made about 2.2 hours after primary minimum, which, according to Stewart's orbit*, would be about an hour after the total phase so that, although it would receive most of the light from the fainter component, about one-fifth would come from the brighter. This spectrum has much the same character as the others, except that the lines are much weaker, and thus is in agreement with the above hypothesis. Further an additional plate was obtained on July 30 on Seed 23 emulsion and the finer grain enables the second spectrum to be more readily and certainly measured. On this plate the enhanced line 4549 is plainly doubled, the intensity of the second spectrum being relatively much stronger than in the other lines. Further the silicon pair 4128, 4131 show fairly strong companions, while the second spectrum in the hydrogen and helium lines is very weak. This would make it appear as if the faint diffuse companion were of Type B9 with relatively weak hydrogen and helium lines, while the bright dense star is B8 or even earlier. The relative intensities of the doubled lines 4549, 4131, 4128 in this spectrum are more nearly equal, being only about one-half as compared with one-fourth for the hydrogen and helium lines. Altogether eleven lines have been measured in the primary spectrum, Hy, H8; He 4472, 4388, 4144, 4121, 4026; Fe-Ti 4549; Mg 4481; C 4267; Ca, K 3934, and in the fine grained plate, Si 4128, 4131. The lines are of only fair quality for measurement, although much better defined than in U Ophiuchi, but the measures nevertheless are satisfactorily accordant, the probable error of measures of the primary spectrum on a plate being only ±1.8 km. per second. In the table of observations given below, column 1 contains the plate number, columns 2, 3 date and Julian date of the observation and column 4 the phase from primary minimum computed from the original phase 2,419, 652.963 with a period of 4.477325 days from Stewart's photometric orbitt. Columns 5, 6 contain the velocities of the primary and secondary stars and columns 8, 9 the residuals, in the sense observed minus computed, from the final orbit. Column 7 contains the number of lines measured in the primary and where a second figure is present the number in the secondary spectrum. *Astrophysical Journal, 42, 315, 1915. *Astrophysical Journal, 42, p. 315, 1915. When these velocities and phases were plotted on cross section paper it was at once seen that the orbit was not circular. The photometric orbit does not show eccentricity, but this element can only rarely be accurately obtained from the light curve. Preliminary elements obtained graphically were assumed as follows: e eccentricity K half-amplitude velocity y velocity of system w longitude of apse T time of periastron 0.05 240° 1.903 days from minimum. An ephemeris and observation equations calculated by means of Lehman-Filhés differential coefficients were computed for applying least squares corrections to e, K, y and w. Owing to the smallness of the eccentricity it was considered useless to apply corrections for both wand T and the latter was considered fixed. From this least square solution we obtain the following corrected elements: The probable error of a single plate for the bright star is ±1.8 km. and for the faint ±8.1 km. per second. A graph of the orbit with the observations of the principal spectrum represented by circles is shown in Fig. 2. Applying the above values we obtain by the well-known for mulae a sin i=3,388,000 km. a2 sin i=10,842,000 km. Stewart's photometric orbit* gives two solutions, a uniform and a darkened. The uniform gives a value of the inclination 69° 45', radius brighter star .090, radius fainter star .450, while the darkened solution gives 68° 25', .0932, .460 for these three quantities. The dimensions, masses and densities in the orbit follow. For comparison the dimensions from Shapley's darkened orbitt are also given and it appears that further photometric work on this star is desirable. If we assume the surface intensity of a B8 star to be -2.2‡ magnitudes and the sun's absolute magnitude to be 4.86 the absolute magnitude of the brighter component of RS Vulpeculae, with apparent magnitude 7.75, is +1.09 and the parallax is 0.0046. TW Draconis. The eclipsing variable TW Draconis (a,15h 32.4m, d,+64° 14′, 1900, Vis. Mag. 7.45; Spectral Type B9) was first observed on April 13, 1919, and the last plate obtained on July 17. During this interval fourteen plates were obtained, all of which are used in the orbit. They are not so well distributed as in RS Vulpeculae owing to the depth of primary minimum, when the star falls to *Astrophysical Journal, 42, 315, 1915. †Contributions from Princeton Observatory, No. 3, p. 90. Astrophysical Journal, 40, 415, 1914. 9.8 magnitude, making it impracticable to obtain plates at this epoch. The comparative faintness of the secondary, its light being 0.115 of the system, of course renders its spectrum unobservable. The spectrum classed as B9 is in reality A3 judging by the relative strength of hydrogen and K and the number and intensity of the metallic lines, and in consequence should be capable of accurate measurement. Although the interagreement among the lines is fairly good, the velocities of the plates are disappointing, the residuals unexpectedly high, resulting in a plate error of ±2.6 km per second. This is probably due to the rather. wide and diffuse character of the metallic lines, making the settings uncertain. That the lines are wide should not be a cause for surprise when we consider the nearness of the two bodies and the probable rapid rotation of the bright body in the period of the system. The data of the observations are given in Table III where column 1 contains the number of the plate, columns 2 and 3 the date and Julian date of the observation. Column 4 contains the phase from primary minimum computed from initial photometric phase 2,418,906.453 with period 2.80654 days, and column 5 the velocity determined from measures of the number of lines in column 6. Column 7 contains the residuals in the sense observed minus computed from the final orbit. TABLE III-OBSERVATIONS OF TW DRACONIS. When these observations were plotted it was at once seen that by making the orbit slightly eccentric better agreement could be obtained than with a circular orbit. Although no eccentricity is given by Shapley's orbit,* it is probable that Nijland's observations are *Contributions from Princeton Observatory, No. 3, p. 90. not of sufficient accuracy to determine this and alternative solutions for eccentric and circular orbits gave considerably lower residuals for the former. Preliminary elements which were obtained graphically are as follows: Owing to the smallness of the eccentricity it was considered useless to apply least square corrections to both T and w and, in this case, as the latter seemed better determined by the graphical elements, a correction for T was used. The result of the least square solution gives for corrected elements: This function of the masses, all that can be determined when the second spectrum can not be seen, does not give us information in regard to the dimensions or masses of the system. From the photometric orbit we obtain the diameters of the individual stars in terms of the relative orbit, but the latter can not be known without the ratio of the masses. As a first approximation Shapley assumed the masses equal and later used an empirical formula* for determining the masses of the components. This formula, based on the relative light of the two bodies, has its constants determined from spectroscopic binaries in which both spectra show and the ratio of the masses are known. Using this formula μ-0.4+1.2Lь the ratio comes as brighter star 0.73, fainter star 0.27 total mass. If we use RS Vulpeculæ as an analogy where the system is somewhat similar, a dense bright small primary with a tenuous, large *Contributions from the Princeton Observatory, No. 3, p. 123. |