202 



CARNEGIE INSTITUTION OF WASHINGTON. 



by adding the zero-point corrections to the relative magnitudes, have 

 been formed for the first 67 areas, and the zero-point reductions for 

 areas 68 to 115 are ready for the least-squares adjustment. 



It is highly important that the final magnitudes should form a 

 homogeneous system, in zero-point as well as in scale. To this end 

 all the areas of each zone are intercompared, and at intervals of 4 hours 

 in right ascension comparisons are made directly with the North 

 Polar Standards, whose zero is the point of reference for the entire 

 system of magnitudes. The zero-point determinations are therefore 

 subject to certain closing conditions, similar to those occurring in 

 triangulation operations, which may be expressed by the general 

 statement that the algebraic sum of the zero-point differences along 

 the closed circuit connecting any series of areas must be zero. Thus, 

 for the zone at 45°, intercomparison photographs connect the succes- 

 sive steps in the circuit Pole, 20, 21, 22, 23, 24, Pole (the numbers 

 are those of the areas involved), and 5 other similar circuits, each of 

 whose summed zero-point differences must be zero. Further, there 

 is the condition, superfluous so far as the adjustment is concerned, 

 that the zero-point differences around the zone itself must also be zero. 



To illustrate the accordance of the results, the closing errors now 

 available, expressed in hundredths of a magnitude, are given in the 

 accompanying table. In view of the number of steps in the circuits — 

 usually 6, though the zone circuits include 12 at 75° and 24 for the 

 other zones — the internal consistency appears to be very satisfactory. 



The reduction of the closing errors to zero is accompHshed by the 

 usual least-squares process for the discussion of conditioned observa- 

 tions. The results for each zone are adjusted separately, excepting 

 those for 0° and — 15°, which, because of the nature of the conditions, 

 must be treated as a unit. The number of unknowns in each solution 

 is 12 per zone. The resulting corrections for adjustment average 

 ± 0.03 mag. For the 4 zones now complete, the maximum correction 

 is 0.07 mag. 



The extensive measures and reductions involved in this investiga- 

 tion have been continued by Miss Joyner, Miss Richmond, and Miss 

 Winn. Miss Carolyn Burns and Miss Helen Burns have each given 

 a part of the year to this work, and Miss Wolfe has frequently assisted 

 with the reductions. 



