.Notices respecting New Boohs. 40 D 



necessary. The omission of such experimental detail is scarcely 

 pardonable. The diagrams are usually clear : that one illustrating 

 dispersion is, however, misleading, and the sectional drawing of 

 the eye seems unnecessarily crude. The refraction by the eye is 

 attributed entirely to the lens ; perhaps the author would be 

 astonished to be told that two-thirds of the total refraction occurs 

 at the front surface of the cornea: the lens is a comparatively 

 unimportant organ. It may be doubted whether the gradation of 

 density in the lens is "an admirable provision of nature which 

 ensures that no light is lost by total reflexion."' There would be 

 so little difference of index between the lens and the two humours 

 if no gradation existed, and consequently so little reflexion, that 

 its diminution would be of no importance in view of the fact 

 that the chief loss by reflexion also takes place at the anterior 

 surface of the cornea. 



Plane Trigonometry, an Elementary Text-hook for the Higher 

 Classes of Secondary Schools and for Colleges. By H. S. L'aeslaw, 

 Sc.D. (Camb.), D.Sc. (Glasg.). Macmillan & Co. London, 

 1915. 



The first edition of this book appeared in 1900, and was the 

 embodiment of the methods which Professor Carslaw bad gradually 

 adopted during his experience as a teacher first in Glasgow and 

 then in Sydney. The present edition differs only in slight details 

 from its predecessor, the most important innovation being the 

 indication of the harder portions by means of asterisks. The 

 book is divided into two Parts, the first part containing within its 

 twelve chapters the ordinary elementary trigonometry, which 

 gives the trjgonometrical ratios and their simpler transformations 

 and culminates in the solution of triangles and the measurement 

 of heights of inaccessible objects. In Chapter XII the radian is 

 introduced for the first time and an interesting discussion given of 

 the meaning of the length of a curve. There is also a somewhat 

 isolated section on the Dip of the Horizon, in which no hint is 

 given that the simple calculated result is not in accord with obser- 

 vation on account of refraction of light. Chapter XIII, which 

 opens Part II, is devoted to the properties of triangles and their 

 related circles, a kind of mathematical cid de sac which some geo- 

 metrical minds spend their existence in exploring. The remaining 

 chapters introduce the student to quite a different atmosphere, 

 through which he should pass ere long into the aethereal regions 

 of infinite series and function theory. Professor Carslaw inten- 

 tionally limits his treatment to the Real ; and yet a slight hint 

 now and then might stimulate the intelligent student by giving him 

 a vision of the Imaginary splendours behind the curtains of reality. 

 These limitations, however, in no way detract from the value of 

 the book as a sound exposition of the subject. 



