450 Intelligence and Miscellaneous Articles. 



the manipulation of the machinery of the Differential and Integral 

 Calculus before they have grasped the preliminary notions of a 

 Limit and of an Infinite Series 1 ' he pronounces to be to a large 

 extent an " educational sham," which is a " sin against the spirit 

 of mathematical progress." Hence, after devoting the two opening 

 chapters to the subjects of Permutations and Combinations, and 

 the general theory of Inequalities, he discusses very fully and 

 admirably in the following two chapters the doctrine of Limits 

 and the 'convergence of infinite series and of infinite products: 

 these are followed by chapters applying the previous results to 

 Binomial and Multinomial series for any index, and to Exponential 

 and Logarithmic series. All this forms a good introduction to the 

 theory of Functions, such as has been opened up by the labours of 

 Cauchy, Biemann, Weierstrass, and others, and will enable the 

 student who assimilates the results to get an intelligent hold upon 

 the Calculus. This account of the function-theory is further illus- 

 trated in other three chapters, in which the Author treats of 

 Graphs of the circular functions, Biemann's surface, hyperbolic 

 functions, Gudermannian functions, the numbers of Bernoulli and 

 Euler, and a host of other choice matters, succeeded by explana- 

 tions of the method of finite differences, Becurring series, and a 

 group of miscellaneous methods. The concluding five chapters are 

 devoted to Continued Fractions, properties of Integral Numbers, 

 and, as we have already mentioned, Probability. This is a very 

 scanty account of much admirable work, but the analysis of one 

 chapter would occupy too much space. The dip we have made 

 here and there (on the ex pede Herculem theory) will be enough 

 to assure those of our readers who have not yet got the book that 

 there is a rare treat in store for them if they will but get it. The 

 " get-up " and other features make the volume a handsome addition 

 to one's book- shelf. 



L. Intelligence and Miscellaneous Articles. 



ON ELECTKICAL OSCILLATIONS IN STRAIGHT CONDUCTORS. 

 BY PROF. STEFAN. 



IF a variable current is transmitted through a wire which is sur- 

 rounded by a concentric metal tube, a current is induced in this 

 tube. The direction and magnitude, as well as the distribution in the 

 tube, may be directly deduced from the principle of least magnetic 

 energy when the current in the wire is supposed to be given. The 

 minimum of this energy is obtained by the following arrangement 

 of the currents : — The central current is condensed in an infinitely 

 thin layer on the surface. The induced current flows in an infi- 

 nitely thin layer on the inner surface of the tube, and has at any 

 instant the same intensity as the current in the central wire, but 

 the opposite direction. With this arrangement magnetic forces 

 are only effective in the space between the surface of the wire and 

 the inner surface of the tube. The interior of the wire as well as 

 that filled by the mass of the tube, and in addition the whole 

 external face, are free from magnetic forces. 



