atom can affect others without itself suffering any change, and the denial of this possibility constitutes a postulate more fundamental than that of the conservation of energy.

Hard upon the heels of the matrix theory there followed the theory of Schrödinger. Here again, the endeavor is to provide for a procedure which will determine a set of vibrations with appropriate frequencies for the atom; the procedure in being thus made to provide for the frequencies provides also for the amplitudes, so that we arrive at the same stage as was reached on the matrix theory. The Schrödinger theory proceeds along lines which make in some respects a closer appeal to our physical intuitions, however.

If we should attach a prong to a tuning fork and cause it to set up ripples in a bowl of water, these ripples would be reflected from the walls of the bowl, and very quickly we should realize a steady state of what the physicists call standing waves in the water. The ordinary laws of dynamics would enable us to calculate the nature of these waves. Now, in the hydrogen atom and in the ether surrounding it, Schrödinger supposes that there exists a state of affairs crudely analogous to these standing waves. That which oscillates is not the light itself, but is the source which sends out the light emitted by the atom, and the standing waves are waves of electric density. If we should now endeavor to produce in the light waves the frequencies which we desire by simply assigning those frequencies of vibration in the standing waves, we should accomplish very little from a philosophical standpoint. What Schrödinger does is to start once more with that expression which I have called the nameform of the atom, and devise a system of laws by which one can specify the standing waves in the ether in such a manner that through the name-form as a starting point they shall receive the frequencies which they require. Once more we have the principle of starting with a certain mathematical form which is the thing characteristic of the atom, a form moreover of relatively simple structure and containing but few letters and numbers. We proceed to apply to it a

process of mathematical manipulation, the same for all atoms, with a view to deducing the more detailed and complicated properties of the specific atom itself.

It turns out that while there is no simple electron in the older sense of the word there does exist a close relationship between the electric density distribution as defined in the Schrödinger theory and what was the electron in the old theory. If we should consider the case of a large electronic orbit of the old theory, the Schrödinger picture would correspond not remotely to it, but in place of the electron there would be a distribution of vibrating charge extending over an appreciably large region. The analogy with the older picture would become less and less the smaller the orbit until for such orbits as exist in the hydrogen atom in its unexcited state it would lose its significance completely. The situation. is something like one where we feel perfectly definite in the meaning to be attached to the earth's inhabitants rotating around the sun which is at a distance large compared with their relative journeyings during the process, while it would be perfectly futile to form in our minds a picture of the people on Times Square, N. Y., as describing an orbit about the center thereof; for, in the latter case relative motions of different parts of the crowd would be large compared with any motion concerned in its complete journey around the center of the Square. Thus, while to the large-scaled eye the electron may be still regarded as an entity whose properties are confined to the region of a point, to the eye of an imaginary inhabitant of the atom itself it is merely a vague quivering nebulosity.1

The growth of the new theories during the last three years has taken place with such rapidity that one can hardly expect, as yet, consistency in all their parts. Even when the framework of the theory is consistent in its various funda

1 In developments which have only become elaborated since this address was presented it has become necessary, alas, to discard this concept of the electron, and to demote what is here called charge density to an abstract quantity whose average value in a certain region is merely a measure of the probability of the electron's presence in that region.

mentals, we shall be lucky if, as time goes on, it does not predict some consequences inconsistent with experiment. Or perhaps I had better modify that statement and say that we shall be unlucky unless it does this; for it is a fact which we may regard in the light of comfort, or in the opposite light according to our inclinations, that progress is only to be made in times of trouble. Let us beware of the day when difficulties vanish, when theories hang together and there are no facts that fail to fit them, for then indeed will science be dead and our labors ended.

THE DISTANCES OF THE STARS

By S. A. MITCHELL

(Read April 21, 1928)

THE last ten years has witnessed in astronomy a remarkable series of brilliant achievements that have thrilled and startled the whole scientific world. On the one hand, the astronomer in coöperation with the physicist and the chemist has been making an attack on the structure of the atom. The physicist and the chemist in their investigations have been confined to terrestrial laboratories and their researches. on the practical side have been limited to the range of temperatures and pressures available by mechanical methods. No such limitations however have been placed on the work of the astronomer. He has had at his disposal, with no expense other than that of his astronomical equipment, the celestial laboratories of the sun and distant stars, where high temperatures and minute pressures are readily available to test and extend the physical-chemical theories. Remarkable discoveries have been made, into which subject on account of lack of time I cannot enter today.

The more brilliant of the recent astronomical investigations have been connected with the stars. It is no exaggeration to state that not a single one of these discoveries would have become possible were it not for our ability to measure with a high degree of precision the enormous distances that separate us from the stars.

The astronomers of the sixteenth century saw clearly that if the earth makes an annual journey about the sun, as stated by the Copernican theory, then the near-by stars must show an annual displacement back and forth with respect to the more distant stars. This annual parallax of the stars was too small to be discovered by the telescope invented by Galileo in 1609, and so one was forced to assume that the

universe was made on a much larger scale than had hitherto been thought.

With each increase in telescopic power, with each instrumental improvement which added to the accuracy of stellar measurements, the problem of finding the distance of the stars was again attacked. Hooke, Flamsteed, Picard, Cassini, Horrebow and Halley, each in turn attempted to find the displacements of the stars. Each in turn failed in the attempt though Halley found that three of the brightest of the stars, Aldebaran, Sirius and Arcturus were not in reality fixed, since each star has a slight but unmistakable motion of its own, which we now call proper motion. Halley came to the conclusion that the stars were at least 20,000 or 30,000 times more distant than the sun, though the exact distance of the sun was then unknown.

The first of the world's gigantic telescopes was made by Sir William Herschel. He attempted an ingenious method of detecting the annual displacement of the stars by measuring accurately the relative positions of stars near each other in the sky, one being bright the other faint. Although Herschel did not succeed in detecting the parallaxes of any stars, he did find an entirely new type of stars, of which we now know many thousand, namely double and binary stars.

Following Herschel's time, continued attempts were made to measure the distances to the stars-but these attempts ended only in failure. It remained for the year 1838 to have the honor of measuring the first stellar distance. Singularly enough, the distance of not only one star was measured but three, by three different observers, using instruments of three different types and employing three different methods. The greatest honor probably belongs to Bessel in determining the distance of 61 Cygni. The instrument used was the heliometer which had the peculiarity that its object-glass was cut exactly in halves.

Once started, the work has gone steadily forward from that day to this. In the first fifty years, the total number of parallaxes measured was only about fifty, the difficulty lying