348 Notices respecting New Boohs. 



equation \/ 2 Y—0, 



f(z -f ioo cos u + iy sin u, u)clu, 



-$ 



f being an arbitrary function of its arguments. Thence spherical 

 (and, more especially, zonal) harmonics are deduced. Further, 

 their integral properties are demonstrated, which lead at once 

 to the expansion of a f uuctiou as a series of surface harmonics. 

 Stress is laid (pp. 57-66) on the practical evaluation of the co- 

 efficients, Bauschinger's scheme for the calculation of the auxiliary 

 coefficients being fully explained by means of two numerical tables. 



5. The aim of this Tract is to give an account of various methods, 

 both numerical and graphical, of solution of Spherical Triangles. 

 Every teacher of mathematics will gladly share the author's 

 opinion that this subject is of importance not only in view of its 

 applications, but " has also considerable value from the educational 

 point of view." After a few remarks on the use of Logarithmic 

 Tables (Chap. I.), the fundamental formulas of spherical trigono- 

 metry are developed in Chapter II. in an easily accessible and 

 attractive manner. Chapter III. treats of the numerical solution 

 of the Bight-angled, and Chapter IV. of that of the General 

 spherical triangle. The following chapter contains special appli- 

 cations of the most important and instructive kind : Great Circle 

 Sailing, Finding the Longitude at Sea, Beducing an Angle to the 

 Horizon, and Conversion of Star Coordinates, with numerical 

 examples. The last chapter is dedicated to Graphical Methods of 

 Solution of spherical triangles. 



6. The last of the Edinburgh Tracts hitherto published contains 

 a most fascinating and easily intelligible introduction to the theory 

 of Automorphic Functions which will, doubtless, greatly contribute 

 to the diffusion of this beautiful but by no means very accessible 

 branch of mathematics. The reviewer, tempted to enter upon the 

 numerous attractive details of this beautiful work, regrets the 

 necessity, dictated by reasons of " space," of limiting himself to a 

 mere quotation of the chapters. These are : I. Linear Trans- 

 formations. II. Groups of Linear Transformations. III. Auto- 

 morphic Functions. IV. The Biemann - Schwartz Triangle 

 Functions. V. Non-Euclidean Geometry. VI. Uniformisation. 

 — A very full Bibliography of automorphic functions (pp. 88-96), 

 up to 1913, will be helpful to those who desire to pursue the subject 

 further. 



Bulletin of the Bureau of Standards. 

 (Washington : Government Brinting Office, 1915.) 



Amongst the publications of scientific interest during 1915 we 

 note the following : — 



In the March number is described a determination by the bomb 

 method of the heats of combustion of Cane Sugar, Benzoic acid, 



