posed to the visitor's gaze. Vegetative people in their thoughts and acts seem to "wobble" about, and are uncertain, unstable, and confused in their plans and movements. There seems no fixity of purpose, because they are composed mainly of fluid material, and, like the waters of the ocean, they are ever shifting, and never definite; hence, we cannot expect to find a high phase of either Order or Time in those in whom the vegetative system is supreme. Yet, even in this class of persons, Order can be very much strengthened by commencing early with them, and insisting upon their having a place for everything and compelling them to regard this law. The exercise of the faculty of Order is essential to all the higher mental powers. In combination with Calculation, Time, and Reason, it assists the astronomer and mathematician. Combined with Constructiveness, Weight, Form, and Size, it aids the operations of the mechanic and artist. With Language, Memory of Events, Observation, Constructiveness, Locality, and Time, it is the ally of the historian and editor. Associated with Music, Calculation, Time, Constructiveness, Intuition, and Ideality, it is a valuable assistant to the composer. To the naturalist, teacher, scientist, mechanic, chemist, and physicist, Order is most essential. No high pursuit can succeed with deficient Order, for the arrangement of ideas in an orderly manner, as well as the placing and classifying of substances and articles, demands a good degree of this faculty. Form, Size, and Locality, where they are well developed, assist deficient Order and compensate one measurably for such deficiency. The preceding statements show the origin and action of this high and useful trait. The higher an organism has evolved, the more Order it exhibits; and the lower the organism in the scale of creation, the less accurate, precise, periodic, and orderly is it in its habits, methods, and movements. The numerous signs, together with the very diverse origin of the several phases of Order, as above described, very materially enlarges the phrenological notions in regard to this faculty and its single cranial sign. CALCULATION. Aristotle lays down the general principle of the Pythagoreans in the following terms: "Number," he says, "is, according to them, the essence of all things, and the organization of the Universe in its various determinations is an harmonious system of numbers and their relations." Definition. The science of numbers or computation; capacity for numerical calculation; ability to keep accounts and understand * Basic Outlines of Universology, S. P. Andrews, p. 150. numerical relations; skill in the arts of counting; addition, subtraction, multiplication, and division; memory of dates, figures, and numbers. An excess of this power is rarely met with, and, when it is, we find that it is usually the compensation for some very serious deficiency in some other department of mentality. Where the mind dwells too much upon calculation, to the exclusion of every FIG. 116.-GALILEO GALILEI. (ASTRONOMER, Born at Pisa, 1564. Conspicuous facial sign, Calcu lation, shown by width between the outer terminus of the eyebrow and the outer angle of the eye. The law of the straight line, square, and cube governs this face. The Quality of this subject is very high and Color dense. The domestic and moral signs are large. Although partially hidden by the beard and moustache, the superstructure tells us this is correct. Such a nose and forehead must have a superior vegetative base from which to draw their power. Benevolence, Love of Home and Country can be seen and are large. The mouth, by its size, announces good alimentive capacity. The nose is long, large, high, broad, and bony. In it the signs for Ideality, Mental Imitation, Analysis, Sublimity, Constructiveness, Acquisitiveness, Veneration, and Selfwill are large. Size, Form, Language, Observation, Locality, Weight, and Calculation are uncommonly developed. Mental Order, shown by squareness of the forehead, is most decided, while Reason and Intuition show the highest degree of development. Altogether a physiognomy of transcendent power and scientific beauty. thing else, the character loses a great deal of general power, and the other faculties become weakened through want of use, and the mind is turned into a mere calculating machine. We rarely find, however, such excessive action of this faculty. It more often needs cultivation than restraint. A deficiency causes one to be inaccurate in his count, reckoning, and accounts; dull and slow in arithmetic, and unable to keep the date or number of anything in the mind correctly. Calculation is easily cultivated by persist- Facial and Bodily Signs. outer terminus of the eyebrow and the outer angle of the eye. This peculiarity of formation causes the eyebrow to flex upward and tend toward the upper part of the ear. This sign is found most decided in the faces of the muscular races, and of those who possess not only large arithmetical calculation, but also a shrewd, crafty, cunning, politic, tactful, and worldly disposition. The Mongolian race and face well illustrate this form and phase of numerical talent. The Celtic races also exhibit the mental aspect of this faculty. Like Order and Time, there are several manifestations of this trait. The osseous individual reveals a phase of Calculation different from that which distinguishes the muscular man. The kind of Calculation exhibited by the former is more purely mental and assists him in mechanical pursuits, while the latter is the artistic form; that is to say, the phase of Calculation which can estimate numbers and weights by sight and by lifting. DESCRIPTION.-Calcu lation is a general and principles. Modesty, and Force. Where the brain is large and of good or fine quality, combined with a good endowment of square bones, a high degree of geometric calculation is present, and talent for trigonometry and mensuration will be shown. Born at Turin, 1736. Conspicuous facial sign, Calculation. The law of the curve and square governs this face. The signs for Firmness, Conscience, Love of Home, of Country, and of Young are well defined; so, also, are Benevolence, Friendship, Pneumativeness, Mirthfulness, Amativeness, Approbation, Sanativeness, Modesty, and Force. Alimentiveness and Bibativeness are normal. In the nose, which is arched, long, high, broad, bony, and muscular, we find all of the signs of mental greatness. Hope, Analysis, Mental Imitation, Human Nature, Ideality, Sublimity, Construction, and Acquisitiveness are all very large; while the signs for Executiveness, Veneration, and Self-will are pre-eminent. The region about the eyes and interciliary space is noteworthy. Form, Size, Observation, Weight, and Locality are well defined. Calculation is of the highest order; while Mental Order, Reason, and Intuition are wonderfully developed. The writings of de Lagrange are not only of the highest mathematical value, but are elegantly written and presented. He well deserves the title of a "luminary of mathematical science." A noble and beautiful physiognomy. The muscular form in excess gives the combination for pure calculation, but, when accompanied by a good degree of the brain system and fair development of bone, it manifests talent for mathematics and for calculations of the relations of circular forms and number. The sign for numerical calculation observed in the formation of the terminus of the eyebrow being most decided where the muscular system is dominant is an excellent proof of its muscular origin. It also explodes the phrenological error that this indication is caused by a "cranial organ or accumulation of "brain-matter" at this place. The phrenological idea of "organs" which are said to be observable on the outside of the skull is giving way to recent discoveries of "brain areas or tracts" of the internal cerebral structure, wherein are located the centres of motion or of impulse, which act with and for the several bodily organs and functions. The faculty of Speech, for example, it has been demonstrated beyond a doubt, has its representative in a certain area of the brain, but it is not situated behind the eyeball, pushing the eye outward and forward, as phrenology asserts. The sign for articulate speech, it is true, is shown in the face by prominent eyes, also by the shape of the mouth, lips, and ears; but this same faculty can just as well, or nearly as well, be discerned by the finger or fingernail of those in whom the muscular system is dominant, for the reason that Language and Calculation are both best developed in those races in whom the muscles are in excess of the bones. The Oriental races, for example, exhibit large calculative powers. They also reveal great Acquisitiveness (they are natural gamesters) and other muscular traits in harmony with numerical calculation, such as diplomatic policy, craft, cunning, and deception. All these faculties are the most conspicuous in muscular races, as well as in the muscular animals, and are shown by signs of muscular develop ment, and not by "brain organs" externally on the skull. The basis of everything is (as I have shown in the chapter on the "Basic Principles of Form ") mathematical or numerical. Every separate atom, article, and entity is countable, and holds its rank as number one, two, three, etc., in a certain department of creation; hence Number is a universal element and principle, and enters into all things. It is thus shown to be a prime and primitive element in everything, and also takes its rank among the highest and most perfected aspects of Nature, as in the completion of schemes, plans, and numbers of finished creations; for ex ample, in the numbers of the bones, muscles, and organs in man; the numbers of leaves of plants, which are governed by mathematical precision; by the divisions of the earth into continents, islands, etc. I could pursue this form of illustration almost indefinitely, and then have made only a beginning. The science of numbers has many departments; as, for example, it commences with the primary and simplest aspect of counting or enumerating, and this is the phase first exhibited by children and undeveloped races. The latter never get beyond this stage. The Esquimaux, it is said, can count only ten; while the Greenlanders can reckon only five besides the enumeration of their fingers and toes; yet many dogs, birds, and even pigs, have been trained to count as high as sixty. Dr. Carpenter tells us that the young Yanco of the Amazons can count no higher than three. The powers of enumeration shown by muscular races, such, for example, as the Mongolian, are extraordinary in degree, and universal among them. In their counting-houses they make use of the abacus, sliding-rule, and tallies, and other numerical instruments. This form of reckoning is a primitive one, and is used in many schools by the younger pupils in object-teaching. The other branches of arithmetic and mathematics require the use of memory and the reasoning processes. The science of numbers seems to many persons a very abstruse and profound subject, but to others it is entirely simple. The cause of this is found in inherited differences. The capacity for pure calculation has been exhibited in early childhood by certain persons in a most surprising and precocious manner, but I believe the higher forms of number, such as those used in mensuration, in engineering, and in other departments of applied geometry, have never been exhibited by any very young arithmeticians, because the application of the higher principles of number requires the exercise of a high degree of Reason, and this faculty is never found greatly developed in childhood. George Bidder and Zerah Colburn were precocious arithmeticians, who in early childhood "lisped in numbers" and astonished the world by the exhibition of their wonderful numerical power; yet in adult life they were not celebrated for any very great superiority in any direction, except the power for calculating immense sums. The following account of Zerah Colburn, an American lad, who was brought to London in 1812, at eight years of age, I quote from "Mental Physiology," by Dr. Carpenter. Of the powers of this lad, which he terms most happily "numerical intuition," he states that, upon being examined by several eminent mathematicians, he gave the following test: He raised any number consisting of one figure, progressively to the tenth power, giving the results (by actual multiplication and not by memory) faster than they could be set down in figures by the person appointed to record them. He raised the number eight progressively to the sixteenth power; and in naming the last result, which consisted of fifteen figures, he was right in every one. Some numbers consisting of two figures he raised as high as the eighth power, though he found a difficulty in proceeding when the products became very large. On being asked the square-root of 106,929, he answered 327 before the original number could be written down. He was then required to find the cube-root of 268,336,125, and with equal facility and promptness he replied 645. He was asked how many minutes there are in forty-eight years, and before the question could be written down he replied 25,228,800, and immediately afterward he gave the correct number of seconds. On being requested to give the factors which would produce |