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... be squeezed out unless it is at a distance from O less than r cosec a." Many corrections have to be made in this before any sense can be made of it. A full solution of the problem thus concealed by language is given in the text. Lessons in Geometry. By CHARLES M'LEOD. Pp. 507. 1915. (Aberdeen, The University Press.) Elementary Geometry. By W. E. PATERSON and E. O. TAYLOR. Pp. 327. Part I., Is. 8d.; Part II., Is. 8d. 1915. (Clarendon Press.) In the eighty lessons and six appendices contained in his book, Dr. M'Leod has given us an exceedingly interesting and stimulating account of his subject. The work has a wide scope; the course of geometry is complete from the very beginning, and by the time the last appendix has been mastered, the reader has been through the whole of the ordinary elementary work in plane and solid geometry, in plane trigonometry, in logarithms and in mensuration, and has also learnt something about conic sections and derivative functions. A large number of examples is provided. A paragraph from the preface explains the use to which the book may be put. " With junior pupils the book requires the guiding hand of the teacher. Young teachers may find in it suggestive hints from an old hand. More advanced pupils may derive profit from reading through its pages on their own account." This estimate is more than justified by an examination of the book. Any teacher of elementary mathematics would find it useful to him, and one can hardly imagine a better text-book for a student who is beginning the study of geometry somewhat late in his educational career. The book by Messrs. Paterson and Taylor is a school text-book on the usual lines. It presupposes a preliminary course, and is specially adapted to follow Mr. Taylor's Introduction to Geometry, also published by the Clarendon Press. The proofs of the first eleven theorems are placed in an appendix and are not to be learnt till some considerable number of the succeeding theorems have been mastered. A special feature of the work is that it is divided into Chapters, not into Books. The Theorems (of which there are 77) are thus numbered consecutively, and the same method is used with the Problems. The proofs are sometimes given in outline only, and the book is quite in the fashion in the number of question marks and inconclusive paragraphs which it contains. The printing is good, and the volume would be found quite workable as a text-book for classes which are being taken through the ordinary elementary course in Plane Geometry.