The motion of the stars 



63 



Putting 



X = b log r '.■ r = 



the value of ä-« may be written 



— 00 



+«. 



a[rn) =■ b j dxDe (m — x), 



— 00 



and hence, for 7) = Constans, using the formula I (52), 



. — sb (m —m«) — Ssh'-Oä'^ + ä s-b--3- 



= e -, 



which expression has tlie form 



(33) ■»s=p"q"\ 

 wdiere 



q =e- . 



A comparison with (16) gives 



q' = q\ 



wliere 



'i + V 



z = 



As q is always >^1, we have 



q' ^q- 



Thus the assumption D = constans (as well as the hypothesis I (12)) leads to 

 a still higher value of q than that derived from the discussion in I. 



It follows from (16), as well as from (33), that the mean parallax of the stars 

 of a certain apparent magnitude is very different from the reciprocal value of the 

 mean distance of these stars. We get from (16) 



M{r) = 2)^'q 



and hence : 



(34) mII] = 



M{r) 



The value of q, used beneath, is 



q = 1 .2695. 



Hence we have 



(35) M CA 



rj M[r) ' 



Multiplying by 0". 206265 the formula (35) may be written 



0".3324 



(36) M{k) = 



M{r) 



