Similarly, in the case of a double mirror,

r'=N2N1r,

if O is taken on the common edge of the component mirrors. Thus, in the case of any multiple mirror, we have, as before,

where 1-2n;. n,, provided that all the component mirrors have a common point of intersection, and that this point is taken as the origin of the vectors r, r'.

Under these circumstances, therefore, the treatment of point-objects and their images is formally the same as that of incident and reflected rays.

September 5, 1916.

LII. On an X-Ray Vacuum Spectrograph. By MANNE SIEGBAHN, Dr. phil., and EINAR FRIMAN, Dr. phil.* N order to examine the high frequency spectra of the elements by long wave-lengths the authors have had a vacuum spectrograph built. Hereby, as our former measurements have shown, the following conditions must be satisfied. First, the crystal must be movable, as otherwise irregularities in the structure of the crystal may be of great influence (comp. Rutherford and Andrade and E. Wagner). Secondly, in order to get a good resolving power, besides using a fine slit it is of great importance to focus the rays.

The apparatus built on this principle is shown in fig. 1, in both horizontal and vertical section. The spectrograph consists of a round metallic box of 6 mm. thickness, a height of 8 cm. and an inner diameter of 30 cm. The upper part BB, 3.5 cm. broad, is carefully plane-ground, as well as the corresponding part CC of the cover D. This as well as the bottom is furnished with radial reinforcements in order to resist the pressure better. The cover has a handle and a screw, the latter being used to lift it after the air has been admitted. The box is supported by three set-screws. In the middle of the bottom there is a conical hole with a metallic cone E, fitting well in it. This cone, being kept in the hole by a ring screwed into the box, after lubricating can be turned without the air passing through. The crystal table, placed

*Communicated by the Authors.

+ Phil. Mag. vol. xxxi. p. 403 (1916); vol. xxxii. p. 39 (1916).

on the cone, consists of a slide F, that can be moved by means of the screw H. On the slide the table N is placed, that can be turned round the axis a with the aid of the

screw h. This arrangement allows of a careful adjustment of the crystal K. This is attached to the table by means of a bow and two screws. The lower part of the cone is joined to a metallic arm M, about 20 cm. long, with an index Z.

This moves along a scale S, that indicates the turning angle of the crystal directly in degrees. The arm M can be moved to and fro by a slowly rotating eccentric-pulley. Through the side of the box, placed opposite to one another, two tubes R and U pass. The former is in communication with the pump by means of an indiarubber tube. In the latter there is another tube V, the end of which is covered with a plane-ground plate p, having a slit o 0·1 mm. wide and furnished with edges of gold. Between this slit and the crystal a screen I of lead is placed, with a slits of 2 mm. width. In the tube V is a cylindrical shield of lead 1.5 cm. thick, with an opening of about 1 mm. The X-ray tube (of the construction previously described) is attached to the spectrograph in such a way, that the extended part of it is put into the tube U, and then an air-tight elastic connexion obtained by means of picein.

The photographic plate is placed in the casket G. This is attached to the sledge L by screws passing through the two feet, which are furnished with longilateral openings by means of which the casket can be turned or removed. Through this arrangement the plate (in position 0) can be adjusted perpendicularly to the line first slit-crystal rotation axis, and at the same distance as the slit from the crystal. The sledge is supported by three steel bullets (comp. Moseley), two of which rest in a circular groove, the third in one of the radial cavities. In this way the sledge can take up perfectly fixed positions, the number of which is thirteen, situated at about the same angular distance from each other. These angles have been very carefully determined. In the investigations described in the next paper, only five positions have been used, which are denoted by 0, I-IV. The aperture angle of the casket is about 37°, and thus the plates in two adjacent positions have an angle of 4°-5°

common.

The X-ray tube is evacuated with a molecular air-pump. The fore-pump is employed simultaneously for the molecular air-pump and the spectrograph. If the latter is separated from the X-ray tube through a foil placed on the greased plate p, a suitable vacuum can be obtained in a few minutes. Physical Laboratory, University of Lund,

June 1916.

*Phil. Mag. vol. xxxii. p. 39 (1916).

LIII. On the High-Frequency Spectra (L-Series) of the Elements Lutetium-Zinc. By EINAR FRIMAN, Dr. phil.* [Plate XI.]

Na preceding paper† Dr. Siegbahn and the author have given the results of an investigation of the high-frequency spectra (L-series) of the elements tantalum-uranium. In this domain we found at least 11 line-groups. With the vacuum spectrograph described in the previous paper (p. 494) I have been able to continue these examinations down to zinc (34 elements). Here I have reached a wave-length of 12.346. 10-8 cm. (La-line of zinc), while the greatest wave-length measured by Moseley was 8.364.10-8 cm. (Kxline of aluminium).

Most of the elements examined as compounds were finely pulverized and rubbed on the anticathode, which was scratched beforehand with a file, or still better with a knife. By this method, also used in the investigation above-mentioned, a small quantity of the substance (some mgr.) is enough for an experiment. In some cases, however, the elements in metallic form were soldered on the anticathode (Cd, Ag, Pd, Zn) or pressed in tongs of copper soldered on it (In, Ru).

With the elements lutetium-silver very sharp photogrammes were obtained with a rocksalt crystal as reflector and an exposure time of an hour. In the later experiments a gypsum crystal was used. This also gave several rather sharp lines, but the lines of weak intensity did not appear. As window between the spectrograph and the X-ray tube in the beginning a thin foil of aluminium (0.001 mm.) was used. From tellurium it was replaced by a thin foil of goldbeater's skin that very well transmits the soft rays (Moseley). It has a disadvantage, however, in also transmitting the luminescence light from the anticathode, which often was very strong and blackened the plate. The spectral lines generally were referred to the Ka-line of copper, the wave-length of which has been very carefully determined by Siegbahn and Stenström §. The reflexion angles calculated have an uncertainty of about 03 per cent. As grating-constant of rocksalt the value 2.814.10-8 cm., given by Moseley, was *Communicated by the Author.

+ Phil. Mag. vol. xxxii. p. 39 (1916).

Here a

Some of these photogrammes are reproduced in my doctor-dissertation, Lunds Univ. Arsskr. N. F. Avd. ii. Bd. xii. Nr. 9 (1916). more detailed account of my investigations is given.

§ Phys. Zeitschr. xvii. p. 48 (1916).