to reduce the scales in two directions at right angles in any desired and different ratios? A photograph, or with more labour a pantagraph, will reduce in both directions in the same ratio, but this is not what is needed. A contributor of a memoir rarely pays any attention to the proportions of the page in which he desires his paper to appear, and then it is a mere chance whether his diagrams however neatly constructed can be used without redraughting. The ideal remedy would be a photographic process of bi-directional
One of Galton's original designs for double pantagraph, coloured in the actual drawing.
reduction, because photography is so much shorter and cheaper than pantagraphic work. The difficulties as to distortion of lettering would be overcome by pasting on the printed lettering to the reduced photograph, instead of to the original drawing. But although this topic more than once formed the subject of long talks of the present writer with Francis Galton, no