( 631 ) 



in which [i z= mod. of the Nei)-Log. 



0.4 wi — 2.20 4- Ï' 1 



(t = e & 



fhn 



0.4 m — 2.20 + T 1 



and 



«(2.20-T-0.4m4-2/ow) 1 (13) 



2«fiJ 



«(2.20-T-0.477i + 2%9) I (14) 



4«fiJ 



log h,n — 2.2^ — OAm (15) 



As soon as the (iV,„)^ have become known we find the {JSf^T^ by 

 simple subtraction. 



I have carried through the solution for the values 400, 600, 800 

 and 1000 for ij. It appeared that only when we come to the last 

 value we get satisfactory results. 



It seems superfluous to give all my calculations in full. I will 

 only communicate some of the values obtained with the constant 



^ = 1000 (16) 



which was tinally adopted. The value of the G and H were found 

 to be as follows. (See table I p. 632). 



Now, if for the stars of magnitude 2, 3, 4, 5, we take the numbers 

 found by Pickering for the whole of the sky, viz. resp. 58, 172, 

 577, 1848 ') and for the remaining magnitudes, the numbers which 

 we derive from table 2 of the Groningen Publication N". 18, by 

 snnply multiplying with 41 253 (the number of square degrees for 

 the whole of the sky), we tind equations of condition for the deri- 

 vation of the unknown quantities A(0), Dj^, D^,, such as this : 



•5Ö ^ = 0.2962 + 0.0411 D,, + 0.0244 i>,„ 



140 

 etc. Tl,ey get a more convetaent fc'tn tf we put — =. Z and if 



we then divide all the equations by the coeflicient of Z. In this 

 way the equations of condition become as follows : 



') In Publ. IS. p. 8 I found, by countings made on the materials of Pickering 



^•2.495 — 58 ; iV3.495 — 171 ; iV'l-SS — 574 . ^5.495 _ 1837. 

 1.495 2.49Ü 3.495 ' 4.495 



Willi the aid of the computed values communicated in the same publication it is 

 easy to pass frc 



those of the text. 



easy to pass from tliese to the numbers iV^-^ etc. Tiie results tlms found are 



1.5 



