CURTIS— NUMBER OF SPIRAL NEBULA. 517 



from regions taken in duplicate. I am unwilling at present to admit 

 that as many as five per cent, of the nebulae counted by me are 

 spurious. Even if twenty per cent, were spuriou-s, we should still 

 h?ve to account for over half a million nebulae. 



B. The theory may be advanced that the small spirals occur in 

 greatest profusion in the regions contiguous to the larger members 

 of the class, which might explain why fewer nebulae were found by 

 Fath. His plates were taken at the centers of the Kapteyn areas 

 where the larger nebulae would be included only by chance, whereas, 

 from the purpose of the Crossley nebular program, nearly all the 

 plates have some N. G. C. object central. This point is difficult to 

 prove or disprove without a special investigation comprising many 

 plates taken at random in the galactic north polar region. It is 

 certain that the small spirals frequently show a gregarious tendency ; 

 sometimes one half of a plate will record many small spirals while 

 the other half records very few. The greatest number of nebulas 

 found on a single plate was 304 (checked by a duplicate plate) in 

 the region of 12'' 55"*, -|- 28° 30' (shown in Fig. 2) ; the region about 

 N. G. C. 4826, less than 7° distant from this, shows but 2. While 

 the small nebulas are evidently quite irregular in their distribution, 

 it would seem that the large number of regions included in this 

 discussion is sufficient to afford a true representation of their average 

 frequency. 



C. Sharp focus and perfect images are essential for the detec- 

 tion of the smallest and faintest spirals. On plates where large num- 

 bers of small nebulas are found, the majority are, as a rule, detected 

 in the area 20' in radius about the optical axis as center, comprising 

 only 0.35 of a square degree. At a distance of 30' from the optical 

 axis the parabolic images are very poor, and only the brighter of 

 the small nebulae can be detected in these regions, the faintest nebulae 

 being obliterated by the blurring and spreading of the image. Dr. 

 Fath used very large plates, 6^ X 8^^ inches in size, in his work 

 on the number of the small nebulas, with the 60-inch reflector, and 

 it appears that he used almost this full area, inasmuch as he states 

 that the used area of his plates was 1.88 square degrees. As the 

 full area of the Crossley plate is 0.9 square degrees (and the outer 

 portions of this are so poor because of the parabolic distortions that 



