Book of Alchemy


Chapter 7


Relation of the Law to Light and Matter


    The student recalls when, during his early school years, he studied the science of geometry, it was pointed out to him that most theorems or laws possess corollaries.  He discovered that many laws of nature could be extended and expanded, thus giving rise to new formulas; but only combinations of the same basic laws.


    The student at this stage of development is still so greatly enmeshed in the struggle of comprehending a fundamental law itself that he is chained to its immediate structure and is therefore, neither capable of extending the law further nor deriving the consequences thereof.


    When through additional instruction as to the effects or action of a law, such presentation will have two advantages: (1) It will open an extended field of vision.  (2) It will enhance the clarity of perception of the fundamental law itself, of which the parallel is an effect.


    As we review in this lecture, the law of the triangle, extend its significance and scope and apply it to a series of problems which are of significance to the student.


   Multiple Causes – Chain of Events


    The law of the triangle, as previously stated, has been applied only to the case of a single event.  But in actual experimental practice this is seldom the case.  The common experience is that many events occur in the form of chains.  A cause may give rise to a certain effect.  This effect, in turn, may serve as a cause, producing a new effect.  A pictorial form is shown in Fig. No. 1:   




    Such a chain of events may readily be transformed into the triangular form, as follows:


    We have noted that a positive, active cause when acting upon a negative recipient produces as a result a manifestation.


    This manifestation in a chain of events now serves as a new cause.  Usually it becomes an active cause, which when acting upon a new recipient (negative) will give rise to a manifestation.  Under certain circumstances the manifestation may serve as a passive cause.


    Thus, the chain of events moves on, the manifestation always serving as a renewed active cause.


    As a specific example of a chain of events, we take the case of a man ringing an electric doorbell.  The chain of events is as follows:


The man’s finger pushes against the button and the button

is depressed.  The button, being depressed, pushes against

a spring which closes an electric switch.


The switch is now closed and the voltage of a dry cell

is applied to the resistance of the wires, causing a

current to flow.


This current flows through a coil and produces

therein a magnetic attraction.


The magnetic action attracts a plunger which, when in

motion, causes a metallic hammer to strike the bell.  


    It would be well to study this sample with great care and note the various active and passive causes.  Also note how the manifestation transforms into either an active or a passive cause.


    In the form of a diagram this case is illustrated in Fig. No. 2


Fig. No. 2


    We note that at the point “A”, of the diagram No. 2 there occurs a break in the chain of triangles.  The reason for this is that the action of triangle number II produces a manifestation which serves as a passive cause, or recipient for the voltage of triangle number III.


    Breaks in sequence always occur during trigger or relay actions.  Good examples of such cases are mousetraps, pistols, and relays.


    The importance of such relay actions is that they show how the direction of a course of events may be changed or displaced by other external events.  The illustrations shows why it is so difficult to predict the future from the present.


    If a chain of events were restricted in such a manner that a manifestation could serve only as an active cause and never be a passive cause, then it would be relatively simple to predict the future from the present.


    The possibility that a manifestation may serve as a passive cause and thereby change the direction of events and displace their lines of progression makes the prediction of the future from the present more difficult.


    If the course of a human life is mapped out using this system, it will become a triangular network of an extremely complex pattern.  As a good exercise for the student, it is suggest that he analyze and make a map of the causes and effects which activate his behavior during the relatively short time interval of five minutes.  Such an exercise will reveal to him the immense complexity of the structure patterns of cause and effect.  This is logic of the mind.


    In closing this section, let me point out the fact that the operational form of the triangle is also used to denote the union of opposites.  It asserts that every manifestation must be brought about by the union of two causes of opposite polarities.  Their union produces the equilibration, the arch, the perfect manifestation.


    But let us remember that your word shall be made flesh.


    The Laws of Energy


    The sun, the visible manifestation of an invisible center, is the source of all energy.  From the sun there radiates into the surrounding space the primary energy of nature, Spirit.  This energy is a dual polarity, positive and negative.


    This energy has the nature of a wave and it produces a vibratory condition wherever it strikes and it has the Personality of the Father.


    We use the word energy often. The student is tempted to use the words Force, Energy, and Power synonymously.  If he will look up in a dictionary the precise meaning of these words he will discover that each word has a significance particularly its own – a different state.


    For our purpose now, for the sake of simplicity, let us define the word energy as follows:  “Energy is any positive, or active, cause which has the ability to produce a manifestation.”

    Students are sometimes confused by the meaning of the word manifestation.  By manifestation we denote any event which is able to make itself manifest to us.  Thus by “manifestation” we mean a perceptible effect.  Such effect may be perceptible on the material plane through our objective senses, or it may be perceptible on the immaterial plane through our spiritual senses.


    The first impression is that of “sensing,” “feeling,” or “perceiving”.  This is usually followed by a reinterpretation of these feelings in terms of objective sense perceptive.


    The concept of energy is fundamental in the field of science.  It is as fundamental as the concepts of space and time, which does not exist.


    The science of energy is also called Thermodynamics.  It has been so named because the first experiments concerning the nature of energy were conducted using heat as the form of energy under investigation.  The science of “Thermodynamics” could much better be named Energetics.


    There are two fundamental principles of thermodynamics.  The first law is called the Principle of Conservation of Energy.  This principle asserts that energy can neither be created nor destroyed, but may be transformed.  It insures that the total amount of energy within the universe does neither diminish nor increase, but remains the same.


    Science also asserts that energy may transform from one kind into a different kind.  Mechanical energy may change into electrical; immaterial energy may transform into material.


    The secondary law of thermodynamics is also called the Principle of Degradation of Energy.  It asserts that although energy may transform from one kind to a different kind, it always changes from a higher form to a lower form.  Energy always changes from a form where it is easily available, to perform a manifestation, to a form where it is less available.


    An application of this law is the fact that heat must always flow from a higher temperature to a lower temperature.


    The second law asserts that there exists a certain direction along which energy manifests, from higher forms to lower forms.  From a more organized state to a less organized state.


    The second law of thermodynamics may be regarded as a law of devolution of energy.


    Energy, being an active, positive cause, must obey the law of the triangle.  We shall now consider this law in greater detail.


    The symbol of the triangle


    The earlier statement is the objective representation of a perfect creation.  It is used either with its apex upward, to represent a material creation, or with its base upward, to symbolize an immaterial creation.


    The symbol of the triangle is used in two distinctly different manners.  These are called the operational form and the hierarchical form.  Both applications of the symbol of the triangle apply equally well to a material creation as to an immaterial creation.


    Before discussing the two uses of the law of the triangle in detail, let us briefly state the meaning of the uses.


    The first way in which the triangle is used is to show the manner in which a manifestation is created.  It is the law of dual causes and their effect.  It shows how forces in nature operate in order to produce manifestations.  This is the operational form of the triangle.  Logically?


    The second manner in which the law of the triangle is used is as a representation of levels of development.  It postulates that all levels of development are in steps of three.


    It shows that there are three distinct points required in a perfect manifestation.  This we shall call the hierarchical form or use of the law of the triangle.


    Thus there are these two forms or uses.  The operational form, the law of cause and effect; and the hierarchical form, the law of degree of development.  We shall now discuss each form in detail.


    The operational form of the law of the triangle


    In a previous section of this article, it was stated that the word energy denoted any agent or active, positive cause which has the ability to produce a manifestation.  There is but one basic energy.


    In order to produce such a manifestation, the active or positive cause must always act upon a suitable recipient, which we may call a passive, negative cause.   


    In our studies the active, positive cause is symbolized by the number one, the passive, negative cause is symbolized by the number two, while the manifestation is symbolized by the number three.  Hence, the law of energy, recalling our studies is: 1 + 2 = 3, which is the Law of the Triangle.


    In pictorial form, the law of the triangle is illustrated in Fig. No. 3 on page 47.


    This diagram represents the operational form of the triangle.  It demonstrates how forces in nature must operate in order to produce a manifestation.


Fig. No. 3


    Let us examine the operational law in greater detail.  We note that all causes in nature are dual - positive and negative.  Every cause, in order to produce a manifestation, must commence with two elements.  These two elements must be of different polarity.  One must be active; the other, passive.  One must be strong and forward; the other must be a recipient.


    However, the two causes must be related to one another.  The recipient must bear a definite affinity or attunement to the cause.  Let me illustrate: An electrical force will give rise to a manifestation only when it is permitted to act upon an electrified body.  It will have no effect upon a magnetic object, or upon a non-electric (neutral) object.


    On the other hand, a chemical force will produce an effect only if it is permitted to act upon a chemical substance.


    A psychic force will produce a manifestation only if it permitted to act upon a recipient who is in a state of psychic attunement.


    It is the violation of this principle of attunement between active and passive causes which gives rise to the failure of many experiments.


    If a manifestation is desired, it is always imperative to ascertain whether or not the two causes are properly related to one another.  Except when God given.


    Another fact which the laws of the triangle illustrates is the fact that all manifestations occur on a level different from that of the causes.


    Causes operating in a state of rest will produce a manifestation in a higher level, a state of motion.


    Causes acting in the immaterial plane will produce a manifestation upon the material plane.  This is indicated in the diagram by the words Level “A” and Level “B”.


    We thus see that the operational law of the triangle is the Law of Cause and Effect.


    Our first illustration is taken from the science of mechanics.  It is well known that when a mechanical force is permitted to act upon a mass, it then will produce a change of motion.  If the mass is initially at rest, then upon application of the force, the mass will commence to move and accelerate.  (See Fig. No. 4)

    The “force” is, in this illustration, the active cause, and the “mass” is the recipient or passive, negative cause.  The manifestation or effect is the “acceleration” or “change in motion.”


    In the form of a diagram, this is illustrated in Figure No. 5:


    A very common error, frequently made by beginners, is to interchange one of the causes, usually the active, with the manifestation.


    In fact, it is this confusion between cause and effect which is the reason for the failure of many experiments.


    Unless the three operational points of the triangle are clearly visualized in their proper positions, the law of the triangle cannot operate, the situation under consideration is not understood, and no manifestation can take place in the desired direction.  Unless you use Gods’ word.   


    Reconsidering the example which has just been discussed, let it be desired to set an object, a mass, into motion.  In considering this problem the beginner very often makes a false assumption by assuming that the motion is the active cause; actually, the motion is the effect or manifestation.


    In this particular example, it is clear it is the force which must be the active cause.  It is this force which, acting upon a mass, produces the change in motion (acceleration).


    A second illustration of the operational form or use of the law of the triangle will be taken from the laws of electricity.


    We know that if a difference in electrical pressure – also called by scientists “difference in electrical potential”, or “potential difference” – or voltage is allowed to act upon the ends of a conductor, then a flow of electric current will result.


    The magnitude of this flow is dependent upon the resistance which the conductor offers to the passage of electrical current.


    We may thus say that a voltage, acting upon a resistance produces, as manifestation, an electric current.  Hence the triangle is as follows in Fig No. 6:


    In this example the voltage is the positive cause, while the resistance is the negative cause, and the electric current produced is the manifestation or effect.


    Again, a beginner is very often tempted to interchange active cause and manifestation.  He will speak of “sending a current through a wire,” as if current were the active cause.  However, the applied voltage is the cause; the current is the effect, or manifestation.


    Although mistakes such as these are easily detected in experiments performed upon the material plane, great care must be exercised when the law is applied to experiments performed upon the immaterial plane.


    From this discussion, we now understand the operational form or use of the law of the triangle, the law of cause and effect.


    Before discussing the hierarchical form or use of the law, let us develop the operational form still further.


    The Hierarchical Form of the Law of the Triangle 


    We next discuss the second manner in which the symbol of the equilateral triangle is used.


    The second form or use of the law is based upon the fact that all perfect manifestations in the universe manifest in three levels of development.  For any perfect condition to exist, there must exist three points, three levels.


    There exist three fundamental units within matter: electrons, atoms, and molecules.  Electrons of dual polarity combine to form atoms.


    Atoms of dual polarity combine into a molecule.


    Thus electrons, atoms, and  molecules form three levels of development or evolution.  The lowest level is the electron; the highest is the molecule.


    Thus, these three elements form a hierarchical progression, a complete manifestation, symbolized by the triangle in Fig. No. 7.



    When the triangle is used in this hierarchical form, it used with slightly different emphasis from that of its use in the operational form. 


    Both the operational and the hierarchical forms of use are related to one another.


        From the many illustrations of this Trinity of Points, let us recall two additional groups: Life, Light, and Love; and also Man, the Universe, and God.


       The Relation Between the Operational and Hierarchical Forms 


    Below, in Fig. No. 8,  it is easily seen that the operational form is implicitly contained within the hierarchical form.


    Using the previous illustration of electrons, atoms, and molecules, we note that electrons of opposite polarity combine to form atoms.

Fig. No. 8


    Furthermore, positive and negative atoms or atomic groups combine to form molecules.  Hence, as in Fig. No. 9.

                                    Fig No. 9    Fig.                                            No. 10



    These two triangles are the operational forms.  When their result is combined, we obtain the hierarchical form as in Fig. No. 10.


    We thus see that both forms of the triangle are manifestations of One Single Law.


Application of the triangle law to wave propagation




    Having discussed the law of the triangle in detail, one of the most important applications of the law is to the problem of wave propagation.


    All waves are started by vibrations.  Every vibrating object pushes rhythmically against any substance which surrounds it.  If the surrounding substance is elastic, such as air, a wave is started by the vibrating object. 


    A familiar example of this fact is the vibration of the string of a violin which pushes against the surrounding air and sets up a wave therein which reaches our ears.


    Another example is a stone which, when dropped into a pool of water, causes water waves to spread out over its surface.


    In our studies, we have learned that the nature of the entire universe is vibratory and that vibrations constitute the only Actuality, except the substance of God.  Thus, waves are generated everywhere and their action manifest upon reaching us.  The nature of wave pulse is an attribute of the personality of the Father.


   In many instances, the waves of primary energy, Spirit, spirit of God, upon reaching us, are able to produce definite effects upon special human sense organs, especially equipped to respond to them.


    These sense organs, in turn, activate certain centers within our brains and originate certain realizations or Realities of the vibratory Actualities.


    Such is the case with the vibrations of light and sound.


    The incoming waves are of such a nature that there exist no receptor or sense organ within the human organism to produce any direct Realities.


    However, very frequently, such waves produce certain manifestations which may be transformed into realizations of light and sound by means of suitable instruments created by man’s objective consciousness.


    An example of this is provided by the phenomena of electrical or radio waves.  The discovery of radio waves was delayed for such a long time because the human organism does not possess any special sense organ to perceive them, or neither was the spiritual hearing sensitive enough to receive thought waves.


    For this reason, a radio receiving set is so constructed that it transforms the electric vibrations into vibrations of a different kind, which the human organism is capable of sensing, namely, sound (in the ordinary receiving set) or light (in a television set)


    Fundamental properties of waves


    As the primary energy – God force – has personality (wave properties), the study of the fundamental properties of waves is of importance to us in our studies.


    Remember that the laws and principles of material science are only reflections of the more extended laws of arcane science.


    The laws and principles here do apply to all types of waves: light, sound, electrical and waves of higher frequency.


    We shall consider the familiar example of water waves.  A stone is dropped into a quiet pool of water.  Large circles of ever-widening radii spread from the place where the stone touches the water, out into the surrounding surface.


    After the waves have reached the banks of the pool, they disappear, and the surface of the water becomes quiet again.


    If, instead of dropping a stone, the surface of the water is touched with a finger and the finger is moved rhythmically up and down, the same phenomena will occur.


    We will note, if we perform the experiment, that there exists a definite relationship between the rapidity with which the finger is moved up and down at the place where it touches the water, and the distance between the circles which spread out.


    If the finger vibrates slowly, then the distance between the successive circles is large; whereas, when the finger vibrates rapidly then the circles follow one another closely together.  This is frequency.


    From these simple observations, we conclude that there are two fundamental requirements necessary to generate a wave: (1) a vibrating source; (2) an elastic substance which is in contact with the vibrating source, and is able to transmit the wave.


    Words commonly used by scientists in describing the behavior of a wave, and their meanings:


    The “source” of a wave is the point where the wave originated.

    The “rays” are the directions in which the wave travels.


    The “wave fronts” are the traces formed by all particles of the vibrating substance which are identically disturbed at any instant.  In the example under consideration, the wave fronts are circles. 


    The “velocity of propagation” of a wave is the speed with which the wave advances along any given direction.  (See Fig. 11).  

    We are now in a position to apply the operational law of the triangle to the generation of a wave. 


    We note that the vibrating source is the active, positive cause; the elastic substance is the passive, negative cause (recipient); while the wave is the resultant manifestation.


    Hence, the triangle becomes as shown in Fig. No. 12.


    There is an additional fundamental fact concerning waves. We shall develop it by considering another simple experiment.



    The dot represents the “vibrating source”


    The arrows represent the “rays”


    The circles represent the “wave fronts”





Fig. No. 11


    Let us place small pieces of paper at various points upon the surface of the water.  We next produce a wave once more by dipping a finger rhythmically into the water.


    We observe the waves which are generated and how they spread out into the surrounding water surface.


    We now observe the pieces of paper and note how they are affected by the wave.  The important thing to observe is that the pieces of paper are not pushed along by the advancing wave.


      The pieces of paper will be forced to move rhythmically up and down as the wave passes by, but they remain at their location upon the surface.


    From this simple observation, we may derive one very fundamental fact: It is only the disturbance which is propagated out, away from the surface.


   The elastic substance itself through which the disturbance travels remains at rest as a whole, although each particle of the substance will vibrate back and forth about its rest position.


   In fact, for each particle of the elastic substance, the law of the triangle becomes as follows:   

    The vibratory force of the arriving wave – the positive cause – acts upon the particle of the elastic substance – the recipient – and produces a vibratory motion – the manifestation.


    We thus see that a wave is the propagation of a periodic or rhythmic disturbance through an elastic substance.


    Only the disturbance is propagated; the substance as a whole remains at rest, although its particles are vibrating back and forth about their rest positions.


 The disturbance which is propagated represents energy, the ability to perform a manifestation (work), when acting upon a suitable recipient.


    It is this vibratory energy which forces each particle of the substance located in its path to execute a vibratory motion.


    As the energy moves away from its source, where it is generated, it spreads over an increasingly larger area, thus weakening the effect.


  Definition: A wave is the propagation of a periodic disturbance through an elastic substance.  The following conditions are necessary in order to produce such a wave:


(1)    A vibrating surface


(2)    An elastic substance


(3)    A properly attuned recipient, which has the ability to vibrate.


    Fundamental wave concepts


    In describing the properties of waves, there are certain concepts used, with the meaning of which every student should be familiar.  (See Fig. No. 14).

1.  Wave length:  The length of a wave, or – in short – the wave length, is the distance between two corresponding points of a wave.  It is the length of one complete cycle, thus:

                               It can also be the distance between two wave crests, such as B-B Fig. 14, or between two starting points. ( As shown in the diagram above.)


2.  Amplitude: The amplitude, or half-swing, of any wave is the maximum displacement of any particle of the wave from its rest position.  Thus it is, roughly speaking, equal to a “half-swing” of any vibrating particle.  (See Fig. No. 14).


3.  Frequency: The frequency of a wave is the rate of its vibration.  A wave which vibrates very rapidly is said to be of “high” frequency.


    The frequency of a wave is thus an indication of how frequently a number of complete waves (wave lengths) pass by a given observer during a set time interval.  The frequency equals, more precisely, the number of complete waves which pass an observer stationed at any specified point, during the time interval of one second.


Relation between frequency and wave length


    It was stated that the more rapidly the finger touches the water with a vibratory motion, the more closely spaced were the distances between successive wave crests. 



    This experiment demonstrates that there exists a definite relationship between frequency and wave length.  If the frequency (rate of vibration) increases, then the wave length decreases.  If the frequency is small, then the wave length is large.


    It can be shown that when the frequency of a wave is multiplied by its wave length, then the product equals the velocity of propagation of the wave.      


Wave propagation


    We shall now apply the operational law of the triangle to the case of the propagation of a wave through an elastic substance.  Such a substance consists of molecules which possess forces of attraction between them, having constraining bonds.  We might roughly picture such a substance objectively as consisting of metal spheres which are mutually connected by metallic springs, thus:

    If sphere number 1 is moved to the left, then its motion is transferred to sphere number 2 by means of the spring a, and sphere number 2 is forced to move to the left also.


    If sphere number 1 is given a vibratory motion back and forth, then this motion is transferred through the elastic bond a to sphere number 2.  If sphere 1 is moved rhythmically up and down, then the bond a will force sphere 2 to do likewise.


    There is, however, a time lag between the two motions due to the inertia of the spring.  Sphere number 2 will move at a slightly later time than sphere number 1.


    In a similar manner the vibrations of sphere number 2 are transferred to sphere number 3, etc.  We note that it is the elasticity of the springs which determines the speed with which the disturbance advances.


    It is in a manner such as this that the elastic bonds within an elastic substance operate.


    We are now in a position to apply the law of the triangle to the problem at hand.


    A vibratory force applied at the source of the wave is applied to the first particle of the elastic substance and forces it to execute a vibratory motion.  This vibratory motion is transferred by means of the elastic bond to the next particle, and applies to this particle a vibratory force.


    Now the cycle of events repeats.  This vibratory force sets the next particle into motion, which is, in turn, transferred further.


    It is in this manner that a wave progresses in space according to the law of the triangle.






    It is impossible within the short space of this lecture to discuss the many additional applications of the law of the triangle to the domain of wave propagation.  There exists a large number of additional wave laws.


    In this lecture, the law of the triangle has been applied to the case of the propagation of a wave through a material substance.  Examples of such waves are the waves produced by sound, by water, and the elastic waves which may flow through solids.


    The waves produced by light and electricity – in fact, the waves of the Cosmic Keyboard – differ from the types of waves mentioned above by the fact that they do not require a material substance for their propagation.


    Light and electrical waves may flow through a vacuum, but there is no real vacuum.  Psychic waves do not require any material medium for their propagation.


    For a long time, science believed that there did exist a material substance, the ether, which served as the carrier of the waves of the Cosmic Keyboard.  But when experiments were performed, designed to test the nature and properties of this “ether” it was discovered that if it did exist at all, then it would have to possess a series of mutually contradictory properties.


    For example, it would have to be infinitely rigid and also infinitely elastic at the same time.  For this reason, mundane science has abandoned the concept of the “ether.”  Mundane science now postulates that empty “space” has the property of being able to sustain the propagation of the waves of the Cosmic Keyboard.


    We must clearly keep in mind that this is simply an admission of the fact that the waves of the Cosmic Keyboard are not material.


    At all times we must keep in view the Hermetic axiom “As above, so below.”  The laws of material science, as manifesting “below” to our objective senses, are the reflections of the “above,” the laws of arcane science.


    From what we perceive “below” we may arrive by logical induction at a dim perception of what is “above.”  If we desire to master the laws of the universe, a mastery of the simple mundane laws of the material world is a prerequisite to the study of the laws of the immaterial universe.  The laws of the material world will serve us as a guide in our technique, and as a guide to our imagination.


     All wave laws, of which you will read in the various textbooks, are applicable to all types of waves – I repeat, all waves, material and immaterial.  By mediation, you will gradually learn to perceive the higher laws of which the mundane laws are the reflections.


Remember that the spoken word surpasses all, - but that word god gave us still involves the technology of the known laws as we have been declaring in this lesson.


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