394 
Variable Stars 
[ch. xv 
367 . The duration of these pulsations must of course depend on the 
magnitude of the dissipative agencies which tend to check them. If viscosity 
alone were active, it is readily seen, from a consideration of physical dimen 
sions, that the pulsations would be reduced to half amplitude in a time of the 
order of pr 2 /r), which is probably of the order of 10 u years, but ordinary 
conduction of heat, by preventing the pulsations from being strictly adiabatic, 
must also contribute towards checking the pulsations. Although exact cal 
culations are difficult, it seems very likely that the pulsations are checked 
mainly by conduction of heat, this reducing the duration of the pulsating 
stage to a time of the order needed to account for the observed number of 
irregular long-period variables. 
The different possible pulsations of a sphere of gas correspond to its 
various principal coordinates, and these have periods which are, in general, 
incommensurable. Thus pulsating stars can shew no clearly defined period, 
such as is shewn by most of the Cepheid and regular variables, but their light 
curve must be formed by the superposition of light curves of incommensurable 
periods. The principal radial pulsation of the star will probably have a 
greater amplitude than the other vibrations, and this will determine a period 
in which the light curve ought approximately to repeat itself, although the 
exact positions of its maxima and minima will always be influenced by the 
other vibrations of incommensurable periods. This is precisely what is observed 
in the irregular long-period variables.