December 28, 1906.] 



SCIENCE. 



855 



DISCUSSION AND CORRESPONDENCE. 

 THE TEACHING OF CRYSTALLOGRAPHY. 



Several weeks ago Professor A. F. Rogers 

 called attention through the columns of this 

 journal^ to a number of points concerning the 

 teaching of crystallography, especially as a 

 part of the work in an elementary course in 

 mineralogy. In order to discuss Professor 

 Rogers's paper, the end to be attained by such 

 a course must be clearly understood. If the 

 work in the elementary or heginning course 

 has as its object the training of professional 

 crystallographers much may be said in favor 

 of a course similar to the one outlined by 

 Professor Rogers. If, however, on the other 

 hand, the course is to be only a part of the 

 general education of the geologist, chemist, 

 civil or mining engineer, forester, or teacher 

 of science in the secondary school, the prac- 

 tical side of the work must be emphasized as 

 much as possible. In such a course crystal- 

 logi'aphy must, hence, be considered simply as 

 a means to an end, that is, it should train the 

 student in the rapid recognition of crystal 

 forms. The handling of a large number of 

 forms — models and crystals — tends to train 

 the eye better than do extended discussions 

 concerning the measurement, calculation, and 

 projection of crystals. 



The question which confronts most students 

 of mineralogy — here it may be mentioned that 

 in most institutions where mineralogy is 

 taught at all only a very small percentage 

 of the students have time to pursue more 

 than the elementary course — is the rapid de- 

 termination of minerals and, hence, theoret- 

 ical considerations, which are of vital impor- 

 tance to the crystallographer, may in general 

 be dispensed with. To be sure, some theory 

 must be given, but all the theory necessary 

 can be readily given by means of lectures and 

 the laboratory work devoted entirely to the 

 acquiring of a comprehensive knowledge of 

 forms by contact and inspection rather than 

 by analysis. (Pormenanschauungsunterricht 

 of von Groth.) 



The writer agrees with Professor Rogers 

 that the classification of crystal forms based 



»N. S., Vol. XXIV., pp. 620-621. 



upon symmetry is the best to use even with 

 beginners, but would add that the older ideas 

 of holohedrism, hemihedrism, etc., should^ — 

 even though there be no structural connection 

 between such forms — be retained on account 

 of the many advantages they offer in ac- 

 quiring a clear understanding of the forms 

 possible in the various classes of symmetry. 

 That these advantages are recognized as of 

 considerable importance, it may be well to 

 state that most of the German texts on crys- 

 tallography, designed for heginners, retain 

 them; among such works those of Bauer 

 (1904), Bruhns (1904), Klockmann (1903), 

 Linck (1896) and Namnann-Zirkel (1901) 

 may be mentioned. 



It is also common practise with German 

 mineralogists to follow the older methods in 

 the elementary course of instruction and treat 

 the cubic or isometric system first and then 

 the others in order. Even von Groth, who is 

 no doubt one of the strongest advocates of the 

 newer classification^ retained to the knowledge 

 of the writer, who was a student in his labora- 

 tory during the years 1899-1901, the older 

 method of treatment (including holohedrism, 

 hemihedrism, etc. !) in his beginning course 

 rather than discuss the forms as outlined in 

 his * Physikalische Krystallographie,' the third 

 edition of which had appeared several years 

 before, namely, in 1895.^ In fact Professor 

 von Groth was accustomed to state in an in- 

 troductory lecture that from the theoretical 

 point of view the order as outlined by him — 

 begin with class of lowest grade of symmetry 

 and discard ideas of holohedrism and so forth 

 — was the natural one to follow, but that cer- 

 tain practical and pedagogical reasons de- 

 manded that the reverse order be pursued es- 

 pecially when discussing crystallography with 

 heginners. 



There is no denying the fact that the meas- 

 urement, calculation and projection of crystals 

 are of great value to obtain a clear insight 

 into the true meaning of crystallography and, 

 hence, ought to be pursued by at least all 



* Compare Bruhns, * Elemente der Krystallog- 

 raphie,' 1904, preface and foot-note on page 2. 

 Also Baumhauer, * Die Neuere Entwickelung der 

 Krystallographie,' 1905, pp. 26-53. 



