27 and September 2 (Fig. 1). The points indicated in these curves are normal places, each formed from two to three individual measures. The probable error of a single observatión, as determined graphically, was 1.9 km. for August 27 and 3.2 km. for September 2.

+10

- 10

20

Period. The period previously published rested on observations taken during the years 1913, 1914, 1915, and a few plates taken at the Mt. Wilson Observatory in 1911. Since then, Professor Frost, Director of the Yerkes Observatory, has communicated three additional velocities, of which the earliest was taken in 1908. The last plates here were made over ten years later, so that from the date of the first observation made at the Yerkes Observatory to the date of the last observation here, the star has made more than 19,000 revolutions. There are no indica

tions that the old period should be altered unless it were to add a cipher. The period .1930890 day seems quite satisfactory. Radial velocity curves made on different nights show that the amplitude and shape of the curve vary. It is difficult in a star of this nature to be sure that the correct number of cycles have been assumed to have taken place between individual observations separated by long intervals. It seems unlikely that a mistake has been made, for observations in eight out of ten consecutive years agree reasonably well with the mean curve.

The variation in the amplitude of the orbit, as well as in the shape of the radial velocity curve, is shown by the observations of August 27 and September 2 as plotted in Fig. I. These observations yield the following elements:

The two sets of elements differ in the eccentricity and in the amplitude only, for the agreement of the values of y is well within the probable error and the two values for the time of periastion passage are identical. The observations made on September 11, 13 and October 19 furnish further proof that the velocity of the centre of mass for all the measures made during 1918 has been constant. They show also that maximum and minimum velocity occur on schedule time. While there is some uncertainty in drawing a curve through observations when maximum and minimum are the only points given, especially those taken September 13, there can be no doubt that the amplitude varies between wide limits, probably from fifteen or twenty kilometers to seventy or

more.

The behavior of 12 Lacertae in this respect recalls that of the spectroscopic binary B Canis Majoris. The orbit of this star has been very carefully investigated by Mr. Henroteau. In

Lick Observatory Bulletin, 9, p. 155.

B Canis Majoris not only does the amplitude vary, but a simple period fails to predict the maximum and minimum points. Mr. Henroteau gives a very ingenious explanation to account for the observations. He supposes "two sinusoidal or periodic variations of approximately the same constant amplitude and very nearly the same period exist." Their combination gives a curve of variable amplitude with a constant value for the velocity of the system. When the two variations reinforce each other, i.e., when they are in like phase, then we get a large observed range. The fact that the two variations have unlike periods will soon alter this agreement in phase, and when the phases differ by 180°, then we observe small amplitudes.

In the case of B Canis Majoris there was evidence of the existence of this second period in the variation in the width of the lanes. In 1915 the writer suspected that the lines in the spectrum of 12 Lacertae altered their character at times, but the long exposures and the poor quality of many of the plates prevented this point being investigated. The present series of plates show that not only do the lines become diffuse, but, like the lines in the spectrum of B Canis Majoris, they become wider. Figures 5 and 6 are plots of the measured widths of the lines in the plates taken August 27 and September 2. They show that in these two cases minimum width agrees almost exactly with periastron passage. In this respect the spectrum of 12 Lacertae parallels that of Scorpii, another binary of very short period. A further inspection of the plates shows that when the range is small the lines are fairly wide and always rather diffuse. There is, however, no evidence as yet that the variation in the width and definition of the lines has a period different from that of the velocity variation. although it is possible that such is the case. The evidence is not conclusive on this point.

There are other complications in the measures of 12 Lacertae not yet recorded. If we compare the elements as derived from the 1918 plates with those published in 1915, we find that the velocity of the centre of mass seems to have shifted from 13.7 km. to nearly 20 km. In order to investigate this point more fully and

make sure it was real, the observations taken in 1913, 1914, 1915, 1918 were examined separately. First, the straight algebraic means were taken. If the observations were distributed at random, this would give the value of y. Second, the observations were divided for each year into two parts. The first part comprising all those observations with phases where the binary was approaching us, and the second those observations with phase where it was receding. The means of these were taken separately, and then the mean of the two values should give a value for y. This procedure eliminates an error which would be present in the first method from more observations lying below the axis than above or vice versa. Third, means were taken of a number of observations with phases centered around the maximum and minimum points of the radial velocity curves. This is probably the best procedure when, as in the present case, the eccentricity is small and nearly ninety degrees. The result is shown in the following table.

The center of mass of the binary system 12 Lacertae is approaching the observer at a variable rate. The period suggested is many years. There is a distant companion 72" away, twelfth magnitude. It would hardly appear that this could be concerned in the phenomenon, as in the past century the relative motion has been very small.

Calcium Lines. Since the discovery of the existence of binary stars in which the H and K lines did not share in the variation of the other lines, there has been considerable investigation to find out whether the calcium causing the absorption was surrounding the star as part of its atmosphere or whether it was in the form of a cloud lying between the observer and the star under observation.

The observations of 12 Lacertae, 1918, agree with those taken