admit, that one with another the stars are of a certain physical generic size and brightness, still allowing that all such deviations may exist, as generally take place among individuals belonging to the same species.

With regard to size, or diameter, we are, perhaps, more liable to error; but the extensive catalogue which has already been consulted, contains not less than 14,144 stars of the seven magnitudes that have been adverted to; it may therefore be presumed that any star promiscuously chosen for an experiment, out of such a number, is not likely to dif fer much from a certain mean size of them all.

At all events it will be certain that those stars, the light of which we can experimentally prove to be 1, J., 32, 3, and, of the light of any certain star of the first magnitude, must be 2, 3, 4, 5, 6, and 7 times as far from us as the standard star, provided the condition of the stars should come up to the supposed mean state of diameter and lustre of the standard star, and of this, when many equalizations are made, there is at least a great probability in his favour.

Of various experiments I have long ago tried, the equalization of star-light, which about four years ago I began to put into execution, appeared to be the most practicable.

Of ten highly finished mirrors I selected two of an equal diameter, and focal length, and placed them in two simi larly fitted-up seven feet telescopes. When they were com pletely adjusted, I directed them both, with a magnifying power of 118, to the same star, for instance, Arcturus: and upon trial I found the light not only of this, but of every other star to which they were directed, perfectly equal in both telescopes.

In comparing the light of one star with that of another, I laid it down as a principle, that no estimation but that of perfect equality should be admitted; and as the equal action of the instruments was now ascertained, I calculated the diameters of several apertures to be given to one of the telescopes as a standard, so that the other, called the equalizing telescope, might be employed, with all its aperture unconfined, to examine a variety of stars, til! one of them was found whose light was equal to that of the star to which the standard telescope was directed *.

This method of equalizing the light of the stars, easy as it may appear, is nevertheless subject to great difficulties; for

* Dr. Herschel preferred the limitation of the light by circular apertures to the method of obtaining it by the approach or recess of two opposite rectangular plates, in order to avoid the inflections which take place in the angles.

as the brightness of a star is affected by its situation, with regard to the ambient light of the heavens, the stars to be equalized should, if possible, be in nearly the same region. When the sun is deep in the horizon, this is, however, not of so much consequence as the altitude of the star to be equalized, which ought to be, as nearly as possible, equal to that of the standard star. At great elevations some difference in the altitudes of the stars to be equalized may be admitted; but if they are far from each other, the circumstance of the equal illumination of the heavens, and the equal clearness of the air must still be attended to.

Of the Extent of Natural Vision.

281. The following equalizations were made in August and December, 1803, and February 1814, and are given as a specimen of the method I have pursued.

Taking Arcturus for the standard of an experiment, I directed the telescope, with one quarter of its light, upon it: while the equalizing telescope, with all its light, was successively set upon such stars as I supposed might be at double the distance of the standard star: which, as Arcturus is a star of the first magnitude, I expected to find among those of the second. The first I tried was 6 Pegasi, but I found it not quite bright enough,

α

The light of a Andromeda, which next I tried, was nearly equalized to that of Arcturus; and, the observation being repeated on a different night, gave it equal.

In order to obtain some other stars, whose light might be equalized by one quarter the light of Arcturus, I tried many different ones; and found among the a Polaris, y Ursæ, and

Cassiopeæ. These stars, therefore, may also be put into the class of those whose light is equal to the stars of the second order of the distance of Arcturus.

As the foregoing experiments can only shew that a star of the light of Arcturus might be removed to eight times its distance, and still remain visible to the naked eye as a star of between the fifth and sixth magnitude; it will be proper to take also other stars of the first magnitude, for the original standards.

For instance, if we begin from Capella as the standard star, we may, with of its light equalize ẞ Auriga, and ß Tauri; which stars will, therefore, be of the second order of distances. With of the light of Tauri: we equalize (Tauri and Aurigiæ; they will then be of the fourth order. With of the light Aurigiæ, we can equalize e Persei, and H Geminorum,-which will be of the eighth order, And, with af

the light of H Geminorum, we equalize d Geminorum,which makes it a star of the tenth order. That is to say, if Capella were successively removed to two, four, eight, and ten times the distance at which it is from us, it would then have the appearance of the stars which have been named.

To find stars of the intermediate orders of distances, the following table gives the proportional light that should be used with the star which is made the standard; for instance, a star of the second order of distance, with of its light, will equalize a star of the third order; of the light of a star of the third order of distances will give one of the fifth order, and

n

But the extent of natural vision is not limited to the light of solitary stars only; the united lustre of a number of them will become visible when the stars themselves cannot be seen. For instance, the milky-way; the bright spot in the sword handle of Perseus; the cluster north of and H Geminorum ; the cluster south of Fl. 6 and 9 Aquile; the cluster south of "Hercules, and the cluster north preceding Pegasi. But their distances cannot be ascertained by the method of equalizing star-light: their probable situation in space may, however, be deduced from telescopic observations.

To these very faintly visible objects may be added two of a very different nature, namely, the nebulosity in the sword of Orion, and that in the girdle of Andromeda.

Of the Extent of Telescopic Vision.

282. The Equalization of star-light, when carried to a proper degree of accuracy, will do away the cause of error to which the telescopic extent of vision has been unavoidably subject.

We may therefore safely apply this vision to measure the profundity of sidereal objects that are far beyond the reach of the natural eye; but for this purpose the powers of penetrating into space of the telescopes that are to be used must be reduced to what may be called guaging powers; and, as √x. A2-b2 the formula gives the whole quantity of the spacepenetrating power, a reduction to any inferior power, p may

α

be made by the expression/pu2 +b2 A; when the

x

aperture is then limited to the calculated value of A, the telescopes will have the required guaging power. Or we may prepare a regular set of apertures to serve for trials, and find the guaging powers they give to the telescope by the original formulæ.

Application of the Extent of Natural and Telescopic Vision to the Probable Arrangement of the Celestial Bodies in space.

283. When the extent of natural and telescopic vision is to be applied to investigate the distance of celestial objects, the result can only have a high degree of probability; for it will then be necessary to admit a certain physical generic size and brightness, of the stars. But, when two hypotheses are proposed to explain a certain phenomenon, that which will most naturally account for it ought to be preferred as being the most probable.

Now, as the different magnitudes of the stars may be ascribed to a physical difference in their size and lustre, and may also be owing to the greater distance of the fainter ones, we cannot think it probable that all those of the 5th, 6th, and 7th magnitude, should be gradually of a smaller physical construction than those of the 1st, 2d, and 3d: but shall on the contrary, be fairly justified in concluding that, in con

formity with all the phenomena of vision, the greater faintness of those stars is owing to their greater distance from us.

I proceed now to consider some conclusions that may be drawn from a known extent of natural vision, a very obvious one of which is, that all the visible stars are probably contained within a sphere of the 12th order of distances. Now as on the principle of equal scattering, we should see about 15625 of them, it may be remarked that the stars of the catalogue, including all those of the 7th magnitude, amount to 14144, which agrees sufficiently well with the calculated number: but the next inference is, that if they were equally scattered, there would be 2402 of the 10th, 2906 of the 11th, and 3458 of the 12th order of distances, which added together amount only to 8766, whereas the number of stars of the 6th and 7th magnitudes that must come into these three orders, is not less than 12249, which would indicate that the stars in the higher order of distances are more compressed than they are in the neighbourhood of the sun; but, from astronomical observations, we also know that the stars of the 6th and 7th magnitudes are very sparingly scattered over many of the constellations; and that, consequently, the stars which belong to the 10th, 11th and 12th order of distances, are not only more compressed than those in the neighbourhood of the sun, but that, moreover, their compression in different parts of the heavens must be very unequal.

Of the Construction and Extent of the Milky-Way.

284. Of all the celestial objects consisting of stars not visible to the eye, the milky way is the most striking; its general appearance, without applying a telescope to it, is that of a zone, surrounding our situation in the solar system, in the shape of a succession of differently condensed patches of brightness, intermixed with others of a fainter tinge.

The breadth of the milky-way appears to be very unequal. In a few places it does not exceed five degrees; but, in several constellations, it is extended from ten to sixteen. In its course it runs nearly 120 degrees in a divided clustering stream, of which the two branches between Serpentarius and Antinous are expanded over more than twenty-two degrees.

That the sun is within its plane, may be seen by