NOVEMBEB 16, 1906.] 



SCIENCE. 



621 



There is weighty argnment in using the 

 Miller symbols even with beginners in crystal- 

 lography. In elementary work only type sym- 

 bols are used and for these the Miller system 

 is as easy as any. One only has to replace 

 one index of the symbol hkl by a zero when 

 a face is parallel to an axis. When it comes 

 to a question of actual symbols the Miller in- 

 dices of course take precedence over the Weiss. 

 If one learns Miller from the start there is 

 never the necessity of translating back and 

 forth from Weiss, which is a waste of energy. 

 And lastly the Miller is the only universal 

 system. 



The fact that the axial ratios are irrational 

 and that the indices are rational is a thing that 

 always gives many students trouble. Thus 

 most students can not see why the symbol 111 

 does not represent a face that cuts the three 

 axes a, h and c at equal lengths. The writer 

 has used a homely illustration that usually 

 makes it clearer at least. Take two cities, 

 laid out in different ways. A pedestrian on 

 inquiring about a certain building in either 

 place might be told : Go two blocks north, three 

 blocks east. Yet the actual distance he had 

 to walk in the two cities would be different, 

 for the lengths of the blocks are different. 

 These distances are on record and correspond 

 to the axial ratios. Yet the pedestrian is 

 not concerned directly with them. The two 

 blocks and three blocks correspond to the in- 

 dices. 



In order to really understand some of the 

 essential points of crystallography the student 

 must devote some time to crystal measurement, 

 calculation and drawing. And without some- 

 thing of the sort, the time given to crystal- 

 lography may almost be a waste of time un- 

 less it is taken up at some future time. To 

 accomplish this in the limited time available 

 in a general course in mineralogy is difficult. 

 The writer has had partial success with the 

 following method. Selected crystals or wooden 

 models preferably orthorhombic with 110, 

 hkO, Oil and one or more of 100, 010 or 001 

 are chosen. 



(1) Free-hand sketch of the crystal. 



(2) Number faces and indicate zones. 



(3) Measurement of interfacial angles with 

 the contact goniometer. 



(4) Stereographic projection on sheets de- 

 vised by Penfield. 



(5) Graphic determination of a and c from 

 110 and Oil. 



(6) Graphic determination of indices hkO. 



(7) Orthographic projection (plan and ele- 

 vation) from stereographic. 



Taken up in this manner the work is not at 

 all difficult for the drawing of zone circles is 

 not necessary in the stereographic projection 

 and the tedious clinographic projection is re- 

 placed by the orthographic. Yet the student 

 appreciates something of the meaning of axial 

 ratios and indices and is ready, if need be, to 

 take up more advanced work. 



Austin F. Eogebs. 



Stanford University, Cal. 



SPECIAL ARTICLES. 

 IS THERE DETERMINATE VARIATION? 



However willingly we 'incorporate in our 

 general conception and knowledge of variation 

 the special conception of mutations (in the 

 de Vriesian sense) and however implicitly we 

 accept de Vries's primrose species by muta- 

 tion, we must none the less hold clearly in 

 mind that the kind of variation still most 

 familiar to us all is that kind variously called 

 individual, fluctuating, continuous or Dar- 

 winian variation, and we must not for a 

 moment, because some species may have been 

 shown to have arisen in some other way, deem 

 ourselves absolved from the responsibility of 

 further testing the Darwinian assumption of 

 species-forming by the natural selection of 

 individuals possessing advantageous slight 

 variations. 



If new species arise by virtue of a cumula- 

 tion or progressive increase of small fluctu- 

 ating variations in continuous series, they can 

 apparently only do so through (a) natural 

 selection, or (h) determinate or orthogenetic 

 variation. The principal argument for a be- 

 lief in determinate variation so far advanced 

 seems to be that natural selection is unable to 

 make use of fluctuating variation because (1) 

 this variation is too small and useless to be a 

 handle for life and death selectivity, and be- 



