while their recess from the pole would be comparatively slight. To render this reasoning still plainer, imagine this room to be pierced on every side, so that an eye placed at the centre could see every star in the heavens through the openings. Through each of these holes conceive iron rods to pass, all meeting at a point in the centre, and all directed exactly to the stars. On the outside let golden balls be fixed to the extremities of these rods, to represent the stars. Now, grasping the extremities of all these rods in the hand, urge the point where they all unite towards the north pole, and watch the movement of the balls at the outer extremities of the rods. The ball corresponding to the north star will scarcely seem to move, because the eye travels directly towards it. The balls corresponding to the stars on the equator, having their rods perpendicular to the direction of the motion of the central point, will sweep swiftly towards the south. The idea once gained, there is no difficulty in its application.

The visual rays drawn to the stars correspond to the rods, and these rays, meeting in the eye of the observer, are carried forward by the sun in its progression through space. I have supposed the system to move due north; but in case the motion be assumed in any other direction, it is easy to compute the changes consequent. Understanding these preliminary statements, we are prepared to follow Argelander in his investigation.

The five hundred stars selected for examination were divided into three groups, according to the amount of annual proper motion. The first contained only such stars as were seen to move with a velocity not less than one second of space in a year. Although this motion may appear excessively slow, yet its direction in one hundred years may be determined with very great precision. A general examination of the direction in which the stars of this first group appeared to move, indicated the quarter of the heavens towards which the solar system must be progressing; and now commenced the investigation, having for its object the discovery of the exact point. To accomplish this, a point was assumed, and on the hypothesis that it was correctly chosen, the directions of the motion of all the stars composing the first group were computed, and the angles formed by their lines of direction with the meridian were determined.

If the motion of these stars was the effect of systematic parallax, and if the direction of the solar movement had been

accurately chosen, then would the computed angles of direction agree exactly, in every instance, with the observed angles of direction. The comparison of these angles having been made, it was easy to see the discrepancies; and by shifting the assumed point, these differences could be reduced to their minimum value. The point which gave the smallest differences between the observed and computed angles would be the one towards which the solar system was progressing. Such was the reasoning of Argelander, and such the train of investigation on which he relied for the resolution of this great problem.

Having closed his examinations based on the group of stars with the most rapid motion, and having found the point in the heavens which corresponded to their motions, he proceeded to execute his calculations with reference to his second group. The stars of this group moved annually an amount greater than half a second of space, and less than one second. The result was again reached, and the direction of the solar motion thus derived agreed, in a remarkable manner, with that obtained from the first group. A further confirmation was obtained by executing the calculation founded on the motions of the third and last group into which he had divided his five hundred stars. The final result settled, probably for ever, the grand fact that the sun, with its entire cometary and planetary system, is sweeping through space towards a point whose place must fall somewhere within the circumference of a circle whose diameter is about equal to four times that of the moon.

The reality of the solar motion once determined, astronomers have not been wanting to verify and extend this wonderful examination. Argelander's results have been confirmed by the investigations of M. Otho Struve, the son of the distinguished director of the Imperial Observatory of Pulkova; and if, on any fair night, you direct your eye to the constellation of Hercules, and select from its stars the two marked on the globe with the Greek letters and μ, on the line joining these stars, and at a distance from T equal to one-quarter of the distance which divides the stars, will be found the point towards which the sun was directing his course in the year 1840.

Having obtained the direction of the solar motion, we proceed to investigate its actual velocity. How swiftly does the sun, with its retinue of worlds, sweep onward through space? It will not be possible to present here even an outline of the reasoning

of Struve in the resolution of this intricate question.

Two

points are involved. The determination of the annual angular motion of the sun, as it would be seen by a spectator situated at a distance equal to that of the stars of the first magnitude. This being determined, the angular motion can readily be converted into linear velocity, in case the mean distance of the stars of the first magnitude can be satisfactorily obtained After an elaborate inves

tigation, guarded by every care, and open, as it would appear, to no well-founded objections, M. Otho Struve has finally resolved the first of these wonderful questions. It is curious to see how nearly the results agree, which were obtained from data entirely different, and in no way dependent on each other.

By an examination based on observed right ascensions of the stars, he finds that the space passed over by the sun in its progressive movement through the heavens, seen from the mean

M. Otho Struve.

distance of stars of the first magnitude, is 321-thousandths of a second of arc. The result obtained from observed declinations gave for the same quantity 357-thousandths of one second of

arc.

Here is a difference amounting to only 36-thousandths of a second, a quantity exceedingly small, when we consider the extraordinary difficulty of the investigation.

Let us now convert these numbers into intelligible quantities. In case the sun be supposed to be revolving about some mighty centre, at a distance equal to the mean distance of stars of the first magnitude, the period necessary to accomplish its stupendous revolution will be 3,811,000 years!

Vast as this period appears, we shall see hereafter that we have no right to suppose that the centre about which the solar system is revolving, can be located at a distance nearly so small

P

as the mean distance of the larger stars. But what is the actual velocity? How many miles does this mighty assemblage of flying worlds accomplish in its unknown journey in every year? This is the last question, and even this has not escaped the successful examinations of the human mind. The discovery of the parallax of one or two fixed stars has already been referred to. Within a few months an elaborate work, by Struve, on the Sidereal Heavens, has reached us, containing some remarkable investigations on the mean distances of the stars of the various magnitudes.

Struve, by a most ingenious and powerful train of investigation, obtains a series representing the relative mean distances of the stars of all magnitudes, up to the most minute visible in Herschel's twenty-feet reflector. From the sun, as a centre, he sweeps successive concentric spheres, between whose surfaces he conceives the stars of the several magnitudes to be included. The radius of the first sphere reaches to the nearest stars of the first magnitude; that of the second sphere extends to the farthest stars of the same magnitude; and the mean of these two radii will be the mean distance of the stars of the first magnitude. The same is true with reference to the concentric spheres embracing within their surfaces the stars of the various orders of brightness.

Having, from his data, computed a table exhibiting the relative distances of the stars of the different magnitudes, an examination of these figures revealed the singular fact that they constituted a regular geometrical progression; and having assumed the distance of the stars of the sixth magnitude as the unit, the distance of the stars of the fourth magnitude will be one half; that of those of the second magnitude will be one quarter, and so of the even numbers expressing magnitude; while the distance of the stars of the fifth magnitude is obtained by dividing unity by the square root of the number 2, and from this the distances of the odd magnitudes come by dividing constantly by 2. In mathematical language, the distances of the stars of the various magnitudes form a geometrical progression whose ratio is equal to unity divided by the square root of 2.

Having thus obtained the relative mean distances of the stars, in case we can find the absolute mean distance of those of any one class, that will reveal to us the absolute mean distances of the stars of every class. For the approximate accomplishment

of this last great object, we are again indebted to the astronomers of Russia. As early as 1808, M. Struve, then of Dorpat, attempted the determination of the parallax of a large number of stars, and obtained results so small that, in the state of astronomical science as it then existed, no confidence could be placed in them. The final value of the numerical co-efficient of the aberration of light had not been then absolutely determined. Subsequent investigations by Struve and Peters have fixed this quantity, and the actual determination of the parallax of eight stars recently, has shown that confidence may now be placed in the results obtained by Struve nearly twenty-five years ago.

By combining all the results, M. Peters finds no less than thirty-five stars whose parallaxes have now been determined, either absolute or relative, with a degree of accuracy which warrants their employment in investigating the problem of the mean parallax of stars of the second magnitude. Excluding from this number the stars 61 Cygni, and No. 1830 of the Grombridge catalogue, on account of their great proper motion, there remained thirty-three stars to be employed in the investigation.

From a full and intricate examination of all the data, by a process of reasoning which I will not attempt to explain at this time, M. Peters finds the mean parallax of stars of the second magnitude to be equal to 116-thousandths of one second of arc, with a probable error less than a tenth part of this quantity. Returning now, with this absolute result, to the table of the relative distances of the fixed stars of different magnitudes, it is easy to fix their absolute distances, as far as confidence can be placed in this first approximation. We find the stars of the first magnitude to be located between the surface of two spheres, whose radii are respectively 986,000 times the radius of the earth's orbit, and 1,246,000 times the same unit. We will express the distance in terms of the velocity of light, as no numbers can convey any intelligible idea. Stars of the first magnitude send us their light in about seventeen years; those of the second magnitude in about thirty years; stars of the third magnitude send their light in about forty-five years; those of the fourth magnitude in sixty-five years; those of the fifth in ninety years; those of the sixth magnitude, the most remote visible to the naked eye, send us their light after a journey through space of one hundred and thirty years! while the distance of the