directly behind the wheel, with a rectangular opening in it. The form of the opening in the diaphragm and in the teeth of the wheel are seen enlarged in a part of the wheel c', figure 18. As the wheel c revolves, the opening in the diaphragm is successively opened and closed with great rapidity. If it were to be permanently open, then the light from the lamp would fall upon the plane glass m, a portion would be transmitted and a portion reflected, which latter portion would pass through the lenses x and y, be reflected at n, return again, fall a second time upon m, and be transmitted to the eye at e. In this state of the apparatus the eye sees a bright point at the focus o. The bright point continues visible until the velocity of the wheel c is such that one of its teeth passes over the notch in the diaphragm and thus prevents the reflected light from coming to the eye. The bright point is then eclipsed. This will necessarily take place whenever the time occupied by the tooth in passing the space of the notch is the same as that required by light in going from o to n and returning.

When the velocity of the wheel becomes so great as to close and open the notch again while the light is going and coming, the bright point will reappear. As the rotary speed of the wheel increases, the point will be successively eclipsed. The rotary velocity of the wheel is registered by appropriate mechanism so as to mark with precision the number of turns to a second, while the number of teeth in the wheel will serve to determine the time in which one tooth passes the notch. The distance between the stations was 8,633 metres, equal to five and one-eighth miles nearly. The apparatus indicated the time of traversing the double distance, or ten and two-third miles, to be about or of a second, which makes the velocity of light very nearly the same as that given by the preceding methods. Physical science presents few more striking results than this of M. Fizeau.

From the near agreement of these three independent methods of determining the velocity of light we may safely conclude that the probable error is small. Light moves with the amazing velocity of 192,000 miles per second.

We shall now proceed to inquire into the distance of the fixed stars. And we may state, in the outset, that the only means of arriving at an indication of this is an annual change in the position of the star. But there are certain changes which are dependent upon known causes which must first be allowed for. These are refraction, aberration, and nutation. The refraction varies with the altitude of the star; aberration for any particular star depends on the season of the year; nutation, (another fine discovery of Dr. Bradley, in consequence of which the star describes a little ellipse about its mean place once in about nineteen years,) depends upon the position of the nodes of the moon's orbit. This inequality is due to the action of the moon upon. the spheroidal figure of the earth. The amount of these corrections is well known. Now, if there is any change in the position of a star over and above what is due to the above causes it must be referred either to its own proper motion or to the change of position of the earth in its orbit. But these two are not liable to be confounded the one with each other. The proper motion will be progressive from year to year in the same direction. Any change due to the motion of the

earth will necessarily be periodic and the star must return to the same place at the expiration of a year. A proper motion has been detected in many of the stars, amounting in some to 4" or 5" in a

year.

Any change due to the motion of the earth is called the annual parallax. The only means within the reach of astronomy of finding the distance is by means of this parallax.

An obvious proof that the stars are immensely distant is that, except under the severest possible scrutiny, they appear to hold the same relative places at all seasons of the year. Our change of position, involving a distance of nearly 200,000,000 of miles, dwindles down to nothing in comparison with the line which extends from the earth to the star.

In figure 19, let S be the sun, A E B the earth's orbit, and s a

star; then the angle A s S, or the angle subtended by the radius of the earth's orbit, as seen from the star, would be the annual parallax of the star. If this angle were so much as 1", it would follow that the distance of the star must be 206,265 times the distance of the sun. In that case light would require more than 3 years in coming from the star to us. But in no case is the parallax of a star so large as 1". As Biot has remarked, "an angle so large as 1" could not have escaped universal recognition.' What we are now entitled to say then is, that light from the nearest fixed star would require at least more than 3 years to reach our earth.

There is no presumption that the stars are all equally distant. On the contrary there is every probability that their distances are very unequal, and hence that some stars of the first order of intrinsic splendor appear faint from their vast distance. Huyghens, assuming that Sirius was equal in intrinsic brightness to our sun, concluded from a computation based upon the well known law that the intensity of light diminishes inversely as the square of the distance, that Sirius must be 28,000 times more distant than the sun; in other words that our sun at that distance would appear no brighter than Sirius does now. But this estimate of the distance, as we now know, is far too small. At only that distance the parallax would be four times as great as that of the nearest known star. Dr. Wollaston, by very ingenious photo

metric measurements, concluded that Sirius must be 140,000 times more distant than the sun. But even this is much within the true distance. But let us glance at the actual measurements which have enabled the astronomer, in some few cases at least, to sound the amazing depths of the heavens.

The star 7 Draconis, of Flamsteed's catalogue, has a very large proper motion, amounting to nearly 5" annually. Under the supposition that those stars which have the greatest proper motion are nearest to us, and therefore most favorable to researches on the parallax, this star was selected by Dr. Bradley for special observations, with a view to detect this element. It had also the great advantage of passing near the zenith of the Wansted observatory, by which the troublesome irregularities of refraction would be avoided. He failed to detect any parallax, but his labor was rewarded by the beautiful discovery of the aberration of light. Bradley depended upon finding a variation in the elements of right ascension and declination. But this is by no means the most delicate test which can be applied for the determination of a minute annual change in the position of the star.

Galileo was the first to suggest that where a large and a small star are very close together the smaller star might appear faint from being placed at a vastly greater distance than the larger. If this were not always the case, of which there is no probability, it would be likely to occur in some instances. Wherever this holds good the stars will undergo an annual change in their relative positions, either approaching and receding from each other, or the one revolving about the other. Thus, in figure 19, if we suppose s and s to be two stars situated in a right line from the sun and in the direction of the pole of the ecliptic, as the earth goes round in her orbit A E B the star s may appear to revolve round s', and it must do so if the radius of the earth's orbit. holds any assignable ratio to the distance of the nearer star. Thus, when the earth is at A, s will appear at a in the distant heavens; when the earth is at E the star will appear at e; the earth at B will carry the star to b; and hence while the earth goes round in the orbit A E B the star S will appear to go round s' in the curve a e b. No instance has been discovered where this idea has been fully realized. Nor indeed could any available results be obtained from it until a very late period, for the want of instruments fitted to measure so small. an angle as the largest annual parallax. The micrometer in its different forms supplies this want. The manner in which very minute angles are measured by this appendage to the telescope will be understood by a reference to figure 22, which is a rectangular frame with a fine screw at each end passing through the frame and attached to sliding pieces within it. These sliding pieces carry the spider lines a and b, which by turning the screws are made

Fig 22

a

to approach or separate from each other. Graduated circles are fixed to the heads of the screws. Suppose one complete revolution of the screw changes the position of the spider lines by 2' or

120", and let the circles be divided into 360 parts, then one division on the circle will correspond to one-third of a second between the spider lines. This apparatus, called the micrometer, is placed in or across the tube of the telescope near the eye piece. It is sometimes furnished with a slip of metal just below the spider lines, which marks the interval in seconds between them. The distance between two stars or the diameter of a planet is measured by adjusting the instrument so that the stars shall be bisected by the lines, or the disk of the planet will lie exactly between them. The turns and divisions of the screw which bring the lines together will give the angular distance sought in this case to the one-third of a second. Large telescopes fitted with micrometers are indispensable to researches upon the distances of the fixed stars. The value of one turn of the screw is fixed by directing the telescope to two well defined objects of a known angular distance apart.

Special researches upon this branch of astronomy have been made by Struvè, Bessel, Peters, Henderson, Maclean and Groombridge.

In 1835 Struvè, then of Dorpat, now of the Great Russian Observatory at Pulkowa, near St. Petersburg, commenced a series of observations on the bright star in the Lyre. This star has a very minute companion at the distance of 43". Struvè was able to detect an annual variation in this distance, from which he deduced the annual parallax of a Lyræ to be 0.261, from which it follows that light would be about fourteen years coming from that brilliant star to us. The light which it sheds upon us to-night started on its career fourteen years ago.

But the researches of Bessel in connexion with the star 61 Cygni, form an important epoch in the history of stellar astronomy. He was furnished with a magnificent heliometer, made by Frauenhofer, with a micrometer of the greatest delicacy. He brought to the research an array of instrumental means which no previous astronomer had been able to command. His consummate skill as an observer, in connexion with the exquisite instruments in his hand, enabled him to furnish results which have commanded universal confidence. His observations were commenced at Königsberg in 1835, and continued to 1840. His field of view is presented in figure 20, where S is the

Fig 20

double star 61, a and b are two minute stars, situated nearly at right angles from S, the former at the distance of 7', the latter at 11'; the middle of the two stars S was the point from which the distances of a and b were measured. From the configuration of the stars, if S approached a, it would, three months later, approach b; at the expiration of another three months it would have receded from a, and then after the same interval, from b. This, in fact, was the order of change which was observed. In other words, S revolved in a little orbit about its mean place. In

S

the discussion of his observations, on which, as Herschel remarks, "every imaginable cause of disturbance was taken into careful consideration and its effects rigorously calculated," he reached the conclusion that the parallax of 61 Cygni was 0".348.

From this we infer that light would reach us from this star in 91 years. This result of Bessel has received the most ample confirmation by Peters of Pulkowa, who, in a series of observations, made in 1842 and 1843, with consummate address in the use of every refinement which could insure accuracy, found the parallax of this same star to be 0.349, differing from the result of Bessel by only theo of a second. Such a coincidence between the results of different observers, with different instruments and in different places, cannot but inspire great confidence in the conclusion to which they have come.

The star a Centauri, the brightest star in the southern constellation, has been much observed with a view to its parallax; first by Henderson in 1832 and 1833, then by Maclean in 1839 and 1840, and again in 1848, both at the Cape of Good Hope. The mean of the results gives for the parallax of this star 0".915, which places it nearer to our system than any star whose parallax has been determined. And yet light would be nearly four years in coming from this our nearest stellar neighbor.

The parallaxes of the following stars have been proximately determined. I give them in a tabular form, with their parallax, the name of the observer, and the number of years required for light to come from the star to us :

The parallax bears no definite ratio to the magnitude of the star. The severest scrutiny of the bright star a Cygni, by the powerful instruments of Peters, shows absolutely no indication of any measurable parallax.

We can now give at least a partial answer to the question, how far off are the stars? An infant is born, and at the same time a beam of light starts from the bright star in the Swan on its way to our distant world. The child passes through the slow-recurring stages of life, reaches manhood and old age, and lingers his full century and dies; and the light has not yet reached us! Such is the distance which we vainly try to contemplate.