318 Life and Letters of Francis Galton
drawn by hand and therefore inexactly, there was no inducement to consider the possibilities of this converse process, for which exactitude in the picture is essential to success, but now that photography has become common the old difficulty has disappeared, and the possibilities of the neglected process well deserve consideration. The applications would be numerous and especially valuable in determining and measuring restless animals in their momentary attitudes, or even when in rapid motion, which could not otherwise be measured without difficulty, or when in rapid motion be otherwise measured at all. The object I have especially in view is to establish a system of measuring a large number of domestic animals of various pedigree stocks, whether horses, cattle, sheep, dogs, poultry etc., in order to provide material to advance our knowledge of }heredity of a kind that is greatly needed. It is not qualitative facts and exceptional instances that are now wanted by students of heredity, but a large collection of quantitative facts in the form of trustworthy measurements. They are needed to determine with far greater precision than they are at present known the statistical laws and coefficients of heredity. Among these are the conditions and rate of ' regression' of the offspring of exceptional parents; the gradual or sudden alterations of position of the point towards which regression tends, as the breed becomes more- pure; the relative influence of the male and female parent in respect to various measurable peculiarities; the intensities of prepotencies; the frequencies and magnitudes of sudden sports, and the degrees of their subsequent stability through successive generations .... I should add that the direct measurement of creatures so sensitive, timid and sudden in their actions as thoroughbred horses, who at the same time are often vicious, is difficult and dangerous; similarly as regards bulls and some of the breeds of dogs. Photography is a simpler, more exact and far safer method of measurement in these cases than the direct application of rod, tape and callipers."
We shall consider later Galton's method of determining lengths parallel to or nearly parallel to the focal plane of the camera. This he has published (see our p. 320). His two-camera method of determining the three coordinates in space of any point of a subject has not, as far as I know, been published and deserves a paragraph here.
Diagram vii, figs. 1-5, is taken from Galton's manuscript. Fig. 3 represents the plan on a working scale; M1, M2 are the plans of the optical centres of the two camera lenses; bak, fed are 1 ducial lines drawn on the base plane upon which the object stands; b, a and c, d are fiducial points, M1a and M2c being the traces of the vertical planes through the optical axes of the two cameras, and these are so arranged that M1a and M2c are accurately at right angles to bk and fd. Figs. 1 and 2 represent the two photographs, and p, and p2 the point P in them whose coordinates are to be determined. From pl, p2 perpendiculars pig and p2 f are dropped on the images of the fiducial lines ba and cd in the photographs. But clearly ag/ba = ag/ba and fc/cd = fe/cd. Hence g and f on the plan drawing can be scaled. Produce Mfg and M2f to meet in Q, then Q is the plan of the given point P. If S be the perpendicular from Q on M1a, we may take SQ and aS for our coordinates x and y. Now draw to the same scale an elevation (fig. 4) of the system on the vertical plan through the optical axis; N, M, is the height of the optical centre, ST is the elevation of P. Since Sa is known, by joining S to N, we obtain s. If the elevation of P, or z, be TS, we require to determine ts, for knowing it we have TS/ts=M,S/M,a. But to is pig the apparent height in the first photograph altered in the ratio of ab to ab. Fig. 5 illustrates this clearly. Of course we must settle the scale for the drawing-board ab by the value of the fiduciary distance ab in the reticulation on the base plane of the object photographed. Such is Galton's very simple process of taking measurements on photographs