VII. On the Means of discovering the Distance, Magnitude, &c. of the Fixed Stars, in consequence of the Diminution of the Velocity of their Light, in case such a Diminution should be found to take place in any of them, and such other Data should be procured from Observations, as would be farther necessary for that Purpose.
By the Rev. John Michell, B. D. F.R.S.
In a Letter to Henry Cavendish, Esq. F.R.S. and A. S.
Read November 27, 1783.
Thornhill, May 26, 1783.
DEAR SIR,
THE method, which I mentioned to you when I was last in London, by which it might perhaps be possible to find the distance, magnitude, and weight of some of the fixed stars, by means of the diminution of the velocity of their light, occurred to me soon after I wrote what is mentioned by Dr. PRIESTLEY in his History of Optics, concerning the diminution of the velocity of light in consequence of the attraction of the sun; but the extreme difficulty, and perhaps impossibility, of procuring the other data necessary for this purpose appeared to me to be such objections against the scheme, when I first thought of it, that I gave it then no further consideration. As some late observations, however, begin to give us a little more chance of procuring some at least of these data, I thought it would not be amiss, that astronomers should be apprized of the method, I propose (which as far as I know, has not been suggested by any one else) lest, for want of being aware of the use, which may be made of them, they should neglect to make the proper observations, when in their power; I shall therefore beg the favour of you to present the following paper on this subject to the Royal Society.
I am, &c.
1
THE very great number of stars that have been discovered to be double, triple, &c. particularly by Mr. HERSCHEL* , if we apply the doctrine of chances, as I have heretofore done in my "Enquiry into the probable Parallax, &c. of the Fixed Stars," published in the Philosophical Transactions for the year 1767, cannot leave a doubt with any one, who is properly aware of the force of those arguments, that by far the greatest part, if not all of them, are systems of stars so near to each other, as probably to be liable to be affected sensibly by their mutual gravitation; and it is therefore not unlikely, that the periods of the revolutions of some of these about their principals (the smaller ones being, upon this hypothesis, to be considered as satellites to the others) may some time or other be discovered.
*See his Catalogue of Stars of this kind, published in the Philosophical Transactions for the year 1782, which is indeed a most valuable present to the astronomical world. By a happy application of very high magnifying powers to his telescopes, and by a most persevering industry in observing, he has made a very wonderful progress in this branch of astronomy, in which almost nothing of any consequence had been done by any one before him.
2
2. Now the apparent diameter of any central body, round which any other body revolves, together with their apparent distance from one another, and the periodical time of the revolving body being given, the density of the central body will be given likewise. See Sir ISAAC NEWTON's Prin. b. III. pr. VIII. cor. I.
3
3. But the density of any central body being given, and the velocity any other body would acquire by falling towards it from an infinite height, or, which is the same thing, the velocity of a comet revolving in a parabolic orbit, at its surface, being given, the quantity of matter, and consequently the real magnitude of the central body, would be given likewise.
4
4. Let us now suppose the particles of light to be attracted in the same manner as all other bodies with which we are acquainted; that is, by forces bearing the same proportion to their vis inertiae, of which there can be no reasonable doubt, gravitation being, as far as we know, or have any reason to believe, an universal law of nature. Upon this supposition then, if any one of the fixed stars, whose density was known by the above-mentioned means, should be large enough sensibly to affect the velocity of the light issuing from it, we should have the means of knowing its real magnitude, &c.