of gravity, the wire being arranged as in the figure, so as to relieve the rod of the weight of the balls, its office being solely to keep them apart at a given horizontal distance. It is evident that when suspended from C, and allowed to take its position of equilibrium undisturbed by any external force, the rod will assume such a situation that the wire CD shall be quite devoid of torsion; but that if the rod AB be disturbed from this neutral position, C D remaining vertical, the elastic force of the wire called into action by the torsion so induced will tend to bring it back to the point of departure by a force proportional to the angle of torsion. When so disturbed then, and abandoned to itself, it will oscillate backward and forward in horizontal arcs, the oscillations being all performed in equal times; and from the time observed to be occupied in each oscillation, the weights of the balls and that of the rod being known, we are able, from dynamical principles, to determine the motive force by which the wire acts on the balls, or the force of torsion. Suppose, now, two heavy leaden spheres to be brought, laterally, up nearly into contact, the one with A, the other with B, but on opposite sides of them, they will attract A, B, and their attractions will conspire in twisting the wire the same way; so that the point of rest will be changed from the original neutral point to one in which the torsion shall just counterbalance the attractions. By shifting the attracting balls alternately to the one and the other sides of A B, these will assume positions of rest alternately on opposite sides of the original neutral point, and equidistant from it, so that the deviation, if any, shall thus become doubled in its effect on the readings off of a scale marked by a pointer at the end of the rod, which may be observed through a telescope placed at a distance, so that the approach of the observer's person may create no disturbance. (776 j.) Practically, the observation is not so simple as in the above statement. The balls can hardly ever be brought completely to rest; and the neutral point has to be concluded by noting the extremes of the arc of oscillation, perpetually diminishing by the resistance of the air. And when the attracting balls are brought into action, their attraction (acting laterally, according to the inverse squares of the distances) mixes itself with the force of torsion, to produce a compound law of force, under whose influence the times, velocities, and arcs have a different relation from those due to the torsion alone, and which, when investigated rigorously, lead to calculations of great complexity. Fortunately, the extreme minuteness of the attractive forces dispenses with a rigorous solution of this problem, and allows of a very simple and ready approximation, quite exact enough for the purpose. But besides these, a host of disturbing influences, arising from currents of air induced by difference of temperature, has to be contended with or guarded against, so as to render the experiment one of great difficulty and full of niceties, the mere enumeration of which here, however, would lead us far beyond our limits. * (776 k.) The experiment, as conducted by Cavendish, afforded as its final result 5.480. Repeated since, with greater precautions, by Professor Reich, 5.438 was obtained; and still more recently, by the late F. Baily, in a series of experiments exhibiting an astonishing amount of skill and patience in overcoming the almost innumerable obstacles to complete success, 5.660; a result undoubtedly preferable to the two former. Thus the final result of the whole enquiry will stand as below, the densities concluded being arranged in order of magnitude: Schehallien experiment, by Maskelyne, calculated by Playfair D= 4·713 4.950 5.316 Reich, repetition of Cavendish experiment 5.438 Cavendish, result 5.480, corrected by Mr. Baily's recomputation General mean Mean of greatest and least 5.639 The reader is warned to be on his guard against accepting as correct an account of the principle of the Cavendish experiment, professing to emanate from one very high astronomical authority, and passed without note or comment (and therefore so far sanctioned) by another, but which involves a total misconception of its true nature (Arago, Lezione di Astronomia tradutte ed annotate di E. Capocci, Napoli, 1851, p. 238.) Newton, by one of his astonishing divinations, had already expressed his (776 7.) Calculating on 5 as a result sufficiently approximative and convenient for memory; taking the mean diameter of the earth, considered as a sphere, at 7912-41 miles, and the weight of a cubic foot of water at 62-3211 lbs.; we find for its solid content in cubic miles, 259,373 millions, and for its weight in tons of 2240 lbs. avoird. each, 5842 trillions (= 5842 × 1018). opinion that the mean density of the earth would be found to be between five and six times that of water. (Princ. iii. 10.) 561 PART III. OF SIDEREAL ASTRONOMY. CHAPTER XV. OF THE FIXED STARS. THEIR CLASSIFICATION BY MAGNITUDES. CONVENTIONAL OR VULPHOTOMETRIC COMPARISON OF STARS. PHOTOMETRIC SCALE OF MAGNITUDES. GAR SCALE. -- DISTRIBU TION OF STARS OVER THE HEAVENS.- OF THE MILKY WAY OR GALAXY. - ITS SUPPOSED FORM THAT OF A FLAT STRATUM PARTIALLY SUBDIVIDED. ITS VISIBLE COURSE AMONG THE CONSTELLATIONS. ITS INTERNAL STRUCTURE. -ITS APPARENTLY INDEFINITE EXTENT IN CERTAIN DIRECTIONS. OF THE DISTANCE OF THE FIXED STARS. -THEIR ANNUAL PARALLAX. PARALLACTIC UNIT OF SIDEREAL DISTANCE.- EFFECT OF PARALLAX ANALOGOUS TO THAT OF ABERRATION.- HOW DISTINGUISHED FROM IT.-DETECTION OF PARALLAX BY MERIDIONAL OBSERVATIONS. HENDERSON'S APPLICATION TO a CENTAURI. -BY DIFFERENTIAL OBSERVATIONS. DISCOVERIES OF BESSEL AND STRUVE. LIST OF STARS IN WHICH PARALLAX HAS BEEN DETECTED.- OF THE REAL MAGNITUDES OF THE STARS. COMPARISON OF THEIR LIGHTS WITH THAT OF THE SUN. - (777.) BESIDES the bodies we have described in the fore going chapters, the heavens present us with an innumerable multitude of other objects, which are called generally by the name of stars. Though comprehending individuals differing from each other, not merely in brightness, but in many other essential points, they all agree in one attribute, — a high degree of permanence as to apparent relative situation. This has procured them the title of "fixed stars;" an expression which is to be understood in a comparative and not an absolute sense, it being certain that many, and probable that all, are in a state of motion, although too slow to be perceptible unless by means of very delicate observations, continued during a long series of years. (778.) Astronomers are in the habit of distinguishing the stars into classes, according to their apparent brightness. These are termed magnitudes. The brightest stars are said to be of the first magnitude; those which fall so far short of the first degree of brightness as to make a strongly marked distinction are classed in the second; and so on down to the sixth or seventh, which comprise the smallest stars visible to the naked eye, in the clearest and darkest night. Beyond these, however, telescopes continue the range of visibility, and magnitudes from the 8th down to the 16th are familiar to those who are in the practice of using powerful instruments; nor does there seem the least reason to assign a limit to this progression; every increase in the dimensions and power of instruments, which successive improvements in optical science have attained, having brought into view multitudes innumerable of objects invisible before; so that, for any thing experience has hitherto taught us, the number of the stars may be really infinite, in the only sense in which we can assign a meaning to the word. (779.) This classification into magnitudes, however, it must be observed, is entirely arbitrary. Of a multitude of bright objects, differing probably, intrinsically, both in size and in splendour, and arranged at unequal distances from us, one must of necessity appear the brightest, one next below it, and so on. An order of succession (relative, of course, to our local situation among them) must exist, and it is a matter of absolute indifference, where, in that infinite progression downwards, from the one brightest to the invisible, we choose to draw our lines of demarcation. All this is a matter of pure convention. Usage, however, has established such a convention; and though it is impossible to determine exactly, or à priori, where one magnitude ends and the next begins, and although different observers have differed in their magnitudes, yet, on the whole, astronomers have restricted their first magnitude to about 23 or 24 principal stars; their second to 50 or 60 next inferior; their third to about 200 yet |