Interference Methods in Astronomy 148
respectively. The important point to be noted is that the results by the interference method are near the mean of the other results, and that the results obtained by the other method differ widely among themselves.
It is also important to note that, while an eleven-inch glass was used for the observations by the interference method, the distance between the slits at which the fringes disappear was very much less than eleven inches; on the average, something like four inches. Now, with a six-inch glass one can easily put two slits at a distance of four inches. Hence a six-inch glass can be used with the same effectiveness as the eleven-inch, and gives results by the interference method which are equal in accuracy to those obtained by the largest telescopes known. If this same method were applied to the forty-inch glass of the Yerkes Observatory, it would certainly be possible to obtain measurements of objects only one-sixth as large as the satellites of Jupiter.
The principal object of the method which has been described was not, however, to measure the diameter of the planets and satellites, or even of the double stars, though it seems likely now that this will be one rather important object that may be accomplished by it; for some double stars are so close together that it is impossible to separate them in the largest telescope. A more ambitious problem, which may not be entirely hopeless, is that of measuring the diameter of the stars themselves. The nearest of these stars, as before stated, is so far away that it takes several years for light from it to reach us. They are about 100,000 times as far away as the sun. If they were as large as the sun, the angle they would subtend would be about one-hundredth of a second. A forty-inch telescope can resolve angles of approximately one-tenth of a second, so that, if we were to attempt to measure, or to observe, a disc of only
Light Waves and Their Uses
one-hundredth of a second, it would require an objective whose diameter is of the order of forty feet — which, of course, is out of the question. It is, however, not altogether out of the question to construct an interference apparatus such that the distance between its mirrors would be of this order of magnitude.
But it is not altogether improbable that even some of the nearer stars are considerably larger than the sun, and in that case the angle which they subtend would be considerably larger. Hence it might not be necessary to have an instrument with mirrors forty feet apart. In addition it may be noted that it is not absolutely necessary to observe the disap|>earance of the fringes in order to show that the object has definite magnitude; for if the visibility of the fringes varies at all, we know that the source is not a point. For, suppose we observe the visibility curve of a star which is so far away that we know it has no appreciable disc. The visibility curve would correspond to a straight line. There would be no appreciable difference in distinction of fringes as the distance between the slits was increased indefinitely. If we now observe a star which has a diameter of one-hundredth of a second, we need only to observe that the visibility for a large distance between the slits is less than in the case of the distant star, in order to know that the second object has an appreciable disc, even if the instruments were not large enough to increase the distance sufficiently to make the fringes disappear. From the difference between two such visibility curves we might calculate rather roughly the actual magnitude of the stars.
1. The investigation of the size and structure of the heavenly bodies is limited by the resolving power of the observing telescoj>e. When the bodies are so small or so