MancJiester Memoirs, Vol. I. (1906), No. 1. 23 



NOTE I. 



In Table II. of Professor Schuster's paper (yMon. Not.., 

 vol. 40, p. 55) the brightness of the stronger component at 

 different distances from the sun's centre is calculated for 

 different laws of distribution of particles. To get the whole 

 light /, -f /j we must combine Tables II. and III., forming 



Let us form this quantity for 6 = 30°, i.e.., 2 radii from the 

 centre : and 6 = 90° or i radius (the sun's limb). The ratio of 

 the distances is thus 2 ; and the brightnesses observed are in the 

 ratio 2'' or 64. We have to find what law of density of particles 

 gives us this law of brightness. Writing down the brightnesses 

 for different laws of density from Professor Schuster's paper, we 

 have 



Value of I^ + Ii 



Law of density r° 



At distance i, I„ + 1^ = yo 



2, /„ + /i=r22 

 Ratio of brightnesses 2 "46 

 Ratio as power of 2 i'3 

 Power of 2 for density o 

 Difference +i"3 



Thus if the density falls off as the wth power of the distance, 

 the brightness falls off about as the {;« + i7)th power, when tn 

 is near the value we require. And since we have observed 



;;/ + I • 7 = 6 



we find )n = 4"3. 



But it is perhaps scarcely advisable to choose as one of the 

 points the actual limb of the sun, since the chromospheric 

 phenomena complicate matters here ; and indeed the measure- 

 ments of brightness were not made quite so close to the sun as 

 this. Let us rather take the pair of points for which (^ = 52°"5 

 and 0= 22'''5. 



