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ASTRONOMICAL NOTES

VERIFICATION OF THE EINSTEIN THEORY OF RELATIVITY FROM THE ECLIPSE PHOTOGRAPHS

Foremost of

There are several items of astronomical interest this month. course, is the report which comes from England, of the successful outcome of the observations made during the eclipse of last May to determine whether rays of light passing close to the sun are deflected from their course. This report affords one of the rare instances in which a topic of pure science assumes sufficient journalistic importance to justify cable despatches a column long; and in this case at least the real importance of the discovery is commensurate with the popular attention which is devoted to it.

The observed facts are easy enough to understand. At the time of the eclipse, the sun stood in a region of the heavens which is rich in bright stars—the Hyades, the well known cluster near the bright star, Aldebaran. When the sun's disc was obscured by the moon, these stars became visible, and could be photographed -the duration of totality being long enough to permit of several successive exposures. On the plates so obtained, the apparent positions of the stars could be accurately measured, and compared with those on other plates of the same regions taken when the stars were visible at night, remote from the sun. The comparison showed beyond question that those stars whose images fell near the occulted sun were apparently shifted in position, in comparison with the remoter stars in the field, which served as standards of reference—the shift being, in all cases, away from the sun's centre.

This taking and measuring of photographs of the stars is an everyday matter in observatories and the precautions necessary to insure accuracy are well known. The astronomers who are responsible for the present investigation-Prof. Eddington of Cambridge and Dr. Crommelin of Greenwich Observatory—are thoroughly familiar with work of this sort, and have undoubtedly taken every precaution to insure accuracy. Their conclusion that the shift of the star image actually occurs is accordingly unchallengeable.

What this discovery means is, obviously, that rays of light which pass near the sun are deflected towards it-so that looking back along the deflected rays toward the star, the latter appears to be shifted away from the sun. Crudely put, it is evident that the sun, and presumably any other large body, attracts passing waves of light and deviates their paths. The deviation is small, only 134 seconds of arc for a ray which has passed close to the sun; but it is twice as

great as the deflection which would be produced according to the familiar theory by the sun's attraction on the motion of a material particle moving past it with the velocity of light.

The most remarkable feature of the situation is that this deflection, both in direction and amount, has been predicted theoretically by Einstein, a physicist of Swiss birth, resident in Germany, who has long been recognized by students of mathematical physics to be worthy of the high place which will doubtless now be his by acclamation.

His theoretical discussions are far too complicated to speak of here: indeed, the mathematical developments are of so unfamiliar a nature that very few living men are competent to analyse them critically. But it may be possible to give some idea of the nature of the concepts which led to the development of his theory.

The theory of Relativity, which has excited the lively interest of physicists for some years past, and now appears to be firmly founded in fact, is based on the hypothesis that Nature is so constituted that it is impossible, by any physical experiment, to distinguish whether a given “system," including the observers, their instruments, and everything they can detect and observe, is at rest in space; or whether all parts of it are moving in the same direction and at the same rate. In both cases, the relative motions of the various parts of the system will be the same; and if the theory is true, only these can be the objects of physical investigations. Einstein, starting from this hypothesis, considered a further question which may be illustrated as follows. Assume an observer who, with all his instruments, is enclosed within a large, perfectly tight box, inside which he can live and work indefinitely. Now imagine, first, that the box and its contents are at rest in space (except in so far as he, in his experiments, sets various contained objects in relative motion). Second, suppose that the box and everything inside it are all falling freely in a uniform gravitational field (as bodies do near the earth's surface). Since the box and its contents are all falling at the same rate, the observer will not feel the pull of gravity, nor can he detect its existence by any experiment involving the motions of material bodies. But, according to the theory of light which was accepted until recently, the presence of the gravitational forces will not affect the motion of the light waves at all. If this is true, it ought to be possible, by suitably designed optical experiments, to detect the motion of the box and its contents in the second case. This would be true, even if the older theory of relativity were accepted, since the box with everything in it are not moving uniformly, but at an ever accelerating rate.

On the other hand it may be that the general principle or relativity applies even here, and that no experiment could detect anything beyond the relative motions of the contents of the box (including the waves of light). Einstein started with this latter assumption-which necessarily involved the belief that the motion of light is in some way affected by the presence of a gravitational field of force. Following out the consequences through the intricate analysis aforesaid, he reached the conclusion regarding the deflection of rays of light passing near the sun, which has just been so brilliantly confirmed by observation.

Two other natural phenomena (and only these two, as far as yet is known) should also be necessarily different according to the Einstein theory and the older one. Firstly, the elliptical orbit of a planet should not be quite fixed in space, but its perihelion should slowly advance, by an amount which can be definitely calculated. If there are other planets attracting this one, the purturbations due to their influence must of course be added. Now the perihelion of Mercury, after correction has been made for the effects of the attraction of the other planets, is actually moving forward in a manner not explicable by the classical theory, and to an extent about fifty times as great as the probable error of the observations. Now this "inexplicable" advance is found to take place at exactly the rate which has been predicted by Einstein's theory.

Secondly, his theory predicts that all the lines in the solar spectrum should be very slightly shifted towards the red, in comparison with the lines of the same elements, produced in terrestrial laboratories. This effect has been looked for, notably by Dr. St. John at Mount Wilson, and has not been found. There are, however, so many other things that may shift the lines in the sun's spectrumpressure, currents in the sun's atmosphere, etc.-that this unfavorable evidence is not so strong as the positive and very favorable evidence of the two phenomena previously discussed.

At the present time, therefore, Einstein's theory appears to be very probable, if not altogether proved. Much is being said about the radical changes in our conceptions which will follow; but it is easy to exaggerate the significance of such remarks.

The central fact which has been proved-and which is of great interest and importance is that the natural phenomena involving gravitation and inertia (such as the motions of the planets) and the phenomena involving electricity and magnetism (including the motion of light) are not independent of one another, but are intimately related, so that both sets of phenomena should be regarded as parts of one vast system, embracing all Nature. The relation of the two is, however, of such a character that it is perceptible only in a very few instances, and then only to refined observations.

The mathematical relations involved are most elegantly, and, to the trained mathematician, most simply expressed in terms of the non-Euclidean geometry, in which the properties of "parallel" lines are not those assumed by Euclid; and of space of four or even five dimensions. But these are only ways of expressing the facts, and ways that are likely to appear simple only to the trained mathematician. The important physical fact is the relation between gravitation and electro-magnetism, as explained above.-HENRY NORRIS RUSSELL in Scientific American.

MY THEORY.

The special relativity theory which was simply a systematic extension of the electro-dynamics of Maxwell and Lorentz, had consequences which reached beyond itself. Must the independence of physical laws with regard to a system of coordinates be limited to systems of coordinates in uniform movement of

translation with regard to one another? What has nature to do with the coordinate systems that we propose and with their motions? Although it may be necessary for our descriptions of nature to employ systems of coordinates that we have selected arbitrarily, the choice should not be limited in any way so far as their state of motion is concerned. (General theory of relativity.) The application of this general theory of relativity was found to be in conflict with a wellknown experiment, according to which it appeared that the weight and the inertia of a body depended on the same constants (identity of inert and heavy masses). Consider the case of a system of coordinates which is conceived as being in stable rotation to a system of inertia in the Newtonian sense. The forces which, relatively to this system, are centrifugal must, in the Newtonian sense, be attributed to inertia. But these centrifugal forces are, like gravitation, proportional to the mass of the bodies. It is not, then, possible to regard the system of coordinates as at rest, and the centrifugal forces of gravitation? The interpretation seemed obvious, but classical mechanics forbade it.

This slight sketch indicates how a generalized theory of relativity must include the laws of gravitation, and actual pursuit of the conception has justified the hope. But the way was harder than was expected, because it contradicted Euclidian geometry. In other words, the laws according to which material bodies are arranged in space do not exactly agree with the laws of space prescribed by the Euclidian geometry of solids. This is what is meant by the phrase "a warp in space". The fundamental concepts "straight", "plane", etc., accordingly lose their exact meaning in physics.

In the generalized theory of relativity, the doctrine of space and time, kinematics, is no longer one of the absolute foundations of general physics. The geometrical states of bodies and the rates of clocks depend in the first place on their gravitational fields, which again are produced by the material systems concerned.

Thus the new theory of gravitation diverges widely from that of Newton with respect to its basal principle. But in practical application the two agree so closely that it has been difficult to find cases in which the actual differences could be subjected to observation. As yet only the following have been suggested: 1. The distortion of the oval orbits of planets round the sun (confirmed in the case of the planet Mercury).

2. The deviation of light-rays in a gravitational field (confirmed by the English Solar Eclipse expedition).

3. The shifting of spectral lines towards the red end of the spectrum in the case of light coming to us from stars of appreciable mass (not yet confirmed).

The great attraction of the theory is its logical consistency. If any deduction from it should prove untenable, it must be given up. A modification of it seems impossible without destruction of the whole.

No one must think that Newton's great creation can be overthrown in any real sense by this or by any other theory. His clear and wide ideas wil! for ever retain their significance as the foundation on which our modern conceptions of physics have been built.-ALBERT EINSTEIN in The Times, London, Eng.

J. R. C.

NOTES AND QUERIES

Communications are Invited, Especially from Amateurs. The Editor
will try to Secure Answers to Queries

PROGRESS TOWARDS THE PROPOSED OBSERVATORY FOR TORONTO.

In the July-August issue (p. 299) is given an account of efforts being made to establish an astronomical observatory in Toronto. The chief features of the project were: (1) that the City should supply the site; (2) that the University should maintain the observatory; (3) that the Royal Astronomical Society should have accommodation for its various activities..

On June 11 last a deputation waited upon the Board of Control of the City and explained the nature of the project. It was favourably received and the Board requested that a committee be appointed to meet a committee of permanent city officials. Accordingly a committee, consisting of Messrs. A. F. Miller, John A. Paterson and J. R. Collins, representing the Society, and Messrs. A. T. DeLury, J. C. Robertson and C. A. Chant, representing the University, had a conference with the Commissioner of Finance, the Commissioner of Parks, the Assessment Commissioner and the City Solicitor; and a form of agreement was drawn up. This was reported to the Board of Control on August 6th. On November 26th the report was considered by the Board and approved, and on December 4th it was finally ratified by the City Council.

Its provisions are as follows:

1. The City shall dedicate the property as shown on plan herewith, as a park for the citizens.

2. The north-easterly portion, comprising approximately three acres, shall be leased for one dollar per year, to a Board of Trustees, composed of the Mayor of the City, the President of the University, and the President of the Royal Astronomical Society, the lease to run for forty-two years, and thereafter to be perpetually renewable for twenty-one-year periods at the same rate.

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