158 Scientific Intelligence. 



infinitesimal, and that on warming thin sections, in which the 

 hexagonal crystals were visible, with nitric acid and ammonium 

 molybdate, no deposit of yellow ammonium phospho-molybdate 

 could be detected by the microscope. A spectrograph^ analysis 

 showed that these crystals were really beryls, and similar crystals 

 a millimeter in length were picked out of the granite. They were 

 found to contain between 10 and 11 per cent of beryllia. Since 

 then beryllia has been separated from the alumina of feldspar 

 obtained from the granite in Glen Cullen in proximity to a vein 

 of coarse granite in which beryls were found by Dr. John Joly. 



From numerous experiments on the analytical processes em- 

 ployed in the separation of beryllia from alumina, it was found 

 that it remained combined with the sesquioxide bases in so per- 

 sistent a manner as to lead to the belief that ordinary alumina 

 might be found more often than not to contain traces of beryllia, 

 particularly as there is no easily applied chemical test for detect- 

 ing its presence in small quantities, nor a simple means of sepa- 

 rating it. It has, however, been found that such is not the case, 

 though gallium has been ascertained to be present in almost all 

 minerals which contain aluminum. As they belong to the same 

 group, the two elements aluminum and gallium may be expected 

 to form isomorphous mixtures, which would account for their 

 being so constantly associated in nature ; but the position of 

 beryllium in the periodic sytem of classification shows that a sim- 

 ilar behavior with that element is scarcely probable. 



13. Vector Analysis : a Text-book for the use of Students of 

 Mathematics and Physics, founded upon the lectures of J. Wil- 

 lard Gibbs ; by Edavin Bid well Wilson. Yale Bicenten- 

 nial Publications. New York and London, 1901. (Charles Scrib- 

 ner's Sons.) Pp. xiii-436. — As indicated by its title, this book 

 embodies the substance of Professor Gibbs' lectures on Vector 

 Analysis, with such illustrations and extensions as seemed neces- 

 sary to the editor, Dr. Wilson. Since the publication, over 

 twenty years ago, of Professor Gibbs' small pamphlet on the sub- 

 ject, there has been a growing need for some more elaborate 

 text-book which should contain such theorems, examples and 

 problems as would enable one who mastered it to apply its 

 methods to the fields of mathematical physics and pure mathe- 

 matics. University students have felt the need of such a book 

 also, for the number of writers who are making use of the 

 methods and symbols of Vector Analysis is increasing each year. 

 Mention need be made of only a few, such as Heaviside, Foppl 

 and Walker. 



This is not the place nor the occasion to discuss the general 

 question as to the usefulness of Vector Analysis : it may in fact 

 be said to be decided. Whether new theorems can be deduced 

 by means of it may be doubted ; but no one can deny that new 

 points of view may be obtained and that more elegant solutions 

 may be given. 



In the work under review, there is a general discussion of 

 Vector Analysis, together with its most important applications. 



