the name and character of the Highest, the Earliest, the Endless. One is the centre of all, the foundation of every being, and all particular properties which are not absolute and necessary, but direct or indirect radiations of the absolute unity. Ten ones form again an unity of tens up to a hundred; ten tens an unity of hundreds, &c. All the higher comprehend the lower unities, and insomuch as the lower is contained in the higher, so far is the reciprocal community shown. Thus is it also with the universe. Each higher world embraces all the unities or inferior worlds subject to it, and the lower take part in the higher worlds, spheres, and creations, as far as they, as inferiors, can be embraced by them. In the hundred, all numerals, from 1 to 100, are contained; under the class animal all creations of animated nature; and as the numerals from 1 to 100 become more similar as they progress, equally do the lowest in the ranks of animals rise higher and become more developed, till at length the highest members are united to man, without ever being able to reach him. The endless variations of animals, as well from as among themselves, agree also with the normal conditions, where one link can divide itself into endless portions. The Eastern theory of radiation is the same, according to which the lower orders arise from the higher, and embrace and permeate them.

The application of the primary numerals to the spiritual and material world we find in the Magicon as follows:

"True mathematics is something with which all higher sciences are connected; common mathematics is but a deceitful phantasmagoria, whose much-praised infallibility only arises from this-that material conditions and references are made its foundation. As long as it is only confined to this it can certainly not fail; but as it is far different in respect to those things which do not regard it, it can never attain the object of a true science. Above all things it depends upon the knowledge of the straight and crooked lines. If the former is explained as a continuation of many infinitely small straight lines, this is just as radically false and far from the true laws of Nature, as it is a proof of how much men are inclined to confound all things together. As in Nature everything has its distinctive nume

ral, thus are there two lines also. Emanations into the infinite is the subject of the straight, and restriction or deviation from this infinite progression the subject of the crooked line."

"These two numerals, with which the knowledge of everything intellectual and material is connected, remain through all gradations of quantity the same; for greater or lesser expansions of the straight and crooked line are but gradations and varieties of action and duration, as all results of their various gradations must always be to each other as 4 to 9. Herein we find all individual as well as generic differences of intellectual and material nature explained. From this it arises that individuals of the same class differ, and yet have one common law, source, and numeral. This also explains the nullity of all arbitrarily accepted conventional numerals in geometry. The signification of the straight and crooked line may be a key to many secrets of physiology and physiognomy. For here the straight line always shows strength, central energy, reason; while, on the contrary, circular formation is associated with less firmness and more material insolidity. Moreover, the signification of the numerals 4 and 9, the straight and crooked lines, does not only extend to the form and action of the human soul, but also to the whole sensitiveness and energy of its principles. Men of the highest order shew themselves in thought like brilliant rays of light, as their style is straightforward; others of a low grade, on the contrary, spend and write in circles and periods, and therefore are so agreeable to material ears."

From these extracts we may perceive that the characteristic of numerals of the present day is connected with one of much more ancient date, upon which still more might here be said, if the primitive and perfect theory of Pythagoras had been preserved. He was certainly not the discoverer of his cosmological theory of numerals, but, like Thales, had been led thereto by the Egyptians, whose sacred numbers of the Universe were known as the Hermetic numerals; but the true Pythagorean theory is much more closely related to the source of this species of symbolism, than that which the later Half-Pythagoreans and New

Patonists said of it; upon whose speculations and expla Iations we can seldom rely.

Pythagoras was personally a handsome man, and of such a majestic appearance that his scholars believed him to be Apollo. He was clothed in white, and wore always spotlessly clean linen, holding that light and everything good was white, while night and evil were black. The number of his listeners was sometimes stated to be two thousand. But he admitted few to his nocturnal instructions. He divided his instructions into daily and nightly. To the first every one might be admitted, because his lectures consisted in admonitions to virtue and warnings against vice. To the second, however, his scholars were alone admitted, who were chosen only after many examinations and trials, and lived in a community of property. A Pythagorean disciple was especially obliged to overcome all desires, and live strictly in the prescribed manner. Whoever did not persist in the trial was looked upon as dead. The Pythagorean silence which his scholars maintained is well known, and which, according to their capabilities, usually lasted two, three, or even five years. During this time they were only listeners, and did not even see their master Pythagoras during the hours of instruction, but sat behind a curtain. He at first instructed by allegories and symbols, which were usually taken from geometrical and numerical figures, and, when they had comprehended these, by short and enigmatical sentences, which contained either natural or moral truths. It was only after all these preparations that the perfect instruction followed in the profounder sciences. (Diogenes Laertius, Of the Life and Teachings of Celebrated Philosophers, Bohn's Classical Library; Büsching, History of Philosophy, Part. I.: Pythagoras.)

Plato deserves an especial mention, not only because he purified and raised to philosophical theories the various popular superstitions on magic, demons, and spirits, which are said to reveal themselves in the air, in water, &c., and in various shapes to men, but also because his spiritual theory is materially a magical one, and gave rise to the institution of a school, called by his name, whose members may be counted as among the most energetic defenders of magic;

I mean the New-Platonists at Alexandria. I shall here make a few extracts regarding his principal views, and shall commence with what he says about numerals.

Plato calls him happy who understands the spiritual numerals, and perceives their mighty influence. The knowledge of the natural numerals serves, according to Plato, to the investigation of the good and beautiful; without this divine gift one can neither know human nature in its divine and mortal parts, nor yet the foundation of true religion. The numerals are the cause of universal harmony, and the proEduction of all things. Whoever, therefore, abandons his numeral, loses all community with good, and becomes the prey of evil. Even the worship of God, from which all other virtues proceed, rests upon a true knowledge of numbers; the wise man must, therefore, study them ahove all things. The soul is immortal, and has an arithmetical as the body has a geometrical beginning; it, as the image of an universally distributed soul, is self-moving, and from the centre diffuses itself over the whole body. It is, however, divided according to fixed spaces, and forms as it were two connected circles. The one he called the movement of the soul, the other the movement of the All and the erratic stars. In this manner the soul is divided into two portions; and, placed in connection with the outward, perceives that which is, and exists harmoniously because it comprehends in itself. the elements of a certain harmony.

If I make mention here of this mystical theory of numerals, it is not without special intention. On one hand, we hear the heroes of scientific antiquity, who lived not far removed from that age when mysticism treated not only of religious and poetical subjects, but also of certain unknown truths of nature; on the other hand, we cannot be blind to the fact that, in such a theory of numerals, a real and profound signification may be contained, and not alone an idle speculation or fantastical subtlety. For, through the wonderful progress of modern chemistry, the old axiom that determined numerical conditions govern the material world has gained an unexpected signification. Stechiometry shows indisputably in the combination of molecular atoms, a regularity of number as strictly observed by God in the minutest forms as in the

majestic nature of the heavens. If the modern philosopher feels his insignificance with a profound humility in presence of the admirable powers of nature, and as it were unavoidably falls into a religious feeling; if he become dumb before the Almighty, and feels himself inwardly and profoundly impelled to adore Him, does he not stand in a certain relationship to Pythagoras and Plato ?

Plato's other teachings regarding the soul, which the Alexandrians so greedily seized upon, are as follows: "Our soul is a particle of the divine breath, and therefore we are related to God: our soul's divine ideas are natural, and are created by the contemplation of divine things. Before it was associated with the body, it existed in God; even now, though enveloped by the body, it may participate in that divine contemplation through the subjection of the passions and through a contemplative life (Plato in Phædro). Whoever has elevated himself to truth-(ovTwç 8v)—that is, above that which is without change, without creation and decay, he lives truly and according to the divine nature. (Plato de republica, vi.) We may therefore read God through our soul, may approach and regard Him; and this contemplation fills us with the highest and truest pleasure, and makes us happy." God has implanted in the human as well as in the universal soul, of which it is a particle, the conceptions or images of all things, which, however, are obscured in it as soon as it enters the dark cavern of the body. That which Plato says of God and matter, which are the eternal causes of all things; of the world and its connection; of the universal soul, may be seen in many of his dialogues, -for instance, in Timæus, &c.,—and these are true magnetic doctrines; many passages have already been extracted from them at an earlier time.

We must not wholly pass over what Plato says of an early celestial history of man, considering this, as he does, one of the chief reasons for a belief in a future existence. As this later, present life, is simply a loss of man's wings, his whole endeavour ought now to be to regain them. To this end, the purification of true philosophy is beyond everything else, and to it must be added the initiation into the mysteries and perfection in them. For by means of the true phi