in the Study of Crystallography. 159 



which cannot with the greatest ease be performed by the use 

 of the globe. 



In bringing this matter before the Society I have not been 

 concerned to produce anything very new or very original. 

 It has been my object to draw the attention of other 

 chemists to a method of studying Crystallography which 

 I myself have found- profitable. It is true that 1 had never 

 seen a globe used in the study of Crystallography, nor 

 had I met with any suggestion of its applicability. I looked 

 through all the available crystallographic literature without 

 finding any indication of it. When the projection on the 

 sphere is mentioned, it is always with a view to dealing with 

 it according to Miller's method by spherical trigonometry. 



In May J 893 I gave a demonstration to the Philosophical 

 Society of Cambridge (in connexion with globes generally) 

 of the suitableness of black globes for studying crystals. 

 When I began to prepare this paper I made a further 

 thorough search through the literature, because I could not 

 believe that the person who first had the idea to project the 

 crystal on the sphere had done so with any other view than to 

 study it when he had got it there. I could not meet with a 

 copy of either Neumann's i Beitrage zur Krystallonomie,' or 

 Grassmann's work ' Zur Krystallonomie unci geometrischen 

 Combinationslehre,' which are alluded to in the beginning of 

 Miller's Treatise on Crystallography, and I suspected that 

 one or both of these authors might have recommended the 

 use of the globe itself. A few days ago, through Messrs. 

 Mayer and Mtiller of Berlin, I procured a copy of Grassmann's 

 book. Its full title is ' Zur physischen Krystallonomie und 

 geometrischen Combinationslehre/ Yon Justus Gunther 

 Grassmann, Professor am Gymnasium zu Stettin : Stettin, 

 1829. It is the first number of the first volume of a com- 

 prehensive work entitled ' Zur Mathematik und Naturkunde,' 

 which the author proposed to complete by degrees. Nothing 

 further was, however, published ; but the single number is a 

 sufficiently remarkable work. It is worthy of note that he 

 was obliged to publish it at his own expense, as it found no 

 acceptance at the hands of the Scientific Societies or the 

 Journals of the day. This is no doubt the cause why it pro- 

 duced so little effect in its time and is so difficult of access now. 



Of Neumann's Beitrage also only the first fascicule ap- 

 peared, and I have not yet been able to see a copy of it. I am 

 informed that it is excessivelv rare. In Grassmann's work, 

 however, the use of the globe is expressly recommended for 

 presenting clearly to the eye and mind the combination of 

 directions out of which he develops the systems of Crystallo- 



