128 



NATURE 



[March 31, 1910 



of which is perpendicular to its face, but the edge of 

 which is not blunted, only too readily makes a gash. 



The arcs of 45° in Fig. 2 all refer to the cutting edge, so 

 to speak. The direction of the lines within which the 

 cutting edge is situated is determined by the adjacent 

 cardinal points towards which they point. 



Referring back to Fig. 3, OP = OM = r, the radius, 

 ON = rx 1-082, therefore the distance between N and t'-e 

 circle is only rxo-82, which for a radius =10 mm. is about 

 three-quarters of i mm. This small value is diminished 



formulae. Twenty figures enter into each formula ; 

 they are arranged, as for telegraphy, in the way 

 already described, into four groups of five figures in 

 each group. A "figure," in telegraphic language, 

 includes not only the ten numerals, o to 9, but the 

 three symbols in addition, of a stop ( . ), a hyphen (-), 

 and a short oblique line ( / ), such as is used in 

 fractions. The arrangement in groups of five, or in 

 "quintets," proved suitable to other similar work on 



in proportion for lesser values of r (see Fig. 2), so for I which I was engaged, so it has been adopted through- 

 4..„„i -NT /__j 1--.1.. r>\ .._ .J , ^^j. j^^ ^j^^ four quintets, or, we may say, in the four 



words that compose a formula, the first three refer 

 respectively to N, U and L, and in that order. The 

 first two and the last two figures, in each of the first 

 three quintets, give the position of the point in ques- 

 tion in X and in Y to the nearest whole millimetre. 

 The middle figure of the quintet is derived from 

 Fig. 4 to describe the peculiarities of the profile 

 at and immediately adjacent ta that point. The 



practical purposes N (and similarly C) may be considered 

 to lie only just outside the convex circumference of the 

 arc by which they are in each case represented. 



The values of r which are used as standards for the 

 lesser curvatures are 2 mm., 6 mm., and 10 mm. The 

 drawings in Fig. 4 are not exactly on this scale, but the 

 differences are unimportant. It is unnecessary to divide 

 these small curves into concave and convex, as their con- 

 dition in that respect is indicated by the part they play 

 in the profile. Two other curvatures of the larger radii. 



25 mm. and 30 mm., are used to express and to define j fourth and last of the quintets /is preceded by a dot 

 the concavity or the convexity of the ridge of the nose. 1 ( • )> to show that it belongs to a separate category, 



It is well, at the risk of some repeti- 

 tion, to describe in a single paragraph | 234567890 

 the nomenclature of the five cardinal 

 points in the original portrait. B' is 

 the point in the fronto-nasal notch at 

 what is judged to be its deepest part; 

 N' is the tip of the nose, found in the 

 way already described; U' is the point 

 of contact between the naso-labial notch 

 and a tangent, drawn diagonally to it ; 

 L' is a point half-way between the 

 furthest positions at which the lips 

 would touch one another if they were 

 lightly closed ; C is found by a similar 

 method to that used for N'. 



The portraits are described by 

 numerical formulae. Each formula 

 consists of four groups of figures, five 

 figures in each group. The shapes of 

 the profile at and immediately adjacent 

 to the cardinal points, and those of the 

 intermediate links, are expressed by 

 single numerals, as set forth in tabular 

 form in Fig. 4. Not more than o to 

 9, or 10, varieties of shape are provided 

 in each case. Thus, the radius of the 

 standard curve that best fits the fronto- 

 nasal notch, b, is expressed by its 

 appropriate numeral, as shown in the 

 first line of Fig. 4 ; also the inclination 

 of the brow immediately above b, 

 whether it slopes forwards, back- 

 wards, or is upright. The ridge of the 

 nose g is counted as either sinuous, concave, or convex, 

 in two or three different degrees, or else as straight. 

 The letter n includes both the very tip of the nose and 

 the outline underneath it, which leads towards the 

 naso-labial notch. The letter u includes the naso- 

 labial notch and the first portion of the upper lip. 

 The lips require two statements, and therefore two 

 separate figures ; the former, Ip, shows whether the 

 lips are shut, parted in the portrait by i or 2 mm., or 

 open by 3 mm. or more, and, again, whether they 

 project evenly, are overhung or underhung. The latter 

 notation, II, expresses the sizes of the upper and lower 

 lips respectively, whether they are small, medium, or 

 large. The outline between the lower lip and the 

 chin is always notched, and k describes the size and 

 position of the notch, whether it be small, medium, 

 or large, and whether it be high, medium, or low. 

 The curve of the chin itself at C' is not given. 



I have called these profiles "numeralised" to express 

 the fact that they are transformed into numerical 

 NO. 2109, VOL. 83] 



Fig. 4. 



namely, to the peculiarities of b, g, II, and k, as set 

 forth in Fig. 4, and in that order. When pro- 

 ceeding to draw a figure from a formula, it is advis- 

 able for a beginner to use tracing paper. Then, after 

 drawing an arbitrary line in any convenient place, of 

 50 millimetres in length, to serve for BC and, therefore, 

 for the vertical axis, and another line CX, at right 

 angles to CB at C, for the horizontal axis, to plot the 

 positions of N, U, and L ; then, laying the transparent 

 paper upon Fig. 4, to trace, or copy on an enlarged or 

 reduced form, according to the space available, the 

 figures of n, u, and Ip, very faintly. Next to do the 

 same to b, g, II, and k. Afterwards to harmonise the 

 whole tentatively, with faint and brush-like strokes ; 

 lastly, with a free and firm hand to draw the outline 

 through them. Tracing paper may otherwise be con- 

 venient, because when the original profile looks to 

 the left, by the simple act of turning the traced out- 

 line it affords an almost equally dear profile, looking 

 to the right. 



