BEYOND THE MILKY WAY — PAGE 171 



there are several. The most easily visualized is based on the simple 

 assumption that a cosmic explosion started the nebulae moving apart 

 from a common starting point with speeds which have since remained 

 roughly constant, and that the fastest moving ones have naturally got 

 the farthest. From this simple concept, together with the rate of in- 

 crease of recessional velocity with distance, we can readily compute 

 that the explosion must have taken place some 2 billion years ago, 

 a figure in fair agreement with the age of the earth determined from 

 quite different data (radioactive decay in minerals). However, there 

 are further complications which cast doubt on this simple explanation. 



There are so many nebulae that a plot of each one's position in space 

 would be literally an endless task. The best means of representing 

 their distribution in space so far devised has been to count, or estimate, 

 the numbers out to various distances. For instance, a survey by Shap- 

 ley and Ames at Harvard showed over a thousand nebulae actually 

 brighter than "thirteenth magnitude" (visible in a 6- or 7-inch tele- 

 scope), another by Mayall at the Lick Observatory shows an estimated 

 9 million over the whole sky brighter than "nineteenth magnitude" 

 (corrected for obscuration by local interstellar dust) from sam- 

 ple plates taken with the 36-inch reflector, and two other sampling 

 surveys by Hubble with the 100-inch telescope at the Mount Wilson 

 Observatory indicate that there are an estimated 70 million brighter 

 tiian the "twentieth magnitude" — as faint as the 100-inch telescope 

 can conveniently photograph. From the average intrinsic bright- 

 nesses of nebulae we can convert these figures to (roughly) : 2,000 

 within 13 million light-years, 9,000,000 within 200 million light-years, 

 and 70,000,000 within 450 million light-years. 



These numbers are about what we would expect if the nebulae were 

 evenly distributed, about 2 in each 10-billion-billion cubic light-years. 

 The numbers would then increase with the cube of the distance, since 

 the volume of a sphere is proportional to the cube of its radius. The 

 two deepest surveys, however, depart slightly from the cube law, indi- 

 cating a thinning out of nebulae the farther we go from our galaxy. 

 Now it has been repugnant to astronomers since the time of Copernicus 

 to consider ourselves "at the center," as this thinning out would imply ; 

 hence a number of efforts have been made to interpret this last result, 

 tentative though it may be, in such a way that no "center" is necessary. 

 A number of difficulties arise ; for instance, we are seeing the distant 

 nebulae not where they are now, but where they were 13 to 450 

 million years ago, the time required for their light to reach us. Their 

 intrinsic brightness, too, may not be constant in time. And it is certain 

 that their light is so changed toward redder color by the Doppler effect 

 that a correction must be made for its reduced power to blacken the 



