It was quite time that we had in English a standard treatise on gyroscopic motion. Space is, of course, devoted to the subject in various well-known text-books on rigid dynamics, and there are one or two good little books of an elementary nature, such as Perry's _Spinning Tops_ and Crabtree's _Spinning Tops and Gyroscopic Motion_, but hitherto the man in search of detailed information on problems concerning tops in the widest sense has had to go to Klein and Sommerfeld's _Theorie des Kreisels_, if he could not find what he wanted in Sir George Greenhill's _Report_. That Professor Gray should be the man to supply our want is only fitting. At the University of Glasgow, where he succeeded to the chair of Natural Philosophy left vacant by Lord Kelvin's death, an interest in gyroscopic motion is traditional, and Professor Gray inherited a collection of apparatus for experiment in this field which he has extended by many ingenious and convenient forms of gyroscope described in the book before us. His own researches on the general dynamics of gyroscopic systems have added clearness to that branch of applied mathematics, and his son is an expert in the design and application of practical gyrostats. A judicious combination of experimental and theoretical treatment forms the great attraction of Professor Gray's book. The problems of gyroscopic motion range from the behaviour of the schoolboy's top to that of this great top, the earth, and include a great number of engineering applications. The torpedo is kept in its course by a gyroscope; the gyroscopic compass, which makes no use of magnetic properties, has rendered possible the navigation of a submerged submarine; Schlich invented a gyroscopic apparatus, which has been tried successfully in small ships, for keeping a vessel from rolling in a rough sea; with Brennan's monorail the car is kept upright by means of a gyroscopic device; and many other ingenious uses have been made of the seemingly paradoxical properties of spinning tops. The gyroscopic compass is, unfortunately, not treated in Professor Gray's book, nor is there any account of other naval and military applications of the gyroscope, since the author, finding that the official secrecy, necessarily imposed at the time of writing, would prevent him giving anything but a fragmentary account, has preferred to reserve his discussion of these appliances to a promised second volume. Very little is said of the monorail (in fact, Brennan's name is not mentioned), which is less explicable. Many practical applications of gyroscopic theory to such problems as the drift of projectiles, golf balls, and boomerangs (the last-named treated necessarily in a very general manner) come up for consideration, and the forgotten diabolo, child of a passing craze, is resurrected to provide an example of the effect of equality of the principal moments of inertia on the stability of rotation of a body under no forces. Most attention is, however, given