278 JSotices respecting New Boohs. 



conditions the relative intensities in two directions changes 



considerably, the ratio — - , dropping from nearly 2 to about 

 -L7772 



1 5. It is, howeve>*, not yet known if the radiation in these 

 cases gave other indications of being a purely scattered 

 radiation. The reasons for the use of a soft beam in these 

 experiments were that possiVe complications due to the 

 fluorescent radiation were avoided, and because only by using 

 such a beam have experiments on absorbability, and polari- 

 zation of primary and secondary beams indicated the greatest 

 perfection of scattering. The phenomena need further in- 

 vestigation together, to explain the results under varied 

 conditions. 



The experiments, however, show such remarkable agreement 

 between the pulse theory and experiment, under limited con- 

 ditions, that it can on'y be concluded the apparent variations 

 are capable of special explanation. They have not yet been 

 fully investigated by the writers. 



The experiments on the fluorescent X-radiation (homo- 

 geneous secondary radiation) more completely confirm 

 previous experiments showing their uniform distribution, 

 and different origin. 



Our thanks are due to Mr. G. H. Martyn, B.Sc, for his 

 valuable help with these experiments. 



XXXII. Notices respecting New Books. 



Mysticism in Modem Mathematics. By Hastings Berkeley*. 



Henry Frowde : Oxford University Press, 1910. 

 r I\HIS book is divided into three parts. The first is devoted to 

 -*- a brief discussion of Thought and its Symbolic Expression ; the 

 second is occupied by a critical examination of Imaginary Quantities 

 in Algebra and Imaginary Loci in Geometry ; and the third and 

 largest part attacks the philosophical foundations of Non-Euclidean 

 Geometry. The mathematician who follows Labatsehewsky 

 and Biemann into the mystical realms where straight lines 

 assume properties which the matter-of-fact Euclidean denounces 

 as not-straights will not probably be diverted from his pursuit by 

 Mr. Berkeley's logic. Nor will the modern analyst or searcher 

 for complex algebras cease to manipulate his imaginaries although 

 he cannot find an explanation of y' — l which can be stated in 

 simple intelligible language. It may be true, as the author 

 suggests, that the modern mathematician has allowed his sym- 

 bolism to run away with him, and that logic demands a reasonable 

 interpretation of this symbolism. What is an imaginary point? 

 "What are imaginary loci? Boole, Cayley, Chrystal, Henrici, 

 Whitehead, among others, are questioned ; but apparently no 



