46 



KNUT LUNDMARK, GLOBULAR CLUSTERS AND SPIRAL NEBULiE. 



between points situated symmetrically about the nucleus, we find that the following 

 expression can be derived, which pretty well satisfies the observations with the 

 exception of the two points next to the nucleus. 



m 



5 I02; h + 1. 



78. 



(12) 



In this förmula m designates the apparent magnitude of a point in the nebula 

 and h its distance from the centre in mm. How Reynolds' measures can be re- 

 presented by the formula is shovvn by the following table. 



5 log h 



wiol)s. — wcalc. 



5 log h 



wobs. — mcalo. 



3,89 



m 

 + 0,23 



2,38 



m 

 + 0,04 



3,70 



+ 0,04 



1,98 



+ 0,07 



3,49 



+ 0,10 



1,50 



- 0,13 



3,27 



+ 0,06 



0,88 



- 0,08 



3,01 



- 0,09 



0,00 



- 0,41 



2,72 



+ 0,01 



-1,51 



- 





This law is the same as the one found by Bergstrand 21 for the light-curve 

 of the solar corona, and implies that the surface-intensity decreases inversely with 

 the square of the distance from the nucleus. 



If we do not take into consideration that at different distances from the 

 nucleus the nebula has certainly not the same extent in a direction at right angles 

 with the plane of the spiral arms, we may as an approximation consider the inten- 

 sities obtained by Reynolds as a measure for the variation of the står density in 

 the supposed Andromeda-galaxy from the nucleus and outwards. We suppose the 

 true dimensions of the nebula to be 28000 light-years in accordance with the paral- 

 lax-determinations from the 11 temporary stars that have appeared in it, and then 

 obtain, from Reynolds' measurements and Schwarzschild's treatise 183 concerning 

 the variation of the står density in our stellar system, the two curves in fig. 7. 



Owing to the great uncertainty regarding our knowledge of the decrease of 

 står density within our stellar system, as well as the uncertainty of the value we 

 have employed for the truc dimensions of the nebula, no certain conclusions are to 

 be drawn from the two curves. Yet, it seems to be evident that the supposed 

 Andromeda-galaxy has a central condensation, to which our stellar system has no 

 analogy. Probably the distribution of the light (står density respectively) within 

 M 33 is rather to be compared with that of our Galaxy. 



A consequence of Reynolds' theory is, that the reflected light from the 

 gaseous atmosphere of the nebulse ought to be polarized. He has also made observa- 

 tions, both visually and photographically, in order to examine this matter and he 

 considers, regarding M 64, that he has found some indices of polarization. Owing 

 to the many difficulties involved in these experiments, it might be considered that 



