ON APIOIDAL BINARY STAR-SYSTEMS. 249 
Apioidal Binary Star-systems. 
By ALexanvER W. Ropzrts, D.Sc., F.R.A.S. 
[Ordered by the General Committee to be printed in ewtenso.] 
I. General Statement. 
Durine the past ten years a notable extension has taken place in the area 
of variable star research. 
The scope of this branch of astronomy is no longer simply the ascer- 
tainment of the period and amplitude of variation of such stars as fluctuate 
regularly in brightness, or even the determination of the form and 
character of their light-curve. Variable star research goes beyond this 
into a region of investigation, where it marches with the great subjects of 
cosmic physics and the evolution of binary systems. 
Thus the study of variable stars, or at least the study of a certain type 
of variable star, includes an inquiry into the conditions of magnitude, 
movement, and position that underlie such changes in brightness as obser- 
vation reveals to us. 
One of the most important of the recent developments in this direction 
is that dealing with the orbital elements, dimensions, density, tidal pul- 
sations, and secular changes of that remarkable class of stars which for 
want of a better name we may call apioidal binary systems. 
I propose in the present paper considering how far variable star 
reseafch has led us in an inquiry of such interest and importance as that 
just indicated. I shall confine myself exclusively to an exposition of the 
practical side of the subject. As is well known, there is a wide field of 
inquiry dealing with the theoretical aspects of the problem. The classical 
researches of Darwin and Poincaré on the evolution and figure of two 
rotating masses of matter are the most valuable contribution to our 
theoretical knowledge in this direction. Indeed, long before observation 
added its testimony in proof of the existence of such strange systems as 
egg-shaped or pear-shaped stars, Darwin,!' from theoretical considerations 
alone, defined their form and described their life-history, thus becoming 
the honoured pioneer in this wide field of astronomical discovery. Such 
intimate relation between theory and observation is happily not rare in 
the history of scientific progress. 
Practical work on the subject of apioidal or prolate binary systems 
dates only from the close of last century ; but to understand the nature 
and importance of the discoveries which made it possible even to enter 
upon a practical consideration of the problem it is necessary to go some 
way back in the history of variable star research. 
In 1784 Goodricke of York discovered the variation of the bright stat 
p Lyre. Goodricke was able, from his own carefully made observations, 
to indicate the principal features of the light-changes of this remarkable 
star, but he was not able to offer any explanation of the peculiar character 
of its variation. 
In 1858 Argelander published his unrivalled series of observations of 
6 Lyre,’ deducing from them a light-curve of such surpassing accuracy 
1 Figures of Equilibrium of Rotating Masses of Fluid, Phil. Trans. R.S., vol. 
elxxvili. pp. 379, 428. 
2 De Stella B Lyre variabili, Commentatio altera, 
