1888.] on Personal Identification and Description. 347 



closer. Continue to act on the same princii)le until a stage is reached 

 when the contour last drawn is undistinguishable from A. Suppose 

 it to be the fourth stage ; then as 2* = 16, there are sixteen grades of 

 least-discernible differences between A and B. If one of the contours 

 differs greatly in a single or few respects from the other, reservation 

 may be made of those peculiarities. Thus, if A has a deep notch in 

 its lower right-hand border, we might either state that fact, and say 

 that in other respects it differed from B by only 16 grades of un- 

 likeness, or we might make no reservation, and continue subdividing 

 until all trace of the notch was smoothed away. It is pui'ely a matter 

 of convenience which course should be adopted in any given case. 

 The measurement of resemblance by units of least-discernible differ- 

 ences is applicable to shades, colours, sounds, tastes, and to sense- 

 indications generally. There is no such thing as infinite unlikeness, 

 because the number of just discernible difference between any objects, 

 however dissimilar, is always finite. A point as perceived by the 

 sense of sight is not a mathematical point, but an object so small that 

 its shape ceases to be discernible. Mathematically, it requires an 

 infinitude of points to make a short line ; sensibly, it requires a finite 

 and not a large number of what the vision reckons as points, to do so. 

 If from thii'ty to forty points were dotted in a row across the disk of 

 the moon, they would appear to the naked eyes of most persons as a 

 continuous line. 



Description within Specified Limits.-:r-lt is impossible to verbally 

 define an iiTegular contour with such jDrecision that a drawing made 

 from the description shall be undistinguishable from the original, 

 but we may be content with a lower achievement. Much would be 

 gained if we could refer to a standard collection of contours drawn 

 with double lines, and say that the contour in question falls between 

 the double lines of the contour catalogued as number so-and-so. This 

 would at least tell us that none of the very many contours that fell 

 outside the specified limits could be the one to which the description 

 applied. It is an approximate and a negative method of identification. 

 Suppose the contour to be a profile, and for simj^licity's sake let us 

 suppose it to be only the portion of a profile that lies below the notch 

 that separates the brow from the nose, and extending only so far 

 downwards as the parting between the lips. Suppose it also to be 

 the mere outline of a shadow sharply cast upon the wall by a single 

 source of light, such as is excellently seen when a person stands side- 

 ways between the electric lantern and the screen in a lecture-room. 

 All human profiles of this kind, when they have been reduced to a 

 uniform vertical scale, fall within a small space. I have taken those 

 given by Lavater, which are in many cases of extreme shapes, 

 and have added others of English faces, and find that they all fall 

 within the space shown in Fig. 2. The outer and inner limits of the 

 space are of course not the profiles of any real faces, but the limits of 

 many profiles, some of which are exceptional at one point, and others 

 at another. We can classify the great majority of profiles so that 



2 A 2 



