128 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1936 



relative brightness — they are of approximately the same candle- 

 power. We reach this conclusion from a study of the nearer nebulae, 

 whose distance can be ascertained, and then assume that it is true 

 of the farther nebulae also. Thus the faintness of the nebulae gives 

 a measure of their distance, and in this way we can estimate the 

 distances of even the faintest of visible nebulae. 



THE VISIBLE UNIVERSE 



Using this method, we find that the faintest nebulae which are 

 visible in our telescopes are at a distance of about 240 million light- 

 years. Before we proceed further, let us try to see all this in pro- 

 portion — let us make a small-scale model on the scale of 2 million 

 iight-years to the inch. Then our visible universe will be a sphere 

 20 feet in diameter. Our galaxy is a small disk of the size of an 

 average pinhead — perhaps one-tenth inch in diameter. The naked- 

 eye stars are all contained in a sphere of about one six-hundredth 

 inch radius — a mere speck of dust. Our sun is a single electron, 

 and the earth is a millionth part of an electron. 



There is no reason to suppose that this sphere of 240 million light- 

 years radius contains the whole of the universe ; we may be sure that 

 a larger telescope would show still fainter, and, therefore, still remoter 

 nebulae, so that there is no means of fixing the total size of the 

 universe — if it has a finite size — in this way. We must turn to other, 

 and less direct, methods. 



RELATIVITY THEORY AND THE UNIVERSE 



According to the theory of relativity, space curves back into itself, 

 so that the total volume of space is finite — just as the total area of 

 the earth's surface is finite. If the earth's surface were plane, the 

 area within a distance x of any given point, say Charing Cross, would 

 be exactly proportional to x-. But, because of the curvature of the 

 earth's surface, the actual area increases less rapidly than a?^. A circle 

 1 mile in radius has an area of 3.1416 square miles, but a circle 100 

 miles in radius has an area of less than 31,416 square miles. If space 

 is curved in a similar way, the volume of space which lies within a 

 distance x of the earth would increase less rapidly than a;% so that if 

 the nebulae are uniformly distributed in space, the number of nebulae 

 would also increase less rapidly than x^. 



Efforts are being made at Mount Wilson to examine whether the 

 number of nebulae falls off in this way at great distances, but so far 

 the number appears to vary approximately as the cube of the dis- 

 tance — there are no signs of falling off as yet. Indeed, preliminary 

 statistics which have only reached Great Britain within the last few 

 days seem to indicate the exact reverse. This may perhaps mean that 



