July 17, 19 15] 



NATURE 



521 



stances show differences among themselves to the 

 extent of a definitely measurable number of minutes. 

 But such perfection of growth is not easy to attain, 

 and, in ordinary crystallisation without special pre- 

 caution against disturbance, is rarely found. The 

 essential crystallographic measurements can, however, 

 be made in an hour's time, provided use be made of 

 the two- or three-circle form of goniometer, such as 

 the excellent one devised by Dr. Herbert Smith. This 

 form of goniometer enables all the needful measure- 

 ments of the interfacial angles to be made with a 

 single setting of the crystal on the wax of the holder. 

 But practical difficulties have hitherto still stood in 

 the way. Excellent as is von Groth's classification — 

 and the most suitable for a work of reference of the 

 full and comprehensive character of this permanent 

 monument of the master's industry and wide know- 

 ledge of chemistry, related compounds being arranged 

 and compared in close proximity — the very nature and 

 size of such a work renders it unsuitable for the 

 purpose of discovering rapidly the chemical composi- 

 tion of a substance from its geometrical elements. 

 An index of substances arranged in the order of their 

 symmetry and the numerical values of the crystal 

 constants within the system is what is needed, and 

 this has now for the first time been drawn up for 

 the ten thousand measured substances by Prof, von 

 Fedorow. 



Another difficulty then presents itself. It often entirely 

 depends on how a crystal is held in space, that is, 

 which direction in it is regarded as the vertical axis, 

 which the right-and-left axis, and which the front- 

 and-back axis, as to what the nature of the crystal 

 constants (elements) will be. Moreover, even if two 

 different observers choose these similarly, they may 

 select a different parametral plane (a fourth face other 

 than the three faces parallel to the axes, and cutting 

 off unit lengths from the latter) to determine the 

 axial ratios. Hitherto, beyond a few arbitrary rules 

 — for instance, that the right-and-left axis of a rhom- 

 bic crystal shall be longer than the front-to-back axis 

 — there has been no definite guiding principle for the 

 determination of the setting. Prof, von Fedorow has 

 now given us one, by means of which we can be 

 sure which are the real vertical faces (prismatic or 

 pinakoidal), which is the basal plane (the pair of top 

 and bottom faces), and which set of pyramid faces 

 are the important ones fixing the relative axial 

 lengths. The true setting has been determined by 

 Prof, von Fedorow for every one of the substances 

 in his index, and the crystal elements for such setting 

 calculated. 



The mode of classification adopted in this index- 

 catalogue is based on the values of the five funda- 

 mental angles which, in general, characterise the 

 crystals of anv specific substance. A cubic crystal 

 has definite angles which are entirely fixed and ren- 

 dered invariable by reason of the perfect symmetry. 

 At the other extreme come triclinic crystals, the 

 general case, in which all five fundamental angles 

 are different and auite independent of each other. 

 On monoclinic crystals there are three independent 

 angles, from which the other two can be calculated. 

 Rhombic crystals have only two independent angles, 

 which, if measured, enable the other three to be 

 calculated. Hexagonal, tetragonal, and trisronal 

 crystals possess only one angle independent of the 

 symmetry, determinative of the relative length of the 

 unique axis of hexagonal, tetragonal, or trigonal 

 symmetry. 



The first object of von Fedorow in order to arrive 



at the correct setting is to decide which are the 



primary axial-nlane and parametral faces; and he is 



wonderfully aided here bv the discovery of the fact 



NO. 228l. VOL. Oil 



that the faces most extensively developed under ideal 

 conditions of growth are those over which the points 

 of the space-lattice are most densely strewn. Hence, 

 von Fedorow tries to discover the faces of greatest 

 reticular density, the primary faces, by calculation. 

 For it is a well-known fact that the most diverse 

 habits — due to different faces being most prominently 

 developed under different conditions of environment — 

 are shown by the crystals of the same substance. 



Having thus determined the correct setting, and 

 measured the principal angles, including the five 

 fundamental angles, the results are recorded in the 

 index-table in an abbreviated symbolic form if the 

 substance be a new one, or, if it has previously been 

 measured, and therefore appears in his index-table, 

 he discovers the fact at once by the identity of the 

 elements found with those of a substance given in 

 the table. The average time occupied in all this by 

 Prof, von Fedorow or one of his skilled assistants is 

 about two hours. Mr. T. V. Barker, who studied 

 with Prof, von Fedorow before acting as demon- 

 strator of mineralogy at Oxford, has been of con- 

 siderable help in submitting the new method to a 

 very severe test, from which it has emerged with 

 flying colours. He collected, at Prof, von Fedorow's 

 suggestion, fifty specimens of substances which had 

 been crystallographically examined in this country 

 and described in the recognised publications. Five 

 of these were furnished by the lecturer, six others by 

 Prof. Armstrong, with the aid of Messrs. Colgate 

 and Rodd, others by Drs. Chattaway and Drugman 

 and Mr. Marsh at Oxford, and the remainder by 

 Mr. Barker himself. Each specimen was only 

 marked by a number, no name or formula being 

 given, on its dispatch to St. Petersburg. The result 

 was that Prof, von Fedorow identified without any 

 difficulty forty-eight of the fifty- substances. The 

 crystals of one of the two others were too imperfectly 

 developed to be of use, and the fiftieth specimen was 

 that of a substance which it was afterwards dis- 

 covered had never hitherto been measured, a fact 

 which was first indicated by its elements not tallying 

 with those of any substance mentioned in the table. 

 This latter occurrence confers even greater confidence 

 in accepting the new method. 



It thus appears that in Prof, von Fedorow's hands, 

 or those of his pupils, the method is practically in- 

 fallible, provided the crystals are well developed and 

 not of cubic symmetry. If the latter perfect sym- 

 metry be developed, reference must be made to the 

 optical properties, which the lecturer has always in- 

 sisted have been far too much neglected, and are 

 here seen to be indispensable. The optical methods 

 themselves, moreover, as regards their use with small 

 crystals on the polarising microscope, have been fur- 

 ther perfected by von Fedorow, his universal stage 

 placing the rapid methods of two- and three-circle 

 goniometry at the disposal of the microscopist. It 

 must also be remembered that Prof, von Fedorow's 

 method does not discriminate between the members 

 of isomorphous series, as the crystals usually avail- 

 able are not of the high degree of perfection requisite 

 in order clearlv to substantiate the last few minutes 

 of any particular angle; for the differences of ancle 

 between the members of series formed by metallic 

 familv analogues have been shown by the lecturer to 

 be very minute, although unmistakable given the 

 most perfect crystals, and have also been found to 

 obev the law of progression according to the atomic 

 weight of the metal. For instance, ammonium zinc 

 sulphate was simply returned by Prof, von Fedorow 

 as a member of the isomorphous series of monoclinic 

 double sulphates and selenates crystallising with 

 6H.O. Qualitative analysis would be necessary after 



