THE OUTSIDE OF A STAR 
341 
/ 
By the continuity at r x 
which gives 
Also by (236-1) we have at the boundary 
H' = H — B 
(236-3). 
237. Thirdly, let the absorbing material be near the surface and not 
extend below r/ so that k' = k when r' > r /. The appropriate solutions 
are - . . 
238. Certain general conclusions can be drawn from the formulae in 
quantity of the first order k/k' will be a small quantity of the second order. 
Thus to the first order the boundary value of H'\H in (235-4) is 
This requires that both k/k' and e shall be less than § (H'/H) 2 . 
To obtain a line of blackness 1 : 10 {H'/H = -j^) we must have— 
Firstly, e< 1/133. Such a line can only be formed in gas at low 
pressure where superelastic collisions are infrequent and transform less 
than 1 per cent, of the energy of excitation. 
(237-1), 
J' — J — 2 B cosh pr + ^ (H ( 1 — k/k') — B) sinh pr 
H' = H W -^ Bsmhpr' + (H (1 — k/k') — B) cosh pr' 
(237-2). 
The latter values satisfy J = 2 H, J' = 2 H' , at r' = 0. 
From the continuity at r' = r x ' we have by eliminating A 
(l — ("cosh+ — sinhpr/ — 1 
(i +>/) cosher,' + (| +/ 3 ) sinh^T,' 
At the boundary (237-2) gives 
H' = H- B. 
the last three sections. Since p is not less than -^/(3 k/k'), when p is a small 
h'/h = ip 
(238-1). 
(238-2). 
Hence by (234-3)