THE GREAT STAR MAP 249 



of proportion to our visual expectations : and it is a fair 

 conclusion that the difficulty arises from the characteristic 

 property of a fog. There is room for difference of opinion 

 as to the intensity of the fog, for the observations are difficult 

 to interpret and even treacherous : but two separate discussions 

 indicate as rough limits the figures which were given above. 

 A discussion by the present writer,^ assigning the whole of 

 the difficulty to the fog and thus giving probably a maximum 

 density to it, made it extinguish half the light in about 4,000 

 billion miles. A more conservative estimate by Professor 

 Kapteyn of Groningen, who allowed for other possible con- 

 tributing causes, makes the density about one-tenth as great. 

 We must hope that further research will narrow the trail but 

 it will be surprising indeed if we find that we are altogether 

 on a false scent. 



This rather long digression has not taken us so far from the 

 topic immediately concerning us as might at first appear. With- 

 out some such explanation it would not have been easy to realise 

 the importance of mere counts of the number of star images of 

 a certain size. They might have been regarded as of academic 

 interest merely, whereas we now see that they furnish evidence 

 on two fundamental questions : firstly, is our Sun merely an 

 individual star or is it associated with other stars in a family or 

 cluster ? secondly, is there an extremely tenuous " fog " of matter 

 pervading the spaces between the stars and if so what is its 

 density? We shall find that the first of these questions is pre- 

 sented again in another connection when we come to the move- 

 ments of the stars : but the existence of some sort of solar cluster 

 is established by simple numeration combined with measures of 

 brightness. 



How are we to measure the brightness of stars photo- 

 graphically ? In approaching any measurement of differences 

 we must first satisfy ourselves that we can recognise equality. 

 Let us define as of equal photographic magnitude two stars 

 which impress the same plate equally in the same time and we 

 need go no further to encounter trouble. Suppose we pick out 

 two stars by this rule, will they remain equal if we substitute a 

 different plate ? The answer is in the negative : for if one of 

 the stars be a red star and the first plate be isochromatic, we shall 

 » Mon, Not. R.A.S. Ixix. p. 61. 



