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46   Life and Letters of Francis Galton

practical photographic scheme was then evolved'. The difficulty of bi-projection met Galton at a very early stage of his meteorological work, and he solved it by the construction of a compound pantagraph. He gave a great deal of thought to the subject, and his papers contain numerous devices and suggestions for an instrument of this character. His work upon it began in 1867, but was not completed till 1869, when the first compound pantagraph constructed by Mr C. Beck was placed in the Meteorological Office.

The general idea is that of a double or compound pantagraph. The tracing pointer has a horizontal and a vertical motion. The former is conveyed through one pantagraph to the drawing-board on which the paper for reproduction is set and the latter through a second pantagraph to the reproducing pencil or style. The design on page 45-not the one finally adopted-in Galton's autograph indicates his ideas. The two pantagraphic linkages aACBb and a'A'C'B'b' are the fundamental features. C is a fixed pivot which may be either in AB or in a continuation of the rod AB; then if the lengths of aA, CA, CB and Bb be so adjusted that the triangles CAa and CBb are similar for any one position of those triangles, they will be similar for all positions, and consequently the distances a and b move in their constrained horizontal paths will be in the adjustable ratio of CA to CB'.

(xalton's double or drill pantagrapb.

' We shall see later that Galton actually solved the problem, but did not publish his solution. A simple 'bi-projector' was made for the writer by' Mr Horace Darwin many years ago for drawing parabolae, ellipses, probability curves, etc., but it involved the cutting of a definite metal template for each type of curve; it might possibly be adapted for reducing drawings.

2 This fundamental principle of Galton's compound pantagraph is discussed by him with proof in a letter of July 1 .5, 1869, but he was inquiring for a maker even in May of 1869.