( 630 ) 



ÖA 



that — vanishes foi' q = 0. As a consequence A(10) will certainly 

 dg 



be little different from A(0). Therefore, in order to reduce the 

 number of unknown quantities as much as possible, I took, in 

 agreement with what was formerly found : 



A(10) = 0.97 A(0) (9) 



The number of unknown quantities is thus lowered to 4. 



Putting 



A(0) - ^' 



(10) 



we have 



B, = A(>-^B (11) 



in which, for the several intervals, A and B have the following 

 values : 



A 



to 10 



10 „ 30 



30 „ 50 



50 „ g 



10 



1 



20 



D. 



A„- 



1 

 10 



1 



20 



n. 



20 20 ' 



1 



50 



n. 



B 



3 1 



— Ao A 



2 10 2 ^ 



(12, 



D, 



9 



D. 



g-bO 



D. 



The practical advantage of the present form is that the expression 

 (1) for N,n can now be reduced to the well known integral 



G{z)= \e-^\Lv (11) 



00 



Numerical integration is thus avoided and we obtain relations 

 Avhich are linear in respect to the unknown quantities D^^ , D^^ and 



A(0) 



If we denote by (^w)q ^he number of stars between apparent 



magnitude m ~ and m -f — existing between the distance and 



g, we get, substituting (2) (10) ^11) in (1) : 



f 



{NX::=.\_GA-YHB]L^^) 



(12) 



