52 



Hans Henie 



5 Reduction of the Star Density to the eleventh Magnitude. 



If the star density is to be reduced to the same magnitude i. e. to the ele- 

 ventl), it is necessary to know: 



1. Tlie relation between tlie star density and the magnitude. 

 This is given by the equation 



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



and Tab. VII. 



2. The relation between tlie limiting magnitude and the distance from the 

 centre of the plate. 



This is given by the equation 



m„ = W(, — 0,16 It. 



3. The limiting magnitude of at least one point of the plate. 

 This is for most of the plates given in Tab. VI. 



The plates with known limiting magnitude are now reduced in this manner. 

 The plates with centra on the circle of declination — 60°, have unknown limiting 

 magnitude. For these plates I have made use of those parts of the negatives, that 

 are covered by the more northern ones with known limiting magnitude and I have 

 adopted those values of the limiting magnitude, that agree best. My mode of 

 proceeding has been that I have supposed one value of the magnitude of the plate 

 in question and calculated the reduced densities on this suppo.sition. The part in com- 

 mon between the plate in question and the more northern one at once shows if the sup- 

 posed value is correct. If this has not been the case, the value has been modified until 

 the best agreement has been obtained. In this way the limiting magnitude may be found 

 with an error af about 0,1 relative to the more northern plate. The same method has 

 been used for the few more northern plates with unknown limiting magnitude, and 

 also for the south pole plates. 



The following table contains the adopted values of the limiting magnitude in 

 the centre for all the plates of the Harvard Map. 



TABLE VIII. Limiting magnitude in the centre of the plates. 



PI. 





PI. 





PI. 





PI. 





PI. 





1 



11,7 



12 



12,5 



23 



11,6 



84 



10,8 



45 



11,0 



2 



11,8 



13 



11,4 



24 



11,T 



35 



11,2 



46 



11,7 



3 



10,6 



14 



11,4 



25 



11,7 



36 



11,2 



47 



10,8 



4 



10,7 



15 



12,0 



26 



10,4 



37 



11,2 



48 



11,6 





11,0 



16 



12,0 



27 



11,4 



38 



11,4 



49 



11,7 



(J 



11,5 



17 



12,5 



28 



11,4 



39 



11,3 



50 



12,8 





11,3 



18 



11,1 



29 



11,8 



40 



10,5 



51 



11,7 



8 



10,7 



19 



10,9 



30 



10,8 



41 



11,1 



52 



11,4 



9 



10,1 



20 



10,7 



31 



10,4 



42 



11,2 



53 



11,0 



10 



12,1 



21 



10,7 



32 



10,6 



43 



11,3 



54 



11,6 



11 



11,6 



22 



11,4 



33 



10,7 



44 



11,4 



55 



11,6 



