December 5, 1901] 



NA TURE 



117 



curriculum. A detailed table of the schools of Berlin is given 

 in the report, and it shows a surprising variety of educational 

 agencies in the German capital. The table reveals the fact that 

 Berlin has 103 secondary schools and 306 elementary schools. 

 It is evident from the table that the city is making great efforts 

 to assist the industrial education of its youth. Another article 

 in the report contains a statement of the number of students in 

 higher institutions of learning in fifteen prominent countries. 

 The tables show, first, that the Teutonic nations — Germany, 

 Austria, Switzerland, Belgium and the Netherlands — are in the 

 front rank, not only in the number of students in higher insti- 

 tutions, but also in the ratio of increase. Second, that the per- 

 centage of increase in students of technical institutions, such as 

 polytechnic institutions, agricultural and mining schools, is 

 everywhere larger during the year 1S9S-99 than in those of 

 universities and colleges. We note, for instance, that the atten- 

 dance in universities in Germany increased 65 per cent., but 

 that of technical institutions increased 8'2 per cent. In Austria 

 the increase in universities was 4 per cent. ; in technical insti- 

 tutions it was 7 '8 per cent. In Russia the increase in univer- 

 sities was 1 '2 per cent. ; in technical institutions it was 77 per 

 cent. Such figures are significant, inasmuch as they indicate 

 that the industries of Europe and America are claiming more 

 thorough and more special preparation than formerly. 



SCIENTIFIC SERIAL. 

 Transactions of the American Mathematical Society, vol. ii. 

 No. 4, October. — Geometry of a simultaneous system of two 

 linear homogeneous difl'erential equations of the second order, 

 by E. J. Wilczynski, is a continuation of a previous paper (in 

 No. I of the present volume), entitled " Invariants of Systems 

 of Linear Differential Equations." In this some new theorems 

 are deduced, but it is mainly concerned with geometrical inter- 

 pretations. The author confines himself to the special case of 

 the equations 



f + P\\y' + A2=' + i\\y + ?i2= = o. 

 s" + Pi\y' + P-n?' + q-i\y + '/^i^ = o, 



the independent variable being x. The consideration of con- 

 figurations in hyperspace is avoided. The treatment is con- 

 nected with the work of Halphen and Fano upon the single 

 linear differential equation (</'. Math. Annal. vol. liii. ), — The 

 chief result of Dr. L. E. Dickson's theory of linear groups in an 

 arbitrary field is the exhibition of four infinite systems of groups 

 of transformations which are simple groups in every domain of 

 rationaJity. For the case of the field of all complex numbers 

 these groups are the simple continuous groups of Lie. The 

 chief results in a finite field are given in the author's "Linear 

 Groups" (Teubner, Leipzig, 1 901). Corresponding to the 

 isolated group of 14 parameters, there exists in the Galois 

 field of order /" a new system of simple groups of order/"" 

 (/>'"- !)(;>-" - I). — On certain aggregates of determinant minors, 

 by W. H. Metzler. In 1888 Dr. t. Muir showed (Proc. Roy. 

 Soc. Edin., pp. 99-105) that a linear rotation exists between 

 certain minors of a centro-symmetric determinant similar to 

 Kronecker's relation between the minors of an axi-symmetric 

 determinant ; and in 1900 he gave two theorems connecting the 

 minors of any determinant, the first of which reduces to 

 Kronecker's relation and the second of which reduces to his 



tions <|),i|/„ - (|)„i(,,, <fj',^., - ,^j,^„' + ^^- + p^,^^ + t/(pj, 

 ;^lV■J - <Pf4'-2 + 'Pi' + Hi'l'i + 'I'I'-i' vanishes at any point of the 

 interval in question. Certain extensions of the above theorem 

 are also established.— On the system of a binary cubic and 

 quadratic and the reduction of hyperelliptic integrals of genus 

 two to elliptic integrals by a transformation of the fourth order, 

 by J. H. Macdonald, effects the reduction by a special involu- 

 tion of order four containing a form which is the square of a 

 quadratic. Reference is made to Prof. Bolza's inaugural 

 dissertation (Gottingen, 1S86). The sections discuss theorems 

 on the biquadratic involution having a complete square, the 

 system of a cubic and two linear forms and their conjugate 

 system, the system of a cubic and quadratic and their conjugate 

 system, certain involutions, and miscellaneous results on bi- 

 quadratic involutions containing a complete square. — On the 

 theory of improper definite integrals, by E. H. Moore. In the 

 paper the author discusses the types connected with the names 

 of Cauchy, Riemann, du Bois-Reymond, Dini, Schoenflies, 

 Harnack and Jordan, Holder, and de la Vallee-Poussin. 

 Prof. Moore himself defines a system of types, which differ 

 according to the way in which the integral depends (by 

 definition) upon the sets of points of singularity of the 

 integrand function with respect to definite integration.— On 

 the convergence and character of the continued fraction 

 Oj^ a„: fljS 

 I '*' J "•" ~ _,_...., by E. B. Van Vleck, is a portion 



of the paper, contributed by the author to the August meeting 

 of the Society, on the convergence of the continued fraction of 

 Gauss. In this portion the theorem established is— if, in such 

 a fraction, the greatest modulus of any point of condensation of 



the sequence flj, a„, a.. is /C-, then within a circle of 



radiiis 1/4/-, described about the origin as centre, the continued 

 fraction will represent an analytic function, and the only 

 singularities of the function contained within the circle will be 

 poles. In any region excluding these poles and lying in the 

 interior of the circle the convergence will he imiform. 



SOCIETIES AND ACADEMIES. 

 London. 

 Royal Society, November 21.— "The Pear-shaped Figure 

 of Equilibrium of a Rotating Mass of Liquid." By Prof G H 

 Darwin, F.R.S. 



"Sur la Stabilite de I'fiquilibre des Figures Pyriformes 

 affectees par une Masse Fluide en Rotation." By H. Poincare 

 For. Mem. R.S. 



"On the Process of Hair Turning White." By E. 

 Metchnikoff, For. Mem. R.S. 



Although the fact of hair turning white is a most familiar one, 

 its mechanism has not as yet been unveiled. The authors of 

 works on hair and dermatology acknowledge their ignorance 

 concerning this subject. 



Having undertaken a study on atrophic processes, and espe- 

 cially on senile atrophy, my attention has been called to the 

 atrophy of hair pigment so frequent in old people. 



Observations on grey hair, or on hair beginning to turn grey, 

 showed me that the atrophy of its pigment is due to the inter- 

 vention of phagocytes of the hair. 

 I ,. D r -vi . 1 .11. , • - These cells have a single nucleus and their very different 



.— relation.— Prof Metzler extends these relations and gives aspect one from another is due to numerous amoeboid prolonga- 

 a series of types of linear relations between the minors of a tions of their protoplasm. They are derived from the medullary 

 centro-symmetric determinant. The present memoir gives the part of the hair and make their way out into its cortical layer 

 number of relations of each type.— Two papers by A. Prints- where they absorb the pigment granules, which they then 



type. — Two papers by A. Prings 

 heim are (i) ueber die anwendung der Cauchy'schen multiplica- 

 tions regel auf bedingt convergente oder divergente reihen, and 

 (2) ueber den Goursat'schen beweis des Cauchy'schen integral- 

 satzes. These, as well as several of the other papers in the 

 number before us, were communicated to the Ithaca meeting of 

 the Society (August 19).— New proof of a theorem of Osgood's 

 in the calculus of variation.?, by Oskar Bolza, is a simple one of 

 the important characteristic property of a strong minimum in 

 the calculus. — On certain pairs of transcendental functions 

 whose roots separate each other, by the same author, proves the 

 theorem, if, in a certain interval, /, q, <p„, <p^, i(,.„ tfi, are con- 

 tinuous real functions of the real variable at," and if the last four 

 of these functions have continuous derivatives, then, y being a 

 solution not identically zero of the differential equation 

 y" + py + '/y = o, the roots of the functions <p„y' - cp-jr, 

 +!!>'' - 'Piy «''l separate each other if no one of the three func- 

 NO. 1675, VOL. 65] 



remove from the hair. 



If we consider hair, one part of which is already white and 

 the other still pigmented, we find a great many of these phago- 

 cytes. They are supplied with greatly developed prolongations 

 and become insinuated between the keratic cells of the peripheral 

 layer. 



In absolutely white hair the phagocytes filled with pigment 

 become more and more scarce, and most frequently completely 

 disappear. 



It is thus indubitable that the phagocytes of the hairs swallow 

 up the granular pigment of the cortical layer and transfer it else- 

 where, the result being the complete whitening of such hair. 

 On observing the root of hair beginning to whiten, we often find 

 a great many phagocytes filled with pigment. 



The whitening of the hair of old dogs proceeds by the same 

 mechanism. We equally find here a great number of phagocytes 



