Notices respecting New Books. 

 whereas we are informed on p. 96 that 



463 



h K 



+ 



+ 



Even this is not all. For according to the definition 



I s and 



I 



a l 



a 2 



\ 



\ 



c l 



c* 



are identical, and the latter is shown on page 96 to be equal to 

 zero. Consequently there are to be found in close proximity three 

 mutually incompatible meanings for 



Messrs. Amoretti and Morales are not altogether to blame ; they 

 have committed the indiscretion of trusting too faithfully an un- 

 reliable European guide. "We put it to them, however, to recon- 

 sider now and decide whether the " multiple " determinant deserves 

 their support. To us, the "bag and biggage" policy seems the 

 only suitable one for such an usurper. 



The Applications which occupy the third " book " are not all of 

 equal importance. The Algebraical and Geometrical are appro- 

 priate and well chosen. Of those which are said to concern Tri- 

 gonometry, the first half is of very doubtful utility, and the second 

 half consists of nothing more than exercises in finding the final 

 expansion of determinants whose elements involve trigonometrical 

 functions. 



As we have implied above, the work of the two Argentine civil 

 engineers is on the whole a very creditable performance, and sure 

 to prove valuable to the mathematical students of the Republic. 

 We trust that the demand for it may be such that a revised and 

 enlarged edition may soon be called for. 



The text-book of Professor Peck belongs to a differeut category, 

 being of an introductory character, and extending only to 48 pages. 

 It is simply and clearly written, giving the fundamental theorems 

 with numerous easy illustrative examples. The term " co-factor" 

 is incorrectly defined ; equations that are consistent are said to 

 " consist " ; and there are other easily remedied slips or needless 

 peculiarities. To beginners the manual should be very serviceable. 



Thomas Muir. 



