36 



Hans Henie 



The extreme values of the average density are 19 stars per square centimeter 

 on plate 5, and 550 on plate 50. This last plate contains the region around the 

 Southern Cross and shows the extraordinarily great densities of as much as two 

 thousand stars per square centimeter. 



6 Reduction from square centimeter to square degree. 



The direct counts have given the number of stars per square centimeter. Now 

 the photographs are projections of parts o C the sky upon a plane. The area of 

 the sky corresponding with one square centimeter on the plate is accordingly dif- 

 ferent in the different points of the plate. 



The next step must therefore be to reduce the density from number of stars 

 per square centimeter to number of stars per square degree. 



This reduction is determined by the dimensions of the instruments and the 

 character of the projection. The two instruments with which the photographs are 

 taken are of the same construction. The focal length of the one inch lenses is 13 

 inches. As to the projection I suppose this to be approxiniately central; i. e. 

 the focal surface is a sphere. I also suppose the plates focussed for the centre. 



Under these suppositions the reduction in question is easily calculated with 

 sufficient accuracy. 



If the focal length = r, and the distance of any square from tne centre of 

 the plate = p, then the value of an area on the plate, da corresponding to a solid 

 angle dw is given by the following equation 



If dw = 1 square degree and r = 33 cm. I get 



da = 0,0000092294 {v' -\- p-f'. 



This value of r is derived from direct measurements on the plate and agrees 

 with the value of the focal length of 13 inches. 



By means of this formula I have calculated the reduction for all the squares 

 in which the density is determined; this reduction is tabulated in table III. The 

 indices of the squares are those of fig 1. 



Owing to the symmetrical distribution of the observations the reductions 

 are to be computed only for two quadrants, the first and second. 



