IV 



Miller proceeded to develop a system of crystallography, which was 

 not published till 1838, but which was the most important work of 

 his life." His system represented the face of a crystal by a symbol 

 composed of three numerals, or indices. Selecting three crystallo- 

 graphic axes, parallel respectively to possible edges of a crystal, and 

 a face of that crystal making certain intercepts on these axes, and 

 taking the three simplest whole numbers (a, b, c, suppose) whose ratio 

 expressed the ratio of these intercepts, he expressed the ratio of the 

 intercepts of any other face of the crystal, by multiplying a, b, c 



respectively by i LI respectively, where h, h, I were integers, and 



formed the symbol of the new plane. 



"The elegant way" (to continue the words of Professor Maskelyne, 

 already quoted) " in which this mode of representing a face lent itself 

 to yielding expressions for the relations between faces belonging to a 

 zone (i.e., faces that would intersect in edges parallel to the same line) 

 gave it a superiority over previous methods, due to its bringing the 

 symbols of the crystallographer into a form similar to that employed 

 in algebraic geometry. Miller's work consisted in working out into a 

 beautiful system the indicial method of notation and calculation in 

 crystallography, and obtaining expressions adapted for logarithmic 

 calculations by processes of great elegance and simplicity. 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 appropriateness of the mathema- 

 tician." He thus, as it has been well said, " placed the keystone into 

 the arch of the science of crystallography," and the " future develop- 

 ment of that science, there can be little doubt, will follow on the lines 

 laid down by Miller." 



Professor Miller's shorter communications, on mineralogy and 

 physics are numerous and valuable, and, in addition to them and to 

 his original treatise, he published, in 1863, a tract on crystallography. 

 In 1852 a work appeared entitled a new edition of the " Elementary 

 Introduction to Mineralogy, by the late William Phillips," by 

 H. J. Brooke and W. H. Miller. It is, however, no disparagement 

 to either the original author or his fellow editor to say that Professor 

 Miller made this volume almost his own. As has been said by the 

 authority quoted above, " The publication of this severe little volume 

 was an epoch in the science which 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 is a monument to Miller's name, though he almost 

 expunged that name from it." 



But Professor Miller's reputation does not rest only upon his work 

 as a mineralogist, great though that was. His name is no less in- 



