S6: 



NA TURE 



[OcTOliEK 4, 1906 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertalie 

 to return, cr to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Measurement of Resemblance. 



At the distance of a few scores of paces the human face 

 appears to be a uniform reddish blur, with no separate 

 features. On a nearer approach specks begin to be seen, 

 corresponding to the eyes and mouth. These gradually 

 mcrease in distinctness, until at about thirty paces the 

 features become so clear that a hitherto unknown person 

 could thereafter be recognised with some assurance. There 

 is no better opportunity of observing the effects of distance 

 in confounding human faces than by watching soldiers 

 at a review. Their dress is alike, the'ir pose is the same, 

 the light falls upon them from the same direction, and they 

 are often immovable for a considerable time. It is then 

 noticeable how some faces appear indistinguishable at 

 distances where great diversity is apparent in others, and 

 the rudely-defined idea will be'justified that the distance at 

 which two faces are just mistakable for one another might 

 serve as a trustworthy basis for the measurement of re- 

 semblance. The same may be said of obscuritv, of con- 

 fused refractions, and of turbid media ; but in this letter 

 I shall confine myself almost wholly to the effects of 

 distance under the conditions of ample light and a trans- 

 parent atmosphere. Beyond this I shall say nothing, except 

 in one paragraph almost at the end. 



The scale of the features has, of ccurse, to be taken 

 into account. This is of much less importance in living 

 persons than in portraits, because the differences in scale 

 of the adult huinan face are not very great, whereas those 

 in photographs and paintings— ranging as they do between 

 miniatures and life-sized portraits — are so. It is necessary 

 to adopt a facial unit, based on some specified dimension. 

 That which I use is the vertical distance between the 

 middle of the line that joins the pupils and the parting 

 of the lips. It is unaffected by head-dress or by the thick- 

 ness of the hair on the top of the head, while its 

 lower termination can be located in a bearded face 

 more accurately than the chin. I call this n. If the por- 

 traits have different units, they are distinguishable as 

 H and u' . If d and d' be the critical distances at which 

 mistakability first occurs, then u/d and u' Id' are neces- 

 sarily equal, and either of them would serve as a measure 

 of mistakability ; but as u is very much smaller than d, 

 this fraction would always be a decimal preceded by one 

 or two zeros. Therefore I take the index of mistakability, 

 which I will call N, as = 1000 ufd. It is, however, con- 

 venient to measure u and d by different scales; « in milli- 

 metres, distinguishing it as u„, ; d in centimetres, dis- 

 tineuishing it as if,.. Then N= ico ;(,„/</,.. 



Of course, N could be expressed by the arc or angle of 

 which 11,'rf is the chord, but it would be a roundabout 

 method, as angles could not be measured directly without 

 special and troublesome apparatus. I find if very con- 

 venient for my purposes to employ a nomenclature for 

 chords based on that of the metrical system, d, the dis- 

 tance, being the radius or " rad." So a chord=i/ioo be- 

 comes a " centirad," and that =1/1000 a " millerad." A 

 centirad is the chord of 34-4 minutes of a degree, and, there- 

 fore, a trifle larger than the apparent diameter of the sun 

 or moon. It is equal to the apparent size of one-tenth of 

 an inch at 10 inches distance from the eye, which is a 

 convenient distance for reading small type. A millerad 

 which subtends between three and four minutes of a degree, 

 and is equivalent to i/ioo of an inch seen at 10 inches, is as 

 small an interval as can usually be detected in photographs 

 without scrutiny, though a normal eye is able to distinguish 

 one-third or even one-fourth of that interval between 

 sharply defined objects. 



Mistakability is only an approximate measure of resem- 

 blance, for it depends more on the scale of the distinguish- 

 ing features than on the amount of difference of those 

 features. This peculiarity is well exemplified, though 

 greatly exaggerated, by what is seen in the time-tables 

 hung up by railway stations. From across the road, sav, 



NO. 1927, VOL. 74] 



they all appear alike as a shade of uniform grey. On 

 approaching nearer, differences are observed in the' head- 

 lines ; nearer still, varieties in paragraphing come into 

 sight, and at a reading distance the figures are all simul- 

 taneously distinguishable. This experience is partly, but 

 only partly, applicable to human faces. Those that are 

 alike are certainly distinguishable at shorter distances than 

 unlike ones, and I notice no excessive clustering of values 

 closely round particular values of N in my results, which 

 there would be if mistakability always occurred near a 

 particular stage, such as that at which the whites of the 

 eyes cease to be visible, or at twice or three times that 

 distance. 



.\ strong likeness in small details may so dominate the 

 perception that a want of likeness in larger features is 

 overlooked. Here the distance of maximum mistakability 

 will be small, the portraits appearing more unlike when re- 

 moved further off, and the small details cease to be visible. 

 Extreme cases of partial likeness, whether in contour or 

 in detail, would, of course, be noted and allowed for. 

 With these exceptions the index of mistakability appears to 

 be a fair, even, as I think, a close, approximation to an 

 index of resemblance when the quality of the observed 

 likeness is recorded by appropriate letters, as will be de- 

 scribed later on. 



The observational value of mistakability lies in its ask- 

 ing a simple question which different persons would answer 

 in the same way, when they had become familiar with 

 the method. On the other hand, likeness includes mutual 

 suggestibility, a highly complex perception dependent on 

 the mind of the observer, and consequently appreciated 

 differently by different observers, as is notoriously the case. 



The apparatus I now use with ordinary photographs acts 

 very well, but I wasted much time before I contrived it, 

 and more before sending it to be made in a workmanlike 

 manner. I think it could still be improved, so I will de- 

 scribe, not my own, which was made for me by Baker, 

 240 High Holborn, but such as I should order if I required 

 another one. 



It is a long, thin, light box or framework 65 feet 

 (2 metres) long, 10 inches (25 centimetres) wide, and 

 2 inches (5 centimetres) deep, which admits of being 

 divided for sake of portability. It stands on two folding 

 supports 25 feet apart, which fold back when out of use ; 

 when in use they can be clamped to any ordinary table. 

 These raise the long box in a sloping position, the end 

 towards the eye being at the most convenient height for a 

 person seated on a chair, but the further end being lower, 

 because it is easiest to look somewhat downwards. Two 

 rollers, .a and b (Figs, i and 2), run independently on a 

 horizontal axis at one end of the box, and two correspond- 

 ing ones, a and b (Fig. 2) at the other end. A light sledge 

 that slides on the top of the box is harnessed in front to a 

 tape graduated in centimetres, which passes over and round 

 A, back to and around a, and thence forwards to the back 

 of the sledge. (By inadvertence the path of the tape 

 between the lower margins of A and a has been omitted 

 in Fig. I. The reader might dot it in pencil.) A similar 

 sledge and tape is adapted to b and b. The tapes lie half 

 an inch above the box (Fig. i), and can be manipulated by 

 the hands severally, so either or both sledges can be easily 

 pulled either backwards or forwards while sitting in the 

 chair, and their distances from the rollers at any moment be 

 read off on the graduated tapes. (A winch and handle are 

 superfluous.) The photos are mounted on two easily de- 

 tachable standards (Figs, i, 2), with clips at the bottom to 

 hold them (not shown in the diagram), and standing on 

 circular bases. These fit quite loosely into shallow hollows 

 in the tops of the sledges. The standards can be lifted 

 out, the photographs inserted, and the whole replaced with 

 perfect ease. The circularity of the bases of the standards 

 enables either of them to be set a little askew, which is con- 

 venient when the broad, full face of one portrait has to be 

 compared with the narrowed, three-quarter face of another. 

 A board stands vertically across a and B, and above them as 

 a bridge. An eye-slit of half an inch width runs below its 

 upper edge (Figs, i, 3, 4), through which the photos are 

 viewed, and from which the distances of the sledges are 

 reckoned. A ledge i inch below the eye-slit (Fig. i), with 

 a parapet a little less than i inch high, forms a long, 



