142 ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1925 



spectrum lines from distant sources must be shifted toward the red 

 even though the source is at rest. A particle once present in empty 

 space will be driven outward wdth an acceleration which increases 

 with the distance. In de Sitter's world there are, therefore, two 

 causes for a shift of the spectrum lines toward the red — the general 

 dispersion of matter outwards toward the limits of space and the 

 slowing up of natural time apparent in all distant objects, even 

 though they are at rest, relative to the origin of coordinates. 



Because of the symmetr}^ of the formula expressing de Sitter^s 

 world, any desired point may be chosen for the zero point of co- 

 ordinates. That means that there exists no difference in the 

 observed run of phenomena no matter what the point of observation, 

 even though at the boundary of de Sitter's space. 



Is it possible to obtain a measure of this slowing up of natural 

 processes at great distance? Yes, and it follows from de Sitter's 

 theory that there is not only the shifting of the spectrum lines to 

 the red but also, as already noted, the increase of this shift with 

 the increasing distance of the object. These facts should occur in 

 the spiral nebulae as follows: The radial movements outward (Dop- 

 pler displacement in spectrum) of the spiral nebuhi' must tend to 

 greater and greater positive values as the diameters of the nebulae 

 decrease. 



A discussion of the observations gave a verification of the above 

 prediction. The cosmos of de Sitter allows yet other predictions, 

 but we will not discuss them, all now. Suflice it to state that we 

 can determine the radius of curvature of the time-space cosmos of 

 de Sitter from phenomena which appear in the spiral nebulie. The 

 curvature is small, its radius is of the order of 100 millions of light- 

 years. In his continual flow of time an object will never return 

 to the zero point of coordinates. Time is single valued and history 

 will not repeat itself. The cosmology of de Sitter furnishes a suffi- 

 cient description of the universe. 



6. Our preceding discussion is based upon the observation of some 

 50 nebulae which are bright enough for the measurement of the line 

 shifts in their spectra. Now^ there are about 20,000 definitely cata- 

 loged nebulae, and the optical means of our present day should 

 render visible about 3,000,000. What new information may we 

 expect from all of these objects? Just as with the fixed stars, sta- 

 tistical discussions of their distribution, color, photometric measures, 

 etc, will lead to many valuable results. 



We will now speak of only one interesting chapter — that relating 

 to the absorption of light in space. It is evidentlj^ very important, 

 for in a last analysis this absorption Avill play a very important 



