CENSUS OF THE SKY SAMPSON. 191 



to a feeling of a kind of relief in finding that the total is measurable 

 and, comparatively speaking, moderate. 



It may be well to add a few sentences in consideration of the 

 validity of the conclusion, which is and must remain, an extrapola- 

 tion beyond knowledge, a summation to infinity of a series not com- 

 pletely known. 



We begin by admitting that we are dealing only with the sensible 

 universe. There may be dark stars; in fact, we know that there are, 

 because some of them have been detected in occulting the bright ones, 

 as in the case of Algol. Naturally these are not counted. Nor do we 

 reckon with the possible presence of absorbent matter in space, by 

 which the magnitudes of all the stars seen would recede progressively, 

 so that at the end of the series their light would be extinguished. 

 Nor do we profess to unravel the details of globular clusters — we 

 can not do everything. For that matter, there is infinite detail in a 

 drop of blood or an atom of gas. We take the stars as we find them. 

 The relevant question is the possibility of a sudden break or a gradual 

 change in the progression after the 20 terms that have been so care- 

 fully examined. 



There would seem to be a certain kind of control in the total light 

 received, but this proves illusory. 



The total of starlight is a sensible amount, but it is very small. 

 The table shown above is taken from a paper by Mr. Chapman. It 

 shows that for the ascertained magnitude up to the twentieth the 

 total light emitted is equivalent to 687 first-magnitude stars, which 

 again has been put as equal to the hundredth part of full moonlight. 

 If we include all the remaining stars, following the formula, the 

 equivalent addition would be only three more first-magnitude stars. 

 But this tells us very little, for if the progression were so altered 

 that the total number were infinite the total light could easily still 

 be finite, owing to the reducing effect of higher magnitude. 



We leave off our summation at a point where each additional mag- 

 nitude is adding more stars than the last. If this went on the number 

 would be infinite. But, according to the formula, between the twenty- 

 third and twenty-fourth magnitudes there is a turning point, after 

 which each new magnitude adds less than before. The actual counts 

 have been carried so near this turning point that there is no reason- 

 able doubt of its existence. Given its existence, the number of stars 

 is at least finite. That is a conclusion that I regard as open to very 

 little doubt. As to the value of the sum, naturally we can be less 

 positive. But all the indications of the earlier terms must be mis- 

 leading if the margin between one and two thousand millions is not 

 enough to cover the whole. 



It is sometimes said that the British amateur astronomer, to 

 whom in the past so much enterprising construction and so much 



