(m =z 3) 0.186 



[m = 4) 0.272 



(m = 5) 0.375 



{7n = l) 0.527 4-1.474 -Z= 0.595). . (17) 



(m = 9) 0.508 



{m= 11) 0.341 



(m-- 13) 0.159 



{771= 15) 0.050 



In solving these equations I have neglected those corresponding 

 to the magnitudes 2 and 3. The reason is that for these the influence 

 begins to be sensible of stars of so great a luminositj that extra- 

 polation beyond the directly determined part of the luminosity-curve 

 becomes necessary. These stars might therefore rather be used for 

 a cori'ection of this curve at its brighter extremity. 



The remaining equations have been condensed into three by com- 

 bining those for m = 4 and 5, those for 7, 9, 11 and those for 

 13 and 15. The solutions of these three equations is: 



Z = 1.002 therefore A(0) = 139.7 

 />,„:= 0.460 ( . . . . (18) 



i>3„ = 0.1315 



whereas we already assumed 



Z>,. = 970 (19) 



If with these values we compute the numbers Nm and if further 

 we interpolate those for m=zQ, 8, 10, 12, 14 we get the following 

 comparison between theory and observation: 



