188 ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1916. 



The instrument consisted of a 10-inch lens of 45-inch focus, with 

 a 6-inch lens of 27-inch focus, mounted, together with guiding tele- 

 scopes, upon an equatorial mounting of the English pattern. 



With the lO-inch lens, 17° by 17° upon the sky are depicted upon a 

 plate 15 inches square, and to cover the whole sky upon this scale 206 

 plates were requisite. The exposure of each plate was 2 hours or 2 

 hours 20 minutes, so as to reach the faint stars. Northern platen 

 were taken at Mervel Hill, near London; the southern at the Cape 

 and afterwards retaken at Johannesburg. 



There are certain defects in every lens which are practically in- 

 curable when a wide-angle field is desired, namely, curvature of the 

 field and astigmatism or replacement of a point-image by two line 

 condensations at different distances from the lens. It is the art of 

 the lens maker and of the lens user to split the residual errors in the 

 least harmful manner. 



I show two slides taken from the same plate. The first shows the 

 center, with images perfectly round, small, and defined. The second 

 shows the corner. You see the elongations in two perpendicular di- 

 rections succeeding one another separated by forais that suggest 

 flights of beetles. That these forms are so little pronounced at some 

 10° from the center is the proof of the excellence of lens, focussing, 

 and guiding. It is the practice to suppress them somewhat by sac- 

 rificing almost imperceptibly the definition at the center, so that the 

 smallest images are actually not at the center, but half or two-third 

 the radius away. 



But this enlargement of image means diffusion of light, so that the 

 instrument is less sensitive and the stars recorded are less numerous 

 at the margin of the field than at the best focus. In matters of count- 

 ing this is very important, because it would produce a systematic 

 deviation. Accordingly, the average amount of this deviation was 

 determined and allowed for. 



It was proposed to count a sufficient number of plates to determine 

 the number of stars, zone by zone, in each of eight zones of galactic 

 latitude. Actually 30 plates were employed. They are all in the 

 northern hemisphere, but lie both north and south of the galactic 

 equator. In each count it was proposed to detennine the number of 

 stars of each separate magnitude, and here arose one of the most cru- 

 cial, as well as difficult, points. The magnitudes recorded ranged down 

 to the seventeenth, or nearly to the ten-millionth of the brightness of 

 a first magnitude star. It was necessary to have the scale of magni- 

 tude correct over this wide space, because any deviation would here 

 again become systematic, and, altering the number of stars in each 

 grade, would altogether distort the estimated total of the vast num- 

 ber of those beyond the reach of counting. You will understand how 

 difficult it was to establish an absolute magnitude scale when the 



