformity in absolute brightness and their apparently high concentration to dynamically central planes, are of such high value in outlining a stellar system.

The available volumes of the new catalogue of spectra cover less area than shown in figure 1, but the extension to the seventh magnitude (fig. 2) adds definitely to our knowledge of the cluster. Stars of the seventh magnitude are 1.6 times as far away as those of the sixth when the intrinsic brightness is the same. Increasing the depth of our survey by that amount has therefore brought in many B-type stars of the galactic field, objects concentrated to the galactic equator, and it has not introduced a great many stars of the local system. Hence, there is a suggestion in figure 2 that we are attaining the edges of the local cluster when we go out to the B-type stars of the seventh magnitude.

Extending the survey much deeper into space by including the stars fainter than magnitude 7 (fig. 3), we find that outside the relatively small domain of the local cluster the galactic equator has definitely established itself as the central circle for B-type stars.

The very high concentration of these distant stars to the Milky Way is a striking illustration of the great depth of the galactic system when compared with its extent perpendicular to the galactic plane. Probably the most important inference from figures 2 and 3 is, however, that the galactic field is continuous in the immediate environs of the local cluster-that the latter is not a large group or cloud distinctly and distantly isolated in space from other stellar regions. Similar evidence of a surrounding and intermingling galactic field may be deduced from the distribution of Cepheid variables, N-type stars, planetary nebulae, and similar special classes of sidereal objects.

In figures 2 and 3 the crosses indicate the position of stars of the sub-types BO, B1, and B2, and the dots refer to the sub-types B3 and B5. Stars of the first group of sub-types are believed to be intrinsically brighter than those of the second. For a given apparent magnitude, therefore, their distances are greater-possibly even twice as great. It is to be noted that the crosses have completely left the secondary circle in figure 3, indicating that the local cluster is not large enough to include objects as distant as B1 stars must be when they appear fainter than magnitude 7.

1 Shapley, Harlow, these PROCEEDINGS, 4, 1918, (224-229); Mt. Wilson Communications, No. 54. See also Mt. Wilson Contr., No. 157, and a small modification of the original statement of a star-streaming hypothesis, Mt. Wilson Contr., No. 161, section IX.

2 For other properties of the local cluster and for a discussion of the peculiar value of B-type stars in describing its extent, form, and orientation, reference may be made to Mt. Wilson Contr., No. 157, part II. and No. 161, section IX.

3 Strömberg, Gustaf, Astrophys. J., Chicago, Ill., 47, 1918, (7-37); Mt. Wilson Contr., No. 144.

INFLUENCE OF IONS ON THE ELECTRIFICATION AND RATE OF DIFFUSION OF WATER THROUGH MEMBRANES

BY JACQUES LOEB

THE ROCKEFELLER INSTITUTE FOR MEDICAL RESEARCH, NEW YORK

Communicated, August 27, 1919

1. When pure water is separated from a watery solution by a strictly semipermeable membrane more molecules of water will diffuse through the membrane from the pure solvent to the solution than will diffuse simultaneously in the opposite direction; and this difference in the rate of diffusion of water in the two opposite directions will be the greater the higher the concentration of the solution. When the solution is put under pressure, the number of molecules of water diffusing in the unit of time from the solution into the pure solvent will be increased and if this pressure reaches a certain value the number of molecules of water diffusing simultaneously in opposite directions through the membrane will become equal. We may therefore define the osmotic pressure of the solution as the additional pressure which has to be applied to the solution in order to cause as many molecules of water to diffuse from the solution to the pure solvent as will diffuse simultaneously in the opposite direction.

van't Hoff's theory of osmotic pressure assumes that this quantity depends exclusively upon the concentration of the solution. For some

2

time it had been known that in certain cases water is able to diffuse from solutions of higher to solutions of lower concentrations, and it has been suggested by a number of authors, e.g., Girard,' Bartell, Bernstein, and others that these phenomena are due to electrical forces caused by the presence of electrolytes in solution. They assume on the basis of the experimental and theoretical work done by Quincke, Helmholtz, Perrin, and others on electrical endosmose that differences of electrical potential on both sides of the membrane influence the rate of diffusion of water through the membrane.

The writer has recently investigated the influence of electrolytes on the rate of diffusion of water through collodion bags prepared in a definite and uniform way and bathed over night in a 1 per cent gelatin solution. The bags had the shape of Erlenmeyer flasks with 50 cc. contents and were closed by rubber stoppers which were perforated by a glass tube with a bore of 2 mm., the tube serving as a manometer.

When such a bag was filled with watery solution and was dipped into distilled water the level of the water in the manometer rose owing to the fact that more water diffused from the pure water into the solution than diffused simultaneously in the opposite direction, as was to be expected. It was found that the initial rate of diffusion of water was influenced in an entirely different way by electrolytes and non-electrolytes. The solutions of non-electrolytes, e.g., sugars, influenced the initial rate of diffusion of water through the membrane in proportion to their concentration and this influence began to show itself when the concentration of the sugar was above M/64 or M/32. Sugar solutions of lower concentrations than M/64 caused no rise in the manometer. We will call this effect of the concentration of the solute on the initial rate of diffusion the gas pressure effect. Solutions of electrolytes show this gas pressure effect also, but it commences at somewhat higher concentrations than M/64, namely at M/16 or even M/8. Solutions of electrolytes of a lower concentration than M/16 or M/8 have a specific influence on the rate of diffusion of water through the membrane which is not found in the case of non-electrolytes.

When we separate a watery solution of an electrolyte of a concentration below M/16 from pure water by a collodion membrane, the water molecules diffuse through the membrane as if they were electrically charged-positively or negatively according to the nature of the ions present and as if they were attracted electrostatically by ions of one sign and repelled by ions of the opposite sign. When we used solutions of electrolytes theoretically isosmotic with a M/64 cane sugar solution

it was found that the influence of the nature of the electrolytes on the rate of diffusion of water through a collodion membrane could be expressed in the following two rules:

(1) Neutral solutions of salts possessing a univalent or a bivalent cation influence the rate of diffusion of water through a collodion membrane as if the water particles were charged positively and were attracted by the anion and repelled by the cation of the electrolytes; the attractive and repulsive action increasing with the number of charges of the ion and diminishing inversely with a quantity which we will designate arbitrarily as the 'radius' of the ion. The same rule applies to solutions of alkalies.

(2) Solutions of neutral or acid salts possessing a trivalent or tetravalent cation influence the rate of diffusion of water through a collodion membrane as if the particles of water were charged negatively and were attracted by the cation and repelled by the anion of the electrolyte. Solutions of acids and of neutral salts with monovalent or bivalent cation when rendered sufficiently acid obey the same rule."

Thus the rate of diffusion of water into a neutral solution was considerably greater when the solution was M/128 NaCl than when it was M/64 cane sugar; and when different sodium or potassium salts were compared it was found that the rate increased with the valency of the anion of the salt in solution, sulfates and oxalates acting more powerfully than chlorides and nitrates, and citrates and ferrosulfocyanides more powerfully than sulfates and oxalates. The rate of diffusion of water was less when the solution was M/192 CaCl2 than when it was M/64 cane sugar, and the same was true for all solutions of neutral salts with bivalent cation and monovalent anion. The attraction of M/128 solutions for water increased in the order Li<Na<K, showing the influence of the radius of the ion.' Solutions of alkalies like NaOH or KOH acted similarly to solutions of NaCl or KCl. All this was to be expected if water particles behaved as if they were positively charged, being attracted by the anion and repelled by the cation of the electrolyte.

In the case of electrolytes falling under rule 2, water particles behave as if they were negatively charged and attracted by the cation and repelled by the anion of the electrolyte with a force increasing with the number of charges of the ions. Thus solutions of AlCl attract water very powerfully, solutions of Al2(SO4)3 of the same theoretical concentration act much more feebly and solutions of aluminium citrate have practically no more influence on the rate of diffusion of water than cane sugar solutions of the same concentration. When we render M/128 so

lutions of NaCl acid (by dissolving the salt in M/1024 HCl) the water particles diffusing through the membrane are negatively charged and are attracted by the Na ion of the solution. This is supported by the fact that M/192 CaCl, dissolved in M/1024 HCl (or HNO3) attracts water much more powerfully than does M/128 NaCl of the same hydrogen ion concentration; and the attraction of M/512 AlCl of the same hydrogen ion concentration for water is still more powerful than that of CaCl2. All this is intelligible on the assumption of an electrostatic influence of the ions upon negatively electrified particles of water-no matter what the nature or source of electrification of water may be. That water is indeed electrified in the sense expressed in the two rules. was proved directly by experiments on electrical endosmose.

The collodion membranes are not only permeable to water but also to crystalloids in solutions. It could be shown by analytical experiments that the phenomena expressed in the two rules were not due to differences in the rate of diffusion of the solute. The reader will find a full description of these experiments in a recently published paper."

3. The two rules mentioned before were based on experiments with solutions of about the same gas pressure, namely that of a M/64 sugar solution. When we compare the osmotic effect of different concentrations of sodium (or Li, K, NH1) salts within the limit of M/8192 to about M/16 we find a curious phenomenon. In these experiments the solution of the electrolyte was put inside the collodion bag and the latter was dipped into a beaker with pure water. It was found that under these conditions the initial rise (i.e., the rise in the first ten or twenty minutes) of water in the collodion bag increased rapidly with the increase of the concentration of the solution, this initial rise reaching a maximum when the concentration of the electrolyte was about M/256. With a further increase of the concentration of the electrolyte the initial rate of diffusion of water from pure solvent into the solution dropped rapidly, reaching a minimum at about a concentration of M/16. We therefore notice the paradoxical fact that M/256 solutions of all these electrolytes attract water more powerfully than M/16 solutions of the same electrolytes. Thus in the case of a neutral solution of sodium oxalate the level of water rose in the manometer of the flask in twenty minutes to about 100 mm. when the concentration of the solution was M/1024, to 220 mm. when the concentration was M/256, but only to 100 mm. again when the concentration was M/16. While I do not wish to make any assumption concerning the source of the electrification of water and the mechanism by which