786 



NATURE 



[February 17, 192 1 



unity between the categories of space and time 

 that was suggested by Einstein's work. A uni- 

 verse of determinate relations, in which every- 

 thing proceeds according to known laws, is one 

 which may be surveyed as a great whole in which 

 past, present, and future are one. It is a four- 

 dimensional unity, and for Einstein any plane 

 se(Won through it could be the present. The his- 

 tory of a particle is a simple chain of points in 

 that whole, a "world-line." 



Now events moved fast. Minkowski gave the 

 notion of a four-dimension universe. Riemann 

 had initiated a method of geometry in any number 

 of dimensions ; Einstein had glimpsed the possi- 

 bility that, taking gravitation into account, light 

 might be subject to acceleration, which, being 

 interpreted in Minkowski's fashion, meant that 

 the ordinary Euclidean expression for the element 

 of length in a four-dimension space must be 

 generalised. This made the work of Riemann not 

 only useful, but also prophetic. In 1853 he had 

 written that " the ground of the measure rela- 

 tions existing in the universe, if continuous, must 

 consist in the binding forces acting upon it." This 

 really implies the whole relativity doctrine ; it 

 asserts that the measure relations of the pheno- 



mena perceived in the universe are incapable of 

 determination on any absolute scale, independent 

 of the phenomena themselves. Sixty years later 

 Einstein perceives that the gravitational field must 

 be included among those binding forces, and must 

 affect profoundly the measure relations in every 

 physical aspect. Having foreseen this, Riemann 

 had proceeded to develop a non-Euclidean geo- 

 metry in any number of dimensions, and thus the 

 germ of the calculus that Einstein needed was 

 created. With what success it was wielded is 

 now well known. 



Not so well known is the more recent work of 

 Weyl. Einstein finds in universal gravitation the 

 ground of the measure relations of the universe. 

 But equally universal is the fact of electricity, and 

 this universal "binding force" must equally take 

 a part in those relations. The acuteness of Rie- 

 mann 's vision is doubly emphasised when we hear 

 that \Veyl discovers a further generalisation of 

 his geometrical method which provides for elec- 

 tricity a place as natural and convincing as that 

 taken by gravitation in Einstein's theory. But 

 that is history yet in the making, and this article 

 seeks only to traverse the course of history 

 already complete. 



Relativity and the Eclipse 

 By Sir Frank 



IN 1915 Prof. Einstein predicted, as a conse- 

 quence of the generalised theory of relativity, 

 that a ray of light from a star would be bent in 

 its passage through the sun's gravitational field. 

 The amount of this deflection he gave as i-75"(a/»'), 

 where a. is the sun's radius, and r the nearest 

 distance of the ray to the sun's centre. As a ray 

 of light reaches us in the direction of the tangent 

 to its path, the apparent position of a star, photo- 

 graphed during an eclipse of the sun, should 

 therefore be displaced by an angle i75"(a/r) out- 

 wards from the sun's centre. The field of stars 

 surrounding the sun should thus be distorted in 

 a definite manner by an amount within the range 

 of accurate astronomical observation. In Fig. i, 

 if a, b, c are the positions of the stars as seen at 

 ordinary times, and if S is the centre of the sun 

 during an eclipse, then the positions in which the 

 stars are seen or photographed during an eclipse 

 will be A, B, C. If a were at a distance 30' from 

 the sun's centre the displacement a A would be 

 087", and if B were at a distance 90' from the 

 sun's centre its displacement would be 0-27". 

 These are, roughly speaking, the greatest and 

 least displacements which can be obtained in prac- 

 tice. Nearer than 30' from the sun's centre a 

 star's image is liable to be drowned in the corona. 

 At greater distances than 90' good images can 

 scarcely be obtained with a simple object glass, 

 while a doublet or other combination introduces 

 some difficulties. 



These displacements, though small, are ten 

 times as large as those met with in determina- 



NO. 2677, VOL. 106] 



Observations of May, 1919. 



Dyson, F.R.S. 



I tions of stellar parallax, and are determined in 

 a precisely similar manner by comparison of 

 photographs taken at different epochs. The field 

 of stars photographed during the eclipse must 

 be compared with the same field photographed 

 when the sun is in another part of the sky. Ex- 

 perience shows that telescopes of as long focal 

 length as practicable should be used, and that the 

 i eclipse field and comparison field should be photo- 

 i graphed under as nearly as possible identical con- 



FlG. I. 



ditions as regards both the instruments them- 

 selves and the position of the field in the sky. 

 With these precautions there was every reason to 

 suppose that, given favourable weather, successful 

 results would be obtained. 



In the short time available for preparation it 

 was not possible to arrange for the telescopes to 

 be mounted equatorially, and the field of stars 

 was reflected into fixed telescopes by coelostat 



