to be. It was found to be 42-9" a century, a figure which agreed with observation to well within the limits of error of these observations. The motions of the other planets, as predicted by the theory of relativity, have also been found to agree with those observed to within the errors of observation. This latter test, however, is not a very stringent one, since the departures from the motion predicted by the Newtonian law are too small to admit of very precise measurement.
Einstein's theory requires us to suppose that the world line of a ray of light also shall be a geodesic in the continuum. In a gravitational field the curvature of the continuum will impose a twist on the path of a ray of light. Einstein found in particular that a ray of light which comes from a distant star and passes near the edge of the sun on its journey ought to be bent, in its passage past the sun, by an angle which should be 1-75" if the ray just grazes the sun, and would be less in proportion to the inverse distance from the centre of the sun for other rays. The observatories of Greenwich and Cambridge dispatched expeditions to test this prediction at the eclipse of 1919. It was found that the stars which appeared near to the sun at the instant of eclipse showed an appreciable displacement, as compared with their normal positions, of the type required by Einstein's theory. Exact measurement confirmed that the dis- placement varied approximately as the inverse distance from the sun, and that the displacement at the limb was sensibly equal to Einstein's predicted value of 1-75". The Cambridge observers, hampered by cloudy weather, obtained for this quantity the value 1-61" =*= 0-30". The Greenwich observers obtained a value of 1-98" =t 0-12", but it has sincebeen pointed out by Prof. II. N. Russell that their photographs indicate a horizontal and vertical scale difference of the order of i part in 12,000, almost certainly due to a distortion of the coelostat mirror under the sun's rays, and if the measures are corrected for this the result is brought much closer to the theoretical prediction.
The theory makes one further prediction which admits of experimental test. The atoms of any element, say calcium, may be supposed to be formed according to a definite specification, the terms of which depend neither on the velocity of a particular observer nor on his position relative to the gravitational fields of the universe. It can be deduced that the light received from a calcium atom situated in the intense gravitational field near the sun's surface ought to be of slower period, and therefore of redder colour, than the similar light emitted by terrestrial atoms. To be more precise, the Fraunhofer lines in the solar spectrum ought to show a displacement to the red; this displacement ought to be homologous, and should be of amount 0-008 A units at the cyanogen band X 3883 at which observations have been chiefly made. Attempts to test this prediction led to strangely discordant results. All observers agreed in finding some effect of the kind predicted, but its amount was always less than the predicted amount, varying from almost nil (St. John, 1917) to nearly the full amount to be expected (Evershed, 1918; Grebe and Bachem, 1919). In 1921 the position with regard to this test still remained one of great uncertainty and confusion.
It will have been seen that the restricted physical theory of relativity introduced a revolution into the foundations of scientific thought by destroying the objectivity of time and space. The gravitational theory has effected a hardly less important revolution by destroying our belief in the reality of gravitation as a " force." The physicist has, however, to deal with other " forces " besides those of gravitation, and the question inevitably arises as to whether these too must be regarded as illusions, arising only from our faulty interpretation of the special metrical properties of the continuum. Prof. H. Weyl has pointed out that the continuum imagined by Einstein, and found to be adequate to explain gravitational phenomena, is not, in respect of its metrical properties, the most general type of continuum imaginable. A further generalization is possible and the new curvatures introduced must of necessity introduce new apparent forces other than gravitational. Wcyl's investigation shows that these new forces would have exactly the properties of the electric and magnetic forces with which we
are familiar. Indeed, the predicted forces coincide so completely j with known electromagnetic forces that no experimental test of \ Weyl's theory is possible. Had there been the slightest divergence between the forces predicted by Weyl and those predicted by ordinary electromagnetic theory, experiment could have been i asked to decide between the two, but no such divergence exists. It may, however, be said that Weyl's theory makes it highly probable that all forces reduce to nothing more than our sub- jective interpretations of special properties of the continuum in which we live our lives.
Finally a thought may be given to the position, under the new conceptions introduced by the theory of relativity, of the electro- magnetic aether. At one stage in the history of science there was a tendency to fill space with aethers, to the extent almost of one aether for every set of phenomena requiring explanation. That stage passed, and by the end of the igth century only one aether received serious consideration, the so-called electromagnetic aether of Faraday and Maxwell. This aether gave a plausible mechanical explanation of electrostatic phenomena, although it was more than doubtful whether it could account for (-he electromagnetic phenomena from which it took its name, and it was comparatively certain that it could not account for gravita- tion. It gave, however, a satisfactory explanation of the prop- agation of waves of light they were simply waves in the aether and travelled with an absolute velocity c determined once and for all by the structure of the aether. On this view it was quite certain that an observer moving through the aether with a velocity u would measure the velocity of light travelling in the same direction as himself as c-u. Relativity teaches that this velocity is always precisely c, and this in itself disposes of the aether of Faraday and Maxwell. Whether any new aether will be devised to replace it remains to be seen, but none appears to be necessary. Any aether which can be imagined would appear to depend upon an objective separation of time and space. Relativity does not deny that such an objective separation may, in the last resort, really exist, but it shows that no material phenomena are concerned with such a separation. By a very slight turn of thought, the primary postulate of relativity may be expressed in the form that the material world goes on as thouh no aether existed.
To the relativist the essential background to the picture of the universe is not the varying agitation of a sea of aether in a three-dimensional space but a tangle of world lines in a four- dimensional space. Moreover, it is only the intersection of the world lines that are important. An intersection at a point in the continuum represents an event, while the part of a world line which is free from intersections represents the mere uneventful existence of a particle or a pulse of light. And so, since our whole knowledge of the universe is made up of events, it comes about that the tangle of world lines may be distorted and bent to any degree we please; so long as the order of the intersections is not altered, it will still represent the same universe. And so the last function of the aether, that of providing a scale of absolute measurements in space, becomes a superfluity. To the physicist who urges that space measurements without an underlying aether become meaningless, the relativist can reply that time- measurements without an underlying " time-aether " are equally meaningless. A " time-aether " has never been regarded as a necessity, and the relativist feels that the " space-aether " has no greater claim to retention. (J. H. JE.)
RENEVIER, EUGENE (1831-1906), Swiss geologist (see 23.98), died at Lausanne May 4 1906.
RENNENKAMPF, PAUL (1854-1918), Russian general, was born in 1854 and entered the army in 1873. On passing out of the Academy of the General Staff in 1882, he was appointed to the General Staff. From 1895 to 1899 he commanded a regiment and in IQOO he was promoted to the rank of general. In the war with China in 1900 he distinguished himself by his resolute action when commanding a column in Manchuria. In the war with Japan 1904-5 he commanded first a Cossack division, and later large forces of all arms, and again won distinction by his energy. From 1905 to 1913 he was a corps
