140 ANNUAL BEPOET SMITHSONIAN INSTITUTION, 1925 



radial motion, there can be obtained a lower limit for the distance 

 of the spiral nebulae. There results a value of 80,000 light-years. 



If we are convinced that the spirals are distant milky-way systems, 

 there is available yet another method which allows us to push yet 

 further the lower limit of their distance. New stars (novae) appear 

 from time to time in certain spiral nebulae. We can compare these 

 with those which appear in our own milky way. Let us assume 

 that their greatest brightness is the same no matter in which system 

 they occur. Tliis leads to an estimate of 000,000 light-years for 

 the nearest spiral nebulae. This further signifies that their linear 

 dimensions are of the same order as those of our own galaxy. 



4. Now, convinced that the light from the spirals must travel this 

 immensely long journey through space to reach us, let us recall 

 our earlier query : Does this light bring us in its aspects any trace 

 of the structure of this space which does not correspond to the 

 structure of infinite Euclidean space? 



Perhaps. First let us consider the apparent dispersion outwards, 

 relative to our position of observation, of the matter concentrated 

 in these nebulae. In this in itself remarkable phenomenon we will 

 find something further to strike us. AVe will probably not be greatly 

 wrong if, as a first approximation, we ascribe the same linear dimen- 

 sions to all of the spiral nebulae. Then in their apparent angular 

 extent we have a measure of their individual distances. Using this 

 assumption as the basis of our inquiry we reach a startling result: 

 With increasing distance of the nebulae the observed outwardly 

 directed velocity increases, and it increases at a rapid rate, such that 

 when the distance increases tenfold the radial velocity increases 

 about 1,200 kilometers (745 miles) per second. This must mean 

 that the farther away the object is in the depths of Euclidean 

 space the more rapid is the dispersion of its matter into that space. 



Is this interpretation of the observed facts, which assumes infinite 

 space, necessary ? Naturally not. There are no absolutely necessary 

 descriptions of observed facts. We should try to formulate that 

 description which is the most satisfying in the sense that it explains 

 a greater number of isolated phenomena than the older conception. 



5. There is a structure of space in which the phenomena which we 

 have observed in the spiral nebulae will be accurately reproduced. 

 This structure occurs in the cosmology of the Dutch astronomer, 

 W. de Sitter. The world of de Sitter is a four-dimensional con- 

 tinuum of space and time, forming the surface of a sphere in five 

 dimensional coordinates. This sounds richly complex, indeed incom- 

 prehensible. It is not possible to represent it graphically. Jiut 

 representation is a product of our imagination, knowledge of our 



