Notices respecting New Books. 449 



these gases when cold, nor will a current go through NO 

 when the electrodes are made to glow by insulated batteries ; 

 so that in this case the want of conductivity cannot be due to 

 the electricity being unable to get from the gas into the elec- 

 trodes. These experiments show that the molecules of those 

 gases are electrically neutral. This cannot be the case if we 

 suppose the atoms to be charged with definite and equal 

 quantities of electricity ; for if this were so, 3 , the molecule 

 of ozone, would have a resultant charge. We must therefore 

 either suppose that the charges on the atoms are capable of 

 variation, or else that the resultant effect of the charges on 

 the atoms is to be got by combining the charges like vectors 

 and not like scalars, for if this were so it would be easy to 

 explain the neutrality of 3 . 



„ XLIX. Notices respecting New Books. 

 Algebra: an elementary Textbook for the hiylwr classes of Secondary 



Schools and for Colleges. By G. Chrystal, LL.D. Part II. 



(Edinburgh: Black. 1889. Pp. xxiv + 588.) 

 TN this splendid volume we have the fulfilment of the Author's 

 J- promise, and, we presume, the completion of his labours upon 

 Elementary Algebra. Of what sort this work is will be recog- 

 nized by readers of the first volume when they are assured that the 

 present instalment is even more worthy of praise, if that be pos- 

 sible, than its predecessor. There is no shirking of difficulties, for 

 our Author is a past master of his subject ; and from a large 

 acquaintance with what has been written upon it, both recently 

 and long ago, is able to bring forth things new and old out of his 

 ample store. Still he does not exhibit his wares from a vain 

 desire to show off, but has ever an eye to what will be useful to 

 the student subsequently. Hence in his chapter on Probability 

 he omits " matter of doubtful soundness, and of questionable 

 utility,"' and fills the place usually occupied therewith with " a 

 useful exposition of the principles of actuarial calculation." There 

 is a very full analytical Table of Contents which puts the student 

 easily in possession of the heads of the matters discussed in the 

 text. There are, as before, valuable historical notes, and to 

 crown all there is a full Index of Names of Mathematicians whose 

 works have been cited in the two volumes. Much time has been 

 devoted to the construction of the work ; this is evident on the 

 most cursory examination, but we feel convinced that Dr. Chrystal 

 has an ample reward in the admiring gratitude of his readers. 

 They feel that if the Author has given so much of his valuable 

 labour to make the path, if not smooth for them, at least plain, 

 and has collected so many objects of interest for their inspection, 

 it is but meet that they should not flinch from doing their best 

 to master what he has put before them. Our Author, it is well 

 known, has clear and pronounced views on the teaching of Mathe- 

 matics, and in his preface he comments on points to which we will 

 now briefly refer. The practice of " hurrying young students into 



Phil. Mag. S. 5. Vol. 29. No. 180. May 1890. 2 M 





