OCTOBEK 1, 1915] 



SCIENCE 



459 



M. Fr^chet : ' ' Sur les f onetionnelles bilinSaires. ' ' 

 D. F. Barrow: "Oriented circles in space." 



D. Buchanan : "A new isosceles triangle solu- 

 tion of the three-body problem." 



L. P. Eisenhart: "Surfaces and their trans- 

 formations. ' ' 



E. J. Wilczynski ; "The general theory of con- 

 gruences. ' ' 



J. H. M. Wedderburn : ' ' On matrices whose co- 

 efficients are functions of a single variable. ' ' 



E. Kasner : ' ' Conf ormal classification of analytic 

 arcs or elements : Poinearg 's local problem of con- 

 formal geometry. ' ' 



D. E. Curtiss: "Extensions of Descartes' rule of 

 signs connected with a problem suggested by 

 Laguerre. ' ' 



J. B. Shaw : " On parastrophic algebras. ' ' 



The concluding (July) number of Vol. 21 

 of the Bulletin of the American Mathematical 

 Society contains : Report of the April meeting 

 of the society in New York, by F. N. Cole; 

 " An elementary double inequality for the 

 roots of an algebraic equation having greatest 

 absolute value," by G. D. BirkhofP ; " Certain 

 non-enumerable sets of infinite permutations," 

 by A. B. Frizell; "George William Hill, 1838- 

 1914," by E. W. Brown; Eeview of Dickson's 

 Linear Algebras, by W. C. Graustein ; " Shorter 

 Notices " : Poincare's Wissenschaft und Meth- 

 ode, by J. B. Shaw; Martin's Test-book of 

 Mechanics, Vol. 5, by F. L. Griffin ; " Notes " ; 

 " New Publications " ; Twenty-fourth Annual 

 List of Published Papers ; Index of Volume 21. 



SPECIAL ARTICLES 



THE THEORY OF MAGNETIZATION BY ROTATION 



The experiment which I described in a 

 recent number of this journal may be con- 

 sidered as a modification of an experiment 

 made long ago by Maxwell,^ who appears to have 

 been the first to conceive the idea that a mag- 

 net should behave like a gyrostat if its Am- 

 pereian currents are actually material, as 

 modern theory assumes. In Maxwell's experi- 

 ment an electromagnet, mounted in a frame 

 in such a way as to be free to move about a 

 horizontal line through its center of mass and 



1 Elec. and Mag., § 575. 



perpendicular to its magnetic axis, was rotated 

 at high speed about a vertical line, and optical 

 observations were made to see whether the 

 angle a between the vertical and the magnetic 

 axis was altered as the speed increased from 

 zero, stability being secured by properly adjust- 

 ing the moments of inertia. No change in a 

 was observed, but only rough experiments were 

 possible. 



In my experiment the electromagnet is re- 

 placed by each of the countless multitude of 

 molecular magnets of which the iron rod is 

 constituted, and the total change in the orien- 

 tation of all the magnets with reference to the 

 axis of rotation of the rod is determined mag- 

 netically instead of optically. 



In the complete paper it is shown that the 

 angular momentum M of the simplest type of 

 molecular magnet possible, constituted of a 

 negative electron with mass m and charge e 

 revolving with angular velocity w in a circular 

 orbit about a positive nucleus with charge — e 

 at rest, is related to the magnetic moment /* 

 by the equation 



M=:2(m/e)ii. (1) 



If now the rod of which the molecular magnet 

 is a part is set into rotation about its axis AB, 

 with angular velocity O, the angle a between 

 the vector M and AB will decrease, just as in 

 the case of a gyroscope, until the torque T' on 

 the system brought into existence by this dis- 

 placement is just equal to the rate of increase 

 of its total angular momentum in the steady 

 state when kinetic equilibrium has been 

 reached and the vector M is tracing out a 

 conical surface with constant semi-angle a and 

 angular velocity Q. The efl^ect in this steady 

 state is exactly the same as if the rod were at 

 rest and the molecular magnet were acted 

 upon by a torque T" =■ — T' due to an extra- 

 neous magnetic field of strength E, where H 

 is the intrinsic magnetic intensity of rotation. 

 The complete expression for the torque T" is 

 known (and can readily be shown from first 

 principles) to be 



T" = — 2" = — Mfi sin a — BQ- sin a cos a, (2) 

 where B denotes the difference between the 



