391 
361-364] The Fission Theory 
Finally the star breaks into two. When this happens, the two periods of 
rotation and pulsation become equal, both now coinciding with the orbital 
period of the star. On the fissional theory the sequence of Cepheid variables 
ought in all respects to join on to the series of spectroscopic binary stars which 
have just broken up by fission, and this provides further opportunities for the 
testing of the fissional theory of Cepheid variation. 
From Kepler’s third law (or equation (215‘9)), the orbital velocity K of 
either component of a binary system must be connected with the period P 
of the system by a relation of the type 
K=CP~* (3631), 
where C is a constant. Otto Struve* has found that this relation is well 
satisfied in binary systems in which the period is less than about 2'4 days. 
But for periods of less than this, the law begins to fail. As the period de 
creases to below this value, C also begins to decrease, and finally K attains a 
constant value. He has calculated the period at which the law (363T) must 
necessarily begin to fail through the two components of the binary system 
coming into contact, and finds that the period so calculated agrees for each 
spectral type separately with the observed period at which failure begins. 
Further the constant value attained by K is found to be equal to the value 
of K for the Cepheid variables, this being approximately constant for all 
Cepheids of the same spectral type. The Cepheids are accordingly seen 
to fit exactly on to the spectroscopic binaries, thus providing a satisfactory 
confirmation of the fission theory f. 
Long Period Variables. 
Regular Variables. 
364. The investigation of Adams and Joy to which we have already referred 
(§ 353) have shewn that the long-period variables, the Cepheids and the 
cluster-variables form a continuous series in respect of the correlation between 
period and spectral type, but that the periods fall into three distinct groups 
centring round periods of approximately 300 days, 10 days and 0'5 days. 
Otto Struve X has carried out a similar count for spectroscopic binaries, and 
finds that their curve of period-frequencies shews well-defined maxima at 400 
days, 3 days and 0-5 days. He interprets this as evidence that a close relation 
ship exists between variable stars and spectroscopic binaries, and considers 
that the fission theory of variable stars fits in with the various characteristics 
of the latter remarkably well. 
The position of these maxima and minima—or rather lacunae —in the 
frequencies of periods of variable stars makes it clear that they merely 
* Astrophys. Journ. lx. (1924), p. 167 and M.N. lxxxvi. (1925), p. 63. 
Zessewitsch (Ast. Nach. No. 5534) finds further support for the fission theory in the 
behaviour of the stars RW Draconis and XZ Cygni. 
J M.N. lxxxvi. (1925), p. 75.