The genus Orestias belongs to the highlands about Lake Titicaca and the desert of Death Valley, Nevada.

The genus Pygidium pertains to the highlands of South America. Of the rest of the genera Nematogenys, Brachygalaxias, and Percilia are peculiar to Chili; Basilichthys, Hatcheria, Diplomyste, Aplochiton, and Percichthys are common to Chili and Patagonia; Galaxias, Velasia, Geotria, and Caragola are common to Chili and Australia or New Zealand.

The Calle Calle basin, which includes Lake Rinihue, contains, as far as known, the richest fauna of any river basin in Chili.

So great is the similarity of the Austro-Chilian fauna of Chili with that of Patagonia, that there can be no doubt of the common origin of the two faunas.

Of the three forms of the genus Cheirodon in Chili C. Galusda found about the Bio Bio is most typical. Both the species north of this area and the one south of it have diverged from the typical form. Possibly this indicates that the connection of the Chilian Cheirodon with its Cisandean relatives remained longest near the Bio Bio basin.

MEASUREMENT OF STAR DIAMETERS BY THE

INTERFEROMETER METHOD.

By F. G. PEASE.

(Read April 22, 1921.)

The idea of measuring the angular diameter of a fixed star by the method of interference of light beams was suggested by Fizeau in his report on the Bordin Prize to the French National Academy in 1868. Stephan spent the year 1874 examining all the brighter stars by this method with the 31.5-inch telescope of the Marseilles Observatory, and rightly found that the telescope was altogether too small for the purpose. The papers relating to this work will be found in Comptes Rendus, LXVI., p. 1008, 1873, and LXVIII., p. 1008, 1874.

Nothing further appeared on this subject until Michelson in 1890 published a masterly paper in the Philosophical Magazine, “On the Application of Interference Methods to Astronomical Measures." He pointed out that the telescope itself need not be large, and that the results desired might be accomplished by the use of a double periscopic arrangement consisting of four small auxiliary mirrors placed in a frame on the end of the telescope. Designs for a periscopic attachment are shown by Michelson in his paper but his successful measures of the satellites of Jupiter with the 12-inch refractor of the Lick Observatory in 1891 were made with two apertures placed directly in front of the objective. Aside from this question of size, the interferometer was considered an instrument of the utmost precision requiring the best of optical conditions, and the belief was general that the disturbances of the atmosphere would probably be such as to prevent its successful use even if a large telescope should be built. After the 100-inch Hooker telescope had been completed and excellent results obtained with it at the full aperture of the mirror, Director Hale invited Dr. Michelson to investigate the question of interference with this large instru

ment. Stephan had already found fringes with apertures separated by 25.6 inches; Michelson found the same result in turn, first with the full aperture of the 40-inch Yerkes Refractor, then with the 60-inch reflector at Mount Wilson and finally the 100-inch Hooker Reflector, even though the seeing was not very good. The immediate result was the application of interference methods to the measurement of double stars, and Anderson developed a method by means of which he determined the distance between the components of Capella with a very great degree of precision, it being impossible to do this by ordinary methods on account of the closeness of the companions to one another. The next step undertaken was to adapt the great reflector in accordance with Michelson's plan of 1890, by mounting four auxiliary small mirrors on a beam placed across the upper end of the telescope tube. Success attended its installation and in August, 1920, the interference fringes obtained on Vega with an aperture equivalent to 18 feet were as easily seen as those at 6 feet.

Meanwhile, Eddington, Russell, Shapley, and others had made calculations of the diameters of a number of stars based on estimates of their surface brightness, and their results indicated that a Orionis. would be an excellent object for an attempt to measure the diameter. Merrill first examined the star with the apparatus used by Anderson in the measurement of Capella and found a definite decrease in the visibility of the interference fringes with the slits separated the full aperture of the mirror. An actual measurement of the diameter of a Orionis was then made by the writer on Dec. 13, 1920; a description of the instrument and method is given below.

Before describing the 20-foot interferometer in detail it may be well to recall a few of the principles of interferometry. Thomas Young found that two pencils of light from a point source, when brought together again, can be made to produce interference bands or "fringes." A pinhole in a screen A (Fig. 1) in front of a candle will, for laboratory experiments, serve as a source of light. Light spreads from this pinhole in concentric spherical waves and is intercepted by a screen B, having in it two pinholes equidistant from the axis so that ACAD. These openings furnish the two pencils of light and interference takes place where the wave fronts

intersect, say at a screen E. Having left B at the same instant, the two pencils arrive at the screen E on the axis at the same time, the crest or trough of one wave falling upon the corresponding crest or

trough of the other wave, each thus reinfocing the other. At F, F are points on either side of the axis where the crest from one wave falls in the trough of the other; the result is the complete neutralization of the one by the other (and the total absence of motion) and consequently darkness at that point. Between these two points there is a gradual change in intensity, so that one grades into the other. The observed result is a series of parallel bands, alternately bright and dark, lying on both sides of the axis, bright wherever the path difference from the screen E to the two apertures is equal to any number of even half wave-lengths of light as 2, 4, 6, etc., and dark when the number of half waves in the path difference is an odd number as 1, 3, 5. No light is lost in the mutual action of the two pencils on one another; it is simply redistributed, and what is removed from the dark region is to be found in the brighter portion.

Fresnel improved the method of observing the bands by setting

two prisms of equal angle side by side as indicated in Fig. 2. Light from a source G passing through the two prisms arrives at a screen H, and here the same principle of crest on crest or crest on trough produces interference fringes. It should be borne in

mind that light from two separate sources cannot interfere; it is only two pencils of light from the same source that produce the phenomenon in question. As the size of the source of light is slightly increased, each point in it produces a series of concentric spherical waves and there are therefore at the screen a great many overlapping interference fringe patterns slightly displaced with respect to one another, which reduce the contrast between the dark and light bands. Without going into detail, it is found mathematically and experimentally that for a given distance between the slits there is a certain size of source for which this overlapping is complete, fringes are not visible and ordinary illumination takes place. As the source is slightly increased in size the fringes reappear much less conspicuous than before and then vanish again.

In the application of this principle to the telescope, the wave front from a distant star is considered a plane although it is actually a portion of a sphere. Each point of the star produces a wave which is inclined slightly to that from the central point. All these waves superimpose in apparently one wave front on the axis of the telescope and for a distance of a foot or two on either side. When the telescope is covered with a screen having two apertures