In conclusion, we may recall the purpose of the discussion, the precise formulations of the laws of red-shifts and of nebular distribution, using two different scales of distances corresponding to alternative, possible interpretations of red-shifts. It was hoped that the wrong scale, the wrong interpretation, might lead to anomalies or discrepancies which could be detected or at least suspected. The hope is only partially realized. Suspicions are aroused, but they have not been fully substantiated. The observations now available furnish a consistent picture on either scale.
The facts of the case may be presented in a brief table where the laws are expressed both with symbols and with numerical terms. The table also includes the elements derived from the recession factor which identify our universe among the possible worlds offered by relativistic cosmology. The unit of time is the year, and the unit of distance, the light-year, except that the mean density is expressed in grammes per cubic centimetre.
PLATE VII. A SAMPLE OF THE UNIVERSE
The photograph shows a small region of a typical field in the deepest survey using two-hour exposures with the 100-inch reflector. The faintest nebulae identified with confidence are about the 21st (photographic) magnitude; or a million times fainter than the faintest naked-eye stars. These vague spots are the images of great stellar systems, averaging about 210 million times as bright as the sun. They appear so faint because their average distance is of the order of 400 million light-years. The survey records, on the average, about 38 nebulae in each area of the sky equal to that of the plate (about 2/15 the area of the full moon).
As the depth of the explorations increase, the stars in the stellar system tend to thin out while the recorded nebulae steadily accumulate. About half a magnitude beyond the limit of the survey, and in the directions of the galactic poles, the nebulae should be as numerous as the stars. This level of equality has actually been reached on a few photographs made under exceptional conditions with the 100-inch reflector.
The bright star, surrounded by a halation circle (light reflected from the back of the plate), is B.D. +35° 2731. Nebulae are indicated by arrows.