September 2, 1909J 



NATURE 



299 



the emetic. He knows many of our standard remedies, 

 while of others equally accessible to him he is ignorant. 

 Thus he uses indigenous species of Nephrodium for the 

 relief of tape-worm, and croton as a purgative, but it is 

 apparently from the white man that he has learned that 

 the Ipomoea purpurea has qualities analogous to jalap, 

 and though castor-oil is used for dressing hides he is not 

 aware of its medicinal value. But he undoubtedly is 

 acquainted with a great number of simples, mostly 

 vegetable ; and Father Bryant believes that the further 

 investigation, and in particular the chemical examination, 

 of many of the drugs which he names will in all proba- 

 bility add valuable remedies to our pharmacopoeia. Dr. 

 E. Warren, curator of the museum, promises that his 

 department will provide all possible assistance in material 

 and information to any competent chemist who is pre- 

 pared to undertake such an inquiry. 



B' 



AMERICAN INVERTEBRATES. 



;ULLETIN No. 63 of the United States National 

 Museum is devoted to a monographic revision, by 

 Mr. F. E. Blaisdell, of the beetles of the Eleodine section 

 of the family Tenebrionida; inhabiting the United States, 

 Lower California, and the adjacent islands. The memoir 

 includes 534 pages of te.\t and thirteen plates. 



In No. 2 of the Leland Stanford Junior Publications of 

 the University of California Prof. F. M. Macfarland 

 describes in considerable detail the anatomy of the opistho- 

 branchiate molluscs obtained during the Brauner-Agassiz 

 expedition to Brazil in 1899. The collection, although 

 small, adds seven to the list of Brazilian species of the 

 group ; and since little was previously known with regard 

 to the structure of the opisthobranclis of the district, the 

 opportunity was taken of studying this as minutely as 

 the amount of material permitted. A number of diagram- 

 matic figures of the radula in different genera is given. 



The feather-stars, or ophiurids, of the San Diego region 

 form the subject of vol. vi.. No. 3, of the University of 

 California Publications in Zoology. The author, Mr. J. F. 

 McCIendon, began his investigation in the hope that a 

 taxonomic and biological study of the local members of 

 the group might facilitate work in which it was important 

 to know the breeding-seasons and habitats of different 

 species, but, unfortunately, he could not remain long 

 enough to obtain all the data desired. It is believed, 

 however, that the height of the breeding-season for most 

 of the species is in the spring, although individuals full 

 of apparently unripe eggs were taken in spring. 



A number of new fossil echinoderms from the Cretaceous 

 and Tertiary Ripley beds of Mississippi are described and 

 figured by Mr. A. W. Slocum in vol. iv.. No. i, of the 

 Geological Publications of the Field Museum, Chicago. 



The re-arrangement of the large collection of graptolites 

 which for many years has been in course of formation in 

 the U.S. National Museum has afforded to Mr. R. S. 

 Bassler the opportunity of revising the species of the 

 dendroid group from the Niagaran Dolomite of Hamilton, 

 Ontario, and the results of his studies are published, with 

 a large number of illustrations, in Bulletin No. 65 of the 

 museum. 



THE SEVEN STYLES OF CRYSTAL 

 ARCHITECTURE.^ 

 'T'HE proverbial importance of the number seven is once 

 more illustrated in regard to the systems of symmetry 

 exhibited by solid matter in its most perfectly organised 

 form, the crystalline. For there are seven such systems or 

 styles of architecture of crystals, just as there are seven 

 distinct notes in the musical octave, and seven chemical 

 elements in the octave or period of Newlands and 

 MendeWeff, the eighth or octaval note or element being 

 but a repetition on a higher scale of the first. 



A crystal appeals to us in two distinct ways, first com- 

 pelling our admiration for its beautifully regular exterior 

 shape, and next impressing us with the fact of its internal 



1 Svimmary of evening disccmrse delivired before thp British Asscciation 

 at Winnipeg on .\ugiist 26 hy Dr. A. E. H. Tutton, F.R.S. 



NO. 2079, VOL. 81] 



homogeneity, expressed in the cases of transparent crystals 

 by its perfect limpidity, and the obvious similarity through- 

 out its internal structure. As it is with human nature at 

 its best, the external appearance is but the expression of 

 the internal character. 



The purpose of this discourse is not so much to dilate 

 upon the seven geometrical systems of crystals as to show 

 how they are occasioned by differences in the internal 

 structure, and to demonstrate this internal structure in an 

 ocular manner, unfolding at the same time some interest- 

 ing phases of recent investigation. 



To the Greeks, whose wonderfully perfect knowledge of 

 geometry we are ever admiring, the cube was the emblem 

 of perfection, for like the Holy City, lying " foursquare," 

 described in the inimitable language of the book of Revela- 

 tion, " The length and the breadth and the height of it 

 are equal." Moreover, even when we have added that all 

 the angles are right angles, these are not the only perfec- 

 tions of the cube, for they carry with them, when the 

 internal structure is developed to its highest possibility, no 

 fewer than twenty-two elements (thirteen axes and nine 

 planes) of synunetry. 



At the other extreme is the seventh, the triclinic, system, 

 in which the symmetry is at its minimum, neither planes 

 nor axes of symmetry being developed, but merely 

 parallelism of faces, sometimes described as symmetry 

 about a centre, and in which there are no right angles 

 and there is no equality among adjacent edges. Between 

 these two extremes of maximum and minimum symmetry 

 we have the five systems known as the hexagonal, tetra- 

 gonal, trigonal, rhombic, and monoclinic, possessing, re- 

 spectively, 14, 10, 8, 6, and 2 elements of symmetry. All 

 crystals do not possess the full symmetry of their system, 

 each system being subdivisible into classes possessing a 

 definite number of the possible elements. Altogether there 

 are thirty-two such classes, and their definite recognition 

 we owe to the genius of von Lang and Story Maskelyne. 



The characteristic property possessed in common by all 

 crystals is that the exterior form consists of and is defined 

 by truly plane faces, inclined, in accordance with one of 

 the thirty-two classes of symmetry, at specific angles which 

 are characteristic of the substance. This has only been 

 proved to be an absolute fact within the last few years, 

 although asserted by Haiiy so long ago as the year 1783 ; 

 for the numerous cases of so-called " isomorphous " salts, 

 the first of which were discovered by Mitscherlich in the 

 year 1820, were for long believed to be exceptions, and 

 until the year 1890 no actual evidence one way or the 

 other was forthcoming. But it was eventually shown that 

 the crystals of the members of an isomorphous series did 

 differ, both in their angles and in all their other crystal- 

 lographic and physical properties, although in the cases of 

 the angles the differences were very small. Moreover, the 

 differences were shown to obey a simple but very interest- 

 ing law, namely, that they were functions of the atomic 

 weight of the chemical elements of the same family group 

 the interchange of which gives rise to the series. 



All crystals possess one other obvious property, that of 

 homogeneity, and we now know that it is the character 

 of the homogeneous substance which determines the ex- 

 ternal form. There are no fewer than 230 different kinds 

 of homogeneous structures, neither more nor less, the 

 elucidation of which we owe to the independent recent 

 labours of Schonflies, von Fedorow, and Barlow ; and it 

 is a significant fact that the whole of them fall naturally 

 into the thirty-two classes of crystals, leaving no class un- 

 accounted for. Of these 230 modes of regular repetition in 

 space fourteen are the space-lattices long ago revealed to us 

 by Bravais, and all recent investigation concurs in indicating 

 two facts, first, that it is the space-lattice which determines 

 the crystal system, and second that it is the arrangement of 

 the chemical molecules which is represented by the space- 

 lattice. Each cell of the space-lattice corresponds to a 

 molecule. The structure is certainly not solid throughout, 

 however, part only being matter, and the rest aether-filled 

 space, the relative proportions and the shape of the material 

 portion being as yet unknown. We limit ourselves, there- 

 fore, to considering each molecule as a point, and we draw 

 the lattice as a network of three systems of parallel lines, 

 parallel to the directions of the three principal crystal 

 edges, analogous, according to the system of symmetry, to 



