October 18, 1901.] 



SCIENCE. 



611 



aware, is quite so successful in producing for 

 the student the right combination of physical 

 and mathematical difficulties. 



The first volume is divided into three princi- 

 pal parts and into twenty-three sections. The 

 first part is devoted to pure analysis, with sec- 

 tions in order on definite integrals, Fourier's in- 

 tegral, infinite series, Fourier's series, multiple 

 integrals, functions with complex arguments, 

 differential equations, and Bessel's functions. 

 The second part treats of geometrical and me- 

 chanical theorems, with sections on linear in- 

 finitesimal deformation, vectors, the potential 

 function, examples of potential function, spher- 

 ical harmonics, and the fundamental principles 

 of mechanics. The third part is devoted to ap- 

 plications in the fields of electricity and mag- 

 netism, with sections on electrostatics, prob- 

 lems in electrostatics, magnetism, electrokinet- 

 ics, electrolytic conduction, steady electrical 

 currents, flow of electricity in surfaces, flow of 

 electricity in space and electrolytic displace- 

 ments. 



The second volume is divided into five parts 

 and into twenty-three sections. The first part 

 is concerned with the theory of linear differ- 

 ential equations, with sections on integration 

 by .means of hypergeometric series, integration 

 by means of definite integrals, the P-function 

 of Eiemann, and, under the heading Oscilla- 

 tionstheoreme, a section treating very fully 

 the equation d^y j dx^ + py=0, where p is in 

 general a function of x. The second part is 

 devoted to heat diff'usion, with sections on the 

 differential equation of heat diffusion, the prob- 

 lem when dependent on a single coordinate, 

 and the problem of diffusion in a sphere. The 

 third part is devoted to the theory of elasticity, 

 with sections on the general theory of elas- 

 ticity, statical problems, equilibrium and de- 

 formation of an indefinite isotropic solid, vibra- 

 tions of stretched cords, Elemann's method of 

 integration, vibration of membranes and the 

 general theory of the differential equation of a 

 vibrating membrane. The fourth part is oc- 

 cupied with electrical oscillations, with sections 

 on electric waves, linear electric currents, and 

 reflection of electric oscillations. The fifth 

 part treats of hydrodynamics, with sections on 

 general theorems, motion of rigid bodies in 



fluids (two sections), discontinuous fluid mo- 

 tion, propagation of an impulse in a gas and 

 aerial vibrations of finite magnitude. 



When all parts of a work like this one 

 are noteworthy for their unsurpassed excel- 

 lence, it is difficult to cite parts specially com- 

 mendable or to call attention to small defects. 

 Every reader, according to his bias, will be 

 drawn first to those sections in which he has 

 special interest, and he must be a narrow special- 

 ist if he does not find many such sections. Gen- 

 erally, the work is to be praised for its admirable 

 clearness. Some of us foreigners find the Ger- 

 man frequently lacking in directness and per- 

 spicuity ; and we are especially mystified often 

 by the offensive use of italics so common with 

 writers whose thoughts are unclarifled. Pro- 

 fessor Weber's style, however, is as transpar- 

 ent as that of the best French standards, and 

 in this respect his work recalls the faultless ex- 

 position of such great masters as Gauss and 

 Kirchhoff. 



The typography of the work is likewise un- 

 surpassed. It, like the selection of the subject- 

 matter and the treatment thereof, is a model 

 for all makers of mathematical books. Book 

 makers and publishers in America should take 

 note of the fact that each of the volumes of this 

 work ( comprising over 500 pages per volume) 

 ' made in Germany,' is beautifully printed, on 

 excellent paper, and is yet less than 30 milli- 

 meters thick over all, including the rather 

 stout half-morocco binding. To do as well in 

 our country it will be essential to discard the 

 miserable, thick, talc-loaded or lead-loaded 

 paper now so commonly used here. 



It would be possible to find some small faults 

 with the presentation and treatment of the 

 topics, here and there. ' There are spots on 

 every sun ' ; but in this case, as with our orb, 

 they do not disturb the general luminosity, and 

 we may expect to see them disappear from 

 future editions. In the meantime, students of 

 mathematics and physics generally will find 

 this work a mine of instructive and inspiring 

 information accessible by the aid of a full table 

 of contents and a good index. Every worker 

 in mathematical physics should have the 

 volumes constantly within an arm's reach. 



R. S. W. 



