1915-1916.] Explanation of the Satellites of Spectral Lines. 201 
the spectrum specified by /3 ; this line is, however, more diffuse than in the 
previous case, and is not accompanied by fainter components. 
Let the oscillator emit a wave given by cos /3t from t — 0tot — l; let it 
then rest from t = l to t = l + k, and again emit the wave given by cos fit 
from t = l + k to t = 2l + Jc; there are thus two periods of activity of equal 
duration separated by a period of rest. The sole difference between this 
case and the first one lies in the limits of integration. The second term 
may be neglected as before. After the limits are substituted the Fourier 
integral takes the form 
i r 1 
-J g^[sin J(a - f3)l cos{ J(a - f3)l - at) + sill J(a - (3)1 cos{ J(a - (3)(Sl + 2k) - at)]da 
*)j Z* 30 SJJ} 1/ n I3}1 
= ~ I' 2 Q ~ COS ^(a - (3)(l + k)cos{^{a - (3)('2l + k)- at) da. 
77 J 0 CL — fj 
The energy contained between the periods specified by 
consequently 
4 sin 2 -|(a - (3)1 
tv(<x - (3f 
cos 2 i(a -/?)(/ + A;). 
a and a + da is 
The first factor is the same as occurs in the first case ; it has a maximum 
at a = /3, whence it descends to minima at (a — (3)1 = z3z2tt. The second 
factor is zero at (a — /3)(l + k) = ±(2n+ l) 7 r. Let l = k\ then three of the 
zeroes occur in the original central part of the pattern. Considering the 
two factors together, we see that the main part of the original line is now 
resolved into five components. 
We might proceed further in the same way, making suppositions as to 
the manner in which the oscillator starts and stops, or introducing sudden 
changes of phase, and calculating the way in which this affects the 
appearance of the line. Generally speaking, however, the calculation 
becomes heavy, and it will probably bring out no new features. It seems 
to me more promising to follow up the investigation experimentally. 
The analysis here is practically the same as that used in the calculation 
of Fraunhofer diffraction patterns. Our first case is the case of the single 
slit; our third case is the case of the two parallel slits separated by an 
opaque interval ; and similarly we might have passed to the case of the 
diffraction grating. The integration with respect to ^ is simply the 
summation of the S.H.M.s which according to Huygen’s principle take 
place at each point in the aperture. To every Fraunhofer diffraction 
pattern there corresponds a method of stopping and starting the oscillator. 
The question, therefore, as to whether the structure of a certain line can be 
explained on the method suggested in this paper resolves itself into the 
