second to every sq. cm. on the earth which is exposed normally to its rays. To measure this quantity, the energy is absorbed by a blackened surface and thus converted into heat, which is measured directly by a rise of temperature in water or some other body, or else compared to an equal emission of heat from a source of known output. The great problem in the measurement of the solar constant was to correct for the absorption in the atmosphere. This was done by Langley and Abbot, who have compared readings on the surface of the earth with readings on the tops of high mountains. The final value obtained for the constant is .033 calories per sq. cm. per second, or .033 x 4.2 x 10' ergs per sq. cm. per second.

We have now all the material to hand for calculating the effective temperature of the sun. We do not say the actual temperature of the sun, because there may be considerable variation in temperature throughout the sun's mass. The solar disc, however, radiates energy, and when we speak of the effective temperature of the sun, we mean the temperature of a full radiator which, if placed in the position of the sun, would radiate just the same amount of energy that is given out by the real sun.

METHOD 1. USING THE DISPLACEMENT LAW.

Langley and Abbot have measured the distribution of the energy throughout the solar spectrum very carefully and found that the waves of wave-length about .490 micron carry the maximum amount of energy.

interior of a sphere whose equator is the orbit of the earth. Therefore, area of sun's surface X aT area of the given sphere X solar constant.

METHOD 3. USING THE THEORY OF EXCHANGES.

Let us assume that the sun and the earth are full radiators, that the temperature of the crust of the earth is nearly the same all over the earth, and the loss of heat from the earth by radiation equals that gained from the sun by radiation. These assumptions are very nearly true; even if not true, the errors involved are small.

What is the ratio of the size of the disc of the sun to the whole area of the celestial sphere?

The angular semi-diameter of the sun is approximately 16' 1", which is

Therefore the fraction of area of celestial sphere occupied by dise of sun

Now, imagine the celestial sphere to be coated with solar discs. The number required would be 184,300, and the earth at the centre of such a sun-lit sky would receive 184,300 times as much radiation as it does at present. The earth would then be in a 'fully-radiating' enclosure and the temperature would rise until it became equal to that of the sun. When this was attained, the earth would be radiating 184,300 times as much radiation as it is at present. But the amount of radiation from a body is proportional to the fourth power of the absolute temperature of the body.

Hence, taking the average temperature of the crust of the earth as 290° absolute, we see that, if T is the temperature of the sun,

A slight correction may be made to this, but it is hardly worth while bothering about it.

We have thus deduced the effective temperature of the sun by three methods and the three results agree fairly well. We may therefore conclude that the effective temperature of the sun is in the neighborhood of 5900 or 6000 degrees absolute.

We might have reversed the arithmetic in the last method quoted above, and, having assumed the temperature of the sun, deduced the temperature of the earth. We should have got somewhere near 290° absolute. Making like assumptions for the other planets, we could work out their temperatures in much the same way. This has been done by the late Professor Poynting, who arrives at the following temperatures: Mercury, 467°A; Venus, 342°A; Mars, 235°A. It is interesting to note that the average temperature of Mars' crust is nearly 40° C. below the freezing point of water. In the same way the effective temperature of space has been found to be 7° C. above the absolute zero.

In 1899, Professor Callendar, in a lecture to the Royal Institution on the temperature of the sun, quoted some of the results obtained by early workers on this subject. Dulong and Petit, in 1817, from a knowledge of the rate of cooling of a body in vacuo, deduced 1900° C. Rosetti, in 1878, using a radiation formula of his own, deduced 12,700° C. Bottomley in 1888 and Paschen in 1893, using a radiation law involving a power of temperature higher than the fourth, both deduced 4000° C. Early workers, using the fourth power law, obtained 6900°, and as late as 1897, Wilson and Gray, from results of experiments with a radiomicrometer, and using heated platinum as a comparison object, deduced 6900°. But we may safely conclude that the results given by the three methods outlined above are much nearer the mark.

UNIVERSITY OF TORONTO.

THE SPECTROSCOPIC BINARY 12 LACERTAE

BY REYNOLD K. YOUNG

TWELVE Lacertae belongs to the same class of binaries as B Cephei, o Scorpii and ẞ Canis Majoris. These stars are similar in having very short periods (41⁄2 to 6 hrs.). All of them are probably variable and their radial velocity curves, without exception, present peculiarities. An orbit for 12 Lacertae has already been published by the writer in the publications of the Dominion Observatory, Volume 3, No. 3. This work was based on measures of 117 plates taken at Ottawa with the one-prism spectrograph of that observatory. The fact that the period proved to be only four times the time required to obtain a single spectrum made the investigation of the details of the behavior of the star's light extremely difficult. Nevertheless the observations did bring out several points of interest and indicated that it would be worth while to pursue the investigations further when an instrument for which the exposure time was shorter was available.

The one-prism spectrograph attached to the 72-inch reflecting telescope will secure a good spectrum of 12 Lacertae, under normal exposing conditions, in five minutes. In the following work, the slit has been set narrower and the spectrum made wider than usual. Ten minutes under these conditions give a strong spectrum extending into the violet well beyond K. Twenty-five to thirty spectrograms can therefore be secured during one revolution of the star. We have secured two series of plates covering a complete period, one series taken August 27 and a second series taken September 2. Plates were taken on three other nights near the times of predicted maxima or minima. These data are given below in Table I.

'See this JOURNAL, September, 1916.

In the third column of the table, the phases are counted from Julian Day 2421833.0. The fourth column gives the velocities. obtained from all the spectral lines, exclusive of the lines H and K of Calcium. The results from the latter lines are found in the fifth column. As a rule, the K line alone was measurable. The sixth column gives the sum of the widths of eight of the principal lines, the unit being 1/200th mm.

A general idea of the precision of the measures may be obtained from an inspection of the radial velocity curves for August