Part 11 (1/2)
Year of observation. Groups of spots observed. Number of days.
1826 118 277 1827 161 273 1828 225 282 1829 199 244 1830 190 217 1831 149 239 1832 84 270 1833 33 267 1834 51 273 1835 173 244 1836 272 200 1837 333 168 1838 282 202 1839 162 205 1840 152 263 1841 102 283 1842 68 307 1843 34 324
Previous to the publication of this table, the author had inferred the necessity of admitting the existence of another planet in the solar system, from the phenomenon of which we are speaking. He found a sufficient correspondence between the minima of spots to confirm the explanation given by the theory, and this was still more confirmed by the more exact determination of Schwabe; yet there was a little discrepancy in the synchronous values of the ordinates, when the theory was graphically compared with the table. Previous to the discovery of Neptune, the theory corresponded much better than afterwards, and as no doubt could be entertained that the anomalous movements of Ura.n.u.s were caused by an exterior planet, he adopted the notion that there were two planets exterior to Ura.n.u.s, whose positions at the time were such, that their mechanical affects on the system were about equal and contrary.
Consequently, when Neptune became known, the existence of another planet seemed a conclusion necessary to adopt. Accordingly, he calculated the heliocentric longitudes and true anomalies, and the values of radius vector, for all the planets during the present century, but not having any planetary tables, he contented himself with computing for the nearest degree of true anomaly, and the nearest thousand miles of distance. Then by a composition and resolution of all the forces, he deduced the radius vector of the sun, and the longitude of his centre, for each past year of the century. It was in view of a little outstanding discrepancy in the times of the minima, as determined by theory and observation, that he was induced to consider as almost certain the existence of a theoretical planet, whose longitude, in 1828, was about 90, and whose period is from the theory about double that of Neptune. And for convenience of computation and reference, he has been in the habit of symbolizing it by a volcano. The following table of the radii vectores of the sun, and the longitude of his centre, for the years designated in Schwabe's table, is calculated from the following data for each planet:
Long. of Planets. Ma.s.ses. Mean distances. Eccentricities. Perihelion.
? 1/1648 494.800.000 0.0481 11 ? 1/3310 907.162.000 0.0561 89 ? 1/23000 1824.290.000 0.0166 167 ? 1/20000 2854.000.000 0.0088 0 ? 1/28000 4464.000.000
No. of spots in Dates. Rad. vector. Sun's long. Ordinates. Schwabe's table.
Jan. 1, 1826 528,000 320 + 84 118 ” 1827 480,000 339 + 36 161 ” 1828 432,000 352 - 12 Max. 225 Max.
” 1829 397,000 38 - 47 199 ” 1830 858,000 71 - 86 190 ” 1831 324,000 104 - 120 149 ” 1832 311,000 144 - 133 84 ” 1833 300,000 183 - 144 Min. 33 Min.
” 1834 307,000 220 - 137 51 ” 1835 338,000 263 - 106 173 ” 1836 380,000 302 - 55 272 ” 1837 419,000 337 + 25 Max. 333 Max.
” 1838 488,000 3 + 44 282 ” 1839 651,000 29 + 107 162 ” 1840 632,000 51 + 188 152 ” 1841 680,000 80 + 236 102 ” 1842 730,000 105 + 286 68 ” 1843 160,000 128 + 322 34 Min.
” 1844 188,000 152 + 339 Min. 52 ” 1845 772,000 174 + 328 114 ” 1846 728,000 196 + 284 157 ” 1847 660,000 218 + 216 ” 1848 563,000 240 + 119 Observed. Max.
” 1849 447,000 261 + 3 Max.
” 1850 309,000 283 - 135 ” 1851 170,000 323 - 274 ” 1852 53,000 41 - 391 Min.
” 1853 167,000 133 - 277 ” 1854 315,000 160 - 129 ” 1855 475,000 183 + 31 Max.
” 1856 611,000 203 + 167 ” 1857 720,000 225 + 276
It is necessary to observe here, that the values of the numbers in Schwabe's table are the numbers for the whole year, and, therefore, the 1st of July would have been a better date for the comparison; but, as the table was calculated before the author was cognizant of the fact, and being somewhat tedious to calculate, he has left it as it was, viz., for January 1st of each year. Hence, the minimum for 1843 appears as pertaining to 1844. The number of spots ought to be inversely as the ordinates approximately--these last being derived from the Radii Vectores minus, the semi-diameter of the sun = 444,000 miles.
In pa.s.sing judgment on this relation, it must also be borne in mind, that the recognized ma.s.ses of the planets cannot be the true ma.s.ses, if the theory be true. Both sun and planets are under-estimated, yet, as they are, probably, all to a certain degree proportionally undervalued, it will not vitiate the above calculation much.
The spots being considered as solar storms, they ought also to vary in number at different times of the year, according to the longitude of the earth and sun, and from their transient character, and the slow rotation of the sun, they ought, _ceteris paribus_, to be more numerous when the producing vortex is over a visible portion of the sun's surface.
The difficulty of reconciling the solar spots, and their periodicity to any known principle of physics, ought to produce a more tolerant spirit amongst the scientific for speculations even which may afford the slightest promise of a solution, although emanating from the humblest inquirer after truth. The hypothesis of an undiscovered planet, exterior to Neptune, is of a nature to startle the cautions timidity of many; but, if the general theory be true, this hypothesis becomes extremely probable. We may not have located it exactly. There may be even two such planets, whose joint effect shall be equivalent to one in the position we have a.s.signed. There may even be a comet of great ma.s.s, capable of producing an effect on the position of the sun's centre (although it follows from the theory that comets have very little ma.s.s). Yet, in view of all these suppositions, there can be but little doubt that the solar spots are caused by the solar vortices, and these last made effective on the sun by the positions of the great planets, and, therefore, we have indicated a new method of determining the existence and position of all the planets exterior to Neptune. On the supposition that there is only one more in the system, from its deduced distance and ma.s.s, it will appear only as a star of the eleventh magnitude, and, consequently, will only be recognizable by its motion, which, at the greatest, will only be ten or eleven seconds per day.
Ma.s.sES OF THE SUN AND PLANETS.
We have alluded to the fact of the radial stream of the sun necessarily diminis.h.i.+ng the sun's power, and, consequently, diminis.h.i.+ng his apparent ma.s.s. The radial stream of all the planets will do the same, so that each planet whose ma.s.s is derived from the periodic times of the satellites, will also appear too small. But, there is also a great probability that some modification must be made in the wording of the Newtonian law. The experiments of Newton on the pendulum, with every variety of substance, was sufficient justification to ent.i.tle him to infer, that inertia was as the weight of matter universally. But, there was one condition which could not be observed in experimenting on these substances, viz., the difference of temperature existing between the interior and surface of a planet.
We have already expressed the idea, that the cause of gravity has no such mysterious origin as to transcend the power of man to determine it.
But that, on the contrary, we are taught by every a.n.a.logy around us, as well as by divine precept, to use the visible things of creation as stepping stones to the attainment of what is not so apparent. That we have the volume of nature spread out in tempting characters, inviting us to read, and, a.s.suredly, it is not so spread in mockery of man's limited powers. As science advances, strange things, it is true, are brought to light, but the more _rational_ the queries we propound, in every case the more satisfactory are the answers. It is only when man consults the oracle in irrational terms that the response is ambiguous. Alchemy, with its unnatural trans.m.u.tations, has long since vanished before the increasing light. Why should not attraction also? Experience and experiment, if men would only follow their indications, are consistently enforcing the necessity of erasing these antiquated chimeras from the book of knowledge; and inculcating the great truth, that the physical universe owes all its endless variety to differences in the form, size, and density of planetary atoms in motion, according to simple mechanical principles. These, combined with the existence of an all-pervading medium filling s.p.a.ce, between which and planetary matter no bond of union subsists, other than that which arises from a continual interchange of motion, are the materials from which the gems of nature are elaborated. But, simplicity of means is what philosophy has ever been reluctant to admit, preferring rather the occult and obscure.
If action be equal to reaction, and all nature be vibrating with motion, these motions must necessarily interfere, and some effect should be produced. A body radiating its motion on every side into a physical medium, produces waves. These waves are a mechanical effect, and the body parts with some of its motion in producing them; but, should another body be placed in juxtaposition, having the same motion, the opposing waves neutralize each other, and the bodies lose no motion from their contiguous sides, and, therefore, the reaction from the opposite sides acts as a propelling power, and the bodies approach, or tend to approach each other. If one body be of double the inertia, it moves only half as far as the first; then, seeing that this atomic motion is radiated, the law of force must be directly as the ma.s.s, and inversely as the squares of the distances. There may be other atomic vibrations besides those which we call light, heat, and chemical action, yet the joint effect of all is infinitesimally small, when we disregard the united _attraction_ of all the atoms of which the earth is composed. The _attraction_ of the whole earth at the surface causes bodies to fall 16 feet the first second of time; but, if two spheres of ice of one foot diameter, were placed in an infinite s.p.a.ce, uninfluenced by other matter, and only 16 feet apart, they would require nearly 10,000 years to fall together by virtue of their mutual attraction. Our conceptions, or, rather, our misconceptions, concerning the force of gravity, arises from our forgetting that every pound of matter on the earth contributes its share of the force which, in the aggregate, is so powerful. Hence, the cause we have suggested, is fully adequate to account for the phenomena. Whether the harmony of vibrations between two bodies may not have an influence in determining the amount of interference, and, consequently, produce _some_ difference between the gravitating ma.s.s and its inertia, is a question which, no doubt, will ultimately be solved; but this harmony of vibrations must depend, in some degree, on the atomic weight, temperature, and intensity of atomic motion.
That a part of the ma.s.s of the earth is _latent_ may be inferred from certain considerations: 1st, from the discrepancies existing in the results obtained for the earth's compression by the pendulum and by actual measurement; and, 2d, from the irregularity of that compression in particular lat.i.tudes and longitudes. The same may also be deduced from the different values of the moon's ma.s.s as derived from different phenomena, dependent on the law of gravitation. Astronomers have hitherto covered themselves with the very convenient s.h.i.+eld of errors of observation; but, the perfection of modern instruments now demand a better account of all outstanding discrepancies. The world requires it of them.
The ma.s.s of the moon comes out much greater by our theory than nutation gives. The ma.s.s deduced from the theory is only dependent on the relative inertiae of the earth and moon. That given by nutation depends on gravity. If, then, a part of the ma.s.s be latent, nutation will give too small a value. But, in addition to this, we are justified in doubting the strict wording of the Newtonian law, deriving our authority from the very foundation stone of the Newtonian theory.
It is well known that Newton suspected that the moon was retained in her orbit by the same force which is usually called weight upon the surface, sixteen years before the fact was confirmed, by finding a correspondence in the fall of the moon and the fall of bodies on the earth. Usually, in all elementary works, this problem is considered accurately solved.
Having formed a different idea of the mechanism of nature, this fact presented itself as a barrier beyond which it was impossible to pa.s.s, until suspicions, derived from other sources, induced the author to inquire: Whether the phenomenon did exactly accord with the theory? We are aware that it is easy to place the moon at such a distance, that the result shall strictly correspond with the fact; but, from the parallax, as derived from observation (and if this cannot be depended on certainly, no magnitudes in astronomy can), we find, _that the moon does not fall from the tangent of her orbit, as much as the theory requires_.
As this is of vital importance to the integrity of the theory we are advocating, we have made the computation on Newton's own data, except such as were necessarily inaccurate at the time he wrote; and we have done it arithmetically, without logarithmic tables, that, if possible, no error should creep in to vitiate the result. We take the moon's elements from no less an authority than Sir John Herschel, as well as the value of the earth's diameter.
Ma.s.s of the moon 1/80 Mean distance in equatorial radii 59.96435 Sidereal period in seconds 2360591