scientific works. Man is but a part of "one stupendous whole," as we shall have every reason to believe as we progress in the study of scientific physiognomy. The great French philosopher, Comte, recognized the intimate relation between universal existence and mathematical law, and he expresses his sense of it thus. He observes:

It is necessary for physiologists to have geometrical and mechanical knowledge to understand the structure and the play of the complex apparatus of the living, and especially of the animal, organism. The laws of equilibrium and motion are, as we saw when treating of them, absolutely universal in their action, depending wholly on the energy and not at all on the nature of the forces considered, and the only difficulty is in their numerical application in cases of complexity. Thus, discarding all idea of a numerical application in biology, we perceive that the general theorems of statics and dynamics must be steadily verified, in the mechanism of living bodies, on the rational study of which they cast an indispensable light. The highest orders of animals act in repose and motion like any other mechanical apparatus of similar complexity, with the one difference, of the mover, which has no power to alter the laws of motion and equilibrium. The participation of rational mechanics in positive biology is thus evident. Mechanics cannot dispense with geometry, and, besides, we see how anatomical and physiological speculations involve considerations of form and position. *

America has given to the world a philosopher who has perhaps grasped a profounder idea of the unity of law than any philosopher of ancient or modern times, and from his work I have received much instruction, as well as the verification of my theories upon the "Basic Principles of Form." Mr. Stephen Pearl Andrews, in his "Basic Outlines of Universology," formulates a universal basis for everything in existence, and this basis is Number. It is a daring, comprehensive, and masterly undertaking, and its laws can be applied to all other theories, facts, systems, and objects in the universe if they present truthful aspects. I had made all the discoveries pertaining to the law of form as applied to scientific physiognomy before I read Mr. Andrews' work, and I was both delighted and sustained by the support which his larger conceptions and generalizations afforded me. In my own department of research I am constantly surprised and gratified at the breadth of his philosophy and the manifold applications of its logic which I am enabled to make. Just here a temptation arises to give the reader some extended quotations from his work, trusting that as they progress in physiognomy, more particularly as they advance in the practical division, they will see more and more the use and beauty of his discoveries, which both indorse and assist in explaining my own theories on the symbolism and signification of form generally.

* Comte's Positive Philosophy, pp. 325, 326.

I am here undertaking perhaps a most difficult task, that is, to give the reader a tolerably clear idea of what Mr. Andrews deems the absolute basis of all thought and all things. The more I study the subject, the more difficult becomes the undertaking; but, as it corroborates my own theories, and more particularly that of the geometric outlay of the face, as shown in Fig. 1, and as his basis corresponds to and confirms my own ideas of the ruling principles of Nature in chemistry, architecture, and mathematics, and also that these three are a unity, or, in other words, are resolvable into number primarily, I shall attempt in as brief a manner as possible to make it clear to my readers, for in order to comprehend the "grand man" we must have some knowledge of basic or universal principles. No intelligent person should be satisfied with less. And now let us proceed to investigate why and how "Number is the proper index to the whole volume of Being, the inventory and label of the contents of the universe."*

I shall now give the statement of Mr. Andrews in regard to the scope of his discoveries, and shall then proceed to show the correspondencies existing between his discoveries and my own. I hold this to be the mutual corroboration of the truth of both his and my own observations and deductions, for all sciences, if based upon natural law, will coincide and mutually expound and verify each other. Mr. Andrews has made a very free use of capitals, and I have retained his style of printing as nearly as possible. This, together with the coinage of some new verbal forms, shows the marked individuality and strongly assertive selfhood of the man. The same attributes and tendency to originate a new vocabulary are observed in all original minds; besides, the demands of a newly discovered science or principle require new forms of style and expression.

Scientific laws and observations that harmonize are a part of eternal truth, hence incontrovertible and immortal, for "a law once demonstrated is good for all time." The definition given by Mr. Andrews of the science which he has formulated is stated thus. He observes:

Universology is therefore based on finding in the determinate particular (any one thing, however minute) a General Law, or, more properly speaking, a Group of Universal Laws, as a new basis of Generalization distinct from and traversing the law or laws of Being gathered from observation; all generalization (Universal) as distinguished from observational generalization (namely, the collection of numerous facts and the deductions made therefrom). This is analytical generalization (Universal) as distinguished from observational generalization (always partial or fragmentary, or, at all events, less than Universal). It is the Interior and Vital Law of All Organization,

* Basic Outlines of Universology, S. P. Andrews, p. 191.

and hence of the Constitution of Being itself (transcendental), as distinguished from the external and dead law. It is a new or a newly discovered Scientific Entity, a New Element in Science, revolutionary, exactifying, inaugurative of New Careers, and Scientifically Supreme. *

This new element which Mr. Andrews proposes to introduce is Number, the same by which Plato, Pythagoras, and other eminent Greek philosophers sought to pierce the veil of the infinite and open up to the world the secrets of creation. Many modern philosophers have sought from this basis to deduce a law of universal application. Comte, in his "Philosophie Positive," has come perhaps the nearest to it of the moderns up to the time of the appearance of "Universology." In his system he endeavors to make mathematics the basis of all things, yet Mr. Andrews goes farther, both in simplicity and complexity, and founds upon very simple numbers the whole scheme of being, viz., the dominance of the law which he terms "the spirit of the numbers 1, 2, and 3." The arithmetical reader will immediately recognize the fact that these are basic numbers, from the combinations of which all other numerical powers proceed. He says:—

Comte has furnished the rational basis for the first of these beliefs, viz., that the fundamental principles of all science are to be sought in the mathematics by establishing the fact that the mathematics are the basis or fundamentum of the pyramid of the sciences, in virtue of their greater simplicity and generality, properties which constitute the elementary character of this as of other elementary domains. He failed, however, to draw from the demonstration the consequence which I am here deducing from it, namely, that it is in this elementary domain of science that the first principles of all science must be sought. †

I shall now proceed to show Mr. Andrews' ideas of the supremacy of the first of these three units, and thence how they come to stand as representatives of the science of morphology or form; how, in fact, they create the sphere and cube, which he terms the "morphic measurers" of the universe, and which I find, when applied to the forms of man, to be the measurers and revelators of his character. On page 102 he remarks that "the number two (2) is the virtual basis of the whole of mathematics; more properly speaking, it is not a sum. Two (2), the first sum, is the simplest form of division; its included units being divided even before it is a sum, and division by thought lines or real lines is the Essence of Form." Of the dominance of simple numbers in all domains of thought and substance, he remarks:

If mere number is the simplest, most general, and hence the most elementary of the Domain of Thought and Being, we have next to inquire what is most simple, most general, and most elementary within this whole Ibid., page 103.

* Ibid., p. 590.

† Ibid., pp. 137, 138.

Domain of Being. Here the numbers (1), two (2), three (3) answer to our call, and appear as the first heads or principles prima capita of the whole positive numerical Domain. It is here that the Child begins to acquire Science in the pure and exact meaning of the term, and it is with these numbers or with the recognition of the Spirit or Meaning of these Numbers, enlarged into the Universal Principles of Being, that the Thinking World will pass from its infancy-the stage of mere observation and vague speculation to an exact comprehension of the Universe. *

The First law of Universal Being, in the natural order of precedence, has relation to the number one (1), and may be regarded as the spirit of one, whence it is denominated Unism, from the Latin unus, one.

It

It ramifies or permeates all thought, all existence, and all movement, and is one of the two organizing forces, or factors, or principles of all things in the Universe of Matter and Mind. The second law of Universal Being, in the natural order, has a similar relation to the number (2), and may be regarded as the spirit of two, whence it is denominated Duism, from the Latin duo, two. likewise ramifies or permeates constitutively all thought, all existence, and all movement, and is the remaining one of two antagonistic but co-operative organizing forces, or factors, or principles of all things in the Universe of Matter and Mind. The third law of Universal Being has relation to the number three (3), and may be regarded as the spirit of three, whence it is denominated Treism or Trinism, from the Latin tres, three.

From these three laws or principles the whole Universe is wrought out by their successive repetitions in new forms of manifestation in infinite variety, but in serial order and traceable regularity of structure from the lowest to the highest domain, from the basis of the scientific pyramid in the Abstract Mathematics up to its culminating point in Theology, or the science of God.

In quoting so copiously from universological laws as I shall, I leave out, as far as possible, all that pertains to the transcendental, the abstract, and abstruse, and come as quickly as possible to the practical applications of number to form, and as an application of the evolution of form from number I quote the following, which is simply and concisely stated. Mr. Andrews says:—

Posit through the imagination two points anywhere in space, and let these two points represent two units. Conceive of them as the sum called two, that is to say, collectively, or as co-existing at the same time in the mind; and this conjoining of the two individual or separate units into a collective twoness is necessarily effected by drawing a line of abstract thought as a trait d'union or connection between them. This line so improvised and interposed by the operation of the mind itself is then Limit, and as such it is the governing element of Form. Form is thus generated from Number.†

The preceding shows how the mind first by abstract reflection and imagination creates Form mentally. We can illustrate the process practically by placing two articles of any sort whatsoever in space, as, for example, two pencils, and we create a third object, viz., the form resulting from the space inclosed between the pencils; that is the most simple form that can be shaped.

* Basic Outlines of Universology, pp. 139, 140, et seq.

Ibid., p. 356.

Number is, then, the simplest or most elementary and primitive kind or variety of Limitation. The mathematical unit representing the Individual Thing is in turn represented Geometrically by the mere point, and Number is an aggregation of Geometrical Points. This is lower down in the Elementismus of Limitation than the line which pertains to figure or Form, and hence to Geometry, above the domain of mere Arithmetic. It is here, therefore, in Number and in the First Elements of Number that the definite limitations of Being must first be considered. *

Mr. Andrews includes a system of comprehensive analogies, by which Form is made to echo to or repeat Number, and this idea of echo or analogy is carried through everything in Nature, as well as into every human scheme, plan, government, system, and all modes of conduct whatsoever. I can only refer in a meagre manner to these manifold subjects, as I need all my space for the consideration of my own particular branch of science. Suffice it to say that all thinking persons can apply his system infinitely and absolutely unlimitedly. To return to the consideration of the analogies of form and number, Mr. Andrews observes:—

The Morphic Analogies of the 4, the 3, and the 7 are the square, the equilateral triangle, and the House, Edifice, or Temple with its body and its roof. The Compass (dividers) associates with the Circle. This, together with the Square, the Triangle, and the Edifice or Temple, again reminds us of the Symbolism of Masonry, as the Instinctual Stage of the religion of science and of the science of morals.t

The point is a very important factor of Form and Being. Aside from its significance as a unit in mathematics and its import as the type of the "least element of roundness" in general morphology, it is the analogue of the nucleus or "starting-point of development" in all organic processes, and it must also type the centre of the mineral crystal, where the polar forces cross each other in the development of that object. Although here the angle is formed, yet it corresponds to the point. It is the analogue of motion, and hence of development in the egg or vegetable cell, because it is from this central point, as in the germ spot in the animal egg, that the forces of the egg-substance are set in motion which commence the evolution or progressive development of the chick or mammal. It is, therefore, the type-form of Nature dominated by art in its inceptive or embryotic state. Motions are the essential forces of art acting upon substance.

We all know that the ovoid is the primitive type-form of the mineral, vegetable, and animal cell. How, then, do we arrive at the square, cube, and angle in primitive forms? By motion, by segmentation.