274 



SCIENCE 



[N. S. Vol. XXXVIII. No. 973 



Lippmann's achievements. There are many 

 who know the results of his practical work as 

 director of the large sugar refinery at Halle, 

 and of his researches in the laboratory, as 

 comprised in his exhaustive two-volume 

 treatise " Die Chemie der Zuckerarten," but 

 there are fewer, perhaps, who know what he 

 has done during leisure hours in the study 

 along historical and cultural lines, as exem- 

 plified in his masterful book " Die Geschichte 

 des Zuckers " and in these two volumes of 

 scientific papers and essays. To be technolo- 

 gist, chemist, historian and scholar, and all 

 surpassingly well, is a record of accomplish- 

 ment such as few men have realized. Adapt- 

 ing a phrase from that ancient " father of 

 science," Aristotle, of whose works Professor 

 Lippmann is such an enthusiastic commenta- 

 tor, we may say: it is a record of accomplish- 

 ment, " four-square and truly good." 



C. A. Browne 



SCIENTIFIC JOUBNALS AND ARTICLES 



The July number (Vol. 14, No. 3) of the 

 Transactions of the American Mathematical 

 Society contains the following papers : 



L. E. Dickson: "Proof of the finiteness of 

 modular covariants. ' ' 



E. D. Carmiehael : ' ' On transcendentally trans- 

 cendental functions. ' ' 



M. Pr^ehet : ' ' Sur les classes V normales. ' ' 



G. E. Clements: "Implicit functions defined by 

 equations with vanishing Jaoobian. ' ' 



Dunham Jackson : ' ' On the approximate repre- 

 sentation of an indefinite integral and the degree 

 of convergence of related Fourier series." 



L. P. Eisenhart: "Certain continuous deforma- 

 tions of surfaces applicable to the quadrics. " 



The concluding (July) number of volume 

 19 of th'9 Bulletin of the American Mathe- 

 matical Society contains : Report of the April 

 meeting of the Society, by F. N. Cole; Eeport 

 of the twenty-third regular meeting of the 

 San Francisco Section, by W. A. Manning; 

 " The total variation in the isoperimetric 

 problem with variable end points," by A. E. 

 Crathorne ; " A note on graphical integration 

 of a function of a complex variable," by S. D. 

 Killam; " The unification of vectorial nota- 



tion," by E. B. Wilson ; " Shorter Notices " : 

 Kowalewski's Grundziige der Differential- und 

 Integralrechnung, by R. L. Borger; Vivanti- 

 Cahen's Fonctions polyedriques et modulaires, 

 by G. A. Miller; Markoff-Liebmann's Wahr- 

 scheinlichkeitsrechnung, Carvallo's Calcul des 

 Probabilites et ses Applications, and King's 

 Elements of Statistical Method, by A. 0. 

 Lunn ; " Notes " ; " New Publications " ; 

 Twenty-second Annual List of Published 

 Papers; Index of Volume XIX. 



TBE BUTHESFOBD ATOM 

 To explain the observations made by Geiger 

 and Marsden' on the scattering of a particles 

 through large angles by metal foils, Ruther- 

 ford^ suggested that in such cases the deflec- 

 tion of each ray was due to an intimate en- 

 counter with a single atom of the matter 

 traversed. It was necessary to assume that 

 the positive charge is highly concentrated in 

 a very small volume at the center, surrounded 

 by an equal amount of negative electricity 

 distributed throughout the remainder of the 

 volume of the atom. To compare the theoiy 

 with experiment, suppose we consider the effect 

 of allowing a narrow pencil of a rays to strike 

 a thin metal foil from a direction perpen- 

 dicular to its surface. The probable number 

 of reflected or deflected rays which may be 

 expected each second to strike any given square 

 centimeter of a spherical screen whose center 

 of curvature is the point of bombardment, 

 was shovra. by Rutherford to be, according to 

 his theory, 



4r^ \ mw' J 2' 



where : 



Q = number of a rays striking the foil per 



second; 

 nt = number of atoms in the foil per unit area ; 

 r = radius of the spherical screen ; 

 <t> = angle between the radius vector to the area 

 and the direction of the striking beam 

 of rays; or the angle of deflection; 

 A'^e^ central charge of the bombarded atom; 



^Proc. Boy. Soc, 82A: 495, 1909; 83A: 492, 

 1910; Manchester Lit. and Phil. Soc. Proc, 1910. 

 ^Phil. Mag., 21: 669, 1911. 



