In other words, the solar system is situated within the ring of the milky zone, but "much nearer" to the southern inner edge of the ring, where the "considerable inflection" or divergence into two branches takes place, than to the inner edge of the ring in a northern direction. This confirms the wonderful exactness of Swedenborg's statement :

"That our solar vortex is not in the axis, but is near the axis, where there is a considerable incurvation or inflection."

He fixes the position of our solar system by three conditions:-1. It is not in the common axis, as he terms it. 2. It is near the common axis. 3. It is near that portion of it where there is a considerable incurvation or inflection. All of which are wonderfully true, and now regarded as expressive of a most important matter of fact. Let it be observed, this position was assigned fifty years before Herschel first conjectured it, and that no published record exists of its being even surmised before the time of the latter, except in the way pointed out in the introductory remarks to this article.

This striking confirmation of Swedenborg's formula is a hundred-fold more wonderful than the confirmation of Leverrier's formula for the discovery of planets, as much so as the discovery of the situation of planets in a planetary system is to the discovery of the situation of suns in a starry system. Before Herschel confirmed the formula in the manner previously stated, there were as many reasons for doubting the position of our sun among the stars, assigned by this formula, as there are for doubting the position of all other stars. But the formula is like a cornucopia, which, turn it on whatever side you will, something rich and valuable is sure to drop out. For, if you take the data of the distances and elliptic structure of the planetary orbits of any system, you then obtain the situation of its sun, and, by it, of all others in the starry cluster; but, if you reverse the ends of the calculus, and take, for your data, the situation of each one of the suns or stars, you then obtain the form and elliptic character of all the orbits at different distances, forming the system of each. These are the wonderful results which this new formula will realize. Do you ask for proof? Bear in mind that the demonstration has been given,-the strongest, the only one, indeed, which can be demanded. The position of our solar system amongst the stars has been assigned, and observation has since declared, that the sun can be seen to occupy the identical position. And this demonstration will answer for all the stars. And when this is obtained, the character of their respective systems, the form of the planetary motions revolving around each, become, at once, as demonstratively evident as those of our own system. This is, indeed, a mighty achieve

ment of the eminently profound and colossal genius of Swedenborg. By the striking demonstration of this formula, given as a discovery by Herschel, the possibility of informing ourselves of the general character of the planetary motions around each star, is carried to the highest point in the certainty of reason. Besides this information, astronomy will derive some important advantages from its application, inasmuch as it most beautifully developes the mysterious groundwork of those secular inequalities and cycles of incalculable length, to which the solar system, as a whole, is liable. As this is a most important fact, I will briefly furnish the reader with two direct mathematical proofs.

Proposition.The theory declares, that as the solar system is carried along the milky path, and afterwards compelled to diverge therefrom, the planetary orbits will change their form and eccentricity to a certain amount, and then return to their original condition, when they will again change, and again return, and so on to eternity.-Principia, vol. ii. pp. 233-238.

First Direct Proof.-The beautiful demonstration by La Grange* of the stability of the solar system, is a direct proof of Swedenborg's theorem. The changes in the character of the planetary orbits, spoken of in the proposition, were already known and seen to be at work undermining the present form of the system, and fears were entertained that they might become exorbitantly great, so as to subvert those relations which render it habitable to man. This was a difficulty which appeared insurmountable to the astronomers of Swedenborg's day, and for some time afterwards. Theologians everywhere accepted it as an obvious demonstration of their doctrine of the final destruction of all things. Newton and Leibnitz had both bowed with submission to the order of things, which was winding up the operations of the great whole, and bringing on an inevitable doom. Geometers, philosophers, and theologians, accepted the fact as evidence of the common declaration, “that the end of all things," if not at hand, was at least certain. Everywhere the profoundest mathematical resources were employed to their utmost limits, but the equation on one side always equalled nothing, and the quantities only seemed to converge without the slightest possibility of their opening out, and again returning to a new development of being. Only one bright refreshing spot existed, like an oasis, where weary man, had he known it, might have refreshed himself; and that was the Principia of Swedenborg. There alone, amongst all the works of this period, is shewn the now accepted doctrine of a cyclar return. At length, Lagrange appears with a demonstration, grounded on the disco* Memoirs of the Royal Academy of Berlin, 1777.

very of a certain relation which prevails in the system, between the masses, orbital axes, and eccentricities; by which the doctrine is completely established, that though the solar system is liable to certain mutations in the form and eccentricity of its orbits, of very long periods, yet its orbits return again exactly to what they originally were, oscillating between very narrow limits. The same matter has been recently investigated by Leverrier with the same successful results.* So that the doctrine of a cyclar return in the form of the solar system, first propounded by Swedenborg, is now received as one of the most beautiful conceptions of man, under the name of La Grange's Theory of the Stability of the Solar System. †

There is, however, this superiority in Swedenborg's theory, it not only explains the doctrine of a cyclar return, but also most satisfactorily exhibits the reason why it is so, bringing the philosophy down to the very senses, by telling you, Principia, vol. ii., page 230

"In the magnet and its sphere there is a type of the heavens: a mundane system in miniature presented to our senses;

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the philosophy being stated where referred to in the proposition to these remarks. So far, therefore, Swedenborg's Principia is capable of actual demonstration; for La Grange has already done it.

Second Direct Proof.-The proposition of Swedenborg declares, that this doctrine of the cyclar return is grounded on the changes and mutations in the form of the whole system, considered as a unit or globular vortex, in being bent in various directions, and again unfolding itself, according as it happens to be either passing in or out, or along the stream of the milky way; the latter being considered in the light of a magnetic axis. The fact of such a cyclar return has been completely established, as we have shown: nothing now remains but to establish, that these secular outstanding changes are dependent on, and due to, the translatory motion of the solar system. Hitherto, astronomers have admitted only the doctrine that quantity of matter is the only standard of the amount of attractive force; but now, another is added to their formulæ. Specific forces of attraction, coming from adjacent and surrounding systems, which act additionally to those belonging to, and arising out of the system itself, thereby causing additional and unaccountable changes in the form and situation of the system, producing translatory motions in space, these specific forces are now, for the first time, taken into

* Taylor's Scientific Mem., part 18.

+ After Newton's discovery," says Professor Playfair, "of the elliptical orbits of the planets, La Grange's discovery of their periodical (or cyclar) inequalities is with out doubt the noblest truth in physical astronomy."

N. S. NO. 121.-VOL. XI.

B

consideration. Bessel, the great Konigsberg astronomer, was "the first to conjecture" (Cosmos, vol. i., page 137) and practically apply this idea to the solution of planetary disturbances. The solution is similar in character to that given by Laplace to solve the discovery of Halley, in regard to the secular acceleration of the moon's mean motion, at the rate of eleven seconds in a century. Every change in the form of the earth's orbit, causes one in the distance and periodic time of the moon. So also with the sun and its system; every change in the form of the orbit of the sun, causes a change in the distances and form of orbits throughout its system. Accordingly, Bessel has proved, in an article entitled "An Investigation of the Portion of the Planetary Disturbances depending on the Motion of the Sun,” (Abh. der Berlin, 1824, s. 2—6.) that secular inequalities are produced by this motion, and are due solely to its influence; therefore, they change with the relative situation of the solar system amongst the stars; and that, with the return of the whole solar system to the same position in its orbit, and amongst the same stars, the whole planetary system will be brought to its original form and condition. This theory, as we have shown above, Bessel was the first to conjecture and apply. And it is clear, it will most satisfactorily explain the whole doctrine of a cyclar return. The question was also raised by Mayer in a German work (Comment. Soc. Reg. Gotting., 1804— 1808, vol. xvi., pp. 31-68). The learned reader may also consult Arago in the Annuaire, 1842, pp. 388-399.

Thus the whole theory of Swedenborg is capable of actual demonstration. And such is its immense usefulness and extensive applicability, that we have not the slightest hesitation in affirming its capability of solving all the fundamental problems in sidereal astronomy. As we proceed in our report of the discoveries contained in the Principia, this will be abundantly apparent. The reader would be well rewarded by a double perusal of the two demonstrations referred to above. La Grange is the acknowledged first suggestor of the cyclar theory, and Bessel the first suggestor of the theory of its cause. Yet the whole doctrine is repeatedly given, by Swedenborg, in the compass of half a dozen sentences; yea, a score of times in the course of the chapter on "The Heavens," vol. 2. This doctrine was published forty-four years before Lagrange put forth his, seventy-one years before Mayer, and ninety-one years before Bessel.

Having now given this double proof of the important advantages which may be derived from the application of his beautiful formula, I will return to the first demonstration, which is more immediately the object of this article. Of this singular achievement of the genius

of Swedenborg-the most extraordinary on record-there is now no room for doubt. He assigned the exact position of our solar system amongst the stars fifty years before it was even conjectured. Are not these great facts? Are not these discoveries, theoretical though they be, most honourable to the name and genius of Swedenborg? Most truly they are so. When will the world do justice to the memory of his departed genius?

(To be continued.)

S. BESWICK.

NEWTON;-HIS DOCTRINE OF A VACUUM AND OF COLOURS.

(From Swedenborg's Diary.*)

I HAVE spoken with Newton concerning a Vacuum, and concerning Colours. In respect to a vacuum he said, that in the world he believed there was a vacuum; but when the angels perceived that he had the idea of a vacuum as of nothing, they averted themselves, saying that they could not sustain the idea of a nothing, because with the idea of nothing, the idea of the essence of things perished, and together with that idea perished also the idea of thought, of understanding, of affection, of love, and of will, both with men and with angels, all which things cannot exist in nothing, or a vacuum. They inquired from Newton whether the Divine principle from which angels have all their wisdom, and men all their intelligence, both in the spiritual and the natural worlds, is a vacuum, and thus whether any divine operation can flow through a vacuum into their vacuum, and present those effects of thinking, loving, &c. to their perception. Being troubled at this interrogation, he replied that he could not believe that these effects took place in an absolute vacuum, which is a nothing; but by an apparent vacuum, because the Divine principle is the very Esse itself of wisdom and love with the angels in heaven, and with men in the world, and fills all things. But this Divine Esse and this vacuum or nothing are opposites, so much so, that if the one be supposed to exist, the other cannot; wherefore the angels besought him, that he and all others who had cherished the idea of a vacuum as of nothing should desist from that idea, that they might be together; knowing that nothing of their life can possibly exist in a vacuum, or a nothing, but in those things which are and which exist from the Esse of all things [or from the Divine], adding that concerning

* See Appendix, page 5.