( 885 ) 
and the minimum of 7 are found; and, with increasing u, approaches 
zero on both sides. Fig. 1 (taken from Voier Le. p. 115) shows the 
curves representing the two functions. We may consider vas 
measuring the width of the dark line appearing in the spectrum. 
Indeed, the slope of the intensity curve is much steeper than the 
slope of nx, because the strength of the transmitted light (provided 
we are not dealing with the radiation through a thick atmosphere, 
47 
/ 
ef. § 5) is given by =le , 2 being the length of the path 
through the gas. The dotted curve represents the reciprocal value of 
the intensity of the transmitted light on the supposition that for 
a=0 we have /='/,,, /,;.80 that at p= tt '/,v', where nx has 
half its maximum value, we find /—'/,/,. Almost the whole of 
the dark line thus lies between u = —'‘/, rv’ and «= + '/,v'). 
§ 3. Cases in which the anomaly of the dispersion curve is greater. 
Our object being to apply the results of the theory to the inter- 
pretation of the solar spectrum, we must allow for the possibility 
that perhaps not in all cases the modulus of —-—~—__. may be 
taken to be small as compared with 7,* (e.g. when we are concerned 
with very strong lines, like the calcium lines Mand £); we therefore 
return to equation (5). Separating the real from the imaginary part, 
we obtain 
— Zou 1/, ov! 
NN RN = -—____ and_n? x = —_ [26 Saat 
yp, (£ uw? + v”) yp, (tu + vy’) 
The substitution of the second equation into the first one leads to 
— Zou +'/, ov'x — ou + '/, ov'x , 
Re i EES 9 or n—- nN, = vt © - (7) 
v, (4u? + v”) */a(7+-9)0,(4n7 +0") 
from which we deduce 
. ‘/ ,ov'x 9) 
Gre U, +n es (Au? + v’”) i 1] (n +n = (47 _ yl?) (8) 
2 0 0 {2 “0 0\ {t Ae v ) 
A similar position as, according to (6), the curve ” takes with 
respect to the straight line ,, it assumes according to (8) with 
respect to the curve n, +d (if d represents the second term, which 
is variable with m and x). By that term d the character of the curve 
n is, however, scarcely influenced, because '/,v'x is small in com- 
1) We shall see later on that in the light which has traversed the solar 
atmosphere, the apparent width of the real absorption lines must be even less, 
because part of the attenuation depends on scattering, and this part follows a 
law different from the exponential one. 
