ON APIOIDAL BINARY STAR-SYSTEMS. 258 
the revolution in space of the line of apsides, the intricate problem of the 
influence of eccentricity of orbit on prolateness of figure, and the still 
more obscure matter of the gradual recession of the component stars from 
one another. And the datum on which an investigation of this nature 
and scope depended was a variation never much greater than half a 
magnitude, an alteration in brightness inappreciable to an untrained eye. 
If a candle be placed at a distance of 100 yards, and its light estimated, 
it will at once be averred that no eye or instrument can measure the 
change in brightness consequent on the candle being shifted one yard 
nearer the observer. Yet such an apparently inappreciable change in 
brightness is five times greater than the value on which such a determina- 
tion as that of the alteration in figure due to eccentricity of orbit depends. 
lt is evident, therefore, that to arrive at results of any weight or value 
in the cosmical problem of stellar evolution there must be as premises 
observations of great refinement. 
In 1900 I had constructed by Cooke of York a telescope of a peculiar 
pattern (a pattern suggested by Sir David Gill), by means of which I was 
able to obtain observations of far greater accuracy than could be secured 
by an ordinary telescope. The accuracy attained was such as to warrant 
entering upon a systematic observation of all southern close binary 
systems with a view to a definite determination of their form, dimensions, 
movements, and density. 
Four apioidal binary systems are under constant observation at 
Lovedale, and already over 10,000 observations have been secured of one 
of the most remarkable of these stars, viz., RA Centawri. A preliminary 
determination of the orbital elements of this star,! as well as the densities 
of the other four, have ® already been published. It is hoped that in 
1906 this inquiry may be extended to northern stars of the close binary 
type, so that any general consideration of the whole problem may rest on 
a common method of observation. 
Il. Particular Exposition of the Problem. 
If two stars form a binary system there are three ways of arriving at 
a knowledge of the main facts of figure, motion, mass, and density ; but 
no single method yields a full knowledge of these orbital elements. Each 
method has its limits, but each is supplementary of the other. 
It will make for brevity if we state in order the various values which 
fix the dimensions, size, and position of any binary system. 
. The period of revolution, 
. The size of the orbit. 
. The eccentricity of the orbit. 
. The position of the orbit in space. 
. The inclination of the orbit. 
. The size and form of the component stars. 
. The mass of the components. 
. The density of the components. , 
. The surface brightness of the components. 
SOaONOQorwwre 
It is evident that determinations of the value of any of the above 
elements, made at different dates, will yield evidence of any secular 
change. Such determinations are of special interest when the eccentricity, 
distance, figure, and brightness of the component stars are in question. 
} Monthly Notices R.A.S., vol. xiii. p. 527. 
? Astrophysical Journal, vol. x. p. 308; Nature, No. 1663, p. 468. 
