172 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



photographic plate. What is more, a receding source should theoreti- 

 cally be fainter than the same source of light at rest. 



Using the best data available in 1935, Hubble and Tolman concluded 

 that these deepest surveys can be understood if space itself is "curved," 

 somewhat like a two-dimensional surface can be curved into the form 

 of a sphere. Just as there is not as much area in a circle on the surface 

 of a sphere as there is within a circle of the same radius on a flat sur- 

 face, so, too, there would be less "room" in "curved space" than in "flat 

 space," as we normally conceive it, for spirals at great distances from 

 us. This conclusion was inspired by Einstein's General Theory of Rel- 

 ativity, which ascribes what we normally call gravitation to a kind 

 of curvature of space; in other words, space is expected to be curved 

 by the mass of matter contained in it. Unfortunately the curvature of 

 space necessary to explain Bubble's counts of the nebulae is very 

 large — corresponding to a radius of only 500 million light-years or so, 

 which implies a very large amount of matter, not at all in agreement 

 with the observed space density of spirals and the (small) masses 

 measured from their rotations. 



This is the impasse we have reached in our attempt to understand the 

 universe beyond the Milky Way. It may be removed by improving the 

 observational data; by better measurement of the masses of spirals, 

 including the faint outer parts, as we are trying to do at the McDonald 

 Observatory ; by finding evidence for matter between the spirals ; by 

 improving the correction for the Doppler effect as Stebbins and Whit- 

 ford of Wisconsin are doing in their color work at Mount Wilson; 

 or by better and more complete surveys of the nebulae which are soon 

 to be expected from the 48-inch Schmidt telescope and 200-inch tele- 

 scope at Palomar. Or it may be removed by some new line of theoreti- 

 cal reasoning such as the Kinematical Relativity of Milne, in Eng- 

 land, or by taking account of the clustering of nebulae, in a revision 

 of Tolman's calculations, as now being undertaken by Omer at Chi- 

 cago. Probably the solution will be found through some combination 

 of these, but I have no doubt that, when it is reached, some even larger 

 problem will be found to take its place. 



