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 assigned. There may even be a comet of great mass, capable of producing an effect on the position of the sun’s centre (although it follows from the theory that comets have very little mass). 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 mass, 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.
MASSES OF THE SUN AND PLANETS.
We have alluded to the fact of the radial stream of the sun necessarily diminishing the sun’s power, and, consequently, diminishing his apparent mass. The radial stream of all the planets will do the same, so that each planet whose mass 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 entitle 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 analogy 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, assuredly, 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 transmutations, 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 space, 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 mass, 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 space, 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 mass 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 mass 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 latitudes and longitudes. The same may also be deduced from the different values of the moon’s mass as derived from different phenomena, dependent on the law of gravitation. Astronomers have hitherto covered themselves with the very convenient shield 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 mass of the moon comes out much greater by our theory than nutation gives. The mass deduced from the theory is only dependent on the relative inertiæ of the earth and moon. That given by nutation depends on gravity. If, then, a part of the mass 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 pass, 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.
| Mass of the moon | 1 ⁄ 80 |
| Mean distance in equatorial radii | 59.96435 |
| Sidereal period in seconds | 2360591 |
The vibrations of the pendulum give the force of gravity at the surface of the earth, and it is found to vary in different latitudes. The intensity in any place being as the squares of the number of vibrations in a given time. This inequality depends on the centrifugal force of rotation, and on the spheroidal figure of the earth due to that rotation. At the equator the fall of a heavy body is found to be 16.045223 feet, per second, and in that latitude the squares of whose sine is ⅓, it is 16.0697 feet. The effect in this last-named latitude is the same as if the earth were a perfect sphere. This does not, however, express the whole force of gravity, as the rotation of the earth causes a centrifugal tendency which is a maximum at the equator, and there amounts to 1 ⁄ 289 of the whole gravitating force. In other latitudes it is diminished in the ratio of the squares of the cosines of the latitude; it therefore becomes 1 ⁄ 434 in that latitude the square of whose sine is ⅓. Hence the fall per second becomes 16.1067 feet for the true gravitating force of the earth, or for that force which retains the moon in her orbit.