BLUE-VIOLET LIGHT IN THE SOLAR CORONA ON AUGUST 30, 1905. 329 



9. On the Number of Particles and Intensity of Light per Unit Volume of the 



' Corona. 



I shall explain that this problem can be solved on the following assumptions : 



(1) The luminosity of the corona is caused by particles, which are heated to 

 incandescence by solar radiation, and which scatter sunlight. 



(2) The number N (r) of particles per unit volume is a function of the distance r 

 from the sun's centre. 



(3) The apparent intensity is a known function of?- [see formula (D), 7]. 



(4) The ratio g(r) of polarised and total light has been observed and represented 

 as a function of r. 



(5) The intensity of light, T (r), of a particle heated by slar radiation is correctly 

 determined by STEFAN'S and the Wien-Planck formulae.* 



With reference to (5) I have calculated the temperatures of particles at distances 

 h = 50, 100, 200, 300, 400, 600, ..., 1600 from STEFAN'S formula (absolute tempera- 

 ture of the sun = 6000), and the intensities for wave-lengths 3000 to 5000. I find 

 that their integral intensity T(r) appertaining to blue-violet light is very nearly 

 inversely proportional to the sixth power of r, the average error of the intensities 

 between / = 50 and 1200 being only 7 per cent, of the intensity. 



I adopt the following notation : 



C = centre of sun, P = position of scattering particle, r = its distance PC (in unit 

 of the sun's radius), 6 = TJ angle CP Earth, P (r) cos* 6 = light polarised by a 

 particle at P in direction 0, S(r) P(r) cos* 6 = total light scattered by a particle at, 

 P in direction 6, F (r) = N (r) [T (r) +S (r)], f(r) = N (/) P (r). 



The functions are 



->), P(r) = c, (r"-r"),t 

 T(r) = Cl r-. 



Let us find by integration the total light emitted by a channel of unit section which 

 runs in the direction towards the earth. I designate by p(= rcosB = h + 500/500) 

 the shortest distance of this channel from C and introduce 



" sec 6 = 360 (A + 500)-'. 



The element of volume at P = r sec 6d6 = &g<7 



Unit volume at P sends light F (r) -f(r) cos* = F(gcos6) -f(g cos 6) cotf$. 



The total light sent by all the particles in the channel towards the earth equals 



(2) 



* Sci- AKKIIIAM-.S, 'Lick Olwi-rvutory Bulletin,' No. 58. 



t See Dr. SCHUSTER, " On the Polarisation of the Solar Corona," ' M. N.,' voL 40, p. 38 (6). 

 VOL. CX^VII. A. 2 U 



