50 



Hans Henie 





I. 



II. 



III. 





Rim) 



A 



Rini) 



A 



R{m) 



A 



11,5 





- 6 





- c 





- 6 





0,62 



5 



0,5'J 



5 



0,54 



6 



7 



0,58 





0,54 





0,49 





8 



0,53 





0,50 





0,45 





9 



0,50 





0,46 





0,41 





12,0 



0,46 



4 



0,42 



4 



0,37 



4 



3 



1 





3 





3 









0,40 



3 



0,36 



3 



0,31 



3 



3 



0,37 



3 



0,34 



2 



0,28 



3 





0,35 



2 



0,31 



3 





2 





0,32 



3 



0,29 



2 



0,24 



2 



4. The Variation of the Limiting Magnitude. 



As the reduction to the eleventh magnitude has now been calculated, it is 

 possible by means of this reduction to continue the discussion of the decrease of 

 the mean relative density, and on this base to make the variation of the limiting 

 magnitude clear. 



According to page 40 the relative density, d, is defined as the quotient be- 

 tween the mean density of the zone in question, D, and that of the entire plate, 

 i. e. 



With the notions of the preceding paragraph we have 

 D = A{m) 

 Do - Am,) 



The equation for the reduction to the eleventh magnitude is 

 ^(11)== A{m) R{m) 



which applied on gives 



^(11) = ^K) R{m,) 

 By dividing the equations we get the following expression for R{m): 



R {m) = . R{m,) 



