386 C. K. SWARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



law of crystallography; (2) those who have sought to develop only the 

 forms which are possihle in crystals under the above named law. 



To the first class belong Hessel, Bravais, Moebius, Curie, Fedorow, and 

 Minnigerode; to the second, Gadolin and Schoenflies. 



Hessel. — The founder of the modern classification of crystals is J. F. C. 

 Hessel, whose results were published in an article entitled "Krystall/' in 

 Gehler's Physikalisches Worterbuch, in the year 1830. 6 



Unfortunately Hessel's results long rested in obscurity and were prac- 

 tically overlooked. It is only recently that they have begun to be appre- 

 ciated at their true worth. 



Hessel based his discussion upon the conception of symmetry, of which 

 he recognized two types, ebenbildlich (having the same form) and gegen- 

 bildlich (likeness by reflection) ? 



Hessel's method is to develop first all possible symmetrical figures, and 

 then, secondly, to determine which of these are possible in crystals. 8 To 

 do this he shows first that there are seven types of axes about which all 

 symmetrical figures may be developed. The types are as follows : 9 



Types of Axes 



Ends unlike (ungleichendig). { %^e '(tSh). 



Ends alike 

 (gleichendig). 



Forms opposite (gleich- ( Simple (einfach). 

 stellig) .... { Double (zweifaeh). 



Forms not opposite (un- 

 gleichstellig) 



r Alternate ( Simple (einfach). 



(gerenstellig). 1 Double (zweifaeh). 



Oblique Simple (einfach). 



(ebenbildlich). 



The axes are classified accordingly as they are dissimilarly terminated 

 (ungleichendig) or similarly terminated (gleichendig). The latter are 

 divided into those in which the upper faces directly overlie the lower 

 (gleichstellig) or not. The last type is subdivided into those in which 

 the upper faces alternate with the lower (gerenstellig), or are obliquely 



8 Bd. v, Ab. ii, pp. 1023-1360. 

 A separate edition of this article was issued in 1831 under the title "Krystallometrie 

 oder Krystallonomie und Krystallographie." This work is reprinted in Ostwald's 

 "Klassiker der exakten Wissenschaften," no. 88, 1897. An admirable review of Hessel's 

 results is given by L. Sohncke, "Die Entdeckung des Eintheilungsprincips der Krystalle," 

 Zeitschrift fiir Krystall., bd. 18, pp. 486-498, 1891. 



7 Article Krystall, cited above, p. 1035. Reprint, vol. i, pp. 20-21. 



8 He develops his results by means of radii ("strahlen"), which are lines drawn from 

 the center of the figure to the symmetrical parts. He is thus able to discuss the posi- 

 tion of these lines rather than the parts of the figures. Hessel does not recognize planes 

 of symmetry, but develops the figures about axes which comprise in reality both axes 

 and planes of symmetry. 



Article Krystall, pp. 1059-1060. Reprint, vol. i, pp. 44-45. See Sohncke, Zeitschrift 

 fiir Krystall., bd. 18, p. 488, 1891. 



