452 Notices respecting New Boohs. 



same experiment was observed as follows. The meniscus 

 between the two liquids is visible on account of the different 

 indices of refraction. At ordinary temperature the index for 

 chloroform is 1*45, while that of water is 1*33. The index 

 for chloroform decreases more rapidly with rising tempe- 

 rature than does that of water, so that eventually the index 

 of chloroform falls below that of water. When the two indices 

 are equal the separating surface disappears from view to 

 reappear again when the temperature is raised still more. The 

 disappearance is so complete that when the experiment was 

 first made it was given up at this point, as there was every 

 appearance of homogeneity just as though mixture of the 

 two liquids was complete. In the case described above the 

 temperature for disappearance of the meniscus is considerably 

 below that at which the liquids change places. 



The tube used was a thick-walled tube about 6 cm. long 

 with internal diameter of 7 mm. 



XLII. Notices respecting New Books. 



Bibliography of Non-Euclidean Geometry, including the Theory of 

 Parallels, the Foundations of Geometry, and Space of n Dimen- 

 sions. By Duncan M. Y. Sommeeville, M.A., D.Sc. Printed 

 and published by Harrison & Sons, London, for the University 

 of St. Andrews. 1911. 



BY the preparation of this bibliography Dr. Sommerville has 

 earned the gratitude of all students of the branches of mathe- 

 matics which bear upon the modern developments of non-Euclidean 

 space. Begun as a continuation of Halsted's bibliography of a 

 similar nature, which contains short annotations on the principal 

 works catalogued, the present work finally took a different form ; 

 and we have here catalogued the titles of all works from the 

 earliest times to the present which deal with the extended con- 

 ception of space. Fully half the book is a chronological catalogue, 

 beginning with Aristotle and Plato in the fourth century B.C., 

 and coming down to 1911. In each year the authors' names are 

 arranged alphabetically. There then follow a subject index, with 

 the authors' names and dates given under each heading; an alpha- 

 betical index of subjects ; and an author index, giving titles and 

 dates, from which by reference to the chronological catalogue 

 every needed information can be at once obtained. The book 

 should be in every mathematician's library. 



