320 



NATURE 



[August 2, 1900 



plane figure on a plane. Plan and elevation of a line which is 

 inclined at given angles to the co ordinate planes. The meaning 

 of the terms " trace of a line," " trace of a plane." 



The difference between a scalar quantity and a vector quantity. 

 Addition and subtraction of vectors. 



Slope of a line ; slope of a curve at any point in it. Rate of in- 

 crease of one quantity,;/ relatively to the increase of another quantity 



X ; the symbol for this rate of increase, namely, -^ ; how to 



determine — when the law connecting x and y is of the form 



dx 

 y = ax". Easy exercises on this rule. 



In setting out the above syllabus the items have been arranged 

 under the various branches of the subject. 



It will be obvious that it is not intended that these should be 

 studied in the order in which they appear ; the teacher will 

 arrange a mixed course such as seems to him best for the class 

 of students with whom he has to deal. 



ANAL YTICAL FOR TRAITURE. 

 T T seems well to put on record the principal results of 

 -*■ experiments that I have recently made to isolate the 

 particulars in which one portrait differs from another. 

 They had a measure of success, but not enough to de- 

 serve illustration or lengthy description. The objects I 

 had hoped to attain are important ; namely, to define 

 photographically the direction and degrees in which any 

 individual differs from the race to which he belongs, the 

 race being represented by a composite picture of many 

 individuals belonging to it. Or, again, to define the par- 

 ticulars in which any variety of a plant or animal differs 

 from its parent species. Or to define family features ; 

 or to isolate expressions, recollecting that these consist 

 both of subtractions from, and additions to, the features 

 as seen in repose. 



My starting point was that the exact superimposition 

 of a rather faint positive upon its rather faint negative 

 produces an approximately uniform grey, when they are 

 viewed as a single transparency. Thus, I photographed 

 a rotating disc that had been faced with white paper and 

 divided into concentric rings. The innermost disc was 

 left white, the outermost ring was painted black, and the 

 intermediate rings contained successively increasing pro- 

 portions of black to white. The photographic negative 

 showed rings of graded tints, and from this I took a 

 positive by contact. Subsequently applying the positive 

 to the negative, film to film, and viewing them as a 

 transparency, a nearly uniform grey surface was pro- 

 duced. It was necessary to superimpose them with 

 exactness ; otherwise the edges of the rings were con- 

 spicuously dark in one part, and light in the opposite 

 part. Another test experiment was to paste together 

 thicknesses of tracing paper — two-fold, three-fold, &c., 

 up to twelve-fold — to cut distinctively shaped snippets of 

 these and to variously distribute them over the surface of 

 a glass plate, which was then photographed, and a positive 

 taken as well. On treating the positive and negative as 

 above, all the tints between those of the three-fold and 

 the nine-fold inclusive produced a uniform grey. 



Let A and B be any two pictures whose respective 

 negatives and positives will be called neg. a, pos. a, 

 neg. b,pos. b. My object was to produce photographically 

 a third pictue X which should express the difference 

 between A and B ; that is, should be equal to A — B, or 

 else a fourth picture Y which should represent B— A. 



It will, however, be simpler to treat the problem at first 

 as an optical one, based on the following equations : — 

 (I.) pos. a -f neg. a = grey ; (II.) pos. a + x = pos. b 



(if treated as a photographic problem, (11.) would be re- 

 placed by pos. a + X = neg. b). From these we obtain 



(III.) pos. a -f \pos. b -t- neg. a} = pos. b 4- grey 

 and 



(IV.) pos. b -V {pos. a + neg. b} = pos. a + grey. 



NO. 1605, VOL. 62] 



Calling the terms within brackets by the name of 

 "transformers," the transformer oi b into a is the negative 

 of the transformer o'f a into b. The two terms with- 

 in brackets may be " composited " together on equal terms, 

 then the result may be composited with the first term, 

 allowing two-thirds of the total time of exposure to the 

 transformer, and one-third to the first term. Or, what 

 comes to the same thing in the end, all three terms may 

 be composited in equal shares, allowing one-third of the 

 total time of exposure to each. The transformers in 

 (III.) and (IV.) being respectively x -I- grey and/ -V grey, 

 are nearly equivalent for the purposes of the inquiry to 

 X and J/, because the addition of a uniform shade of grey 

 has little or no effect on pictorial resemblance. A portrait 

 does not cease to resemble the original when it has 

 become somewhat browned by exposure to a London 

 atmosphere, or when it is viewed in shade, or under a 

 tinted glass. Its distinctiveness depends on the differences 

 (not the ratios) being preserved between the tints of all 

 adjacent elements of its surface. Of course the grey 

 must not be too dark ; otherwise the deeper tints of the 

 portrait would appear indistinguishably black. 



This method of transformation succeeds fairly well. I 

 changed an F on a white ground into a good G on a 

 grey ground, and I changed with passable success one 

 portrait A on white ground into another portrait B 

 on grey ground, but the transformer itself gave little of 

 that information to the eye which I had expected. It must 

 have nearly isolated, but it failed to exhibit in an intel- 

 ligible form the differences between A and B. Then I 

 photographed two faces, each in two expressions, the one 

 glum and the other smiling broadly. I could turn the 

 glum face into the smiling one, or vice versa, by means of 

 the suitable transformer ; but the transformers themselves 

 were ghastly to look at, and did not at all give the im- 

 pression of a detached smile or of a detached glumness. 



Part of the ghastliness was due to the different den- 

 sities of the superimposed positives and negatives, which 

 did not neatly obliterate one another in the unchanged 

 portions of the face, and part was due to their not being 

 superimposed in the best possible way. There can be 

 no doubt of the best fit when engaged in making the 

 transforjner of an | into an L ; but the eye must deter- 

 mine the best fit and proportions of the two components 

 of the transformer of one portrait into another. I can- 

 not yet make up my mind whether or no the process 

 admits of substantial improvement, but feel sure that the 

 only satisfactory experiments now would be those made 

 by two converging lanterns on a screen, one at least of 

 which admits of easy and delicate adjustment in direction 

 and in the intensity of its illumination. The most suit- 

 able portraits for the attempt are apparently such as are 

 popularly, and sometimes reproachfully, termed " artistic," 

 that is to say, with blurred outlines and medium tints ; 

 certainly not those which in photographic language are 

 called "plucky." I have no means in my house for 

 experiments of this kind, but perhaps a trial might be 

 made in some laboratory where they exist. The point is 

 to ascertain whether the images of neg. a and pos. b can 

 be so combined on the screen as to give an intelligible 

 and useful idea of the differences between A and B. 



Francis Galton. ■ 



A RECOLLECTION OF KING UMBERTO. 



HOW enthusiastically the late King of Italy could 

 devote himself to the welfare of science and art, 

 those of us who were at Como last September had an 

 opportunity, of seeing. One very hot day he arrived 

 with the Queen and the Duke of Naples by train from 

 their palace at Monza, near Milan. First they made an 

 official inspection of the galleries and machinery in the 

 Silk and Electricity Exhibition, then they visited the 

 Exhibition of Sacred Art, and, after lunch, they opened 



