studies in Stellar Statistics 



and for two different h 



A[h,):A{h,) = hf:hT 

 Introducing star magnitudes [m) instead of h through 



m = — 2.5 log h -f- const. 



which gives 



J4.j ^ _ j^qO («1— ma) 



we get 



and for w?^ — Wg == 1 



(5) A{m) : J.(m— 1) = 10°" = 3.981 



the well-known result. 



For obtaining the number of stars of a given magnitude we proceed in the 

 following manner. 



The formula (4) may be written 



^ C'lO"""' ™ 0.4miiat. loglO ^^_0.9jio m 



■ • dh = — 0.9210 Ce~" "'" " dm 



Substituting in (3) we obtain for the number of stars of the mngnitude 

 m ± Vs dm the expression 



(6) a{m) dm = C, dm e'-''''"' 



Integrating between m = — go (corresponding to h = œ) and m we obtain 



(7, e 



A{m) 



1.3816 



giving the number of stars brighter than m. Hence (5). 



Les «m denote the number of stars of the magnitude m ± Va we obtain 



^ 1.B816 ff* / 1.3816 l.aSlö' 



«(m) dm = \e —e ■' 



or 



(7) «^ = C,e^-^'°'" 



which gives 



(7*) a„ : = 3.981 = A,n : Am-i ■ 



The formula (5) is usually said to be confirmed by the observations. Taking 

 the Bonner Durchmust. (B. D) we get from Newcomb-Engelmann. 



Lnnds Umv:s Årsskrift. N. F. Aid. 2. Bd 8. 2 



