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Psychological Investigations   253

and quotes from his paper in the Fortnightly of September 1880 (see our pp. 238-41), and in concluding the subject expands the last paragraph of that paper into his final expression of opinion:

"There can, however, be no doubt as to the utility of the visualising faculty when it is duly subordinated to the higher intellectual operations. A visual image is the most perfect form of mental representation whenever the shape, position and relations of objects in space are concerned. It is of importance in every handicraft and profession where design is required. The best workmen are those who visualise the whole of what they propose to do, before they take a tool in their hands. The village smith and the carpenter who are employed on odd jobs require it no less for their work than the mechanician, the engineer and the architect. The lady's maid who arranges a new dress requires it for the same reason as the decorator employed on a palace, or the agent who lays out great estates. Strategists', artists of all denominations, physicists who contrive new experiments, and in short all who do not follow routine, have need of it. The pleasure its use can afford is immense. I have many correspondents who say that the delight of recalling beautiful scenery and great works of art is the highest that they know; they carry whole picture galleries in their minds_. Our bookish and wordy education tends to repress this valuable gift of nature. A faculty that is of importance in all technical and artistic occupations, that gives accuracy to our perceptions, and justness to our generalisations, is starved by lazy disuse, instead of being cultivated judiciously in such a way as will on the whole bring the best return. I believe that a serious study of the best method of developing and utilising this faculty', without prejudice to the practice of abstract-thought in symbols, is one of the many pressing desiderata in the yet unformed science of education.." (pp. 113-4.)

Galton next passes to "Number Forms" and gives here the fullest account that he has provided of them, although in no way comparable with the range of his collected material. He publishes three plates of "Number Forms" and a fourth plate showing some typical associations of numbers with colours. He also indicates that some persons associate character with numerals, but rarely, except in the case of 12, to which most pay great respect, is there any agreement in the characterisation. Thus 3 may be a "treacherous sneak," a "feeble edition of 9," "a good old friend" and "delightful and amusing." There is no agreement as to the sex of numbers, although Galton himself imagined that the even numbers must of course be male (p. 144).

He then refers to the very strong evidence he had collected for the hereditary character, not of particular number forms, but of the tendency to visualise numbers. He next turns to colour associations and describes them at considerable length (pp. 145-54). He emphasises the fact that while to the ordinary man these associations of colour with letters or numbers appear equally "wild and lunatic," no two colour visionaries agree in their schemes, and one seer is scandalised and almost angry at the heresies of another !

' NapoleonIseemstohaveheldthatmenwhoformedmentalpictures(tableaux),nomatterwhat their intellect, courageand knowledge, were unfit to command. Maximes de Guerre et Pensees, No. 73.

2 Galton, notwithstanding his evidence for the hereditary character of this faculty, yet held that it could be developed by training, and cited Legros' old teacher Lecoq de Boisbaudran, who had developed at the Lcole Nationale de Dessin in Paris a complete training in. visualisation. It can, no doubt, where it exists be developed by practice, but it may be questioned whether it can be originated in an individual without it, any more than musical sense or mechanical ingenuity can be developed in those in whom they are not innate

' The complexity of some of the colour schemes as shown on Galton's Plate IV is marvellous; that plate required 14 colour stones to produce it lithographically; and therefore, fascinating as it is, I cannot reproduce it here!