SOME RESULTS OF STUDIES ON ECLIPSING VARIABLES by S. PIOTROWSKI, Warsaw The present communication deals with certain results of studies on eclipsing variables conducted in the Warsaw Observatory. In the years 1947-48 I worked out^1 an analytical method of determining the intermediary orbit of an eclipsing system. It is characteristic for this method that from the first beginning we apply the fundamental equation of the problem to individual normal points and we do not use the free-hand curve at all. It is because of the mentioned character of the method that we are able to weight in a rational way individual equations and we obtain the elements of the system with their mean errors using the least squares algorithm. In this way we get from the outset an insight into the determinacy of the problem; moreover we can judge whether the degree of approximation is sufficient for applying the - rather laborious - method of differential corrections. The method I am speaking of was applied several times by different authors - most often in the form and with modifications given by Z. Kopal in his monograph "The Computation of Elements of Eclipsing Binary Systems"^2. In the last months we applied in Warsaw this method - together with the method of differential corrections in the final stage - to the eclipsing system WW Aur. Our results must be still regarded as preliminary. The observational material consisted of photoelectric observations in two colours executed with the photometer with the 1P21 cell of the Cracow Observatory. The observations were executed by myself and my collaborators (in the first place A. Strzalkowski) in Cracow; the reductions and computations were performed in Warsaw by K. Serkowski and B. Jun. We had at our disposal more than 1500 sets obtained in the years 1948-51 during 33 evenings. Each set consists of 4 readings of the galvanometer on the variable star (2 through the yellow filter and 2 through the violet one) plus 4 analogical readings on the comparison star plus galvanometer readings of the dark current and of the sky background (in yellow and violet). There is a certain pecularity in the manner in which the individual sets were grouped into "supersets" called observations. We had namely divided the light curve in equal intervals of 0.004p (it is nearly 0.01d) and from all sets (on the average 3) from the same night falling in the given interval one observation was formed. Nearly 500 observations in each colour were obtained - and these observations will be published.^3 Observations from different nights and pertaining to the same phase-interval were afterwards grouped into normal points. Outside eclipses the intervals were taken of course greater. The light curve shows two minima of nearly equal depth (about 0.7m); there is a small ellipticity (the coefficient of cos^2 theta in light units being 0.014) and no observable reflection. Though both components are of the same spectral type (A7) variations of colour index are clearly visible in the primary minimum: the star is growing redder at mid-eclipse by about 0.05m; no variations are detectable in the secondary minimum. There is one interesting feature of the curve of colour variations: just after the beginning and just before the end of the primary minimum the star is bluer than outside eclipses. It is worth-while noticing that the same is true for the system U Oph according to photoelectric observations of N. L. Magalashvili.^4 Fig. 1. WW Aur. The light curve in primary minimum Few years ago the light variations of WW Aur were observed photoelectrically (but without filters) by C. M. Huffer and the elements of the system were determined by Z. Kopal.^5 It is recomforting to see that the system of elements determined by Kopal differs but little from our system, though the observational evidence on which the computations of American authors are basing is in one respect essentially different from Warsaw data. The point is that Kopal used when determining the elements the ratio of brightnesses of both components obtained by R. M. Petrie^6 from spectroscopic observations. Our analysis of Petrie's determination convinced us that his value of L_a/L_b is not reliable and thus in Warsaw we have used only our own photometric data. Though the rejection of spectroscopic observations considerably diminished the determinacy of the problem (one may notice that Kopal had from the first beginning a practically fixed value for L_a/L_b - and in consequence, for k) our results concerning the geometric elements of the system agree rather well with those of Huffer and Kopal (the greatest difference is of course in k). Perhaps the most valuable result of our computations is the relatively well determined value of the difference of limb darkening coefficient in the violet and yellow light (approx. 4200 A and 5300 A). The assumed, starting value of this coefficient, common for both components and both colours was 0.6; the difference came out 1/2 Delta u = 0.09+-0.03, the star discs being more darkened in violet light. Fig. 2. WW Aur. The curve of colour variations In the end of my communication I would like to point at one fact concerning not the system WW Aur itself but the algorithm employed. The values of the elements obtained during the intermediary orbit determination and these computed by the method of differential corrections agree satisfactorily; the same is not true for mean errors obtained in both stages of computation. I know from private communications (in particular from Z. Kopal) that the same fact was noticed by other computers. So this point needs an elucidation. Budapest, August 1956. 1 Ap. J., 106, 472; 108, 36; 108, 510. 2 Harvard Observatory Monographs No. 8, 1950. 3 Acta Astronomica, Vol 6 (in press). 4 Abastumani Bull., 10, 21, Table VI, 1947. 5 Ap. J., 114, 297, 1951. 6 Publ. Dom. Ap. Obs. Victoria, 7, 205, 1939.