84 



Hans Henie 



The decrease of the density from the centre of the plate is consequently very 

 nearly compensated. At the same time the reduction to the eleventh magnitude 

 has made the whole set of negatives homogeneous. The 55 preceding tables of den- 

 sity form in reality a map of density covering the entire sky. 



4 Combination of the different Plates of the Harvard Map. 



In order to carry out a discussion of the apparent distribution of the stars 

 in the sky it is necessary to combine the plates of which the Harvard Map consists. 

 For this purpose I use the graphic method, which is the quickest, and which gives 

 a sufficient approximation. 



The negatives are consequently treated as tangent-planes to the focal sphere. 

 Tlien it is an easy problem of descriptive geometry to transform the system of 

 plates into a plane projection. As projection I choose the gnomonics, this having 

 the valuable property of reproducing straight lines as straight lines. I project the 

 whole sphere in the half scale on six planes, one plane for each polar region, as 

 far as the circle of 50" polar distance, and four planes surrounding the equator. 

 On these planes the contour of the negatives, and the projection of the rectangular 

 axes with the centimeter squares are drawn. Owing to the symmetrical arrange- 

 ment of the plates, the drawing of the projections is not difficult. 



The reduced star densities are now written in the corresponding projected 

 centimeter squares, and in this way the six charts form a map of density contain- 

 ing a total of more than five thousand values of the star density in points distri- 

 buted almost uniformly over the whole sphere. 



For the orientation it is also necessary to have the declination- and hourcircles 

 drawn on the charts. The first are hyperbolas on the equator charts and circles 

 on the polar charts, the latter are straight lines on both. 



5. Division of the Sphere into Areas of about 25 square degrees. 



The sphere is now divided in the following maimer. The circles of declination 

 are drawn for every 6°. 



The 36 zones which this division gives, are divided into squares by equidistant 

 hourcircles after the following scheme: 



00__30o 72 hourcircles i. 



e. 432 squares 



30—40 60 

 40—50 54 

 50—60 42 

 60-65 36 

 65—70 30 

 70—75 24 



120 

 108 



84 

 36 

 30 

 24 



