I 



Notices respecting New Books. 501 



. So much must suffice to give an idea of the object and scope of this 

 small volume, which, it should be said, presupposes " a familiarity 

 with the elemeuts of algebra and trigonometry." To students 

 thus qualified "its subject-matter and treatment constitute a rapid 

 review of the underlying principles of those subjects, including in 

 its most general aspects the algebra of complex quantities." 



J. J. W. 



Elasticity. By Dr. B. Williamson, F.R.S. 

 (London: Longmans, 1894; pp. x + 135.) 



The full title, viz. ' Introduction to the Mathematical Theory of 

 the Stress and Strain of Elastic Solids,' indicates that this little 

 book is an elementary one, and that it does not treat of the more 

 advanced portions of the general Mathematical theory. These, as 

 our readers know, are admirably discussed in Mr. Love's fuller 

 treatise. The subject is of the highest practical importance, and 

 we are glad to have such an Introduction drawn up by so com- 

 petent a writer as Dr. Williamson. Our author states at the 

 outset that he adopts the notation suggested years ago by the late 

 Professor Townsend : a notation which " has the advantage of 

 harmonizing with the generally recognized method of representing 

 the equation of a surface of the second degree." The discussion 

 is in the main confined to the consideration of perfectly elastic 

 solids, so that the results are, of course, only approximately true 

 for actual substances. 



The work is divided into five chapters. In Chapter I., /Strain is 

 treated of under the heads of Homogeneous and Heterogeneous 

 Strain, and Strain in Curvilinear Coordinates. Chapter II. is 

 devoted to Homogeneous and Heterogeneous Stress. The con- 

 nexion between Stress and Strain is the subject of Chapter III., 

 and occupies three sections, on Work and Potential Energy, Case 

 of Isotropic Substances, and Applications. The Torsion of Prisms 

 is considered in Chapter IV., and Elastic Beams in Chapter V. 

 Erom this summary it will be seen that a fair amount of interesting 

 ground is covered. That the text is clearly put goes without 

 saying, but there is no great scope for novelty of treatment. Dr. 

 Williamson takes care to give references, where called for, to 

 recent memoirs and treatises bearing on the subject. It only 

 remains to add that each chapter is closed with a selection of good 

 illustrative exercises from College Problem papers, and that there 

 is an index at the close of the volume. 



On the Definitions of the Trigonometric Functions. By A. MaO 



farlake, D.Sc. (Boston : J. S. Cushiug & Co. ; 49 pp.) 

 This is a paper the substance of which was communicated to the 

 Mathematical Cougress at Chicago on the 22nd August in last 

 year. It is a following up of previous papers by the same author 

 on points connected with Space Analysis. Three of these are 

 respectively entitled ' Principles of the Algebra of Physics/ in 

 which Dr. Macfarlane introduced a certain trigonometric notation 



