( 629 ) 



For III = 14 the values were Jiovv expressly computed. The result 

 is as follows : 



Total number of stars. 



Oomp. I. Comp. 11. 



(8) 



The deviation increases strongly with diminishing brightness and 

 is excessive for magnitude 14. We conclude at once, that for the 

 greater distances the formula (3) furnishes a value of the star-density 

 which is much too small. Calculation shows that some approximate 

 agreement is already obtained if we take the stars between 9 = 140 

 and () = GO to be 21 times more numerous. 



As it thus appears that formula (3) is useless for considerable 

 values of Q, I began by retaining that formula exclusively for the 

 values of {) below 70 whereas for the values exceeding 70 I assumed 

 that the density diminishes regularly (linearly) from 0.214 to zero. 



It was easily ascertained that, if we choose the decrease of the 

 densit}^ in such a way that it vanishes for q = 557, we get consi- 

 derably nearer to the truth, especially if we take : 



A, = 125. 



The values obtained in this way were put down in the above 

 table under the head Comp. II. 



As a further approximation I also derived coi'rections for the star- 

 density at distances below 70. It appeared that the results become 

 more satisfactory if the linear decrease of the densities is assumed 

 to begin for distances somewhat smaller than 70. 



Having obtained this result I have no further continued these 

 approximations, bu( 1 have given up the formula (3) altogether and 

 have tried to determine the luminosity-curve directly in the assumption 

 that, for the intervals between 9 =r and <) = 10; ^ =r 10 ' and 

 ^ := 30 ; 9 =i 30 and 50 ; 9 = 50 and Q ^ g the density changes 

 linearly in such a way that it vanishes for Q =^ g. 



In this way the problem is reduced to the derivation of the 

 5 unknown quantities: 



A(0) ; A(10) ; A(30) ; A(50) ; g. 



For reasons given in the paper quoted above we have to assume 



