364 
THE OUTSIDE OF A STAR 
We write g 2 A?i = <1- There are two 4 X orbits and six 4 2 orbits (four belonging 
to the K line and two to H ); hence q = 3. 
It is found that e hv ^ RTe is large so that we have with sufficient accuracy 
n 2 /% = \qre -hvi°JRT e% 
In this form the result is easily seen to be the appropriate modification of 
Boltzmann’s formula. If the n 2 atoms were excited by full radiation at 
temperature T e we should have щ/щ = qe~ hvi *l RTe -, but n 2 is reduced pro 
portionately to the diminished intensity of the radiation, so long as n 2 is 
small compared with n x . 
Let t x be the average duration of a normal state, t 2 of an excited state. 
^ en t 2 /t x = n 2 )n x = %qre~ hvi *l RTe (253-4). 
The atom will be excited (t x + i 2 ) _1 times per second and absorb 
hv l2 . (t x + i 2 ) -1 ergs per second. For each erg absorbed 1 /с units of momentum 
will be absorbed; this momentum is in all directions over the outward 
hemisphere and the average component in the radial direction will be 
l/2c. (Allowing for the law of darkening the result should strictly be 
4/7c.) For equilibrium this outward momentum must balance the 
momentum communicated by gravity, viz. Анд, A being the atomic weight 
of calcium. Hence , 
hv X2 
or 
Анд — 
+ t 2 = 
2c (t x + t 2 ) 
liv X2 
2c Анд 
.(253-5). 
By (253-4) and (253-5) to our order of approximation 
qrhv 
t 2 = ; . 12 e - hv ”! RT ° (253-6). 
4 cAHg 
Inserting numerical values for the sun the results are 
t 2 /t x = r x 3-54.10- 3 , 
t x + t 2 = 4-6.10- 5 , 
so that t 2 = r x 16-2.10- 8 . 
Since r is necessarily less than unity an upper limit to the duration 
of the excited state giving the H and K emission is 16-2.10 -8 seconds. (If 
this limit were exceeded there could be no calcium chromosphere on the 
sun.) By accurate measurement of the residual intensity at the centre of 
the H and K lines we could determine definitely this physical constant 
of the calcium atom. Provisionally r is believed to be about 0-1 so that 
t 2 — 1-6.10~ 8 secs. 
Values of t 2 have been determined in the laboratory by experiments 
on canal rays for some elements (but not for Ca + ) and these give results 
of the order 10~ 8 secs.; so that the astronomical determination is probably 
near the truth.