138 Notices respecting New Books. 



by passing light the reverse way through an elliptic analyser 

 (t. e. a Nicol prism and quarter undulation-plate), then 

 through the bi quartz, and finally through an analyser. It is 

 found quite impossible to get any match between the two 

 halves of the biquartz when a is large. The actual dispersion 

 of the axes depends upon the variations of /3 with A, and this 

 is very much greater in quartz than in such a doubly refract- 

 ing substance as compressed glass. But in most cases there 

 will always be sufficient variation to make the use of the 

 biquartz a very unsuitable method, and this does, I think, 

 account for the two classes of results mentioned at the begin- 

 ning of this paper. 



In conclusion, I have only to express my gratitude to Mr. 

 Glazebrook for many valuable suggestions, and to Professor 

 Thomson for the use of the Cavendish Laboratory. 



XXI. Notices respecting New Books. 



A Treatise on Spherical Trigonometry, and its application to Geodesy 

 jand Astronomy; with numerous examples. By Dr. J. Casey, 

 F.B.S. (Longmans: 1889.) 



T\R. CASEY has "struck oil" as a writer of Mathematical 

 -*-^ Text-books. It is not so many years since he began this 

 career with his useful and excellent ' Sequel to Euclid,' which has 

 now reached a fifth edition, and since that time he has produced 

 other text-books of like good quality. Having given us an " ele- 

 mentary" and a more advanced Plane Trigonometry, he now 

 completes this special corner of mathematical literature with the 

 work before us. The student will find here all, or nearly all, he 

 wants in a text-book on the subject, illustrated by much matter 

 selected from foreign periodicals, with variety of proofs. Follow- 

 ing a practice which has come much into vogue of late years, many 

 results are ticketed with the names of the earliest publishers of 

 them : for instance, two formulae which frequently occur in the 

 solution of triangles are called the first and second Staudtans of a 

 triangle. Becent points and lines which occur in Plane Geometry, 

 and which have analogues in Spherics, have the like names here : 

 some, as the Lemoine point and the Symmedian point, which are 

 identical in plane, do not coincide in Solids. The specially noteworthy 

 chapters, as might be expected from Dr. Casey's original work in 

 this field, are, in our opinion, those upon the small Circles on the 

 Sphere and on Inversions. There is a large collection of exercises, 

 and, after the author's previous manner, the more noteworthy 

 results are numbered ; of these, 495 are given. In addition to a 

 handy and compact account of the purely Trigonometrical details, 

 there is a final chapter on the applications to Geodesy and Astro- 

 nomy. The text is accompanied by a short index. 



