December 20, 1912] 



SCIENCE 



869 



Also notes and errata to volumes 7 and 13. 



The opening- (October) number of volume 

 19 of the Bulletin of the American Mathe- 

 matical Society contains : " Surfaces of 

 revolution of minimum resistance," by E. J. 

 Miles ; " Shorter Notices " : Riquier's Les Sys- 

 temes d'Equations aux Derivees partielles, by 

 Edward Kasner; Study's Ebene analytische 

 Kurven und zu ihnen gehorige Abbildungen, 

 by Arnold Emch; Coffin's Vector Analysis, 

 by J. B. Shaw; Berichte und Mitteilungen 

 der Internationalen mathematischen TJnter- 

 richtskommission and Auerbach und Eothe's 

 Taschenbuch fiir Mathematiker und Physiker, 

 by E. W. Ponzer; Bonola-Carslaw's ISTon- 

 Euelidean Geometry, by Arthur Eanum; Bar- 

 barin-Halsted's Geometrie rationelle, by E. C. 

 Archibald; Smith and Granville's Elementary 

 Analysis, by Jacob Westlund; Hawkes, Luby 

 and Teuton's Second Course in Algebra, by 

 J. V. McKelvey; Jacob's Calcul mecanique, 

 by C. C. Grove; Schwahn's Mathematische 

 Theorie der astronomischen Finsternisse and 

 Haret's Mecanique sociale, by Kurt Laves; 

 " Notes," and " New Publications." 



The November number of the Bulletin con- 

 tains : Eeport of the nineteenth summer meet- 

 ing of the society, by F. N. Cole ; " A few 

 theorems relating to Sylow subgroups," by G. 

 A. Miller ; " Theorems on functional equa- 

 tions," by A. E. Schweitzer ; " Double curves 

 of surfaces projected from space of four di- 

 mensions," by S. Lefschetz; Eeview of South- 

 all's Geometrical Optics, by E. B. Wilson; 

 "Shorter Notices": Eogers-Salmon's Analytic 

 Geometry of Three Dimensions, by Virgil 

 Snyder; Volume 3 of Picard's edition of the 

 Works of Charles Hermite, by James Pier- 

 pont; Heiberg's Naturwissenschaften und 

 Mathematik im klassiscben Altertum and 

 Mannoury's Methodologisches und Philoso- 

 phisches zur Elementar-Mathematik, by D. E. 

 Smith; Weber und Wellstein's Encyklopadie 

 der Elementar-Mathematik, volume 3, part 1, 

 and Korn's Freie und erzwungene Schwing- 

 ungen, by J. B. Shaw; Eichard's Assurance 

 complementaire de I'Assurance sur la Vie, by 

 C. C. Grove; Vahlen's Konstructionen und 



Approximationen, by E. W. Ponzer; "Notes," 

 and " New Publications." 



The December number of the Bulletin con- 

 tains : General report of the fifth interna- 

 tional congress of mathematicians at Cam- 

 bridge, by Virgil Snyder; Eeport of Section I 

 of the Congress (arithmetic, algebra, an- 

 alysis), by A. B. Erizell; " Shorter Notices": 

 Boehm's Elliptische Eunktionen, Part 2, by 

 L. W. Dowling; Darboux's Eloges aeadem- 

 iques et Discours, by G. A. Miller; Hedrick 

 and Kellogg's Applications of the Calculus to 

 Mechanics, by D. C. Gillespie ; " Notes," and 

 " New Publications." 



CONDITION OF THE EABTH'S CEUST 



The results of measurements of the force 

 of gravity at various points on the earth, as 

 well as the results of triangulation operations, 

 were early recognized as indicating that the 

 earth's crust is in a condition of approximate 

 equilibrium, to which the name " isostasy " 

 has since been given. 



The development by Mr. B[ayford of a new 

 method of reduction of gravity observations, 

 in which for the first time the effect of the 

 topography of the whole earth has been taken 

 into account, has furnished strong additional 

 proof of the general fact that the condition of 

 isostasy exists, that elevated regions, whether 

 plains or mountains, are, so to speak, floated 

 on the earth's surface by reason of the lesser 

 density of the underlying materials, and that 

 ocean bottoms are depressed because of the 

 greater density of the materials beneath. 



The question of how close is this adjust- 

 ment, of how local is the compensation of sur- 

 face irregularities, is of considerable interest. 

 If the compensation is quite complete for 

 each small topographic feature, so that a single 

 mountain or hill or canyon is exactly com- 

 pensated by a less dense or a more dense ma- 

 terial beneath, the surface of the earth would 

 in detail be in a condition of nearly perfect 

 equilibrium, and would largely be free from 

 stresses due to the supporting of topographic 

 features; on the other hand if the compensa- 

 tion is more general such features of moderate 



