VARIABLE STARS 
207 
1 he unpunctuality of the variation is strongly suggestive of an intrinsic 
period rather than a forced oscillation caused by external agency. For an 
extraneous cause could scarcely fail to be strictly periodic; and although 
the response of the star might be irregular there would be no cumulative 
deviation from a periodic ephemeris. But the long-period variables show 
little or no tendency to recover in phase after an irregularity, and the 
deviations pile up in the manner to be expected of an uncontrolled 
accumulation of accidental delays and accelerations. 
It has been suggested that at the low surface temperature (indicated 
by the great difference between visual and bolometric magnitude) the 
material cannot remain gaseous and that condensations will occur. These 
might obstruct the regular flow of energy from the interior, which would 
be dammed back until it had sufficient strength to volatilise or to blow 
away the obstacle. After this relief the clouds would form again, and the 
whole process would be roughly periodic like the spirts from a kettle 
boiling over. It is likely that something of this kind occurs and is a feature 
of the variation absent in ordinary Cepheids, but it is doubtful whether 
it would in itself impose a periodicity. It seems more likely that if no 
other cause of variation were present a balance would be reached between 
the amount of cloud formed and the power of the obstructed radiation to 
disperse it. The alternative is that the period is primarily determined by 
the pulsation of the star as a whole and the above-mentioned skin effect 
is a consequence of this pulsation. The catastrophic skin effect reacts on 
the internal conditions and causes irregularity in the period; that is to 
say, in these extreme conditions of pulsation “the tail wags the dog” to 
some extent. We may test the pulsation hypothesis by examining whether 
the mean period is consistent with what we know of the internal condition 
of these stars. It is first necessary to estimate the mass. 
141. From mean parallactic motions and mean cross motions the 
average absolute magnitude is found to range from — 0 m -6 to + 0 m -6 
according to the division of type from Ml to M 8*. Confirmation is 
obtained from the star X Ophiuchi which has a non-variable companion 
of type K 0. Using the spectroscopic parallax of the companion, the 
absolute magnitude of X Ophiuchi is + 0 m -3 as compared with the average 
for its class (M 6) of + 0 m -5. The heat measurements show that even at 
maximum the reduction to bolometric magnitude is large, the effective 
temperature being well below 3000°. The absolute bolometric magnitude 
is about — 3 m . This refers to maximum and the mean rate of radiation 
may be taken to correspond to — 2 m -5. Assuming ah effective temperature 
* P. W. Merrill and G. Stròmberg, Astrophys. Journ. 59, p. 105. W. Gyllenberg 
finds the average absolute magnitude - 0 m -7, Arlciv for Math., Astr. och Fysik, 14 , 
No. 5 ; his result refers to the extreme maxima whereas that of Merrill and Stròmberg 
refers to the mean maxima of the stars.