intrinsically brighter at A than at D. Such is not the case. This can be explained if these lines are self-reversed, as seen at A. At the constriction the current density is high, and so the electrons are very dense. This is the condition for the absorption of the D-line radiation by atoms from neighbouring atoms. Many of the atoms present will thus be in the condition that the valency electron has been displaced to the 2p ring, and so these atoms are no longer in a condition to absorb the D-line radiation, but rather those lines converging to 2p. Thus the light transmitted by these atoms suffers absorption of the subordinate lines, while the D lines are not affected. In the wider portion of the apparatus the electrons are less dense. There is less chance of the atoms absorbing radiation, and so the subordinate lines no longer show self-reversal. Accordingly, they will appear brighter

than at the constriction.

When the current in the arc is reduced, the density of the electrons and the self-reversal of the subordinate lines are less marked. This is illustrated in the spectrograms IV., V. (Pl. I.).

While the arc is in operation the actual drop of potential across the electrodes is only about 10 volts. At 300° C. the vapour pressure of sodium and potassium is high, and the mean free path of the electrons must be very small. It seems improbable that the bombarding electrons can gain energy sufficient to ionize during the time that this path is traversed. It is more likely that the atoms become partially ionized by the absorption of radiation. The atoms which are in this condition, i. e. those in which the valency electron is in the 2p ring, will then require less energy than 5.1 volts for complete ionization.

White light from an arc was passed through the radiation. at the constriction, and also at D, and the complete spectrum viewed at the windows C and D. Visual observations showed absorption of the D lines only, they of course appearing dark on the luminous background.

The light issuing at D came from a point within the tube at a considerable height above the alloy electrode. There was no possibility of the variation in the relative intensity of the lines being due to the electrode potential gradient.

The spectrograms I., II., III. (Pl. I.) were photographed with exposures of 10 seconds each, and those of IV., V. (Pl. I.) with 20 seconds' exposure.

were photographed.

III. Diffraction Pattern in a case of two very close PointLight Sources. By B. E. MOURASHKINSKY, Optical Laboratory of the Central Chamber of Weights and Measures, Petrograd *.

AS

[Plate II.]

S is well known, the illumination at the point r in the focal plane of a geometrically corrected objectglass with a circular aperture due to a point-light source is expressed by

where

I = M 4J,2(2),

(1)

(2)

R being the radius of the object-glass, f its focal length, A the wave-length of light, r the distance of the considered point from the geometrical image of the point-source (in the focal plane), J1 Bessel's function of order unity. The illumination at the geometrical image of the source is assumed to be equal to unity.

For values of

we have Lommel's tables, in which the argument is varying by tenths from ≈=0 to z= =20.0.

If we take two point-sources, primarily of equal intensity, and denote the illumination at the point r due to the first source by I, and that due to the second by I2, the entire illumination at this point due to both the sources will be

where

and r1 are the distances of this point in the focal

plane from the geometrical images of two sources.

Communicated by the Author, having been read before the Russian Astronomical Society, April 27, 1922.

The distribution of illumination along a meridional line (a line joining two geometrical images) depends on the distance between the sources. If the distance between two

d being a linear distance between these images in focal plane; then

r1 = d−r,

The value may be either positive (towards the image of the second point) or negative (in the opposite direction). The expression (3) may be written

I = M

4J(:) 4J12 (D—~)

+

(D − 2)2

(5)

The factor M is constant for a given instrument, and the illumination at the point r will be

The measured angular distance between two point-sources expressed in are seconds may be converted into D and vice versa by means of the following simple relations :

As two points are of equal intensity, the distribution of illumination along a meridional line will be symmetrical with respect to two geometrical images.

The question is, what value should D attain so that the two images would be just resolved.

The resolving power of an object-glass with a circular aperture depends on: (1) the size of an aperture, i. e. its diameter, (2) the wave-length of light of a source, (3) the contrast between the illumination at the geometrical images of two sources and that at the central minimum in the