1 84 



A^A TURE 



[December 20, 1894 



ON THE USE OF THE GLOBE IN THE 

 STUDY OF CRYSTALLOGRAPHY.^ 



IN modern treatises on crystallography, the crystal is imagined 

 projected radially on the surface of a sphere, and the 

 spherical triangles so obtained aie dealt with hy spherical 

 irigonomeiry. Problems in astronomy and mathematical 

 geography are also commnnly dealt with by the methods of 

 spherical trigonometry. But they can also be dealt with 

 completely by the method of graphical conslrtiction on the 

 surface of a sphere where the sngles and arcs are directly 

 measured with a divided circle ; and the use of spherical 

 trigonometry is dispensed with. Many years ago it occurred to 

 the author that what elimirated the use of spherical trigono- 

 metry in the one case might eliminate it in the others : hence 

 the idea of the use of the globe in the study of crystallography. 

 Various arrangements of globe and circles were described and 

 exhibited. The usual method of mounting globes on a polar 

 a.iis, round which it can revolve inside a metal meridian, 

 snpporied in its turn at right angles to a horizontal circle or 

 equator, was found to be inconvmient. It is necessary to be 

 able 10 reach every part of the globe, and to have it steady for 

 drawing, and the fixed circle and axes stand greatly in the way 

 of this. The instrument found most generally use'ul was a 

 black globe, along with a system of brass circles, divided into 

 degrees, which can be applied directly and exactly to any part 

 of its surface. The .system of brass circles is called the 

 ir.-'ircf'hirt, invented by Captain Aved de Magnac, of the 

 I'rcr.ch Navy, and published by E. Bertau.x, of Paris. With 

 this instrument every problem in the ge metry of crystals can 

 be solved with ease and accuracy by graphic construction alone. 

 T he various manipulations occurring in the use of the globes 

 were described and illustrated. In the practical determination 

 of a crystal, the inclinations of its faces are observed with the 

 goniometer. From these observations, treated usually by the 

 methods of spherical trigonometry, the elements of the crystal, 

 namely, the inclination of its axes and the proportion of its 

 parameters, are deduced. The process is then reversed, and 

 the elements found are assumed, and from them the inclinations 

 of the faces are calculated. The usefulness of the globe was 

 illustrated by demonstrating how these two processes can be 

 carried out by simple graphical construction. On the globe, 

 the face of a crystal is represented by its pole, or the p .int 

 where the radius of the sphere, which is perpendicular to the 

 face, pieices the surface of the sphere. The angle between 

 two faces, measured by the goniometer, is the angle contained 

 between their normals. It is therefore ready to be transferred 

 directly lo the globe on which it is entered as an arc. In doing 

 •so, any point on the globe is taken as the pole of the face from 

 which a start is made. From this a great circle is drawn in 

 any direction. When the first angle has been measured on the 

 goniometer, it is laid off on the globe as an arc, of an equal 

 number of degrees, along this great circle, and from the initial 

 fixed point. The poles of the first pair of faces are situated at 

 the extremities of this arc, which becomes the base line of the 

 survey of the crystal. By Iriangulation from it, the angles 

 being supplied by the goniometer, the positions of the poles of 

 all the faces are placed as points on the globe. 



The interred ion of a face with the surface of the globe is a 

 circle, which may be described on it with a pair of compasses, 

 lakirg the pole of the face as centre. The circles in whieh any 

 two faces, which are not parallel, meet the sphere, cut each 

 other in two points. If lhe>e points be joined by the arc of a 

 great circle, wc obtain the projection of the edge which the 

 two faces male on meeting. It is perpendicular to the great 

 ciiclc passing through the poles of the two faces. If it be 

 carried parallel lo itself to the centre of the sphere, it coincides 

 with a diameter, and its poles are indicated by points on the 

 globe. When the operation has been repeated with all the 

 edges, wc have a second group of points on Ibe globe, which 

 catalogue* the edges occurring on the crystals. 



If the circles f.f intersection, with the surface of the sphere, 

 of any three facet, not in the same zone, be considered, the arcs 

 connecting each pair of intersections meet in a point which is 

 the projection of the comer formed by the three faces which 

 meet there. A third group of points, representing corners, is 

 thus obtained on the globe, and the chaiaclerislics of the 

 cr)stal ate exhausted. 



> Atnlraci of a Paper read before th« Chemical Society, December 6, 1894, 

 J J. V. Itucharwn. F.R.S. 



If the corners be carried parallel to themselves to the centre, 

 they find themselves already represented by the intersections of 

 the diameters representing their edges. If the similar poles of 

 any such group of diameters be connected by arcs of great circles, 

 a spherical triangle or jiolygon is marked out, and its area com- 

 pared with that of a hemisphere is a measure of the corner, 

 just as the arc is the measure of the angle which it subtends. 

 The secondary figures thus described on the sur'.ice of the sphere 

 are always difietent from the primary ones. Thus the corners 

 of the cube, when collected at and radiating from the centre of 

 the sphere, delineate the regular octahedron, which in its turn, 

 when similarly treated, delineates the cube. From this point 

 of view they are reciprocal inversion forms. 



Having got a complete projection of it on the globe, the 

 crystal can be studied. It can be referred with equal ease to any 

 system of coordinates and to any number of different systems ; 

 it is only necessary to shift the nu'trosfhh-e over the surface of 

 the globe. In fact, there is now no question touching the geo- 

 metry of the crystal which cannot be directly answered alter 

 making one or more simple measurements ; and the distinc- 

 tion between easy questions and difiicult ones has almost 

 disappeared. 



The projection of the crystal has been constructed from sup- 

 posed observed angles on the goniometer ; but it is equally easy 

 to construct it from its crystallographic specification — that is, 

 the inclination of the axes and the proportion of the para- 

 meters. 



The projections, of the normals to the faces, or the co- 

 ordinate planes, are found by constructions on these planes. 

 These positions are marked on the sphere by the points on the 

 coordinate circles where they meet its surface. A great circle 

 drawn through any one point, at right angles to the coordinate 

 circle, contains the pole of the face. It is also contained in 

 another great circle, found in the same way. It is fixed in their 

 point of intersection. 



In this way every possible face, permitted by the specifica- 

 tion, can be easily and readily placed on the sphere by its repre- 

 sentative pole ; and the angles between every pair can be at 

 once taken off with a pair of compasses or a tape. In a few 

 minutes a complete catalogue can be made of the angles which 

 each face makes with every other one. The advantage of this 

 is particularly apparent in the oblique systems, which on the 

 globe are dealt with as readily and as easily as those of the 

 regular system. 



In conclusion, the author alluded to other uses of the globe, 

 where it does easily, and without fatigue, work which can he done 

 in no other way without great labour ; and he pointed out an 

 important indirect advantage, gained by its use. in the education 

 of the sense of direction, which is generally only sparingly 

 developed in the mind. 



THE USE OF SAFETY EXPLOSIVES IN 



MINES. 



A LARGE committee wasaoi oinled by the North of England 

 Institute of Mechanical Engineers in iSSS, to investigate 

 and report upon the subject of flamelcss explosives in relation 

 to their dcgrte of safety in mines. Expeiimcnts with various 

 explosives and appliances connected wiih shot-firing were com- 

 menced in 1892 at lleliburnupon-Tyne, and a number of 

 papers referring lo them have been contributed lo the Insti- 

 tute's Transactions. The first part of the Report of the Com- 

 mittee has just been puhlished, and it clears away many ol the 

 doubts and uncertainties connected with the emplo\meiit of 

 safety explosives in underground workings. Into the detail- of 

 the experiments we have not space lo enter, but the following 

 conclusions deduced from them show the kind of results 

 obtained : — 



(1) All the high explosives (ammonite, ardeer powder, bel- 

 lite, carbonitc, roburiie, and sccurite) arc less liable ihan 

 bla-tingpowder to ignilc inflammalilc mixtures of air and lire- 

 damp. Thesi: explosives, however, cannot be relied upon as 

 en-uring absolute safety when u-ed at places where inllamniable 

 mixture- ol air and fire-damp may be present. 



(2) The variable results following upon the delonalion o' high 

 explosives appear to be <luc in some measure lo defective ad- 

 mixture of, or variation in the proportions of, the ingredients 

 used in ihe manufacture of the explosive. 



In view of ihe changes from lime to lime made in the pro- 



NO. 131 2, VOL. 51] 



