154 Scientific Intelligence. 



angles for all the crystal forms of all crystallized mineral species. 

 Such a table is eminently useful to the crystallographer to deter- 

 mine without laborious calculation whether the forms observed 

 on a crystal are already known or are new. But the construction 

 of a complete table, based on the accepted method of interfacial 

 measurements between crystal faces, was impracticable, since it 

 required the presentation of an enormous number of angles for 

 each, form, and would thus be too bulky to be useful. Mono- 

 graphs on various mineral species contained approximations to 

 such tables, but they were not complete even for those species 

 and were widely scattered through the literature. The invention 

 of the goniometer with two circles* by means of which each face 

 on a crystal may be measured independently of all the others, 

 and its position determined with reference to a fixed pole and 

 meridian by two angular coordinates, first made possible the 

 formation of a complete table of angles. For such a table need 

 now contain for each form only these two angular values, <f> and 

 p (corresponding to geographical longitude and latitude for a 

 point on the earth's surface), which fully characterize the form 

 and which may be directly and rapidly compared with the results 

 of measurements. The tables before us contain these values for 

 each well-established form of each mineral, calculated from the 

 axial elements of the substance and the symbol of the form; there 

 are also given for each form several angles which facilitate the 

 comparison of these angular coordinates with the results of the 

 ordinary interfacial measurement ; and lastly a set of linear coor- 

 dinates which enable the rapid plotting of the form in a gnomonic 

 projection. In an introduction of 29 pages necessary explanations 

 of the values contained in the tables are given, and the schemes 

 employed in each system for the calculation of the values are 

 shown. Some idea of the enormous labor represented by this 

 volume may be given by the statement that it contains upwards 

 of 70,000 values ; of this number about half are values recurring 

 more or less often, such as angles of 45° and 60°, but the remain- 

 der required each a separate calculation. An appendix contains 

 notes on the various minerals, indicating the particular orienta- 

 tion adopted in each case. The volume forms a logical conclu- 

 sion to the elegant system of crystal measurement and descrip- 

 tion which the author has developed, and will be a welcome aid 

 to the increasing number of those who are pursuing their crys- 

 tallographic studies in the fruitful fields he has discovered. 



c. P. 

 1. Tabellarische Uebersicht der Miner alien nach ihrer krys- 

 tallographisch-ehemischen Beziehungen geordnet ; von Paul 

 Groth. Vierte vollstandig neubearbeitete Auflage, 184 pp. 

 Braunschweig, 1898 (Fr. Vieweg und Sohn). — The fourth edition 

 of Groth's Mineralogical Tables has just appeared and will be 



* For a brief description of this instrument and the method of using it, as well 

 as for references to the original papers concerning it by Goldschmidt and others, 

 see this Journal, vol. ii, 1896, p. 279. 



