542 Notices respecting New Boohs. 



An Elementary Treatment of the Theory of Spinning Tops and Gyro- 

 scope Motion. By H. Crabtree. Longmans, Green & Co. 

 London: 1909. 

 The history of applied mathematics is full of: illustrations of 

 the truth that problems which tried the powers of the most 

 powerful thinker of one age become the familiar possession of the 

 average student in the succeeding generation. Usually the first 

 presentation of the theory is crude and difficult ; but with the 

 flight of the years the combined attacks of many minds evolve a 

 simpler and generally a more natural way of looking at the asso- 

 ciated problems, which finally And their appropriate place in a 

 so-called elementary textbook. Spinning tops and gyroscopic 

 motion are a case in point. In this refreshing little book which 

 Mr. Oabtree has prepared, the dynamical principles of the con- 

 servation of energy and the conservation of moment of momentum 

 are applied with simplicity and power to many familiar phe- 

 nomena of motion — spinning tops, mono-rail, precession, diabolo, 

 torpedo, golf-ball, rifle- bullet, and so on. Simple diagrams help 

 to elucidate the discussion — with the exception (if a fault must be 

 noted) of the misleading diagram on page 53 of the flight of a 

 rifle-buUet. Here also the attempt to explain the " drift " is not 

 convincing — indeed, the hydrokinetics is not sound. The foot- 

 note on the same page referring to the golf-ball and Tait's investi- 

 gations is so full of misstatement and the mythology of the Club- 

 house that the author had better suppress it altogether in a second 

 edition. These flaws apart, the book deals in an interesting 

 wav with great problems. There are many examples for the 

 student to work at ; the mathematics is kept well under control, 

 and the dynamical ideas are never lost sight of. The book should 

 be in the hands of all students who are beginning their higher 

 studies iu applied mathematics. 



Funlctionentafeln mit Formeln unci Kurven. Von Dr. E. Jahnke 

 unci Ingenieur E. Emde. Teubner : Leipzig und Berlin. 1909. 



These tables of functions of various kinds are a most valuable 

 addition to the many books of tables which have recently been 

 prepared. The mere enumeration of some of the functions which 

 are here tabulated will suffice to show to all interested the real 

 importance of the work: Exponential Eunctions, Hyperbolic 

 Functions, Fresnel's Integrals, the Gamma Eunction, the Error 

 Integral, Elliptic Integrals and Eunctions, Spherical Harmonics, 

 Bessel's Eunctions, etc. Among the elliptic functions there are 

 not only the familiar functions in their earliest form, but also 

 Theta functions, and the Weierstrass functions; and a valuable 

 addition gives the mutual induction and attraction between 

 parallel co-axial circular circuits in terms of a quantity w T hich 

 depends on the radii of the circuits and their distance apart. 



