Jan. 17, 1889] 



NATURE 



^77 



tory of the College de France. I could also have 

 explained the successful syntheses, not less remarkable, 

 of minerals and meteorites made by these experimen- 

 talists or by their pupils, among whom M. Bourgeois 

 occupies a special position. But I must limit myself ; 

 and, indeed, what I have said is sufficient to show how 

 their methods have advanced our knowledge in a dornain 

 to which access had previously appeared shut against 

 investigation. 



Wherever the experimental method has hitherto carried 

 its torch, it has brilliantly illuminated the most striking 

 phenomena in the science of the earth. It suffices to 

 mention the name of Daubrce, the direct descendant of 

 the illustrious geologists of the Scottish school, to indicate 

 the extent of the field of the mineral sciences already 

 explored by the method of experiment. It has been 

 successfully applied to the interpretation of metalliferous 

 deposits and of metamorphic rocks, and to the study of 

 ihe fractures and deformation of the earth's crust, of the 

 bchistosity of rocks, and of certain features in mountain 

 structure. 



Geology, after having passed through the successive 

 phases of observation and analysis, has therefore entered 

 upon that of experiment and synthesis, in which it strives 

 to imitate the creative power of Nature, thus crowning 

 the scientific edifice by processes which allow us to catch 

 ;i glimpse of the operation of causes the knowledge of 

 which is the final aim of physical and natural science. It 

 was this crowning of the work which Leibnitz foresaw when 

 1 e wrote, two centuries ago : — " He will perform, in our 

 '■pinion, an important work, who shall carefully compare 

 the products extracted from the depths of the earth with 

 I hose of the laboratory ; for then will be brought vividly 

 liefore our eyes the striking resemblance which subsists 

 between the productions of Nature and those of Art. 

 Although the Creator, inexhaustible in resource, has at 

 command divers means of effecting His will, it neverthe- 

 less pleases Him to maintain a constancy in the midst of 

 ihe variety of His works ; and it is already a great step 

 towards a knowledge of things to have discovered even 

 one means of producing them ; for Nature is only Art on 

 .1 large scale." 



SOME RECENT ADVANCES IN THE THEORY 

 OF CRYSTAL-STRUCTURE. 



'PHE growth of modern theories concerning the struc- 

 *• ture of crystals is perhaps not so closely followed by 

 i::nglish chemists as might be expected from the inherent 

 interest of the subject, in spite of the attention which is 

 now devoted to all questions of atomic and molecular 

 arrangement in space. 



It is in the morphology of crystals that the geo- 

 metrical arrangement of the atoms or molecules (in the 

 solid) finds, if anywhere, a geometrical expression, and 

 yet little or no account is taken of this subject in text- 

 books of chemistry or physics, so that it is difficult for 

 the student to discover what views are held by modern 

 authors. Moreover, crystallographic observations and 

 'heories are generally pubhshed in journals specially 

 devoted to mineralogy which are not easily accessible to 

 all who are interested in such questions. 



It seems, therefore, advisable to draw attention to the 

 progress which has recently been made in the theory of 

 crystal-structure, and more especially to papers by Prof. 

 .Sohncke, of Munich, published in Groth's Zcitschrift fiir 

 Krystallographie uiid Mincralogie, a journal which is a 

 complete storehouse of information relating to the study 

 of crystals. 



Sohncke's theory, which was published in 1879,1 has 

 now emerged from the purifying fire of recent criticism in 



' " Enfwickelung einer Theorie der Krystallslruktur." (Leipz'g.) 



an emended form in which perhaps it will more readily 

 excite the interest of chemists. 



In order to make it clear in what respects the theory of 

 Sohncke in its latest form differs from those which have 

 been previously advanced it will be necessary to give a 

 brief sketch of the theory of Bravais, of which Sohncke's 

 system is an extension. 



The Abbd Haiiy,i having found that all crystals of the 

 same substance may be reduced by cleavage to the 

 same solid figure, whatever their external form, argued 

 that the cleavage solid has the form of the ultimate 

 particles into which any crystal may in imagination be 

 separated by repeated subdivision, and that this is there- 

 fore the form of the structural unit: it is not, of course, 

 necessary or even probable that the latter should be 

 identical with the chemical molecule. Hence a crystal is 

 to be regarded as constructed of polyhedral particles, 

 having the form of the cleavage fragment, placed beside 

 one another in parallel positions. A crystal of salt, for 

 example, which naturally cleaves parallel to the faces of 

 the cube, is constructed of cubic particles. 



Upon the relative dimensions of the structural unit 

 depends the form assumed by the crystals of a giverv 

 substance. 



It will be found that this theory not only accounts for 

 the existence of cleavage, but further defines the faces 

 which may occur upon crystals of a substance having a 

 given cleavage figure ; for, if once it is assumed that a 

 crystal-face is formed by a series of the particles whose 

 centres lie in a plane, it follows that all such planes obey 

 the well-known law which governs the relative positions 

 of crystal-faces. 



A natural advance was made from the theory of Haiiy,. 

 without detracting from its generality, by supposing each 

 polyhedral particle in Haiiy's system to be condensed into 

 a point at its centre qf mass, so that the positions of the 

 molecules, and therefore of the crystalline planes, remain 

 the same as before ; but the space occupied by a crystal 

 is now filled, not by a continuous structure resembling 

 brickwork, but by a system of separate points. 



It will be found that in such a system of points, if the 

 straight line joining any pair be produced indefinitely in 

 both directions, it will carry particles of the system at 

 equal intervals along its entire length ; in other words, all 

 the structural molecules of a crystal must lie at equal 

 distances from each other along straight lines. The 

 interval between particles along one straight line will in 

 general be different from those along another, but the 

 molecular intervals along parallel straight lines will 

 always be the same. 



Bravais,^ therefore, following in the steps of Delafosse 

 and Frankenheim, treated the subject as a geometrical 

 problem, and inquired what are the possible ways in 

 which a system of points may be arranged in space so as 

 to lie at equal distances along straight lines— in other 

 words, so as to constitute what may be called a solid 

 netivork {assemblage, Raunigitter). 



The geometrical nature of a network may be best 

 realized as follows. Take any pair (o C,) of points in space, 

 draw a straight line through them, and place points at 

 equal distances along its entire length (c^, Q,, . . .) ; such a 

 line may be called a thread oi points {raugce). Parallel to 

 this line, and at any distance from it, place a second thread 

 of points (Ai a^, identical with the first in all respects ; in 

 the plane containing these two threads place a series of 

 similar equidistant parallel threads (.A.^ a.i, &c.) in such 

 positions that the points in successive threads lie .at equal 

 intervals upon straight lines whose direction (o A,) is 

 determined by the points upon the first two threads. Such 

 a system of points lying in one plane may be called a web 

 {reseaii). Now, parallel to this plane, and at any distance 

 from it, place a second web (h, <^i), identical with the first 



' " Trait< lie Cristallographie." (Paris, 1822.) 

 ^ " Etudes cristallographiques." (Paris, 1P66.) 



