irregularity of the precession of the equinoxes, which followed exactly the same period ; whence he concluded that the motion of the poles of the equator, occasioned by this vibration of its plane, was not confined to the solstitial colure. A series of observations on stars differently situated proved that all the phenomena could be explained on the hypothesis that the pole of the equator describes in 18 years a small circle of 18" diameter, contrary to the order of the signs ; or that the axis of the earth, following the circumference of this circle, describes the surface of a cone, the axis of which forms with its side an angle of 9".
This apparent vibratory motion is denominated the Nutation of the Earth's Axis.
We must draw a distinction then, between the mean and the true or apparent obliquity of the ecliptic. The mean obliquity is the obliquity calculated for any particular date on the supposition that there is no nutation, while the true obliquity is that quantity increased or diminished by the nutation. The progressive diminution of the mean obliquity and the nutation of the earth s axis are inequalities distinguished from each other, not only by their being derived from different and distinct causes, but still more by the very great difference of time required for their full development.
The path in which the earth at present travels around the sun is indicated in the elements (p. 782). Plate XXVII. also shows the varying rate at which the earth moves owing to the eccentricity of her orbit. It will be seen also from that plate, and more precisely from the table of elements, that the perihelion of the orbit lies near the place of the winter solstice, so that, in fact, about ten days after midwinter of the northern hemisphere the earth is at her nearest to the sun. An important difference thus exists between the seasons of the two hemispheres. In the northern we have the sun farthest from us a few days after midsummer, while at the corresponding season in winter the sun is at his nearest. So far, then, as the sun s distance is concerned, the seasons are rendered more moderate for the northern hemisphere by the effects of the earth s eccentricity. Nor is the difference on this account by any means inconsiderable. The sun in aphelion is farther from us than in perihelion in the proportion of about 61 to 59, and the earth receives more heat in the proportion of about 31 to 29, or roughly, about ^th more heat in aphelion than in perihelion. There is also a difference due to the varying rate of the earth s real (that is, of the sun s apparent) motion. In winter the earth moves more rapidly than in summer, really as 61 to 59, but the apparent change of the sun s rate of motion along the ecliptic is as 31 to 29, because the increased rate is magnified by the earth s greater proximity. Hence the interval from the autumnal to the vernal equinox is shorter than the interval from the vernal to the autumnal equinox. This also is shown by Plate XXVII., where the number of divisions marking the earth s daily journey is seen to be greater in the summer half than in the winter half of the orbit. Thus the winter cold is less enduring than the summer heat. In the southern hemisphere all these rela tions are reversed. The summer heat is rendered more intense by the greater proximity of the sun, the winter cold is intensified by his increased distance. The summer heat is less enduring than the winter cold. We have in the north a relatively short but moderate winter (so far as the sun s proximity can moderate winter cold), and a long but also moderate summer ; in the southern hemisphere they have a short and intensely hot summer, a long but also intense winter. The presence of a great expanse of sea in the southern hemisphere partially tends to moderate the seasonal changes; but we see in the wider extension of the antarctic snows the effect of the long and cold winter and the short summer. We have, however, referred to these considerations less on account of their intrinsic importance, than to show how the eccentricity of the earth when near its maximum value, and when the perihelion was differently situated from its present position, may have caused the condition of the two terrestrial hemispheres to differ from that now existing. The present value of the eccentricity is nearer the minimum than the maximum value, though the perihelion is at present so placed as to produce almost the maximum possible difference between the two hemispheres, with the present degree of eccentricity. It must not be supposed that the eccentricity, in obedience to the law relating to planetary eccentricities (Chapter VI.), oscillates between the absolute maximum and tho absolute minimum, the perihelion shifting continuously forwards. On the contrary, the successive maxima and minima are very unequal, and are attained after very unequal intervals ; while the perihelion, apart from short periods of regression, and though always progressing on the whole in any considerable period, yet progresses at very unequal rates in different periods. This will be seen from the following table, presenting the eccentricity as calculated for different epochs from 1,100,000 years before our present era till now, chiefly by Mr James Croll, but partly from Leverrier and Stone:—
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Years B.C. Eccentricity Of Earth s Orbit. Longitude of Perihelion. Years B.C. Eccentricity of Earth s Orbit. Longitude of Perihelion. 1,100,000 1,050,000 1,000,000 990,000 980,000 970,000 960,000 950,000 940,000 930,000 920,000 910,000 900,000 0-0303 0-0326 0-0151 0-0224 0-0329 0-0441 0-0491 0-0517 0-0495 0-0423 0-0305 0-0156 0-0102 54 12 4 8 248 22 313 50 358 2 32 40 66 49 97 51 127 42 156 11 181 40 194 15 135 2 720,000 710,000 700,000 0-0422 0-0307 0-0220 125 14 177 26 208 13 650,000 600,000 0-0226 0-0417 141 29 32 34 550,000 600,000 0-0166 0-0388 251 50 192 56 450,000 400,000 0-0308 0-0170 356 52 290 7 350,000 300,000 0-0195 0-0424 182 50 23 29 890,000 880,000 870,000 860,000 850,000 840,000 830,000 820,000 810,000 800,000 0-0285 0-0456 0-0607 0-0708 0-0747 0-0698 0-0623 0-0476 0-0296 0-0132 127 1 152 33 180 23 209 41 239 28 269 14 298 23 326 4 348 30 343 49 25(i,000 240,000 230,000 220,000 210,000 200,000 0-0258 0-0374 0-0477 0-0497 0-0575 0-0569 59 39 74 58 102 49 124 33 144 55 168 18 190,000 180,000 170,000 160,000 150,000 140,000 130,000 120,000 110,000 0-0532 0-0476 0-0437 0-0364 0-0332 0-0346 0-0384 0-0431 0-0460 190 4 209 22 228 7 236 38 242 56 246 29 259 04 274 47 293 43 790,000 780,000 770,000 760,000 750,000 740,000 730,000 0-0171 0-0325 0-0455 0-0540 0-0575 0-0561 0-0507 293 19 303 37 328 38 357 12 27 18 58 30 90 55
Years B.C. Eccentricity of Earth s Orbit. Longitude of Perihelion. Year A.D. Eccentricity of Earth s Orbit. Longitude of Perihelion. 100,000 0-0473 316 18 1850 0-0168 100 22 90,000 89,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0-0452 0-0398 0-0316 0-0218 0-0131 0-0109 0-0151 0-0188 0-0187 340 2 4 13 27 22 48 8 50 3 28 36 5 50 44 78 28 To thes calculatio eccentrici B.C. and i 851,000 850,000 849,500 849,000 e add Crol n for the i y betweer 549,000 B.C 0-07454 0-074664 0-07466 0-07456 s special naximura i 851,000 0-0168 99 30 Determina tion of sun s dis
tance.