the binomial theorem, or pay a little attention to the expansion of infinite series, they would not persist in calling for a degree of accuracy which is impossible, or in neglecting an important element in a calculation, because it is involved in a certain liability to error within very narrow limits. The absurdity of the reason assigned for this omission, is rendered still more apparent by the case of the prismatic spectrum, which I conceive to be exactly in point. Now, what is it that this beautiful phenomenon displays? The seven primary colours, arranged in a peculiar order, and glowing with an almost painful intensity. But each of these colours occupies a certain space in relation to the whole, the boundaries of which it may be impossible for the hand or eye to trace with geometrical precision, although the relative space in question has nevertheless been made the subject of measurement, and a very close approximation obtained from the mean of a vast number of trials. According to the principle followed by some antiphrenologists, however, breadth should be altogether neglected, because the boundaries of the respective colours are, forsooth, "purely ideal," as if a mathematical line were not the most perfect idealism or abstraction which the mind of man can possibly form. This idealism or abstraction, however, has no more to do with those approximations which may be obtained practically by repeated trials, than the mathematical definition of a line with a metallic rod; and it is a mere quibble to pretend, for example, that we ought not to measure the length of the rod, because it may not correspond with the definition of the line. Upon the strange principle which some opponents have adopted, they must be prepared to maintain, that the boundaries of a hill or hillock are purely ideal, and depend in every instance on the fancy of the measurer *.

An organ may thus be likened to an inverted cone, with its apex in the medulla, and its base at the surface of the brain; the broader the base and longer the distance between • Caledonian Mercury, 11th June 1829.

it and the apex, the greater will be the size, or the quantity of matter which it will contain *. This simile, however, is introduced merely as an illustration, and I do not assert that the organs may be seen regularly disposed in the brain in the shape of cones. Hence, if the line from the ear to the forehead be much larger than from the ear backward, and the breadth nearly the same, we infer that the organs in the forehead predominate. If, on the other hand, the forehead be very narrow, as in THURTELL, and the hindhead very broad, we hold the posterior organs to predominate, although the length be the same in both directions. The whole organs in a head should be examined, and their relative proportions noted. Errors may be committed at first; but without practice, there will be no expertness. Practice, with at least an average endowment of the organs of Form, Size, and Locality, are necessary to qualify a person to make observations with success. Individuals whose heads are very narrow between the eyes, and little developed at the top of the nose, where these organs are placed,

• "There are many convolutions," says Dr SPURZHEIM, " in the middle line between the two hemispheres of the brain, and others at the basis and between the anterior and middle lobes, which do not appear on the surface; but it seems to me that a great part, at least, of every organ does present itself there, and further, that all the parts of each organ are equally developed, so that, though a portion only appear, the state of the whole may be inferred. The whole cerebellum does not reach the skull, yet its functions may be determined from the part which does. The cerebral parts, situated in the middle line between the hemispheres, seem proportionate to the superincumbent convolutions; at least I have always observed a proportion in the vertical direction between them.". Phrenology, p. 116.

The cerebral parts, situated around" and behind the orbit, also re. quire some care and experience on the part of the phrenologist, to be judged of accurately. Their development is discoverable from the position of the eye-ball, and from the figure of the superciliary ridge. According as the eye-ball is prominent or hidden in the orbit, depressed or pushed sideward, inward, or outward, we may judge of the development of the organs situated around and behind it.”—Ibid. Particular directions for observing the parts there situated will be given, when treating of the relative organs.

experience great difficulty in distinguishing the situations and minute shades in the proportions of different organs. (See Note as to Dr GALL, No. I. of Appendix). If one organ be much developed, and the neighbouring organs very little, the developed organ will present an elevation or protuberance; but if the neighbouring organs be developed in proportion, no protuberance can be perceived, and the surface is smooth. The student should learn from books, plates, and casts, or personal instruction (and the last is by far the best), to distinguish the form of each organ, and its appearance, when developed in different proportions to the others, because there are slight modifications in the position of them in each head.

The phrenological bust shews the situations of the organs, and their proportions, only in one head; and it is impossible by it to communicate more information *. The different


• Attempts have been made by opponents to represent certain changes, in the numbering and marking of the organs in busts recently published, as a Revolution in Phrenology." A brief explanation will place this matter in its true light. T phrenological bust sol in the shops is an artificial head, the utility of which depends on the degree in which the delineation of the organs on it approaches to the appearances most generally presented by the organs in nature. The first bust sold in this country exhibited the organs as they would be found in a particular head, not very common in this country, the bust having been imported from the Continent, and national heads being modified as much as national features. On 1st October 1824, a new bust was published in Edinburgh, in which the delineation approached nearer to the appearances and relative proportions presented by the organs in this country. Subsequent observations shewed that this bust might be brought still more closely to resemble the most common proportions of the organs in Britain; and, on 1st April 1829, certain modifications were made on it accordingly. The nature of this operation may be explained by a simple illustration. Suppose that, in 1819, an artist had modelled a bust, resembling, as closely as his skill could reach, the face most commonly met with in Scotland, and that, to save the trouble of referring to the different features by name, he had attached numbers to them, beginning at the chin, and calling it No. 1., and so on up to the brow, which we may suppose to be No. 33. In this bust he would necessarily give certain proportions to the eyes, nose, cheek, mouth, and chin. But suppose he were to continue his observations for five years, it is quite conceivable he might come to be of opinion that, by

appearances in all the varieties of relative size, must be discovered by inspecting a number of heads; and especially by contrasting instances of extreme development with others of extreme deficiency. No adequate idea of the foundation of the science can be formed until this is done. In cases of extreme size of single organs, the form delineated in the bust is distinctly perceived.

The question will perhaps occur, If the relative proportions of the organs differ in each individual, and if the phrenological bust represents only their most common proportions, how are their boundaries to be distinguished in any particular living head? The answer is, By their forms and appearances. Each organ has a form, appearance, and situation, which it is possible, by practice, to distinguish, in the living head, otherwise Phrenology cannot have any foundation.

making the nose a little shorter, the mouth a little longer, the cheeks a little broader, and the chin a little sharper, he could bring the artificial face nearer to the most general form of the Scottish countenance; and that he might arrange the numbers of the features with greater philosophical accuracy; and suppose he were to publish a new edition of his bust with these modifications of the features, and with the numeration changed so that the mouth should be No. 1., and the chin No. 5., and the brow No. 35., what should we think of a critic who should announce these alterations as "a revolution" in human physiognomy, and assert that, because the numbers were changed, the nose had obliterated the eyes, and the chin had extinguished the mouth? This is what the opponents have done in regard to the new phrenological bust. In the modifications which have been made on it, the essential forms and relative situations of all the organs have been preserved, and there is no instance of the organ of Benevolence being turned into that of Veneration, or Veneration into Hope, any more than, in the supposed new modelled face, the nose would be converted into the eyes, or the eyes into the mouth.

In regard to the numeration, again, the changes are exactly analogous to those which are before supposed to take place in regard to the features: The organ of Ideality formerly was numbered 16, and now it is numbered 19, but the organ and function are nothing different on this account. Dr

PURZHEIM adopted a new order of numbering, from enlarged observation of the anatomical relation of the organs, and his improvements have been adopted in Edinburgh and Dublin.

When one organ is very largely developed, it encroaches on the space usually occupied by the neighbouring organs, the relative situations of which are thereby slightly altered. When this occurs, it may be distinguished by the greatest prominence being near the centre of the large organ, and the swelling extending over a portion only of the other. In these cases the shape should be attended to; for the form of the organ is then easily recognised, and is a sure indication of the particular one which is largely developed. The observer should learn, by inspecting a skull, to distinguish the mastoid process behind the ear, as also bony excrescences sometimes formed by the sutures, several bony promi. nences which occur in every head, from elevations produced by development of brain.

In observing the appearance of individual organs, it is proper to begin with the largest, and select extreme cases. The mask of Mr JOSEPH HUME may be contrasted with that of Dr CHALMERS for Ideality; the organ being much larger in the former than in the latter. The casts of the skulls of RAPHAEL and HAGGART may be compared at the same part; the difference being equally conspicuous. The cast of the Reverend Mr M. may be contrasted with that of DEMPSEY, in the Love of Approbation; the former having this organ large, and the latter small. Self-Esteem in the latter being exceedingly large, may be compared with the same organ in the skull of Dr HETTE, in whom Love of Approbation is much larger than Self-Esteem. The organ of Constructiveness in RAPHAEL may be compared with the same organ in the New Holland skulls. Destructiveness in BELLINGHAM may be compared with the same organ in the skulls of the Hindoos; the latter people being in general tender of life. Firmness large, and Conscientiousness deficient, in King ROBERT BRUCE, may be compared with the same organs reversed in the cast of the head of a lady (Mrs H.), which is sold as illustrative of these organs. The object of making these contrasts is to obtain an idea of

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