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Photographie,Researehes and Portraiture   311

is a very important point in the case of reduction to an exact size. Galton's papers show a large number of attempts at its solution. He ultimately sought the aid of Mr (now Sir) Horace Darwin, who in 1878 published in Nature' a satisfactory theoretical solution by aid of a double Peaucellier's cell. Galton found, however, that the cells would have to be of unwieldy size, if these arrangements were used. I" am not aware that the problem has even yet been solved practically, although for scientific photography its solution is very important.

(C) Analytical Photography.

At the same time that Galton was working out his idea of composite portraiture a new problem occurred to him, that of creating what he termed a "transformer" which would transform the type into any individual component. The transformer would thus be a measure of the difference between individual and type, or indeed between any two individuals. He proposed by this method to analyse the differences between types (or races), between individuals (or between an individual and his family type), or between an individual on different occasions. Galton termed the production and study of transformers Analytical Photography. The idea appears first to have occurred to him in 1881; but not till 1900 did he write a letter, which appeared in Nature', August 2, on the subject, stating the outlines of the process, and speaking somewhat doubtfully of his own power of carrying it out. In this letter, after describing the theory' and something of the technique, he writes

"I photographed two faces, each in two expressions, the one glum and the other smiling broadly. I could turn the glum face into the smiling one, or vice versd, by means of the suitable transformer; but the transformers were ghastly to look at, and did not at all give the impression of a detached smile or of a detached glumness."

Later Galton realised that transformers were hieroglyphics which required a key to their interpretation; the photograph of a "smile" is really the photograph of facial modifications which failing the stable basis of the face we do not recognise as a smile at all. I owe to Mr Egon S. Pearson the photographs on p. 312. A is the normal, B the smiling subject. C and D are the transformers. D is the "glumness" and C the "photograph of a smile." All that can be said of the latter is that it does not closely correspond with John Tenniel's conception of the grin which remained some time after the rest of the Cheshire cat had vanished'.

' Vol. xviii, p. 383.   2 Vol. Lxir, p. 320. a If x be-the transformer, Galton lays down two equations

(i) pos. a + neg. a = grey, and (ii) pos. a + x = pos. b,

whence he deduces

(iii) pos. a + {pos. b + neg. a} =pos=   b + grey,   (iv) pos. b + {pos. a + neg. b} =pos. a + grey.

Thus the quantities in curled brackets are the transformers, one the negative of the other (the "smile" and the "glumness").

4 Alice's Adventures in Wonderland, Edn. 1872, p. 93.