Notices respecting New Books. 477 



salts dissolve in water. Dalton also experimented upon sugar, 

 but failed to notice that in that case there is no contraction ; 

 and it has been reserved for ourselves, after the lapse of half 

 a century, to record that there are cases, such as that of 

 sugar, where there is rigid maintenance of volume. 

 Laboratory, New Maiden, Surrey. 



LVIIL Notices respecting New Books. 



Theorie der Quaternionen. Von Dr. P. Molekbeoek. 

 Leiden, 1891. 

 ~V\7E are told in the Preface that this theoretical volume, of 284 

 * * pages, is to be followed immediately by another containing 

 systematized applications. It is to be hoped, rather than expected, 

 that this second volume will not exhibit the prolixity and the 

 uncalled-for minuteness of detail which purposely characterize the 

 first. We say purposely because, though Dr. Molenbroek states 

 that Hamilton's great Treatise (which is accessible to continental 

 readers in a German translation) is so extensive in its theoretical 

 part as to frighten readers away from the applications, he complains 

 that the work of Prof. Tait (also accessible in translations) gives 

 an inadequate (durftig) account of the theory. Hence his own 

 work is designed to occupy a position midway, as it were, between 

 these two treatises. And it does so more by laboriously spinning 

 out the parts treated by Tait, than by introducing other material 

 from Hamilton's stores. 



When we examine the work itself, we find that Dr. Molenbroek's 

 notions as to the really important parts of the theory differ very 

 widely from those of Hamilton and his pupil. So far as we can 

 discover, there is not in his work even an allusion to v • How the 

 promised applications, if they are to deal at all with potentials, 

 fluid motion, &c, are to be made in the second volume, must 

 therefore for the present remain a mystery. On the other hand, 

 the subject of powers and roots of quaternions, not at present of 

 much use in applications, is developed at disproportionate length. 



But the novel feature of the work, and one to which special 

 attention is directed in the Preface, is of a really startling cha- 

 racter ; inasmuch as it is entirely at variance with the elementary 

 definitions given by Hamilton, and reproduced by Dr. Molenbroek 

 himself ! Comment on such a proceeding is altogether unnecessary. 

 We need do no more than state that he regards an imaginary 

 scalar multiplier as an undetermined quadrcintal quaternion, which 

 has the singularly felicitous but hitherto unsuspected power of 

 adjusting its axis so as to be perpendicular to any vector to which 

 it may be applied ! His volume of examples and applications will 

 certainly be eagerly expected, if it is to contain other gems like 

 that enunciated (p. 104) in the following words : — 



" Man kann somit sagen, ein doppelbrechender Krystall konne 

 wie ein konisch spaltender Quaternion w T irken." 



We have hitherto admired Hamilton's wonderful dealings with 



