its diameter in miles, as given by Vogel, I find to be only one third of that of water.

Let us now consider the case of Beta Auriga, which spectroscopic observations show to be a close binary star with a period of about four days, and a distance between the components of about eight millions of miles. This period and distance imply that the mass of the system is about five times that of the sun. As in this case the spectral lines are doubled at regular intervals of two days, and not merely shifted from their normal position, as in the case of Algol, we may conclude that both the components are bright bodies, and we may not be far wrong in supposing that they are of equal mass, each having 2 times the mass of the sun. As the spectrum of Beta Auriga is of the same type as Sirius, we may compare it with that star, as we did in the case of Algol. Assuming the same density and intrinsic brightness for both Beta Auriga and Sirius, I find that Beta Auriga should be about twice as bright as Sirius. Now, according to the Oxford photometric measures, Sirius is 2.89 magnitudes, or 14 32 times brighter than Beta Auriga. Hence it follows that the distance of Beta Auriga should be about 5 times greater than that of Sirius, and assuming the parallax of Sirius at o'39", that of Beta Aurige would be about o'061". From actual measures of the parallax of Beta Aurige made by the late Professor Pritchard at Oxford, he found from two comparison stars a mean parallax of o'062", a result in remarkably close agreement with that computed above from a consideration of the star's mass and brightness compared with that of Sirius. As the actual distance between the components of Beta Aurigæ is equal to the sun's distance from the earth divided by 11.625, it follows that the maximum angular separation between the components is equal to o'062" divided by 11625, or about th of a second, or nearly the same as in the case of Algol.

The bright star Spica has also been found by the spectroscope to be a close binary star. Vogel finds a period of four days, with a distance between the components of about 6 millions of miles, and assuming that the components are of equal mass, and are moving in a circular orbit, he finds that the mass of the system is about 2.6 times the mass of our sun. This would give each of the components 13 times the mass of the sun, and it follows that the light of Spica— which has a spectrum of the Sirian type-should for equal distances exceed that of Sirius about 1'4 times. Now, the photometric measures at Oxford show that Sirius is 191 magnitude, or 5-8 times brighter than Spica. Hence it follows that the distance of Spica should be

powerful telescopes which could ever be constructed by man. In some of these remarkable objects, the doubling of the spectral lines indicates that the components are both bright bodies, but in the case of the variable star Algol, at least, as the lines are merely shifted from their normal position, not doubled, it would seem that one of the components is a dark body, or at least gives so little light that its spectrum is not perceptible. In either case the motion in the line of sight can be measured by the spectroscope, and we can therefore calculate the actual dimensions of the system in miles, and thence its mass in terms of the mass of the sun, although the star's distance from the earth remains unknown. Judging, however, from the brightness of the star and the character of its spectrum we can make an estimate of its probable distance from the earth.

Let us first consider the case of Algol. This famous variable star has, according to the Draper Catalogue, a spectrum of the first or Sirian type. It may therefore be comparable with that brilliant star in intrinsic brightness and density. Assuming the mass of Sirius at 2:20 times the mass of the sun, as determined by Auwers, and that of the bright component of Algol at four-ninths of the sun's mass, as found by Vogel, I find that for the same distance Sirius would be about 28 times brighter than Algol. But photometric measures show that Sirius is about 22 times brighter than Algol, from which it follows-since light varies inversely as the square of the distance -that Algol is 277 times farther from the earth than Sirius. Assuming the parallax of Sirius at 0'39", this would give for the parallax of Algol o'14", or a journey for light of about 23 years. From the dimensions of the system as given by Vogel-about 3,230,000 miles from centre to centre of the components-this parallax would give an apparent distance between the components of less than the two-hundredth of a second of arc, a quantity much too small to be visible in our largest telescopes, or probably in any telescope which man can ever construct. It is therefore no matter for surprise that Burnham, the famous observer of double stars, failed to see any trace of duplicity in Algol with the highest powers of the great telescope of the Lick Observatory. From a consideration of irregularities in the proper motion of Algol and in the period of its light changes, Dr. Chandler infers the existence of a second dark body, and a parallax of oo7". As this is exactly onehalf the parallax found above, it implies a distance just double of what I have found, and would, of course, indicate that Algol is intrinsically four times brighter than Sirius. This greater brilliancy would suggest greater heat, and would agree with its small density, which, from

Spectroscopic observations also suggest that the well-known variable star Beta Lyræ may also consist of two or more close components. Bright lines were detected in the star's spectrum by Secchi so far back as 1866. In 1883 M. Von Gothard noticed that the appearance of these bright lines varied in appearance, and from an examination of photographs taken at Harvard Observatory in 1891, Mrs. Fleming found displacements of bright and dark lines in a double spectrum, the period of which agreed fairly well with that of the star's light changes. Professor Pickering thence concluded that the star consists of two components, one stellar and the other gascous ; but this conclusion has been somewhat modified by subsequent investigations. M. Bélopolsky, from photographs taken with the great thirty-inch telescope of the Poulkova Observatory, confirms the periodical displacement in the bright spectral lines, "in a period identical with that of the star's usual double fluctuation;" but Keeler and Vogel agree that the observed displacements are incompatible with the supposed occurrence of eclipses. Vogel, however, is "convinced that Beta Lyræ represents a binary or multiple system, the fundamental revolutions of which in 124 22h in some way control the light change, while the spectral variations, although intimately associated with the star's phases, are subject besides to complicated disturbances running through a cycle perhaps measured by years."

Quite recently (1896) M. Bélopolsky has found with the spectroscope that the brighter component of the well-known binary star Castor is a close binary star with a dark companion, like Algol. The period of revolution is about three days, and the relative orbital velocity about 20 miles a second. Assuming the bright and dark components to be of equal mass, and hence the absolute orbital velocity of the bright components one-half the relative velocity given by Bélopolsky, I find that, if the orbit is circular, the distance between the components is about $54,000 miles-or slightly less than the sun's diameter, and their combined mass about ;th of the sun's mass. This result tends strongly to confirm the opinion which I arrived at some years since from a consideration of the orbit of the two visible components of Castor, namely, that they are masses of glowing gas. Assuming that the visible components are of equal mass, the combined mass of the whole system would be th of the sun's mass. From this result we can easily compute the stars' parallax, which I find to be 0.2873", From heliometer observations made in 1854-55, Johnson found a "relative parallax" of o'198", but as the comparison star used may itself have a small parallax, the

2.85 times the distance of Sirius. This would make the parallax of Spica about o'137". So far as I know, a measurable parallax has not yet been found for this star. Brioschi, in 1819-20, found a negative parallax which would imply either that the parallax is too small to be measurable, or that the small comparison star is actually nearer to the earth than the brighter star. Still, the above result would seem to suggest that its parallax might possibly be measurable by the photographic method. The parallax found above would imply that the maximum distance between the components of Spica would not exceed the one-hundredth of a second of arc, a quantity much too small to be detected by the most powerful telescopes. In addition to its orbital motion, Vogel finds that Spica is approaching the earth at the rate of about nine miles a second.

We now come to Zeta Ursa Majoris, which has also a spectrum of the Sirian type, and which the spectroscope indicates to be a close binary star with a period of about 104 days, and a combined mass equal to forty times the mass of the sun. Proceeding as before, we find that the light of Mizar should be about 8.7 times that of Sirius. But the photometric measures made at Oxford show that Sirius is about three magnitudes, or about sixteen times brighter than Mizar. Hence the distance of Mizar should be nearly twelve times the distance of Sirius. This gives for the parallax of Mizar about o'032". Klinkerfues found a parallax of o'0429" to o'0477", which does not differ widely from the above result. As the velocity of the orbital motion shown by the spectroscope indicates a distance between the components of about 143 millions of miles, or about the distance of Mars from the sun, the maximum distance between the components would be o'032 multiplied by 1 or o'048", a quantity beyond the reach of our present telescopes.

The well known variable star Delta Cephei has recently been added to the list of "spectroscopic binaries." From observations made with the great thirty-inch refractor of the Poulkova Observatory in the summer of 1894, M. Bélopolsky finds that the star is probably a very close double, the companion being a nearly or wholly dark body, as in the case of Algol, the orbit being a very eccentric ellipse. The observed variation of light, however, indicates that there is no eclipse as occurs in Algol, so that the fluctuations in the light of Delta Cephei will have to be explained in some other way. The spectrum of the star is of the solar type, so that in this respect it differs from the other spectroscopic binaries referred to above. The observations show that the system is approaching the sun at the rate of about fifteen miles a second.

Spectroscopic observations also suggest that the well-known variable star Beta Lyræ may also consist of two or more close components. Bright lines were detected in the star's spectrum by Secchi so far back as 1866. In 1883 M. Von Gothard noticed that the appearance of these bright lines varied in appearance, and from an examination of photographs taken at Harvard Observatory in 1891, Mrs. Fleming found displacements of bright and dark lines in a double spectrum, the period of which agreed fairly well with that of the star's light changes. Professor Pickering thence concluded that the star consists of two components, one stellar and the other gaseous; but this conclusion has been somewhat modified by subsequent investigations. M. Bélopolsky, from photographs taken with the great thirty-inch telescope of the Poulkova Observatory, confirms the periodical displacement in the bright spectral lines, "in a period identical with that of the star's usual double fluctuation;" but Keeler and Vogel agree that the observed displacements are incompatible with the supposed occurrence of eclipses. Vogel, however, is "convinced that Beta Lyræ represents a binary or multiple system, the fundamental revolutions of which in 124 22h in some way control the light change, while the spectral variations, although intimately associated with the star's phases, are subject besides to complicated disturbances running through a cycle perhaps measured by years."

Quite recently (1896) M. Bélopolsky has found with the spectroscope that the brighter component of the well-known binary star Castor is a close binary star with a dark companion, like Algol. The period of revolution is about three days, and the relative orbital velocity about 20 miles a second. Assuming the bright and dark components to be of equal mass, and hence the absolute orbital velocity of the bright components one-half the relative velocity given by Belopolsky, I find that, if the orbit is circular, the distance between the components is about 854,000 miles-or slightly less than the sun's diameter, and their combined mass about 7th of the sun's mass. This result tends strongly to confirm the opinion which I arrived at some years since from a consideration of the orbit of the two visible components of Castor, namely, that they are masses of glowing gas. Assuming that the visible components are of equal mass, the combined mass of the whole system would be th of the sun's mass. From this result we can easily compute the stars' parallax, which I find to be 0.2873". From heliometer observations made in 1854-55, Johnson found a "relative parallax" of o.198", but as the comparison star used may itself have a small parallax, the