( 893 ) 
R—2 [((1 Hede at + (eae Serre a 2(S — E) 4 
El (late det — (1—-)?e —2@+s)t ge Re? 
x 
where « means Va ; 
U HS 
In order to study the nature of this rather intricate relation, 
ln 
. . . . . x 
SCHUSTER assigned a number of different values to the ratio - =~? 
Ss 
and to the product s.¢, and constructed several diagrams in which 
R E 
the corresponding values of 8 and g were taken as ordinates and 
al 
\ 
abscissae respectively. 
As to these results, and a great many other interesting conclusions, 
we refer to the original paper. 
SCHUSTER made no special assumptions connecting x and s with 
frequencies. 
It hes in our line to bring the selective character of these 
coefficients to the front. The simple relation to which (14) may be 
reduced for waves suffering no absorption at all, will prove very 
important and useful in this connection. Denoting by R, the value 
which R assumes for x = 0, we “obtain ') 
2 
8 2+s.t 9) 
Let us call to mind, before applying this formula, that in deducing 
(14) Scucsrer supposed the temperature and the composition of the 
mass of gas to be uniform, and the intensity of the radiation not to 
depend on the angle between any direction considered and the 
normal to the radiating surface. These conditions: evidently not being 
satisfied in the atmospheres of celestial bodies, (14) and (15) only 
give a first approximation ; the influence of the said circumstances 
will afterwards have to be separately discussed. 
§4 we introduced the hypothesis that the first term of the 
damping parameter vanishes at a short distance from the proper 
frequencies, which means that the region of real absorptiou is 
confined to the middle-part of each dark line in all cases, where the 
conditions are such as to make scattering effects appreciable. On 
that score we assume tbe equation (15) to hold good for the rest 
of the spectrum, including — in the case of the solar spectrum — 
the outer parts of the Fraunhofer lines. 
Equation (15) shows that, with increasing thickness ¢ of the 
1) ScuustTeER, le. p. 6. 
