the largest member of the group and the farthest about 120" do not share, according to their discoverer, in the rapid proper motion of the two main stars.

In we find a double a little difficult for our three-inch. The

290°. Burnham found four other faint companions, for which it would be useless for us to look. The remarkable thing is that these faint stars, the nearest of which is distant about 50" from

MAP No. 10.

components are of magnitudes four and a half and ninth, distance 57", p. 110°. Burnham discovered that the ninth-magnitude star consists of two of the tenth less than 2" apart, p. 24°.

No astronomer who happens to be engaged in this part of the sky unless his attention is entirely absorbed by something of special interest, ever fails at least to glance at ẞ Libræ, which is famous as the only naked-eye star having a decided green color. The hue is pale, but manifest.*

The star is a remarkable variable, belonging to what is called the Algol type. Its period, according to Chandler, is 2 days, 7 hours, 51 minutes, 22'8 seconds. The time occupied by the actual changes is about twelve hours. At maximum the star is of magnitude five and at minimum of magnitude 6.2.

We may now conveniently turn northward from Virgo in order to explore Boötes, one of the most interesting of the constellations (map No. 11). Its leading star a, Arcturus, is the brightest in the northern hemisphere. Its precedence over its rivals Vega and Capella has been settled by the Harvard photometry. You notice that the color of Arcturus, when it has not risen far above the horizon, is a yellowish red, but when the star is near mid-heaven the color fades to yellow. The hue is possibly variable, for it is recorded that in 1852 Arcturus appeared to have nearly lost its color. If it should eventually turn white, the fact would have an important bearing upon the question whether Sirius was once a red or flame-colored star.

But let us sit here in the starlight, for the night is balmy, and talk about Arcturus, which is perhaps actually the greatest sun within the range of terrestrial vision. Its parallax is so minute that the consideration of the tremendous size of this star is a thing that the imagination can not placidly approach. Calculations, based on its assumed distance, which show that it outshines the sun several thousand times may be no exaggeration of the truth! It is easy to make such a calculation. Dr. Elkin's parallax for Arcturus is 0018". That is to say, the displacement of Arcturus due to the change in the observer's point of view when he looks at the star first from one side and then from the other side of the earth's orbit, 186,000,000 miles across, amounts to only eighteen one-thousands of a second of arc. We can appreciate how small that is when we know that it is about equal to the apparent distance between the heads of two pins placed an inch. apart and viewed from a distance of a hundred and eighty miles!

Assuming this estimate of the parallax of Arcturus, let us see how it will enable us to calculate the probable size or light-giv

* Has the slight green tint perceptible in Sirius deepened of late? I am sometimes disposed to think it has.

ing power of the star as compared with the sun. The first thing to do is to multiply the earth's distance from the sun, which may be taken at 93,000,000 miles, by 206,265, the number of seconds of arc in a radian, the base of circular measure, and then divide the product by the parallax of the star. Performing the multiplication and division, we get the following:

19,182,645,000,000
*018

The quotient represents miles!

= 1,065,790,250,000,000.

Call it, in round numbers, a thousand millions of millions of miles. This is about 11,400,000 times the distance from the earth to the sun.

Now for the second part of the calculation: The amount of light received on the earth from some of the brighter stars has been experimentally compared with the amount received from the sun. The results differ pretty widely, but in the case of Arcturus the ratio of the star's light to sunlight may be taken as about one twenty-five-thousand-millionth-i. e., 25,000,000,000 stars, each equal to Arcturus, would together shed upon the earth as much light as the sun does. But we know that light varies inversely as the square of the distance; for instance, if the sun was twice as far away as it is, its light would be diminished for us to a quarter of its present amount. Suppose, then, that we could remove the earth to a point midway between the sun and Arcturus, we should then be 5,700,000 times as far from the sun as we now are. In order to estimate how much light the sun would send us from that distance we must square the number 5,700,000 and then take the result inversely, or as a fraction. We thus get

1

representing the ratio of the sun's light at half 32,490,000,000,000, the distance of Arcturus to that at its real distance. But while receding from the sun we should be approaching Arcturus. We should get, in fact, twice as near to that star as we were before, and therefore its light would be increased for us fourfold. Now, if the amount of sunlight had not changed, it would exceed the light of Arcturus only a quarter as much as it did before, or in 25,000,000,000 the ratio of 4

= 6,250,000,000 to 1. But, as we have seen, the sunlight would diminish through increase of distance to one 32,490,000,000,000th part of its original amount. Hence its altered ratio to the light of Arcturus would become 6,250,000,000 to 32,490,000,000,000, or 1 to 5,198.

This means that if the earth were situated midway between the sun and Arcturus, it would receive 5,198 times as much light from that star as it would from the sun! It is quite probable, moreover, that the heat of Arcturus exceeds the solar heat in the same ratio, for the spectroscope shows that although Arcturus is

surrounded with a cloak of metallic vapors proportionately far more extensive than the sun's, yet, smothered as the great star

seems in some respects to be, it rivals Sirius itself in the intensity of its radiant energy.

If we suppose the radiation of Arcturus to be the same per unit of surface as the sun's, it follows that Arcturus exceeds the

sun about 375,000 times in volume, and that its diameter is no less than 62,350,000 miles! Imagine the earth and the other planets constituting the solar system removed to Arcturus and set revolving around it in orbits of the same forms and sizes as those in which they circle about the sun. Poor Mercury! For that little planet it would indeed be a jump from the frying pan into the fire, because, as it rushed to perihelion, Mercury would plunge more than 2,500,000 miles beneath the surface of the giant star. Venus and the earth would perhaps melt like snowflakes at the mouth of a furnace. Even far-away Neptune, the remotest member of the system, would be bathed in torrid heat.

But stop! Look at the sky. Observe how small and motionless the disks of the stars have become. Back to the telescopes at once, for this is a token that the atmosphere is steady, and that "good seeing" may be expected. It is fortunate, for we have some delicate work before us. The very first double star we try in Boötes, 1772, requires the use of the four-inch, and the fiveinch shows it more satisfactorily. The magnitudes are sixth and ninth, distance 5"; p. 140°. On the other side of Arcturus we find, a star that we should have had no great difficulty in separating thirty years ago, but which has now closed up beyond the reach even of our five-inch. The magnitudes are both fourth, and the distance about 0'5", p. 285°. It is apparently a binary, and if so will some time widen again, but its period is unknown. The star 279, also known as Σ 1910, near the southeastern edge of the constellation, is a pretty double, each component being of the seventh magnitude; distance 4"; p. 212°. Just above we come upon, an easy double for the three-inch, magnitudes fourth and sixth; distance 6"; p. 99°. Next is έ, a yellow and purple pair, whose magnitudes are respectively fifth and seventh; distance less than 3"; p. 231°. This is undoubtedly a binary with a period of revolution of about a hundred and thirty years. Its distance decreased about 1" between 1881 and 1891. It was still decreasing in 1894, when it had become 2'9". The orbital swing is also very apparent in the change of the position angle.

The telescopic gem of Boötes, and one of "the flowers of the sky," is e, also known as Mirac. When well seen, as we shall see it to-night, Boötis is superb. The magnitudes of its two component stars are two and a half (according to Hall, three) and six. The distance is about 2'8", p. 326°. The contrast of colors-bright orange yellow, matched with brilliant emerald green-is magnifi. cent. There are very few doubles that can be compared with it in this respect. The three-inch will separate it, but the five-inch enables us best to enjoy its beauty. It appears to be a binary, but the motion is very slow, and nothing certain is yet known of its period.