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ASTRONOMY

the earth remained invariable, without any motion of matter on its surface, the result of this non-coincidence would be the revolution of the one pole round the other in a circle of radius Olb" in a period of about 429 days. This revolution is called the Eulerian motion, after the mathematician who discovered it. But owing to meteorological causes the motion in question is subject to annual changes. These changes arise from two causes—the one statical, the other dynamical. (2) The statical causes are deposits of snow or ice slowly changing the position of the pole of figure of the earth. For example, a deposit of snow in Siberia would bring the equator of figure of the earth a little nearer to Siberia and throw the pole a little way from it, while a deposit on the American continent would have the opposite effect. Owing to the approximate symmetry of the American and Asiatic continents it does not seem likely that the inequality of snowfall would produce an appreciable effect. (3) The dynamical causes are atmospheric and oceanic currents. Were these currents invariable their only effect would be that the Eulerian motion would not take place exactly round the mean pole of figure, but round a point slightly separated from it. But, as a matter of fact, they are subject to an annual variation. Hence the motion of the pole of rotation is also subject to a similar variation. The annual term in the latitude may be readily accounted for in this way. But it seems unlikely that a motion thus produced should have a sensible eccentricity. It therefore appears at present more likely that the seeming eccentricity of the annual motion is unreal and due to the cause already mentioned. (4) Six Eulerian periods are very nearly seven years. In consequence, the effect of the annual change is to produce an inequality in the amplitude having a period of seven years. During one part of this period the distance of the two poles is nearly double, being increased to 0‘25" or 0’30". At another part of the period, three and a half years later, the motion almost ceases. Times of greatest motion were in 1890-92, and again in 1897-99; of least motion about 1894, 1901, 1908, Ac. Besides Chandler, Albrecht of Berlin has investigated the motion of the pole P. The methods of the two astronomers are in some points different. Chandler has constructed empirical formulte representing the motion, with the results already given, while Albrecht has determined the motion of the pole from observation simply, without trying to represent it either by a formula or by theory. It is noteworthy that the difference between Albrecht’s numerical results and Chandler’s formulae is generallyJ less than 0 •05". Masses, &c., of the Planets and Satellites. The elements, masses, and other particulars relating to the major planets and their satellites, so far as these were known in 1875, are given in the Ency. Brit., ninth edition, vol. ii. pp. 782-83, and the adopted elements of most of these bodies have been so slightly changed that a repetition of them is not deemed necessary. What we shall now present is a resume of the masses, diameters, and other more important constants which have been worked out to the present time, necessarily limiting our review to what may be considered the best-established results. For ordinary astronomical purposes the masses are not expressed in terms of the gravitational units already defined, but as fractions of the sun’s mass taken as unity. This fraction is commonly written in the form -, y being the number of times that the sun’s mass exceeds that of the planet. The masses of the satellites are expressed in the same form in terms of the mass of the primary. The minuteness of the planet Mercury and the absence of a satellite make the determination of its mass difficult

and uncertain. In the new planetary tables issued from the office of the American Nautical Almanac, and now most used, y is taken as 6000000. Other values of the mass are generally less than this, y rang- Mercurying up to 10000000 or more. G. W. Hill, from a consideration of the probable density, finds values ranging from 10194200 to 10826200. The uncertainty of the diameter renders this result uncertain ; an increase of onetenth in Hill’s adopted diameter, 6‘68", would increase the resulting volume by one-third and the mass by nearly one-half. The value 7500000 seems as likely as any. The best values of the diameter are those found during transits over the sun’s disc. Todd, with double-image micrometer, found the value 6-604" (A = l), and Barnard, with filar micrometer, 6-126". Both results are liable to be too small from the effects of irradiation. Off the sun’s disc, results of measures with the filar micrometer are Lowell at Flagstaff 7-4", and Barnard at Mount Hamilton 6-14". The mass of the planet Venus derived from all the observations of the sun and Mercury, and adopted in the new planetary tables, is p, = 408000. It is not likely to be in error by 1 per cent, of its amount. For the angular diameter at distance unity Auwers, from heliometer measures during the transits of 1874 and 1882, found the value 16-820"; Newcomb, from double-image micrometer measures during the transit of 1882, that of 16-88"; Barnard, off the sun from measures near inferior conjunction, 17-397"; and German observers, with the heliometer, 17 "30". This difference between the results of measures on and off the sun might be attributed to irradiation; but it is singular that a comparison of numerous measures made at widely different distances from the earth seems to indicate the anomaly of negative irradiation, the diameters measured at the greater distances being proportionately too small instead of too large. The mass of the moon has been already derived as one of the fundamental constants. The most exact value of the diameter is that derived from the occultaoon tions of groups of stars, especially when the ‘ moon is totally eclipsed. From occultations of the Pleiades J. Peters found, for the mean semi-diameter 15' 32-49"; Struve, from occultations during total eclipses, 15' 32-65"; while the most likely value, as concluded by Peters, is 15' 32-59". As the apparent diameter varies with the distance, and can be computed only when the moon’s parallax is known, it is common to express the moon’s diameter in terms of that of the earth as unity. From the value of the parallax already found, it follows that Diameter of moon Eq. diam. of earth = 0-272480. For particulars as to the motion of the moon, see article Moon. The motions of the orbital planes and of the pericentres of the satellites of Mars offer interesting problems to both the observing and the mathematical astronomer. These problems have been most successfully attacked by Hermann Struve in a memoir presented to the St Petersburg Academy in 1898. The preliminary results of theory may first be set forth :— Let M (Fig. 3) be the pole of rotation of Mars, O the pole of the orbit of that planet, and S the pole of the orbit of one of its satellites, all projected on the celestial sphere. The arc OM of the sphere will then be equal to that between the equator of Mars and the plane of its orbit; SO will be equal to the inclination of the orbit of the satellite to that of the planet, and SM to the inclination of the same orbit to the equator of Mars. In consequence of the action of the sun, the pole S moves constantly in a direction at right angles to OS, as shown by arrow a ; while the ellipticity of Mars gives it a much more rapid motion in a direction at right angles to MS, as shown by the other arrow b. The actual motion