November 2, 1891 .] 



KNOWLEDGE 



209 



or two months old — and maj' still be seen a fortnight 

 after hatching. Through the small perforation made by 

 this tooth the fluid flows out, softening the adjacent parts, 

 so that the aperture is widened into a cleft. The process 

 of creeping out may take about two hours. The young 

 animal seems large in comparison with the egg ; one 

 measuring 28 cm. in length came out of an egg 8 cm. long 

 and 5 cm. broad. The young Crocodiles are wild little 

 animals, and are led to the water by the mother. They 

 utter sounds, especially when hungry, but the pitch of 

 their call is not so high as it was when they were within 

 the egg. 



ON THE MASS AND BRIGHTNESS OF 

 BINARY STARS. 



By J. E. GoKE, F.R.A.S. 



THE orbit of a binary star having been computed, 

 and its distance from the earth determined, it is 

 easy to calculate the combined mass of the com- 

 ponents m terms of the Sun's mass. We can also 

 compare the brightness of the star with that of 

 the Sun, for as the brightness decreases as the square of 

 the distance, we can compute how much the Sun's light 

 would he reduced if removed to the distance of the star. 

 Photometric comparisons have shown that the Sun's stellar 

 magnitude is about — 25-5, on a scale of which the " light 

 ratio " is 2-512. In other words, the Sun is 25| magni- 

 tudes brighter than a star of the zero magnitude, or 26| 

 magnitudes brighter than an average star of the first 

 magnitude, like Altair or Spica. The parallax of some of 

 the binary stars has been ascertained, and although the 

 results found are perhaps in some cases of rather doubtful 

 value, an examination of the mass and brightness indicated 

 by the most careful measures of the distance may prove of 

 interest to the reader. 



We will take the stars in order of right ascension : — 



1. 1] Cassiopeife. — For this well-known binary star a 

 parallax of 3743" has been found by Schweizer and 

 Socoloff. Several orbits have been computed, none of which 

 are quite satisfactory, but assuming Griiber's jjeriod of 

 195'235 years, and semi-axis major of 8-639", I find 

 the mass of the system equal to 0-32 of the Sun's mass. 

 The star was measured 3-41 magnitude, with the photo- 

 meter at Oxford, and 3-64 at Harvard. \\'e may, therefore, 

 assume its magnitude at 3-.5. Taking the Sun's stellar 

 magnitude at — 25-5, I find that if placed at the distance 

 indicated by the above parallax the Sun would be reduced 

 to a star of magnitude 3-2, or only slightly brighter than 

 r; CassiopeiiE. As the companion is only 7i magnitude, 

 it will not appreciably affect the light of the star, and as 

 the spectrum is of the second or solar type, it should be 

 fairly comparable with the Sun. If the mass were equal 

 to that of the Sun, the parallax would be 0-256", and at 

 this distance the Sun would be reduced to a 4tli magnitude 

 .star. Struve found a parallax of 0-154". Its compara- 

 tively large proper motion of about 1-2" per annum would 

 indicate a comparative proximity to our system. 



2. 40 Eridani. — The binary companion of this triple 

 star is of about the 9th magnitude, and is probably 

 l>hysically connected with the bright star, as all three 

 have a common proper motion. A parallax of 0-223" has 

 been found by Professor Asaph Hall. This, combined with 

 the orbit computed for the binary pair by the present 

 writer, gives a mass equal to tlie Sun's mass — a result 

 which is remarkable, for the Sun, placed at the distance 

 indicated by the parallax, would shine as a star of 4-3 

 magnitude, or about the brightness of the principal star 



of 40 Eridani. This result implies that the Sun is about 

 70 times brighter than the binary pair. Owing to the 

 faintness of the binary star, the character of its spectrum 

 has not been determined. Computed by a well-known 

 formula, its " relative brightness " is very small, but only 

 one orbit has yet been computed, and this will require 

 revision when furthur measures are available. The proper 

 motion of the system is very large, about 4-1" per annum. 



3. Sirius. — The great brilliancy of this .star — the 

 brightest in the heavens — naturally suggests a sun of great 

 size. Recent investigations do not, however, favour this 

 idea. Assuming a parallax of 0-39" (about a mean of the 

 results found by Elkin and Gill) and the elements of the 

 orbit computed by the writer, the mass of the system would 

 be 3-114 times the mass of the Sun. Placed at the dis- 

 tance of Sirius the Sun would be reduced to a star of 3-1 

 magnitude. As Sirius is about one magnitude brighter 

 than the zero magnitude, it follows that it is about four 

 magnitudes, or about forty times brighter than the Sun 

 would be in the same position. Were it of the same 

 density and brightness as the Sun, the mass found above 

 would indicate that its diameter should be 1-4G8 the solar 

 diameter, and its brightness 2-1324 the solar brightness. 

 The spectrum is, however, of the first type, and the star is, 

 therefore, not comparable with the Sun in briUiancy. The 

 result would indicate that stars of the first, or Sirian type, 

 are intrinsically brighter than the Sun. " 



4. Castor. — Assuming a parallax of 0-198" found by 

 Johnson, and a period of 1001-21 years found by Doberck 

 (« = 7'43"), I find the sum of the masses of the components 

 of Castor only 0-052092 of the Sun's mass, a result which 

 would imply that the components are gaseous masses. 

 Johnson's parallax is, however, of doubtfiU value. Placed 

 at the distance indicated, the Sun would be reduced to a 

 star of 4-5 magnitude. The magnitude of Castor is about 

 1-55, so that it is (according to the assumed parallax) about 

 three magnitudes, or about sixteen times brighter than the 

 Sun would be in the same position. The spectrum is of 

 the first type, another example of the great brightness of 

 the stars of this type. According to a well-known formula, 

 the " relative brightness " of Castor is thu-ty-eight times 

 that of the binary star, t Ursie Majoris, taken as a standard. 

 The latter star has a spectrum of the second type. 



5 a. Centauri. This famous star, the nearest of all the 

 stars to the earth, as far as is at present known, forms an 

 object of especial interest, particularly as its spectrum 

 is, according to Professor Pickering, of the second or solar 

 type, although with some peculiarity. Combining Dr. 

 Gill's parallax of 0-76" with Dowuing's elements of the 

 orbit (P = 7C-222 years, (( = 17-33"), I find that the mass of 

 the system is 2-04 times the mass of the Sun. Placed at 

 the distance of a Centauri the Sun would be reduced^o a 

 star of about 1-7 magnitude, or about one magnitude fainter 

 than the star appears to us. This would indicate that 

 a Centauri is about two and a half times brighter than the 

 Sim, and its mass (if of the same density) about four times 

 the solar mass. As, however, there is something peculiar 

 about the spectrum, the density and intrinsic brightness of 

 c. Centauri may be somewhat difi'erent fi-oin that of the Sun. 



6. 70 Ophiuchi. This is another star wliich is fairly 

 comparable with the Sun. as its spectrum is of the solar 

 type, according to Yogel. The orbit found by the present 

 writer (P=87-84 years, n = 4-50"), combined with Kriiger's 

 parallax of 0-102", gives for the combined mass of the com- 

 ponents 2-777 times the mass of the Sun. The star was 

 measured 4-11 magnitude with the photometer at Harvard 

 Observatory. Placed at the distance indicated by the 



* Or that they are of less density than our Sun. — A. C. Rantabd. 



