THE GREAT STAR MAP 243 



illustrative). Of these the brilliant stars will appear of the 

 second magnitude say, the glowing stars of the third. We shall 

 thus recognise 50 stars only of the second apparent magnitude, 

 for the more distant brilliant stars will be fainter than this 

 and the glowing ones fainter still. Coming to the second shell, 

 we should expect to find 4 x 50 or 200 brilliant stars which 

 would now appear as of the 3rd magnitude; and 4 x 50 

 glowing stars appearing of the 4th. Thus altogether we should 

 recognise as of the 3rd magnitude the 200 brilliant stars of 

 the second shell and the 50 glowing stars of the first, making 

 250 or 5 times the 50 of the 2nd magnitude. Splitting up the 

 stars into two classes has thus enhanced the expected ratio 

 4 in this instance and made it 5. If we go to the next magnitude 

 we shall find that the ratio returns to 4 and remains at 4 ever 

 afterwards : it is therefore only altered for one step but this 

 alteration is an increase ; there is no diminution available for 

 explaining the observed drop towards 3. 



We have taken a very simple case : but its characteristics 

 are maintained in the most complex cases we can devise. 

 They may be stated thus : just as the ratio 4 was disturbed 

 for the first two magnitudes by dividing the stars into two 

 classes, so if it be assumed that there are n classes of diminishing 

 intrinsic brilliance (according to steps of a magnitude each), 

 the ratio will be disturbed for the first 11 magnitudes, after 

 which it will return to 4. In whatever way it be disturbed, 

 it is increased and not diminished. 



This avenue of escape is therefore closed and another 

 must be found. Perhaps the figures used are wrong? It is 

 not likely that the counts are wrong for they have been gone 

 over many times ; but is it certain that the drop of a magnitude 

 in brightness is identified correctly? Accurate measures of 

 brightness are not easy to make, as we find in everyday life 

 in connection with candle-power tests : they are harder still 

 for faint lights such as the 'stars and the difficulties increase 

 as we pass to fainter and fainter stars. We shall presently 

 have to consider these difficulties in connection with the 

 project of the Great Star Map itself. But for the moment it 

 need only be pointed out that it seems unlikely that the 

 discrepancy under investigation is attributable to such a cause. 

 It is easy to calculate what must be the error in estimation 

 of a whole magnitude if such were the case : to make the 



