III. ON THE ORBIT OF THE BINARY STAR 35 COMÆ BERENICES = 1687. By J. E. GORE, M.R.I.A., [Read May 25, 1891.] The duplicity of the brighter component of this wide double star was discovered by Struve in the year 1829. The position angle was then about 250. Recent measures kindly made for me by Mr. Burnham, with the great 36-inch refractor of the Lick Observatory (U. S. A.) show that the position is now about 72o. Although the change of position angle is small I find that the motion has been round the apoastron end of the apparent ellipse, and that hence a considerable arc of the apparent orbit has been described. The change in the mean anomaly amounts, according to my calculations, to about 96-5o. I have computed the orbit by the following method :-Having plotted all the observations, and drawn the interpolating curve and the apparent ellipse in the usual way, I computed, by Professor Glasenapp's method (Monthly Notices, R. A. S., March, 1889), the values of the coefficients in the general equation of the second degree axt + By + yx2 + 8xy + cya + 1 = 0, and obtained the following results : a = - 0.01601, + 0·03089, -0.0002123, 8 = -0.000449, E = + 0.00035068. These values were then substituted in the following equations due to the late Polish astronomer, Marian Kowalski : tan’i sin 202 = 8 - jaß, From these equations the geometrical elements of the real orbit were computed. The remaining elements, P, the period, and T, the epoch of periastron passage, were computed by the formule mt + + M + M t – t M' - M where M and M' are the mean anomalies computed from the geometrical elements for the epochs t, and t', and the corresponding values of 0 derived from the earlier and later measures. The following are the resulting elements which must be considered as provisional until further measures are available : The position of the star is for 1890, .0, R. A. 12h 47m 53', The following is a comparison between the recorded measures and the positions computed from the above elements. The formulæ of computation are as follows: (1) 4 – 34:3776 sin d = + 1:576° (6 – 1815172), cos (0. – 27° 45')' where u is the eccentric anomaly, 7 the true anomaly for the time t, 0. the computed position angle, and po the distance. 1829.99 1833.37 1834.38 1842.39 1842.39 1843.32 1843.34 1845.31 1847.57 1848.12 1849.33 1851.00 1852.32 1853.38 1854.38 1854.41 1855:42 1856.39 1856.41 1856.48 1857-28 1857.45 1857.66 1858.12 1858.44 1860.34 1862-95 1863-31 1865-31 1866.94 1866-42 1868.32 1870.15 1871.33 1872-43 1873.24 1873.35 1873.41 1874.26 1874.30 1874.31 1874.34 1874.40 1875-30 1875-31 1875-31 1875-32 1875-39 1875.43 1876.30 1876.34 1876.36 1876.38 1877.00 1877.24 1877.34 1877.38 1881.842 1885.340 1885-423 1886.38 1887.340 1891.24 Dawes, Considering the faintness of the companion star the above comparison is fairly satisfactory. Assuming that the combined mass of the components is equal to the mass of the sun, we have the “hypothetical parallax." a 1.70 R.I.A. PROC., SER. III., VOL. II. ON THE DETERMINATION OF THE MELTING POINTS OF MINERALS. Part I. — THE USES OF THE MELDO- [Read May 11, 1891.] TAERE appears to have been no serious attempt made in recent times by mineralogists to effect the determination of the melting points of minerals, with a degree of accuracy in keeping with our present means of measuring high temperatures. Nor has there been any suggestion, to the best of my knowledge, as to the possibility of providing a simple and accurate means of observation. The present Paper is preliminary to one embodying the melting points of the more abundant mineral species, and is occupied with an account of a method of effecting such determinations which it is hoped possesses qualities of simplicity and accuracy. It will be seen that its use necessitates only the most minute quantities of the substance, and hence the method is applicable for dealing with rare mineral species or small quantities of chemically prepared bodies; other applications of the methods beside the determination of melting points are suggested in this paper. In meeting the expenses connected with the development of the apparatus, I have to acknowledge gratefully a grant made to me by the Royal Irish Academy. Melting points are constants in molecular physics of much theoretic interest. In many cases the naturally occurring mineral is the sole representative of a particular molecular grouping. The theoretic interest attached to the temperatures at which substances cease to retain the solid state is developed in the writings of Kopp, Carnelley, Van der Waal, Pictet, and others. In the case of minerals, in addition, questions of great geological interest are attached, more especially in connexion with the subject of ejected lavas or contemporaneous igneous rocks, into the temperature of which, at the time of ejection, the factor of great pressure did not enter. There remains the value |