July 21, 1898] 



NATURE 



287 



same species has been ascertained. The particular illustration 

 chosen is the reconstruction of probable stature from a measure- 

 ment of the long bones. 



Up till quite recently this subject remained in great obscurity, 

 of absence of " 

 trustworthy data. 



partly on account of absence of theory, and partly for want of 



The estimated statures as obtained by Orfila, Topinard and 

 Beddoe, or by use of their methods, differ widely, and those 

 methods have no satisfactory theoretical basis. It was usual to 

 suppose that there was some mean or average ratio of stature 

 to long bone, and even when it was recognised that this ratio 

 varied with the length of the long bone, it was thought sufficient 

 to determine it for two or three separate ranges of stature, and 

 determine its mean value for these ranges by a very limited 

 number of cases. 



The first stage in advance was taken when Rollet published 

 his measurements, made in the Anatomical Theatre at Lyons, of 

 the stature and long bones of lOO corpses. Rollet's attempt to 

 establish ratios on the basis of his measurements is not very 

 satisfactory, but to him belongs the credit of having first pro- 

 vided a respectable, if not large amount of data. Rollet's work 

 was followed by a very able memoir on the reconstruction of 

 stature by Manouvrier. There are many traces in Manouvrier's 

 paper of the old view of a " coefficient" by which the long bone 

 must be multiplied in order to obtain the stature. Beyond this 

 view, it cannot be said to contain any theory, and it suffers 

 from certain marked defects. 



Manouvrier's memoir was rapidly followed by an excellent 

 piece of work from Rahon, who collected measurements of the 

 long bones of a very wide series of local races of man, and re- 

 constructed their stature by aid of Manouvrier's tables. 



The present memoir starts with the theory of probability, 

 which the author has already applied to other problems in 

 evolution, and deduces the most probable stature for any com- 

 bination of the four long bones. It is shown that for a population 

 with normal correlation, the relation between stature and one or 

 more long bones is always linear. A general theorem is 

 proved to show that no linear function of the long bones can 

 give the probable stature with so small a probable error as the 

 regression formula of the theory of probability. From this 

 result the following conclusions are obtained : 



(a) No constancy of the ratio stature to long bone is theoretic- 

 ally to be expected, but the ratio of deviation from mean 

 stature to deviation from mean long bone, i.e. the regression co- 

 efficient is the quantity, the constancy of which might be 

 anticipated. 



{b) No method of predicting individual stature from the in- 

 dividual long bones, whether one or all are used, can give a 

 result with a less probable error than 2 cm. 



(f) For the same length of femur, tibia, and humerus, the 

 stature is shorter the longer the radius. This result has con- 

 siderable bearing on the relationship of man to the anthropo- 

 morphous apes. 



Formula; are then obtained for the reconstruction of probable 

 stature as measured : 



(a) On the corpse, from the lengths of the long bones con- 

 taining animal matter, and with the cartilages attached. These 

 will possibly be of service for purposes of criminal investi- 

 gation. 



{b) In life, from the lengths of the long bones without 

 cartilages, and free of all animal matter. 



Corrections are given for cases in which the femur is measured 

 in the oblique position ; the tibia is measured with the spine ; 

 and the left-, instead of the right-, hand members are known. 



The manner in which natural selection modifies the regression 

 formula; is indicated. It is pointed out that the divergence 

 between such regression formulae really enables us to predict to 

 some extent the nature of the differential selection which has 

 taken place between two local races. To test how far we may 

 safely apply our formula? to other than French measurements, 

 the stature of the Ainos <J and 9 is reconstructed by means of 

 them from Koganei's measurements of the long bones, and the 

 result is found to be very satisfactory. With a view of illustrating 

 the change in the regression formula; owing to selection, the 

 anthropomorphous apes are considered, and it is shown that 

 the gorilla, in the regression formuhe for femur and tibia stands 

 much closer to man than either the chimpanzee or orang. 



The formulae are applied to reconstruct the stature of pre- 

 historic, mediaivai and modern races. The modern populations 

 occupying the same districts of Europe as Pala;olithic and 



NO. 1499, VOL. 58] 



Neolithic man appear to be taller, but in the case of both south 

 Germany and France there appears to be a slight, but sensible, 

 decrease of stature since proto-historic times. Modern English 

 do not seem to have decreased in stature since the ancient 

 Anglo-Saxons. In the estimates of stature for the above races, 

 the author differs, in some cases very considerably, from previous 

 writers. 



Beyond the range of normal population (say from 157 to 

 175 cm. for <J ), the line of regression ceases to be linear. An 

 attempt is made, such as existing data will allow of. to express 

 the line of regression by the equation to a curve. The predic- 

 tion of the stature of dwarfs from the curve obtained from the 

 data for giants shows only 2 25 cm. mean error, and must be 

 considered satisfactory. Application is then made of the results 

 to reconstruct the stature of Bushmen, Andamanese, Akkas, and 

 of European neolithic dwarfs. 



Paris. 

 Academy of Sciences, July 11.— M. Van Tieghem in the 

 chair.— On the decomposition of nitric acid by heat at mod- 

 erately high temperatures, by M. Berthelot. Pure nitric acid is not 

 decomposed when kept in the dark at the ordinary temperature, 

 but at 100° measurable amounts of oxygen and nitrogen peroxide 

 are produced. Nitric acid of specific gravity 1*333 'S not 

 appreciably decomposed under similar conditions. — On the 

 compressibility of air considered as a gaseous mixture, by 

 M. E. H. Amagat. In air, the oxygen and nitrogen appear to 

 be compressed, as if each were at the pressure of the mixture ; 

 the volume of the mixture is sensibly equal to the volume of the 

 constituents. A table is given showing the deviations found 

 experimentally for pressures between 100 and 3000 atmospheres, 

 deviations which are within the known experimental error. — On 

 the systems of differential equations satisfied by quadruply 

 periodic functions of the second species, by M. .Martin Krause. 

 — On a mode of supporting the motion of a pendulum, by 

 M. A. Guillet. The impulses are given electrically by induction 

 currents at the same point in its path, one as it ascends, and 

 the other as it descends, the disturbances thus set up being 

 exactly equal and of opposite sense. Comparisons with a free 

 pendulum showed that the time of vibration was unaltered by 

 the use of the mechanism described. — On the passage of electro- 

 magnetic waves from a primary wire to a secondary wire parallel 

 to it, by M. C. Gutton. — On the mode of oxidation of cobalt 

 salts in alkaline solutions, by M. Andre Job. It has been 

 known for some time that cobaltous salts, treated with potas- 

 sium bicarbonate and hydrogen peroxide, give a higher oxidation 

 product having a green colour, the exact composition of which 

 has not hitherto been proved. By means of the ferrous reducing 

 agent recently described by the author, it is now shown that the 

 oxygen taken up corresponds to Co^Oj. The estimation of cobalt 

 in presence of nickel and iron is easily carried out by this 

 method. — Action of heat upon the double nitrites of the alkalis 

 and metals of the platinum group. — Compounds of rhodium, 

 by MM. A Jolly and E. Leidie. At 440" the double nitrite 

 Rh(N02)«.6KN02 is decomposed into nitrogen, nitric oxide, 

 and a salt having approximately the composition KjRhgO,3 or 

 KjO. 6Rh02. These results are considered as affording evidence 

 in support of the oxide RhOj. — On the producticm of tungsten 

 blue, by M. Albert Granger. By the use of a mixed tungstate 

 of barium and sodium a fine indigo-blue glaze is imparted to 

 porcelain, if the temperature is about 1250°, and the heating 

 carried out in a reducing atmosphere. — On the yttrium earths 

 arising from the monazite sands, by M. G. Urbain. — On the 

 brominating action of aluminium bromide in the fatty series, 

 by M. A. Mouneyrat. Ethylene bromide, treated with AlBr^ 

 at 110° C. gave acetylene. With bromide and aluminium 

 bromide, ethyl bromide is readily converted into ethylene 

 dibromide, and the latter again into symmetrical tetra-brom- 

 ethane. From this hexabromethane can be obtained without 

 difficulty. — On some mixed phenyl-alkyl-carbonic ethers, by 

 MM. P. Cazeneuve and Albert Morel. A description of the mode 

 of preparation and physical properties of the phenylmethyl, 

 phenylethyl, phenylpropyl, phenylisopropyl, phenylisobutyl, 

 phenylisoamyl, and ethylallyl carbonates. — On the saponifica- 

 tion velocity of some phosphoric ethers, by M. J. Cavalier. — 

 Action of tetrazodiphenyl, tetrazodiorthotolyl, and tetrazodf- 

 orthoanisyl chlorides upon methyl and ethyl cyanacetates, by 

 M. G. Favrel.— On the phosphates in urine, by M. L. Jolly. 

 The facts noticed by MM. Lupine and Aubert, and explained by 

 them by the assumption of incomplete oxidation of phosphorus 



