ON APIOIDAL BINARY STAR-SYSTEMS. 255 
In diameter 8 Lyre is equal to fifty suns, and in mass sixty-eight. 
Yet the density is indeed small, being only 0-0003 of that of the Sun. 
The component stars though nearly equal in size are very unequal in 
brightness, one star being two and a half times brighter than the other. 
The amount of flattening is equal to that of / Puppis and X Carine. 
The present seems a suitable opportunity for the statement that no refine- 
ment of observation or analysis will distinguish between a prolate spheroid 
and an egg-shaped body. It would require an accuracy of observation 
correct to 0™-001 to reveal the difference between a spheroid of two and 
an ellipsoid of three unequal axes. 
V Vulpeciule (ch. 7394). 
This recently discovered variable! will probably supply questions of no 
common interest in connection with the many-sided problem of close 
binary systems. I have in a recent paper to the Royal Astronomical 
Society called attention to the remarkable rarity of this star. Its density 
is only 0:00002, that of the Sun being unity. 
If now we take this value and place it alongside the long period of the 
star, seventy-five days, we are impelled in the direction of assuming that in 
the case of V Vulpecule we have two vast nebulous orbs, the protoplasm 
of worlds in the making, circling round each other in measured motion. 
The component stars of this system are nearly in contact, and the 
prolateness of their figure, evident from the form of the light-curve, 
also points to a distinctly eccentric orbit. 
U Pegast (ch. 8598). 
All our valuable observations of this star—and they are exceptionally 
so—we owe to Pickering. His photometric measures indicate a system in 
direct contrast with that of V Vulpecule. 
U Pegasi fulfils its period in nine hours ; V Vaulpecule in seventy-five 
days. The density of the former star is 0°36 ; that of the latter, as we 
have seen, 0:00002. It would appear that in the case of U Pegasi we have 
a system not materially different from what our Earth and Moon were at 
the genesis of the latter. The density is probably the same, and the 
period of U Pegasi not much greater than that of the Earth-Moon system 
at the critical bipartition stage. 
There is this difference, however, that in the case of U Pegasi the two 
components are practically equal in size, though distinctly unequal in 
brightness. The existence of vast U Pegasid tides is made evident, by the 
slightly unequal brightness of successive maxima. 
IV. General Conclusions. 
From the foregoing considerations of certain close binary systems it is 
evident— 
(1) That density of all stars of this class is exceedingly small. It will 
be found that the average density of the six stars dealt with in this paper 
is 0-13 that of the Sun. 
(2) All stars of this type are prolate in figure, the amount of flattening 
depending roughly on the nearness of the stars to one another. 
' British Astronomical Journal, vol. xv. p. 200. 
? Harvard Circular, No. 23. 
