BIDDER, when a mere child, displayed such astonishing talent as a mental calculator, that several gentlemen in Edinburgh were induced to take charge of his education; and, on the supposition that his abilities extended to mathematical science generally, selected for him the profession of an engineer. Having heard of this intention, and having observed that in his head the organs of the mathematical faculties were not developed in any extraordinary degree, I inferred that his eminence as a mathematician would not equal that which he had attained as a calculator, and communicated this conviction in writing to Principal BAIRD, one of his patrons. Mr BIDDER subsequently pursued the study of mathematics; but, at the end of two years, both he himself and Professor WALLACE informed me, that he was not distinguished for more than common ability in the class. I have since heard that Mr BIDDER has not prosecuted the profession of an engineer; but obtained employment in a public office, in which his great talent for computation renders him particularly useful.

When the group of organs situated at the top of the nose, namely, Individuality, Form, Size, Weight, and Locality, are all large, there is generally a strong talent for dynamics. Persons thus endowed excel in turning, and in archery; and if Constructiveness be also full, and they have been bred to professions in which they find no scope for these faculties, they frequently set up private workshops, and become inventors and improvers of machinery. The organ of Locality is generally much larger in men than in women; and the manifestations correspond.

Dr GALL cites several cases of diseased affection of this organ; and in the Phrenological Journal*, Mr SIMPSON gives a highly interesting detail of symptoms attending disorder of this and the other knowing organs already treated of.

This organ is possessed by the lower animals, and many interesting facts are recorded of their manifestations of the "No. vii. p. 426.

faculty. Dr GALL mentions several instances of dogs returning to their homes from a great distance, without the possibility of their having been guided by smell or sight. "A dog," says he, "was carried in a coach from Vienna to St Petersburgh, and at the end of six months reappeared in Vienna: Another was transported from Vienna to London; he attached himself to a traveller, and embarked along with him; but at the moment of landing, he made his escape and returned to his native city. Another dog was sent from Lyons to Marseilles, where he was embarked for Naples, and he found his way back by land to Lyons." The common hypothesis, he observes, that dogs retrace their way by the aid of smell, appears abundantly absurd, when applied to cases in which they were transported by water, or in a coach; and the idea that these animals can discover the effluvia of their master's person across a space of several hundred leagues, appears equally preposterous. Besides, a dog does not return home by the straightest road, nor even by the precise line in which he was carried away; and some naturalists have therefore been obliged to admit an occult cause of this surprising talent, and named it a sixth sense. Dr GALL considers it to belong to the organ of Locality. The falcon of Iceland returns to its native place from a distance of thousands of miles; and carrier pigeons have long been celebrated for a similar tendency, and have occasionally been employed in consequence to convey dispatches. Swallows, nightingales, and a variety of sea-fowls, migrate from one climate to another at certain seasons of the year, which is attributed by Dr GALL to periodical and involuntary excitement of this organ.

The frontal sinus has been stated as an objection to Locality, but it rarely ascends higher than the lower part of it; and while prominences formed by the sinus are irregular in form, and generally horizontal in direction, the elevations occasioned by a large development of Locality are uniform in shape, and extend obliquely upwards towards the middle of the forehead. Further, the negative evidence

in favour of the organ is irresistible, and it is therefore held as established.

28. NUMBER.

A scholar of St Poelton, near Vienna, was greatly spoken of in that city, on account of his extraordinary talent for calculation. He was the son of a blacksmith, who had not received any particular instruction beyond that bestowed on other boys at the same school; and in all other respects was nearly on a footing of equality with them. Dr GALL made him come to Vienna, and presented him to his audience when he was nine years of age. "Lorsqu'on lui donnait," says Dr GALL," je suppose, trois nombres exprimés chacun par dix à douze chiffres, en lui demandant de les additionner, puis de les soustraire deux à deux, de les multiplier et de les diviser chacun par un nombre de trois chiffres; il regardait une seule fois les nombres, puis il levait le nez et les yeux en l'air, et il indiquait le résultat de son calcul mental avant que mes auditeurs n'eussent eu le temps de faire le calcul la plume à la main. Il avait creé lui-même sa méthode." An advocate of Vienna stated his regret that his son, of five years of age, occupied himself exclusively with numbers and calculation, in such a manner that it was impossible to fix his attention on any other object, not even on the games of youth. Dr GALL compared his head with that of the boy just mentioned, and found no particular resemblance, except in a remarkable prominence at the external angle of the eye, and a little to the side. In both, the eye was in some degree covered by the external angle of the upper eyebrow. These cases suggested the idea that the talent for calculation might be connected with a particular organ; and Dr GALL sought for men distinguished for this power, in order to verify the discovery. He repaired to the Councillor MANTELLI, whose favourite occupation was to invent and solve problems in

mathematics, and particularly in arithmetic, and found the same configuration in him. He next went to Baron VEGA, author of Tables of Logarithms, at that time Professor of Mathematics, and who, in every other talent, "était un homme fort médiòcre," and found in him the same form of head. He then visited private families and schools, and desired the children distinguished for ability in calculation to be pointed out to him; and still the same development recurred. He therefore felt himself constrained to admit a special organ and faculty for this talent.

The organ, when large, fills up the head outside of the external angle of the eye, a very little below the point called the external angular process of the frontal bone.

The special function of the faculty seems to be calculation in general. Dr GALL calls it "Le sens des nombres ;" and, while he states distinctly that arithmetic is its chief sphere, he regards it as also the organ of mathematics. Dr SPURZHEIM, on the other hand, limits its functions to arithmetic, algebra, and logarithms; and is of opinion that the other branches of mathematics, as geometry, &c. are not the simple results of this faculty. In this analysis he appears to me to be well founded. Mr GEOrge Bidder, when only seven years of age, and without any previous instruction, shewed an extraordinary talent for mental calculation; and I have seen him, when only eleven, answer the most complicated questions in algebra, in a minute, or a minute and a half, without the aid of notation. When he first came to Edinburgh, and before I had seen him, a gentleman waited on me, accompanied by three boys of nearly equal ages, and said, "One of these is GEORGE BIDDER, the celebrated mental calculator, can you tell which is he by his head?" On examining the organ of Number in all of them, I replied that one of them ought to be decidedly deficient in arithmetical talent; that another should possess it in a considerable degree; but that the third must be BIDDER, because, in him, the organ was developed to an extraordinary extent. The gentleman then

stated that the indications were perfectly correct; that the first was a boy who had been remarked as dull in his arithmetical studies; the second was the most expert calculator selected from a school in Edinburgh; and the third was BIDDER. Dr GALL mentions a similar experiment which was tried with him, and with the same result. He gives a detailed account of ZHERO COLBURN, the American youth who exhibited great talents for calculation, and in whom also the organ was found large. This young man visited Edinburgh, and afforded the phrenologists of this city an opportunity of verifying Dr GALL'S observations, which were found to be correct. Masks of him and BIDDER were taken, and now form part of the Phrenological Society's collection. These two examples, however, prove that Dr SPURZHEIM is right in limiting the function of this faculty to calculation of numbers; as neither of these young men have proved so eminent in geometry as in arithmetic and algebra. The organ is large also in the mask of HUMBOLDT, celebrated for his powers of calculation. This organ, and Individuality, both large, give the talent of recollecting dates.

I am acquainted with other individuals in whom this organ is deficient, and who experience great difficulty in solving the most ordinary arithmetical questions, who, indeed, have never been able to learn the multiplication table, or to perform readily common addition and subtraction, even after persevering efforts to attain expertness. This organ is small in the mask marked "French M. D. ;" and it serves as a contrast, in this respect, to those just mentioned, in which it is large.

Dr GALL observes, that when this organ predominates in an individual, all his faculties receive an impression from it. He knew a physician in whom it was very large, who laboured to reduce the study of medicine, and even the virtue of particular medicaments, to mathematical principles; and one of his friends, thus endowed, endeavoured to found an universal language on similar grounds.