we can find their relative diameters if their relative distances are known, provided that their intrinsic brilliancy of surface is the same. This latter condition we may assume to be practically true, if the star's spectrum is similar to that of the sun. These two factors of distance and relative brightness being known it becomes possible to compare directly the diameter of the sun (and hence its volume) with that of a star having the same type of spectrum. Now it has been computed that the brightness of the sun may be represented by stating that it is twenty-seven magnitudes above the zero of stellar magnitudes, or twenty-eight magnitudes brighter than an average star of the first magnitude, such as Aldebaran. The meaning of "stellar magnitude" is that a star of the first magnitude is 2·512 times as bright as a star of the second magnitude; a star of the second magnitude 2'512 times as bright as one of the third, and so on. Or, generally, if n be the difference in magnitude, then (2·512) * will represent the difference in brightness. Hence the sun will be (2.512)28 times brighter than an average star of the first magnitude; that is, the sun is equal in brightness to 158,500 million stars of the first magnitude. In the following paper I will consider those stars of which the distance has been determined with some approach to accuracy, and of which the spectrum-according to the "Draper Catalogue of Stellar Spectra," observed at Harvard-is of the solar type (F), and therefore fairly comparable with that of the sun. The first star I will consider is Beta Cassiopeia, one of the stars forming the well-known "Chair of Cassiopeia." For this star the late Professor Pritchard found, by means of photography, a parallax of o'154 of a second of arc, which would place it at a distance of 1,339,380 times the sun's distance from the earth. Were the sun placed at this vast distance-about twenty-one years' journey for light-I find that its light would be reduced to that of a star of magnitude 3'63 (light varying inversely as the square of the distance). Now the photometric magnitude of Beta Cassiopeia, as measured at Harvard Observatory, is 2:42. Hence the star is 121 magnitude, or about three times brighter than the sun would be at the same distance. Hence, if strictly comparable with the sun in physical constitution, the diameter of Beta Cassiopeia would be 1 times that of the sun, and its mass about 5 times the mass of the sun. Eta Cassiopeia. A parallax of 0'465 of a second has recently 1 See my paper in Knowledge for June 1895. The and as the photometric magnitude of Eta Cassiopeiæ is 3'64, it would follow that the sun is ten times brighter than the star, and hence the mass of the star would be only of the sun's mass. The star is a well-known binary, or revolving double star; and an orbit recently computed by Dr. See, combined with the above parallax, gives for the mass of the system 4th of the sun's mass. The discrepancy between the above results may be partly explained by the fact that the comparison, which, of course, has a mass of its own, is faint, and does not perceptibly influence the light of the primary star. For the Pole Star, a parallax of o'015 of a second has been found by De Ball. Placed at the distance indicated by this minute parallax, the sun would be reduced to a star of only 8.69 magnitude, and as the photometric magnitude of the Pole Star is 2:15, we have a difference of 6'54 magnitudes in favour of the star. This would make the star 413 times the brightness of the sun, and its mass no less than 8,395 times the sun's mass! This is a rather startling result, but the small value of the parallax of course makes its accuracy somewhat doubtful. Brioschi found a parallax of o'60 of a second, which would considerably reduce the mass; but most of the results found in recent years have been very small. It would therefore seem that the Pole Star is probably a sun of enormous size. The spectrum is a doubtful one (F?) of the solar type. For the brilliant star Capella a parallax of o'107 of a second was found by Dr. Elkin. This would give a distance of 1,927,700 times the sun's distance from the earth, and at this distance the sun would be reduced to a star of 4'42 magnitude. As the photometric magnitude of Capella is o'18, it follows that the star is 4'24 magnitudes, or 49'66 times brighter than the sun. This would make its diameter about seven times the sun's diameter, and its mass about 350 times the mass of the sun. A considerably larger parallax of 0'522 of a second was, however, found by Glasenapp, which would make the sun but little inferior to the star in brightness and mass. The star's spectrum is very similar to the solar spectrum. Procyon. For this brilliant star Auwers found a parallax of 0'240 of a second, Wagner o229, and Elkin o"266. Elkin's value, which is about a mean of the other two, would place the star at a distance of 775,430 times the sun's distance from the earth. This would reduce the sun's brightness to a star of magnitude 2'45; and as the photometric magnitude of Procyon is 0:46, it follows that the star is 6 times brighter than the sun. This would make its diameter 2} Star, and her 55. The str an orbit parallax, pre The di by the f ONT, IS ry star has bee minute p sults f Its spectrum is of the same type as the sun and Capella, and its brilliancy would lead us to believe that it is a sun of large size. Theta Ursa Majoris. This is another star with a spectrum of the solar type. A small parallax of o'046 of a second was found by Kapteyn. Placed at the distance indicated by this parallax the sun would shine as a star of 6.26 magnitude. But the star's photometric magnitude being 3:22, it follows that the star is 3'04 magnitudes, or 16:44 times brighter than the sun. Its mass would therefore be about 66 times the mass of the sun, so that if the parallax is at all reliable we have here another sun of large size. 85 Pegasi. For this star Brünnow found a small parallax of 0'054 of a second. The sun if placed at the distance indicated by this parallax would shine as a star of 5'91 magnitude, and as the star's photometric magnitude is 5'83, we have the sun and star almost exactly equal in brightness, and therefore probably nearly equal in mass. The star is a binary, and from an orbit recently computed by Dr. See and the above parallax, I find that the mass of the system would be nearly eight times the mass of the sun. The star's spectrum (E) is, however, not exactly the same as that of the sun, and the star may therefore not be strictly comparable with the sun in brightness. If we assume that the intrinsic brilliancy of its surface is somewhat less than that of the sun, then its diameter, and therefore its mass, may be greater than our sun's. Although stars with spectra of the Sirian type are not directly comparable with the sun in brightness, being probably much hotter, it will be interesting to consider some of the stars having this type of spectrum. In the case of Sirius itself, I find that the sun placed at the distance indicated by a parallax of 037 of a second, found by Dr. Gill, would shine as a star of 173 magnitude, and as the photometric magnitude of Sirius-as measured at Harvard-is +143, or 143 magnitudes brighter than the zero of stellar magnitudes, it follows that the star is 3'16 magnitudes, or 18:37 times, brighter than the sun. Dr. See finds from his orbit that the combined mass of Sirius and its companion is 3'473 times the mass of the sun, the mass of the primary star being 2:36, and that of the companion-which is faint-1113. From this it follows that if Sirius had the same density and intrinsic brightness of surface as the sun it would be only 1'773 times brighter. Hence its brightness is over ten times greater than it would be if its physical constitution were the same as that of the sun. It would seem therefore that the great apparent brightness and as the photometric magnitude of Eta Cassiopeia is 3'64, it would follow that the sun is ten times brighter than the star, and hence the mass of the star would be only of the sun's mass. The star is a well-known binary, or revolving double star; and an orbit recently computed by Dr. See, combined with the above parallax, gives for the mass of the system 4th of the sun's mass. The discrepancy between the above results may be partly explained by the fact that the comparison, which, of course, has a mass of its own, is faint, and does not perceptibly influence the light of the primary star. For the Pole Star, a parallax of oo15 of a second has been found by De Ball. Placed at the distance indicated by this minute parallax, the sun would be reduced to a star of only 8.69 magnitude, and as the photometric magnitude of the Pole Star is 2'15, we have a difference of 6.54 magnitudes in favour of the star. This would make the star 413 times the brightness of the sun, and its mass no less than 8,395 times the sun's mass! This is a rather startling result, but the small value of the parallax of course makes its accuracy somewhat doubtful. Brioschi found a parallax of o'60 of a second, which would considerably reduce the mass; but most of the results found in recent years have been very small. It would therefore seem that the Pole Star is probably a sun of enormous size. The spectrum is a doubtful one (F?) of the solar type. found by Dr. Elkin. For the brilliant star Capella a parallax of o'107 of a second was This would give a distance of 1,927,700 times the sun's distance from the earth, and at this distance the sun would be reduced to a star of 4'42 magnitude. As the photometric magnitude of Capella is o'18, it follows that the star is 4°24 magnitudes, or 49.66 times brighter than the sun. This would make its diameter about seven times the sun's diameter, and its mass about 350 A considerably larger parallax of o‘522 the mass of the sun. times of a second was, however, found by Glasenapp, which would make the sun but little inferior to the star in brightness and mass. spectrum is very similar to the solar spectrum. The star's Procyon. For this brilliant star Auwers found a parallax of 0'240 of a second, Wagner o229, and Elkin o266. Elkin's value, which is about a mean of the other two, would place the star at a distance of 775,430 times the sun's distance from the earth. This would reduce the sun's brightness to a star of magnitude 2'45; and as the photometric magnitude of Procyon is o'46, it follows that the star is 64 times brighter than the sun. This would make its diameter 2 istin ar, and here S. The s Its spectrum is of the same type as the sun and Capella, and its brilliancy would lead us to believe that it is a sun of large size. Theta Ursa Majoris. This is another star with a spectrum of the solar type. A small parallax of 0.046 of a second was found by Kapteyn. Placed at the distance indicated by this parallax the sun would shine as a star of 6·26 magnitude. But the star's photometric magnitude being 322, it follows that the star is 3'04 magnitudes, or 16:44 times brighter than the sun. Its mass would therefore be about 66 times the mass of the sun, so that if the parallax is at all reliable we have here another sun of large size. 85 Pegasi. For this star Brünnow found a small parallax of o'054 of a second. The sun if placed at the distance indicated by this parallax would shine as a star of 5'91 magnitude, and as the star's photometric magnitude is 5'83, we have the sun and star almost exactly equal in brightness, and therefore probably nearly equal in mass. The star is a binary, and from an orbit recently computed by Dr. See and the above parallax, I find that the mass of the system would be nearly eight times the mass of the sun. The star's spectrum (E) is, however, not exactly the same as that of the sun, and the star may therefore not be strictly comparable with the sun in brightness. If we assume that the intrinsic brilliancy of its surface is somewhat less than that of the sun, then its diameter, and therefore its mass, may be greater than our sun's. Although stars with spectra of the Sirian type are not directly comparable with the sun in brightness, being probably much hotter, it will be interesting to consider some of the stars having this type of spectrum. In the case of Sirius itself, I find that the sun placed at the distance indicated by a parallax of 0'37 of a second, found by Dr. Gill, would shine as a star of 1.73 magnitude, and as the photometric magnitude of Sirius-as measured at Harvard-is +1'43, or 1'43 magnitudes brighter than the zero of stellar magnitudes, it follows that the star is 3'16 magnitudes, or 18:37 times, brighter than the sun. Dr. See finds from his orbit that the combined mass of Sirius and its companion is 3'473 times the mass of the sun, the mass of the primary star being 2:36, and that of the companion-which is faint-1113. From this it follows that if Sirius had the same density and intrinsic brightness of surface as the sun it would be only 1773 times brighter. Hence its brightness is over ten times greater than it would be if its physical constitution were the same as that of It would seem therefore that the great apparent brightness the sun. |