﻿446 Notices respecting Xew Boohs. 



sentences from the Prefaces. "... a projective treatment 

 introduces the student to a region of geometrical thought, unlike 

 anything he has seen in the past — a transition as abrupt and 

 fertile as the crossing from algebra to the calculus. There are 

 constant surprises, apparent contradictions, features of absorbing- 

 interest, and principles which, by the generality of their application 

 and the variety of their expression, cannot fail to fascinate the 

 reader. . . . The theory of ideal elements in pure geometry, the 

 notion of one-to-one correspondence and its application to holo- 

 graphy and involution, the principles of conical projection are 

 undoubtedly illuminated by a joint use of geometry and 

 analysis. ■"' Chapters are devoted to such questions as orthogonal 

 projection, conical projection, general projection, reciprocation, 

 nomographic ranges, involution ranges, etc. ; and in almost every 

 case each chapter is preceded by a short historic note tracing the 

 origin and development of the idea or method. In many eases the 

 proofs of important theorems are merely indicated and must 

 be supplied by the student, and in addition there are numerous 

 examples for exercise. 



Homogeneous Coordinates for use in Colleges and Schools. By W. 

 P. Milne, M.A., D.Se. Edward Arnold : London, 1910. 



Dr. Milne has placed in the hands of the student a very 

 serviceable exposition of the method of homogeneous coordinates, 

 particular attention being paid to Areals and Trilinears. The five 

 chapters treat respectively of the Straight Line, the Conic, 

 Tangential Coordinates, the Circular Points at Infinity, and Para- 

 metric Representation. The discussion is simple and clear, and 

 numerous examples are appended to the chapters for the student 

 to test and strengthen his powers. In the preface Dr. Milne 

 refers to certain methods in which " much memory work is 

 avoided," Yet on page 71 he gives an '* easy rule " in which 

 an unnecessary appeal to memory is given for writing down the 

 minors of a symmetrical determinant of the third order. The 

 following is surely more satisfactory. Knowing the rule that a 

 determinant of the third order is unchanged by cyclical permutation 

 of row T s or columns we get the minor with its proper sign by 

 simply passing diagonally from left to right downwards to obtain 

 the positive product in the minor. Could anything be simpler ? 



The Propagation of Electric Currents in Telephone and Telegraph 

 Conductors. By Professor J. A. Fleming, M.A., D.Sc,, F.R.S. 

 Pp, xiv + 316. London: Constable & Co. Ltd., 1911. Price 

 8s. 6d, net. 

 This book is an amplification of the notes of two courses of post- 

 graduate lectures given by the author in the Pender Electrical 

 Laboratory, University College., London, in 1910 and 1911, A 

 considerable part of the subject matter has not hitherto found its 

 way into textbooks. Professor Fleming has therefore rendered 



