248 



NATURE 



\_yuly 15, 1880 



historian of the inductive sciences resigned his chair and 

 used his disinterested influence to obtain the appointment 

 of Miller as his successor. 



Previously to this, in 1825, Miller had taken his degree 

 as a fifth wrangler, and he obtained some reputation as a 

 tutor. In 1 83 1 he published an elementary treatise on 

 hydrostatics, and in 1835 one on hydrodynamics. They 

 bore the mark of the same concise and precise treatment, 

 and e.xcision of all that was merely explanatory, which 

 gave afterwards its character to his treatise on Crystallo- 

 graphy, and probably deterred the ordinary student from 

 that subject far more than any real difficulties inherent in 

 the science. 



Already in 1829 he had published a crystallogi-aphic 

 notice of the forms of ammonium carbonate, followed in 

 1830 by two other memoirs, and thenceforward notices 

 from time to time emanated from his pen on crystallo- 

 graphy and on optical and physical subjects. 



Miller was thirty when he succeeded to the chair, which 

 he occupied forty-eight years. 



The system of Weiss indicated the position of a face 

 on a cr>-stal by expressing its intercepts on a system of 

 axes in the form of integer multiples of the intercepts 

 (parameters) of some other selected crystal-face on the 

 same axes. 



The system of Miller represented the face by a symbol 

 composed of three numerals, or indices, which are the deno- 

 minators of three fractions with unity for their numerator 

 and in the ratio of the multiples of the parameters ; and 

 he asserted the principle that his axes must be parallel to 

 possible edges of the crystal. 



The elegant way in which this mode of representing a 

 face lent itself to yielding expressions for the relations 

 between faces belonging to a zone (/.<•. faces that would 

 intersect in edges parallel to the same line) gave it 

 superiority over previous methods, due to its bringing the 

 symbols of the crystallographer into a form similar to that 

 employed in algebraic geometry. But though expressions 

 were given for the relations connecting four crystal planes 

 in a zone, the principle lurking in them of the rationality 

 of the anharmonic ratios of four such planes was not 

 recognised, or at least was not announced as such, by 

 Miller till 1S57, nor were the further results deducible 

 from this principle ever propounded by him. It was bv 

 a pupil of A.xel Gadolin's and by V. von Lang inde- 

 pendently that the limitations imposed by this principle 

 on the varieties of crystal symmetry were first set forth ; 

 but Bravais had already deduced the necessity for these 

 hmitations by a parallel method of reasoning founded on 

 the idea of what may be termed a net-pile of the centres 

 of mass {Rainiigit/cr), that is to 'say, a parallepipedal 

 system of arrangement of molecules. But Miller's work 

 consisted in working out into a beautiful system the 

 indicial method of notation and calculation in crystallo- 

 graphy, and obtaining expressions adapted for logarithmic 

 computation by processes of great elegance and simplicity. 

 The faces of a crystal he followed Neumann, Whewell, 

 and Grassmann in representing by normals to the faces, 

 which are conceived as all passing through a common 

 point ; and this point is taken as the centre of an 

 imaginary sphere, the sphere of projection. The points, 

 or poles, in which the sphere is met by these normals, 

 and which therefore give the relative directions in space 

 of the faces of the crystal, can have their positions on the 

 sphere determined by the methods of spherical trigono- 

 metry. Moreover a great circle (zone circle) traversing 

 the poles of any two faces will ti - . crse all the poles cor- 

 responding to faces in a zone with them. 



By the aid of the stereographic projection, ■which 

 ^liller also adopted from Neumann, he was able at once 

 to project any of these great circles on a sheet of paper 

 with a ruler and compasses, and for the purposes of the 

 crystallographer elaborate edge-drawings of crystals be- 

 come of comparatively little importance. Miller's system 



then gave expressions for working all the problems that 

 a crystal can present, and it gave them in a form that 

 appealed at once to the sense of symmetry and appro- , 

 priateness of the mathematician. 



His book at length became recognised by physicists 

 and by the higher school of crystallography as one to 

 supersede what had gone before it, as is evidenced by its 

 having been translated into French by no less a man 

 than Senarmont, into German by Grailich, who added a 

 valuable chapter to it on crystallographic physics, and 

 into Italian by Ouintino Sella, and by its being now 

 almost universally employed in crystallographic physics. 



The future development of crystallography, there can be 

 little doubt, will follow on the lines laid down by Iililler, 

 whatever may be the direction that development will take ; 

 and in the cause of higher scientific education, it is much to | 

 be regretted that in a National School of Mining and Mine- 

 ralogy like that established in Jermyn Street the elaborate 

 and relatively clumsy system of notation introduced by 

 Naumann shoidd still be retained, to the exclusion of an 

 incomparably more comprehensive and reasonable system 

 which has at least the advantage not only of being English 

 in its completed form, but of having been originated by 

 mathematicians so eminent as Neumann, Grassmann, 

 Whewell, and Miller. For it is to be borne in mind that 

 the (so-called) system of Naumann, ap.art from his long 

 superseded geometrical treatise, is nothing but a system 

 of notation for the general forms, and not for the particular 

 faces of a crystal, and becomes more complicated in 

 proportion as the symmetry of the crystal is more simple, 

 while it is entirely useless in the methods of computa- 

 tion, its symbols being actually converted by the modern 

 crystallographer who uses them into the Millerian symbols 

 on every occasion when he wishes to deduce relations 

 between faces and the zones to which they belong. 



Besides his memoirs describing the results of crystallo- 

 graphic measurement and certain tracts such as that on 

 the gnomonic projection and on the crystallographic 

 method of Grassmann, Miller published in 1S63 a tract on 

 crystallography which was, in fact, a second edition of 

 his original treatise. 



In 1852 he published his great work, for it was all his 

 own, on Mineralogy, modestly entitled a new edition ot 

 the "Elementary Introduction to i\lineralogy, by the 

 late William Phillips," by H. J. Brooke and W. H. Miller. 

 The publication of this severe little volume was an epoch 

 in the science it illustrated. It contained a mass of 

 results obtained by Miller with all his accuracy and all 

 his patience through many years, and tabulated in his 

 usual concise manner. It may be said to have fired the 

 zeal and directed the general form of the greater but still 

 uncompleted work of his friend Des Cloizeaux. It is a 

 monument to Miller's name, though he almost expunged 

 that name from it. Like other \vork of his it may be 

 merged in the larger works of newer men, but it will not 

 be superseded, and will always have to be referred to. 



One of the great works of Miller's life was the 

 restoration of the standards lost in the fire which 

 destroyed the Houses of Parliament. The micro- 

 scopic accuracy of his mind here had a congenial 

 task ; and another conspicuous ciuality of that mind 

 had to be brought into play in devising the elaborate 

 precautions to be taken in order that the balances and 

 apparatus employed might be sufficiently sensitive, and 

 at the same time absolutely accurate when considerable 

 weights were under determination. Indeed there was no 

 faculty for which ]\Iillerwas more remarkable than this of 

 devising readily the most simple means of making an 

 experiment and the apparatus needed for it. 



His room at the Cambridge Museum was a storehouse 

 of such simple and almost improvised furniture, embrac- 

 ing forms of apparatus needed by a crystallographer and 

 observer using optical instruments : a little heliotrope 

 suggested to him by a crack in the window of a railway 



