1835 



• 

 (lei-ably less than those resulting from tlie former investigation (now 

 0,52 from 13,5 to 14,3, tlien 0.72 from 13,5 to 14,4) which clearly 

 pointed to the presence of large, more distant star-condensations. 

 Now the photographic scales are absolutely independent of one 

 another, and therefoie they are not pei'haps immediately compai-able. 

 If e.g. the i-ediiction-factor employed, 0,884, were somewhat too 

 large, (so that a tenfold exposure would mean a gain of a little 

 under 2 X 0"",884) in the present investigation all. the in's and all 

 their differences would become smaller, and the gradients larger. In 

 how fiir this is actually the case cannot be asceitained with accu- 

 racy, in any case by means of these triplet-photographs we pene- 

 trated less deeply into the fainter stars than at the former investi- 

 gation. When the project for these photographs was made it did not 

 seem really difticult to peneti-ate further than Herschei.'s gauges, 

 the limiting magnitude of which then was found to be 13,9. On 

 account of the scale-reductions since obtained, this purpose, as has 

 now become evident, has not yet been accomplished. It would have 

 required an instrument with a larger opening, or a far greater time 

 of exposure. 



In order to advance further. Prof. Hertzspkung, at my request, 

 made a few more photographs with the 80 cm. refractor at Potsdam. 

 To immediately (ix the scale of magnitudes on the plate, a coarse 

 grating was placed before the objective, so that the central image 

 is weakened 0,'"748 and the J'^ and the 2"fUiiffraction-image become 

 2, '"242 and 3, "'317 fainter than the central image. (>n a plate with 

 the centre on 46 Aquila (19"37,"'5 -|- 1 ^>57') on 0,343 square degrees 

 858 stars were counted, of which 101 present tfie first, and 24 the 

 second diffraction -image. From this we find for 



m„ m, — 2,24 ni^ — 8,82 



hi/ N 3,398 2,469 1,845 



ciLog N ,„, . 



from which result the gradients " — =0,41 and 0,58. I Ins |)late 



dm 



penetrates somewhat further than the Triplet, for from the compari- 

 son with the numbers round about 46 Aquilae that were found in 

 Table 1, there results 7?i(, = 14,8. Here the gradient from 12,6 to 

 14,8 proves to be only 0,41. The smallness of this amount is pro- 

 bably due to the fact that fai- fainter side-images were included 

 than principal images, their place being accuiately known. Here 

 again it is evident, how easily, through dissimilai'ity of conditions 

 .systematic differences may occur in the amounts of stars counted, 

 which rendei' them useless for the deduction of gradients. 



