Another proof that the skull is formed without regard to the brain is the following: "The bony cabinet and its contents are developed, to a certain extent at least, independently. This is very clearly demonstrated by a fact which was observed by Gratiolet, and is too frequently forgotten. The subject is an infant in whom the cranium presented the normal conformation. The brain was, nevertheless, almost entirely wanting."[40] Dr. Gall was a poor arithmetician, and his biographer says that every kind of numerical calculation fatigued him. He could not go through a process of multiplication or division that was at all complicated, and knew nothing of geometry or of the problems of mathematics.[41] George Combe said of himself: "Arithmetic has always been to me a profound mystery, and to master the multiplication table an insurmountable task.... This faculty in me is, in fact, idiotic." Again he said: "When a boy, I never could learn arithmetic. At the end of five years' teaching I could not subtract, divide, or multiply any considerable number of figures with accuracy and facility, and can not now do so.... At the present day I can not sum a column of figures correctly."[42] With these facts in view, our wonder at finding the theories of these men at variance with all exact calculation is considerably diminished. We propose to test some of their theories by arithmetical processes. We found that the sixty famous men entered in the table of authenticated brain weights show an average of 51.3 ounces. We now take all the idiots and imbeciles in the table of "Large Brains and Small Minds," and find the average 59.4 ounces; so that the matter is left to stand thus: Ten idiots and five imbeciles average 59.2 ounces; sixty famous men average 51.39 ounces: in favor of idiocy and imbecility, 7.9 ounces. The heaviest brain in the table of small minds is that of Rustan, an ignorant and entirely unknown laborer. He was a healthy man, and his brain, when it was weighed, was in a healthy condition. Its weight was recorded by Dr. Carl A. Rudolphi, a Swedish naturalist and physiologist of Stockholm, who became professor of anatomy and physiology at Berlin in 1810. It reached the unexampled figure of 78.3 ounces; while the brain of Turgenieff, the heaviest among famous men, was 71 ounces--showing a difference of 7.3 ounces in behalf of the inferior mind. Since writing the above, the following appeared in Tit-Bits, a weekly paper published in London, England, March 19, 1898: "It must not be assumed, however, that intellect is in direct ratio to the weight of the brain; for while the brains of certain intellectual men, such as ... Dr. Abercromby, weighed more than 60 ounces, a certain Strand newspaper-boy, who was in intelligence almost an idiot, had a brain which weighed no less than 80 ounces."