We have seen that the distances of the stars from the solar system are immense beyond conception, and millions upon millions of them are probably forever beyond our power of ascertaining by direct measurement what their distance really is. After we had found the sun's distance and measured the angle filled by his disk, it was easy to calculate his actual size. This direct method, however, fails when we try to apply it to the stars, because their distances are so vast that no star's disk fills an angle of any appreciable size; and even if we try to get a disk with the highest magnifying powers of a great telescope our efforts end only in failure. There is, indeed, no instrumentally appreciable angle to measure.
How then shall we ascertain the actual dimensions of the vast spheres which we know the stars actually are, as they exist in the remotest regions of space? Clearly by indirect methods only, and it must be said that astronomers have as yet no general method that yields very satisfactory results for stellar dimensions. The actual magnitude of the variable system of Algol, Beta Persei, is among the best known of all the stars, because the spectroscope measures the rate of approach and recession of Algol when its invisible satellite is in opposite parts of the orbit; the law of gravitation gives the mass of the star and the size of its orbit, and so the length of the eclipse gives the actual size of the dark, eclipsing body. This figures out to be practically the same size as that of our sun, while Algol's own diameter is rather larger, exceeding a million miles.
If we try to estimate sizes of stars by their brightness merely, we are soon astray. Differences of brightness are due to difference of dimensions, of course, or of light-giving area; but differences of distance also affect the brightness, inversely as the squares of the distances, while differences of temperature and constitution affect, in very marked degree, the intrinsic brilliance of the light-emitting surface of the star. There are big stars and little stars, stars relatively near to us and stars exceedingly remote, and stars highly incandescent as well as others feebly glowing.
We have already shown how the angular diameters subtended by many of the stars have been estimated, through the relation of surface brightness and spectral type. Antares and Betelgeuse appear to be the most inviting for investigation, because their estimated angular diameters are about one-twentieth of a second of arc. This is the way in which their direct measurement is being attempted.
As early as 1890, Michelson of Chicago suggested the application of interference methods to the accurate measurement of very small angles, such as the diameters of the minor planets, and the satellites of Jupiter and Saturn, as well as the arc distance between the components of double stars. Two portions of the object glass are used, as far apart as possible on the same diameter, and the interference fringes produced at the focus of the objective are then the subject of observation. These fringes form a series of equidistant interference bands, and are most distinct when the light comes from a source subtending an infinitesimal angle. If the object presents an appreciable angle, the visibility is less and may even become zero.
Michelson tested this method on the satellites of Jupiter at the Lick Observatory in 1891, and showed its accuracy and practicability. Nevertheless, the method has not been taken up by astronomers, until very recently at the Mount Wilson Observatory, where Anderson has applied it to the measurement of close double stars. It is found that, contrary to general expectation, the method gives excellent results, even if the "seeing" is not the best—2 on a scale of 10, for instance.
To simplify the manipulation of the interferometer, a small plate with two apertures in it is placed in the converging beam of light coming from the telescope objective or mirror. The interference fringes formed in the focal plane are then viewed with an eyepiece of very high power, many thousand diameters. The resolving power of the interferometer is found to be somewhat more than double that of a telescope of the same aperture. By applying the interferometer method to Capella, arc distances of much less than one-twentieth of a second of arc were measured. More recently the method has been applied to the great star Betelgeuse in Orion, whose angular diameter was found to be 0".46, corresponding to an actual diameter of 260,000,000 miles, if the star's parallax is as small as it appears to be.
