Studies in Stellar Statistics 



33 



am 



(63**) a{m] = Ce , 



winch is indeed the case as we have found in the 2:d paragraph. 



In this manner, using the formula (63**), we can deduce the approximate 

 values of C and a from the BD-stars and then, using (63*), obtain the approximate 

 value of b from the C. du C. More accurate values may afterwards be obtained 

 through usual correction formulae. 



It is however possible to solve the problem exactly. Let A(m), as in the 2:d 

 §, denote the number of stars having a magnitude brighter than m, then 



(64) A{m) 



Ç N Ç — (™~»'o)° 

 aim] dm = -= e 2ifc2 



— 00 — 00 



or putting 



(64*) m — = fe ".• dm = hdx 



m—Ttio 



(64**) A{m) = — = \dxe~2 



1/271 



• 00 



Introducing the probabilité/ integral P{x) ^through the formula 



P{x) - ^ \ dx e 2 = I dx e 



l/27cj l/27tj 



—X U 



we have 



(64**=^=) A{m) = f (l - P (|^~'"' 



or (putting x = nijh; y = Ijk) 



(64****) P{x — mij) = 1 - . 



If II = P{x) is the probability integral, I have called in my lectures on statistics 

 the inversion of this integral {i. e. x considered as function of u) the Error-function, 

 denoted by Err u. Investing (64****) we hence have 



(6o) x — my — iLrr 1 1 



For determining x, y and iV we ought to have three such equations: 



x — y = Ürr 11 ~^ 



(65*) x--m.^y = ^rv\\ 



x—m^ y = hjYV 1 - 



N 



Lunds Univ. Årsskrift. N. P. Afd. 2. Bd 8. 



