(35) The following interesting quotation from a writer on the subject serves to bring out some of the main points concerned in the consideration of the activities of this particular principle: "Cyclicity is akin to Rhythm, and arise by reason of it. All events tend to move in cyclic trend—in constant circular movement. The Law of Cyclicity manifests in the universal tendency of things to swing in circles. Cyclicity is the outgrowth, or more complex form, of Rhythm. The primal manifestation of Rhythm is action to-and-fro in. a straight line or path—a movement backward and forward between two extremes or poles of action. This would be the invariable movement if the particular force manifested were the only manifestation of force or energy in that particular field of the Cosmos. But when the swinging pendulum (free to move in any direction) is subjected to the conflicting attractions and repulsions of other manifestations of force and energy, then there is manifested the universal tendency toward the circular trend—the tendency to convert the straight path of the swing into a circular path or cycle. The action and reaction, the attraction and repulsion, arising from the conflict between the force of the rhythmic swing in a straight line on the one hand, and the attractive and repellant forces from without, on the other hand, tend to swing the moving thing in a perfect circle around a central point, axis, or pivotal centre. And these conflicting forces are in operation through the Cosmos, and the manifestation of Cyclicity may be noticed on all planes. There is ever the evidence of the cyclic trend of things and events—the tendency to move in circles. The electrons in the atoms move in circles, just as do the planets around the sun, and just as does the sun move around some other centre in space.

(31) The term "periodicity" so often employed in connection with the subject of Rhythm, means "state of occurring or recurring at fixed intervals of time." Every phenomenal thing manifests periodicity, by reason of the presence and activity of the Principle of Rhythm. Every phenomenal thing has its own rhythmic beat, or measure of periodicity. All scientific investigation tends to corroborate the ancient occult axiom: "Everything beats time." A leading scientist has said: "Rhythm is a necessary characteristic of all motion. Given the co-existence everywhere of antagonistic forces—a postulate which is necessitated by our experience—and Rhythm is a necessary corollary. All motion alternates—be it the motion of planets in their orbits, or ethereal corpuscles in their undulations—be it the cadence of speech, or the rise and fall of prices—it became manifest that this perpetual reversal of motion between limits is inevitable." The atoms in their vibrations manifest Rhythm. The swing of the planets and the whirling of the earth manifest Rhythm. The rise and fall of the tides manifest Rhythm. The swing of the pendulum is interrupted Rhythm. Completed Rhythm is represented only by a completed revolution or circular movement—uninterrupted Rhythm always manifests as a complete movement in an orbit. But inasmuch as the centre between the two extremes is, itself, moving in response to a higher order of Rhythm, we see at last that all completed Rhythm manifests as a spiral—a circular movement which at the same time is moving forward.

(28) So truly does advanced modern scientific thought recognize the nature of vibrations, that the axiom is announced that "The difference in things consists entirely of difference in vibrations." This axiom is akin to the ancient occult aphorism that "Things manifest differences according to their rate of vibrations." So, it is seen, all human investigation tends to prove the truth of the old occult axiom that "Everything vibrates." IV. The Principle of Rhythm The Principle of Rhythm manifests that universal regular swing or time-beat which is apparent in all the manifested world, from its highest to its lowest manifestation. The ancient occult axiom "Everything beats time" expresses this fundamental fact of the Cosmos.

(30) In all Rhythm there is recurring motion, change, and activity; action or motion in opposite directions; alternations between the opposite poles of action or motion; and a regular interval of time between the alternating actions or motions. In all phenomenal change or motion there is to be always found the existence of two opposite extremes between which the rhythmic change or motion is manifested. Rhythmic change and motion proceed by alternating swings between these two extremes, with a regular period of time elapsing between each beat, swing, or impulse in either direction. The period of "time" between the two alternating impulses constitutes the rhythmic rate, degree, or beat—its rhythmic measure of periodicity.

(32) By the Principle of Rhythm day is followed by night, and night by day. Summer and winter alternate in their appearance. Sleeping and waking alternate. Work and rest exchange places. Involution is followed by evolution, and evolution by involution. All changes proceed according to rhythmic order and sequence. The conduct of mankind is regulated by Rhythm. Fashions in dress, in taste, and in feeling, all come and go, and come again. Everything "comes back" in time. Races rise and fall, and then rise again, again to fall. The course of empire wends its way in cyclic procession around the earth. History repeats itself. Even our emotions have their tidal movements.

(25) And the same thing becomes the cause of contrary effects; sometimes through the magnitude of the cause and its power, and sometimes in consequence of the susceptibility of that on which it acts. According to the nature of the force, the same string, according to its tension or relaxation, gives a shrill or deep sound. And honey is sweet to those who are well, and bitter to those who are in fever, according to the state of susceptibility of those who are affected. And one and the same wine inclines some to rage, and others to merriment. And the same sun melts wax and hardens clay.

(46) Sometimes there is a rapid change and shift on the scale of the opposites. Love is quickly transmuted to hate; the best friends and most ardent lovers become the bitterest enemies. And, on the other hand, persons who originally detest each other frequently become ardent lovers after a time; and old enemies, when reconciled, frequently become the closest friends. The swing is often as far in one direction as was its former swing in the opposite direction. Up changes to down, as the earth revolves; and hot becomes cold when the vibrations are changed. This also applies to hard and soft, tenuous and solid, etc., the conditions depending entirely upon the rate of vibrations and relative positions of the particles of the matter of which the things are composed. Moreover, constant emphasis or activity of one opposite frequently leads to a manifestation of the other opposite. We often fly to the other extreme of feeling and action, when we have over-emphasized the former emotional states. We get tired and disgusted with one set or condition of things, and feel a desire to fly to the opposite condition or set. Too much of a good thing often causes us to dislike it. Likewise, if we travel far enough west, we finally reach the extreme east, and vice versa. If we travel far enough north, we pass the pole and find ourselves proceeding south. At the North Pole, no matter in what direction we may travel, we always find ourselves travelling south; while at the South Pole, we can travel north only, no matter which way we may step out.

(33) A writer has said of an important fact concerning Rhythm in our emotional states: "Nothing swings beyond the limit of its extremes—nothing can pass beyond its rhythmic limits. Consequently, if a thing swings far in one direction, it swings back equally far in the other. Its reaction is in the measure of its action, though in an opposite direction. If its swing is great, its extremes are widely apart—if the swing is small, then the extremes are close together. The pendulum illustration may be applied to the phenomena on all planes. A short beat of the metronome allows the rod to move only a short distance each way—the long beat admits of a wide swing. And, in the same way, those who suffer keenly also enjoy keenly, while those whose natures admit of but little suffering are also incapable of more than a limited capacity for enjoyment. A pig suffers little, and enjoys but little; while a highly organized, sensitive individual suffers the torments of emotional and mental hell at times, while at others he mounts to the heavenly emotional and mental realms. The pendulum swings as far in one direction as in the other." In some of the higher teachings of the Rosicrucians the student is instructed in the application of the Principle of Rhythm to the mastery of his emotional states and feelings. The essence of this secret teaching is that the wise, perceiving the inevitable reaction following action, the ebb tide following the high tide, manage to escape the consequences of the reaction by rising to their higher realms or planes of consciousness just before the time of the backward swing of the emotional pendulum, thus allowing the reactionary movement to be manifested only on their lower planes of consciousness while the Ego dwells serenely on the upper plane.

(41) Whenever we see a phenomenal quality, property or characteristic, a state or a condition, we are fully justified in assuming the existence of an opposite to it, which opposite thing will be found to act in the opposite and contrasted direction to it. This is an infallible and invariable rule of phenomenal existence.

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.

(1) [This chapter is supplementary to ch. v.] "The sky turns round; the earth stands still; sun and moon pursue one another. Who causes this? Who directs this? Who has leisure enough to see that such movements continue? "Some think there is a mechanical arrangement which makes these bodies move as they do. Others think that they revolve without being able to stop. "The clouds cause rain; rain causes clouds. Whose kindly bounty is this? Who has leisure enough to see that such, result is achieved? "Wind comes from the north. It blows now east, now west; and now it whirls aloft. Who puffs it forth? Who has leisure enough to be flapping it this way or that? I should like to know the cause of all this." Wu Han Chao said, "Come here, and I will tell you. Above there are the Six Influences and the Five Virtues.

(23) In the above we have but one of the many applications of the Principle of Correspondence, which teaches that "As above, so below; as below, so above;" and that "From One know All." II. The Principle of Law and Order The Principle of Law and Order manifests in the presence and manifestation of a regular sequence, and orderly procession of phenomena in the universe of things. It is voiced by the celebrated axiom of a leading scientist that "The Universe is governed by laws." The spirit of this principle of truth is embodied in the very term "The Cosmos," which term is derived from the Greek term "Kosmos," meaning: "The world or universe considered in connection with perfect order and arrangement, as opposed to Chaos." In the occult teachings of the Rosicrucians it is impressed upon the student that "there is no such thing as Chance," in so far as Chance is used in the sense of "uncaused happening." The student is taught that even in the instances in which Blind Chance seems to rule, there is still the manifestation of Law and Order and Causation, though the Causes may lie outside of human knowledge. The term "Chance" is now employed by careful thinkers only in the sense of "The unknown, or unforeseen cause or causes of an event." In the Cosmos the same Causes, manifesting under the same circumstances always produce the same Effects. All of our science and thought is based upon this universal fact, and intelligent reasoning would be impossible without the tacit assumption of the truth of this principle. There is no room for Chance or haphazard, lawless happenings in the Cosmos. Everything, every happening, and every event, must have its "causes" and its "becauses." Everything happens "because" of so-and-so. Given certain causes, there must ensue certain results and effects. "Nothing ever happens" says the old proverb—and nothing ever does "happen" except for definite causes, and in pursuance with universal laws. As someone has said: "There is no room in the universe for anything outside of and independent of Law and Order. The existence of such an outside Something would render all Cosmic Law ineffective, and would plunge the universe into chaotic disorder and lawlessness." A writer has said regarding this: "A careful examination will show that what we call 'Chance' is merely the idea of obscure causes, causes that we cannot understand. The word 'Chance' is derived from a word meaning "to fall" (as the falling of dice from the box onto the board), the essence of the idea being that the fall of the dice are merely 'happenings' unrelated to any cause. And this is the sense in which the term is generally employed. But when the matter is closely examined it is seen that there is no chance whatsoever about the fall of the dice. Each time a die falls, and displays a certain number, it obeys a law as infallible as that which governs the revolution of the planets around the sun, and the movement of the sun itself. Back of the fall of the die are causes, or chains of causes, running back further than the mind can follow. The position of the die in the box; the amount of muscular energy expended in the throw; the condition of the table; etc., etc., all are causes, the effect of the combination of which may be seen in the fall and position of rest of the die. But back of these perceived causes there are chains of unseen preceding causes, all of which have had a bearing upon the position of the die as it comes to rest on the table. If the die be cast a great number of times, it will be. found that the numbers shown will be about equal, that is, there will be an equal number of one-spot, two-spots, etc., coming uppermost. Toss a penny in the air, and it may come down either heads' or tails.' But make a sufficient number of tosses, and the heads and tails will even up. This is the operation of the Law of Average. But bath the average and the single toss come under the Law of Cause and Effect." The same writer says: "There is no original happening; and every happening is merely a link in a great chain of happenings. There is a continuity between precedent happenings, the present happenings, and future happenings. There is always the relation between what has gone before, and what is happening now, and what will happen in the future. For instance: A stone is dislodged from the mountain-side and crashes through the roof of a cottage in the valley below. At first sight this seems to be a chance effect, but when we examine the matter we find a great chain of causes behind it. In the first place, there was the rain which softened the earth supporting the stone and which allowed or caused' it to fall. Then back of that there was the influence of the sun, other rains, etc., which gradually disintegrated the rock from a larger piece. Then there were the causes which led to the formation of the mountain, and its upheaval by convulsions of nature, and so on ad infinitum. We might follow up the causes behind the rain. Then we might consider the existence of the cottage just at that place at that particular moment. In short we would soon find ourselves involved in a mesh of cause and effect from which we would soon strive vainly to extricate ourselves." But the Rosicrucians do not believe in Fatalism in the ordinary sense of that term. Fatalism denies that preceding events have any causal relation to preceding events, and holds that the fated event would have happened in spite of any precedent event. Fatalism makes the fated event stand apart from the Law of Cause and Effect, and implies that the event arose from the operation of some arbitrary degree or will. The following quotation from an authoritative source will serve to point out the essential distinction between Fatalism and the Determination of Cosmic Law: "Fatalism is the doctrine that the course of events is so determined that what an individual wills can have no effect on that course. Fatalism must be carefully distinguished from Determinism, as the confusion of these two conceptions has been responsible for much of the popular prejudice existing against Determinism. Fatalism, as has been said, denies that Will has efficacy in shaping events. Determinism maintains that this causally efficient Will is itself to be causally accounted for; this is entirely different for the fatalistic assertion that Will counts for nothing. In fact Determinism and Fatalism are fundamental antagonistic. Determinism asserts that events are determined by some of the events that immediately precede them; that if the latter were different the former would be different. Fatalism denies that immediately preceding events have anything to do with the origination of events immediately following: it asserts that the latter would occur even if the former were changed. To say that one's death is fixed by Fate is to deny that it takes place by natural law. Or, more accurately, it is to say that however much one varies the cause, one cannot vary the effect. The fatalist's position is that the end is predetermined, but not the means; the determinist's position is that the events now occurring lead by causality to other events, which are thus fixed because their causes are actually existent. Or, to put it still another way, for the fatalist what actually determines the event is not another event immediately preceding, but some mysterious decree issued by some mysterious agent ages before the event. This enables us to see that Fatalism gives no scope to the Will. But Determinism, which merely asserts that every event has its determining conditions in its immediate antecedents, includes among those antecedents the human Will. Thus Determinism is consistent with a belief in the efficacy of Will, and Fatalism is not." In the above we have illustrations of some of the many applications of the Principle of Law and Order, which teaches that "Nothing happens by Chance, but everything happening is in accordance with Law, Order, and Causation." III. The Principle of Vibration The Principle of Vibration manifests in the manifestation of a state of vibration in everything in the Manifested Cosmos. It is voiced by the old occult axiom: "Everything vibrates." Modern science has advanced to the position of the ancient occultists who asserted that everything in the Cosmos was in a state or condition of continuous vibration. Science now tells us that not only is every particle of matter, or every mass of matter, in a state of continual vibration, but also that light, heat, magnetism, electricity and every other form of natural force results from a state of vibration.

(16) I. The Principle of Correspondence The Principle of Correspondence manifests in a certain correspondence or analogy or agreement between manifestations of the various planes of activity in the Cosmos. It is indicated by the old Hermetic aphorism: "As above, so below; as below, so above," and by the Arcane axiom: "Ex Uno disce Omnes," or "From One know All." The Rosicrucians, and other ancient occultists, hold that the laws governing the nature and activity of the amoeba, likewise govern the nature and activity of man and beings higher than man. What is true of matter is true of energy and of mind. The occultists make a practical application of this universal principle, in the direction of studying the unknown by means of the known, with the knowledge that the same laws govern each. Thus, just as the solar system may be known by means of studying the atoms and molecules, so may the higher planes of being be studied by an examination of the lower planes in manifestation before us.

(69) The Pythagoreans declared arithmetic to be the mother of the mathematical sciences. This is proved by the fact that geometry, music, and astronomy are dependent upon it but it is not dependent upon them. Thus, geometry may be removed but arithmetic will remain; but if arithmetic be removed, geometry is eliminated. In the same manner music depends upon arithmetic, but the elimination of music affects arithmetic only by limiting one of its expressions. The Pythagoreans also demonstrated arithmetic to be prior to astronomy, for the latter is dependent upon both geometry and music. The size, form, and motion of the celestial bodies is determined by the use of geometry; their harmony and rhythm by the use of music. If astronomy be removed, neither geometry nor music is injured; but if geometry and music be eliminated, astronomy is destroyed. The priority of both geometry and music to astronomy is therefore established. Arithmetic, however, is prior to all; it is primary and fundamental.

(18) A writer has said of this Cosmic Principle: "There is always a correspondence between the laws and phenomena of the various planes of life and being. The grasping of this truth gives one the means of solving many a dark paradox, many a hidden secret of Nature. There are planes beyond our knowing, but when we apply the Principle of Correspondence to them we are able to understand much that otherwise would be unknowable to us. This principle is of universal application and manifestation, on the various planes of the material, mental and spiritual universe—it is an universal law. The ancient Hermetists considered this principle as one of the most important mental instruments by which man was able to pry aside the obstructions which hid from view the Unknown. Its use even tore aside the Veil of Isis to the extent that a glimpse of the face of the goddess might be caught. Just as a knowledge of the principles of Geometry enables a man to measure distant suns and their movements, while seated in an observatory, so a knowledge of the Principle of Correspondence enables man to reason intelligently from the Known to the Unknown. Studying the moneron, he understands the archangel.

(5) One day while meditating upon the problem of harmony, Pythagoras chanced to pass a brazier's shop where workmen were pounding out a piece of metal upon an anvil. By noting the variances in pitch between the sounds made by large hammers and those made by smaller implements, and carefully estimating the harmonies and discords resulting from combinations of these sounds, he gained his first clue to the musical intervals of the diatonic scale. He entered the shop, and after carefully examining the tools and making mental note of their weights, returned to his own house and constructed an arm of wood so that it: extended out from the wall of his room. At regular intervals along this arm he attached four cords, all of like composition, size, and weight. To the first of these he attached a twelve-pound weight, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight. These different weights corresponded to the sizes of the braziers' hammers.

(34) In this diagram two interpenetrating pyramids are again employed, one of which represents fire and the other earth. It is demonstrated according to the law of elemental harmony that fire does not enter into the composition of earth nor earth into the composition of fire. The figures on the chart disclose the harmonic relationships existing between the four primary elements according to both Fludd and the Pythagoreans. Earth consists of four parts of its own nature; water of three parts of earth and one part of fire. The sphere of equality is a hypothetical point where there is an equilibrium of two parts of earth and two parts of fire. Air is composed of three parts of fire and one part of earth; fire, of four parts of its own nature. Thus earth and water bear to each other the ratio of 4 to 3, or the diatessaron harmony, and water and the sphere of equality the ratio of 3 to 2, or the diapente harmony. Fire and air also bear to each other the ratio of 4 to 3, or the diatessaron harmony, and air and the sphere of equality the ratio of 3 to 2, or the diapente harmony. As the sum of a diatessaron and a diapente equals a diapason, or octave, it is evident that both the sphere of fire and the sphere of earth are in diapason harmony with the sphere of equality, and also that fire and earth are in disdiapason harmony with each other.

(530) other proportion. No, he replied, such an idea would be ridiculous. And will not a true astronomer have the same feeling when he looks at the movements of the stars? Will he not think that heaven and the things in heaven are framed by the Creator of them in the most perfect manner? But he will never imagine that the proportions of night and day, or of both to the month, or of the month to the year, or of the stars to these and to one another, and any other things that are material and visible can also be eternal and subject to no deviation—that would be absurd; and it is equally absurd to take so much pains in investigating their exact truth. I quite agree, though I never thought of this before. Then, I said, in astronomy, as in geometry, we should employ problems, and let the heavens alone if we would approach the subject in the right way and so make the natural gift of reason to be of any real use. That, he said, is a work infinitely beyond our present astronomers. Yes, I said; and there are many other things which must also have a similar extension given to them, if our legislation is to be of any value. But can you tell me of any other suitable study? No, he said, not without thinking. Motion, I said, has many forms, and not one only; two of