344 SCIENCE PROGRESS 



well treated in the chapters on the numerical aperture, and the testing of 

 objectives. In the latter chapter, among other methods, Abbe's test plate is 

 very clearly described. 



One of the most useful chapters, especially for the private student, is that 

 devoted to microscopes and objectives for different purposes. The distinctive 

 features of the instrument as modified for special subjects, such as botany, 

 physiology, etc., are well described and illustrated. 



It may be useful to indicate briefly the ground covered by the book. After 

 a short introductory chapter on prisms and lenses, there follow discussions on the 

 simple microscope, the compound microscope with its various fine adjustments, 

 objectives — semi-apochromatic and apochromatic, "dry" and "homogeneous" 

 systems — and eyepieces. These give very detailed accounts, and contain illus- 

 trations of the work of the more important makers. Then follow chapters on 

 magnification — the difference between what Abbe termed " empty magnification " 

 and useful magnification is emphasised— substage condensers and diaphragms, 

 methods of illumination (including Siedentopf's method of oblique and dark-ground 

 illumination for ultramicroscopic particles, but, unfortunately, not Cotton and 

 Mouton's simple and convenient modification), the use of the microscope, the 

 binocular microscope, and stereoscopic vision. The rather long chapter on the 

 instrument as modified for use in the particular subjects follows, succeeded by 

 that on the testing of objectives. 



The two chapters by Mr. Conrady precede one on accessories, and the last 



chapter contains a number (thirty-eight) of " hints upon correcting several common 



faults " met with in using the microscope and its accessories, evidently the work 



of a skilled and experienced microscopist. 



H. Thirkill. 



An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic 

 Motion. By Harold Crabtree, M.A. [Pp. xii + 140, with 3 plates.] 

 (London : Longmans, Green & Co. Price 5^. 6d. net.) 



This book is primarily designed " to bring within the range of the abler 

 mathematicians at our Public Schools and of first-year undergraduates at the 

 Universities, a subject which has hitherto been considered too difficult for any 

 but the more advanced students in mathematics." Appearing at a time when 

 investigations of the conditions determining dynamical stability are very much 

 " in the air," this work can be recommended strongly to those concerned with 

 the applications of the gyroscope to practical engineering problems. 



The book can be divided roughly into two parts. In the first part (chapters 

 i. to v ) the necessary mathematical equipment of the student has been reduced 

 to a minimum. Most of the phenomena with which we have been familiar since 

 our "spinning-top days" are here shown to be direct consequences of the existence 

 of a gyroscopic torque when the top or gyroscope is free to precess. The author 

 emphasises the necessity for freedom of precession before any gyroscopic resistance 

 is called into play — a fact too often lost sight of by practical engineers. A short 

 treatment of moments of inertia is given. This part might have been extended 

 very profitably. Considering that a large number of the moments of inertia used 

 in subsequent parts of the book are about axes not through the centre of gravity, 

 the inclusion of the theorem relating to change of axes is very desirable. Although 

 a minor point, the distinction drawn in chapter i. between the angular velocity of 

 a point and that of a line is misleading, considering that the velocity is really 

 about an axis in each case. Too great praise cannot be given for the excellent 



