‘CASS 
STELLAR NUMBERS AND DISTANCES. 107 
As a specimen of a photographic gauge-field on a small scale, we may 
take Prof. Pickering’s catalogue, from the Harvard plates, of 947 stars 
within 1° of the north celestial pole.* The region examined lies about 
27° from the zone of the Milky Way, but is nearly reached by a faint 
extension from it. Since only one eighth magnitude star, and none 
brighter, are included in it, the study of distribution, for which it offers 
some materials, may be said to begin with the ninth magnitude. <A 
single glance at the synoptical table suftices to show that the numerical 
representation of the higher magnitudes is inadequate. The small 
stars are overwhelmingly too few for the space they must occupy if of 
average brightness; and they are too few inaconstantly increasing ratio. 
Hither, then, the diminishing orders form part of a heterogeneous col- 
lection of stars of all sizes at nearly the same distance from us about 
Distribution of 934 stars within 1° of the pole, showing the ratio of numbers to space for each half- 
magnitude. 
that corresponding to ninth magnitude), or they belong to attenuated 
star-layers stretching to a much vaster distance. <A criterion might be 
supplied by Prof. Holden’s plant of charting separately stars of succes- 
sive magnitudes over the same area, and judging of their connection or 
disconnection by the agreement or disagreement in the forms of their 
groupings. 
The accompanying diagram shows graphically the decrease of density 
outward, deducible from Prof. Pickering’s numbers on the sole suppo- 
* Harvard Annals, vol. Xvul, p. 138. a 
+t Recommended in the Century Magazine for September, 1888, as well as in ‘‘Wash- 
burn Publications,” vol. 11, p. 113. 
