Part 11 (1/2)
Such an explanation will account for the general appearances of the Milky Way and of the rest of the sky, supposing the stars equally or nearly equally distributed in space On this supposition, the system must be deeper where the stars appear most numerous
HERSCHEL endeavored, in his early memoirs, to explain this inequality of distribution on the fundamental assumption that the stars were nearly equably distributed in space If they were so distributed, then the nue would show the thickness of the stellar system in the direction in which the telescope was pointed
At each pointing, the field of view of the instrument includes all the visible stars situated within a cone, having its vortex at the observer's eye, and its base at the very li 15' Then the cubes of the perpendiculars let fall from the eye, on the plane of the bases of the various visual cones, are proportional to the solid contents of the cones themselves, or, as the stars are supposed equally scattered within all the cones, the cube roots of the nuths of the perpendiculars A _section_ of the sidereal systereat circle can be constructed fro way:
The solar system is within thethe different directions in which the gauging telescope was pointed On these lines are laid off lengths proportional to the cube roots of the nu the ter curve of the stellar systereat circle chosen Within this line the space is nearly uniformly filled with stars Without it is empty space A sireat circle, and a coive a representation of the shape of our stellar system The more numerous and careful the observations, the es of HERSCHEL are sufficient to reat precision the main features of the Milky Way, and even to indicate soularities
On the fundamental assumption of HERSCHEL (equable distribution), no other conclusion can be drawn from his statistics but the one laid down by him
This assuree, and was led to regard his gauges as indicating not so much the _depth of the syste power or tendency_ of the stars in those special regions It is clear that if in any given part of the sky, where, on the average, there are ten stars (say) to a field, we should find a certain s 100 or orously interpreted, it would be necessary to suppose a spike-shaped protuberance directed from the earth, in order to explain the increased number of stars If reat that this explanation is wrong We should more rationally suppose some real inequality of star distribution here It is, in fact, in just such details that the method of HERSCHEL breaks down, and a careful exareatly modified to cover all the known facts, while it undoubtedly has, in thebasis
The stars are certainly not uniforeneral theory of the sidereal systeation in various parts of the sky
In 1817, HERSCHEL published an important ely h not abandoned Its fundamental principle was stated by him as follows:
”It is evident that we cannot mean to affirnitudes are really smaller than those of the first, second, or third, and that we nitudes of the stars to a difference in their relative distances froreat number of stars in each class, we nitude, beginning with the first, are, one with another, further fro The relative ive only relative distances, and can afford no information as to the real distances at which the stars are placed
”A standard of reference for the arrange their distribution to a certain properlyThe equality which I propose does not require that the stars should be at equal distances from each other, nor is it necessary that all those of the sanitude should be equally distant fro a certain equal portion of space to every star, so that, on the whole, each equal portion of space within the stellar system contains an equal number of stars The space about each star can be considered spherical Suppose such a sphere to surround our own sun Its radius will not differ greatly from the distance of the nearest fixed star, and this is taken as the unit of distance
Suppose a series of larger spheres, all drawn around our sun as a centre, and having the radii 3, 5, 7, 9, etc The contents of the spheres being as the cubes of their diameters, the first sphere will have 3 3 3 = 27 tie enough to contain 27 stars; the second will have 125 times the volume, and will therefore contain 125 stars, and so on with the successive spheres For instance, the sphere of radius 7 has roo to the spheres inside of it; there is, therefore, room for 218 stars between the spheres of radii 5 and 7
HERSCHEL designates the several distances of these layers of stars as orders; the stars between spheres 1 and 3 are of the first order of distance, those between 3 and 5 of the second order, and so on
Co the room for stars between the several spheres with the nunitudes which actually exists in the sky, he found the result to be as follows:
-------------------------------------------------------- Order of | Nunitude | Stars of that | is Roonitude
-------------------------------------------------------- 1 | 26 | 1 | 17 2 | 98 | 2 | 57 3 | 218 | 3 | 206 4 | 386 | 4 | 454 5 | 602 | 5 | 1,161 6 | 866 | 6 | 6,103 7 | 1,178 | 7 | 6,146 8 | 1,538 | | ---------------------------------------------------------
The result of this conitudes could indicate the distance of the stars, it would denote at first a gradual and afterward a very abrupt condensation of thenitude stars
If we assuhtness of any star to be inversely proportional to the square of its distance, it leads to a scale of distance different fronitude star on the cohth order of distance according to this schenitude to eight times its actual distance to nitude
On the schened the _order_ of distance of various objects, mostly star-clusters, and his estimates of these distances are still quoted They rest on the fundamental hypothesis which has been explained, and the error in the assumption of equal intrinsic brilliancy for all stars affects these estimates It is perhaps probable that the hypothesis of equal brilliancy for all stars is still more erroneous than the hypothesis of equal distribution, and it e indeed in the actual dimensions and in the intrinsic brilliancy of stars at the sanitude stars, for exahout the spheres which HERSCHEL would assign to the seventh, eighth, ninth, tenth, eleventh, twelfth, and thirteenth nitudes However this roundwork that future investigators must build He found the whole subject in utter confusion By his observations, data for the solution of soeneral questions were accumulated, and in his ht the scattered facts into order and gave the first bold outlines of a reasonable theory He is the founder of a new branch of astronomy
_Researches for a Scale of Celestial Measures
Distances of the Stars_
If the stars are _supposed_ all of the sahtness to the eye will depend only upon their distance frohtness of one of the fixed stars at the distance of _Sirius_, which may be used as the unity of distance, 1, then if it is htness will be one-fourth; if to the distance 3, one-ninth; if to the distance 4, one-sixteenth, and so on, the apparent brightness di as the square of the distance increases The distance nitude Stars at the _distances_ two, three, four, etc, HERSCHEL called of the second, third, and fourth nitudes
By a series of experiiven here, HERSCHEL deter power of each of his telescopes The twenty-foot would penetrate into space seventy-five times farther than the naked eye; the twenty-five foot, ninety-six times; and the forty-foot, one hundred and ninety-two tinitude stars are those just visible to the naked eye, and if we still suppose all stars to be of equal intrinsic brightness, such seventh-nitude stars would remain visible in the forty-foot, even if removed to 1,344 times the distance of _Sirius_ (1,344 = 7 192)
If, further, we suppose that the visibility of a star is strictly proportional to the total intensity of the light from it which strikes the eye, then a condensed cluster of 25,000 stars of the 1,344th nitude could still be seen in the forty-foot at a distance where each star would have become 25,000 times fainter, that is, at about 158 tiht from the nearest star requires some three years to reach the earth From a star 1,344 times farther it would require about 4,000 years, and for such a cluster as we have iined no less than 600,000 years are needed That is, the light by which we see such a group has not just now left it
On the contrary, it has been travelling through space for centuries and centuries since it first darted forth It is the ancient history of such groups that we are studying now, and it was thus that HERSCHEL declared that telescopes penetrated into time as well as into space
Other ht of stars were made by HERSCHEL These were only one more atte to which some notion of the liained Two telescopes, _exactly equal_ in every respect, were chosen and placed side by side