art. 857, has been adopted by the present Astronomer-Royal, by which the assumption of an approximate knowledge of the situation of the "solar apex," is altogether dispensed with. It consists in referring the absolute proper annual motions both of the sun and the stars used in the enquiry, to linear coordinates fixed in space, and treating the question as a purely geometrical one, according to the rules of the calculus of probabilities, basing his procedure on two distinct assumptions, between which the truth must lie, viz.-1. That all the "irregularities of proper motion" (meaning thereby all the residual amounts of annual movement in each case, which are not accountable for by solar motion), are mere results of error of observation and are not caused by any real motions in the stars. This is evidently an extreme supposition.-2. That none of such residual movements are due to error of observation, but all originate in real stellar movement. This is as clearly an extreme supposition the other way. Assuming then M. Struve's classification of the stars according to a scale of distances which has at least no primâ facie improbability, and using for the purpose those 113 stars of a catalogue prepared with great care by Mr. Main, and published in the 'Memoirs of the Astronomical Society,' which indicate great proper motion, he arrives at the following conclusions as to the situation of the apex, and the annual parallactic motion of the sun as seen from a star of the first magnitude, on each of these two suppositions. Solar apex in R. A. 256° 54'; N.P.D. 50° 31'. 1st Supposition Parallactic motion 1"-269. 2d Supposition Solar apex R.A. 261° 29'; N.P.D. 65° 16′′. Parallactic motion 1'9 12. So far as the situation of the apex is concerned, both these results stand in what (considering the nature of the subject) may be called good accordance with those of our art. 854. The parallactic motion (or which comes to the same, the actual velocity of the solar motion), is, indeed, much greater than that of art. 858. But this evidently results from the restriction of the enquiry to stars of great proper motion. (858 b.) These results were deduced by Mr. Airy in a memoir communicated to the Roy. Ast. Soc. in 1859. The subject has since been resumed (avowedly in extension of the same principle to a larger list of stars), by Mr. Dunkin, who, using the same geometrical formulæ, but basing his results on the observed proper motions of 1167 stars, 819 in the northern and 348 in the southern hemisphere, of all magnitudes, and all (sensible) amounts of proper motion, arrives at the following results on either of Mr. Airy's two extreme suppositions. 1st Supposition (Solar apex in R.A. 261° 14; N.P.D. 57° 5′. Parallactic motion 0":3346. Solar apex 263° 44'; N.P.D. 65° 0'. 2d Supposition Parallactic motion 0"-4103. Agreeing remarkably (as to the second supposition, which is by far the most reasonable of the two), with the other, and, as regards both, exhibiting an almost perfect accordance in respect of parallactic motion with M. Struve's results as given in art. 858. (858 c.) A very extraordinary circumstance remains to be noticed. From the general agreement of all the results, of the investigations of so many astronomers and mathematicians, entering on the enquiry in such various ways, and employing such a multitude of stars so variously combined, there cannot remain a shadow of doubt either as to the reality of the solar motion, or as to its direction in space towards a point very near to R.A. 259°, N.P.D. 56°. As to its velocity there is also every reason to believe that it is not extravagantly over- or under-estimated in the statement above given. But when we come to ascertain by calculation how large a portion of the whole proper motions of the stars, how much of that general residuum or caput mortuum alluded to in art. 856, as left outstanding after precession, aberration, and nutation, have exercised their solvent influences on it, remains yet unaccounted for; we shall find it includes by far the larger part of the total phænomenon of stellar proper motion. The sum of the squares of the total residua (in seconds of arc), uncorrected for the proper motion of the sun, for example, in Mr. Dunkin's 1167 stars are, in R.A., 78.7583, and in N.P.D. 63.2668. And when corrected for the effect of that motion (so concluded), they are represented in R.A. by 75.5831, and in N.P.D. by 60-9084. No one need be surprised at this. If the sun move in space, why not also the stars? and if so it would be manifestly absurd to expect that any movement could be assigned to the sun by any system of calculation which should account for more than a very small portion of the totality of the observed displacements. But what is indeed astonishing in the whole affair, is, that among all this chaotic heap of miscellaneous movement, among all this drift of cosmical atoms, of the laws of whose motions we know absolutely nothing, it should be possible to place the finger on one small portion of the sum total, to all appearance undistinguishably mixed up with the rest, and to declare with full assurance that this particular portion of the whole is due to the proper motion of our own system.] |