Notices respecting New Books. 239 



bonic acid, on the other hand, should act in the opposite 

 direction. 



Very little is known about the properties of liquids, but 

 their kinematic viscosity is known to be less than that of 

 gases, and it is supposed to decrease with a rise of temperature 

 (Wullner, Bd. I. S. 326, Flow of liquids through tubes at dif- 

 ferent temperatures). Hence it may be guessed that the 

 maximum-velocity layer in liquids should be much nearer the 

 surface of the solid causing the currents than in gases, and that 

 a rise of temperature would bring it still nearer. On the other 

 hand, it may be expected that cold would drive it further off 

 the solid, so that any phenomena connected with this layer in 

 liquids might be better developed in descending cold currents 

 than in ascending warm ones. 



In conclusion, the writers wish to call attention to a paper 

 read to the Royal Society of Edinburgh, by Mr. John Aitken, 

 on the 21st of January this year, and of which an abstract ap- 

 peared in ' Nature ' of the 31st January last. Judging from 

 the abstract, it would appear that Mr. Aitken, so well known 

 for his previous researches on dust-particles as nuclei, has 

 been travelling over much of the same ground as we have, 

 and that he has arrived on the whole at similar conclusions. 



University College, Liverpool. 



XXVII. Notices respecting New Boohs. 



The Elements of Plane Geometry : Part I. (corresponding to Euclid, 

 Books I.-IL). Prepared by the Committee appointed by the Asso- 

 ciation (for the Improvement of Geometrical Teaching). London : 

 W. Swan Sonnenschein, 1884 (pp. 138). 



A RECENT Presidential utterance on the teaching of Mathematics 

 -*■■*- in England asserts that " the teaching of Geometry especially, 

 as judged by the text-books which have come before me, is somewhat 

 deplorable. And this is so, principally, because the spirit of Euclid 

 and the methods of the ancient Egyptians and Greeks, rather than 

 the fundamentally different ideas and methods of modern Geometry, 

 still rule supreme." 



The same elegant geometer goes on to say that, "when the 

 Syllabus on the Elements of Plane Geometry appeared, I resolved to 

 give it a thorough trial, and took the best means in my power to 

 form an opinion on its merits, by introducing it into one of my 

 classes. The fact that it did not quite satisfy me, and that I gave 

 up its use again, does not, of course, prove that it fails also for use 

 in schools, for which it was originally intended." This, we would 

 fain think, is just the point. The writer above quoted has himself 

 written a beautiful ' Elements of Geometry,' which we dare say 



