WILLIAM HALLOW ES MILLER. 467 



mental dimensions of his " integrant molecules," our indic'ea were his 

 " decrements," and our conceptions of symmetry his " fundamental 

 forms." There has been nothing peculiar, however, in the growth of 

 crystallography. This growth has followed the usual order of science, 

 and here as elsewhere the early, gross, material conceptions have been 

 tlie stepping-stones by which men rose to higher things. In sciences 

 like chemistry, which are obviously still in the earlier stages of their 

 development, it would be well if students would bear in mind this 

 truth of history, and not attach undue importance to structural for- 

 mulae and similar mechanical devices, which, although useful for aiding 

 the memory, are simply hinderances to progress as soon as the neces- 

 sity of such assistance is passed. And when the life of a great mas- 

 ter of science has ended, it is well to look back over the road he has 

 travelled and while we take courage in his success consider well the 

 lesson which his experience has to teach ; and, as progress in this 

 world's knowledge has ever been from the gross to the spiritual, may 

 we not rejoice as those who have a great hope ? 



Although the exceeding merit of the " Treatise on Crystallography" 

 ca^ts into the shade all that was subordinate, we must not omit to men- 

 tion that Professor Miller published an early work on Hydrostatics, and 

 numerous shorter papers on Mineralogy and Physics, which were all 

 valuable, and constantly contained important additions to knowledge. 

 Moreover, the " New Edition of Phillips's Mineralogy" which he pub- 

 lished in 1852 in connection with H. J. Brooke owed its chief value to 

 a mass of crystallographic observations which he had made with his 

 usual accui'acy and patience during many years, and there tabulated in 

 his concise manner. As has been said by one of his associates in the 

 Royal Society, " it is a monument to Miller's name, although he almost 

 expunged that name from it."* It is due to Professor Miller's memory 

 that his works should be collated, and especially that by a suitable 

 commentary his "Tract on Crystallography" should be made accessible 

 to the great body of the students of physical science, who have not, as 

 a rule, the ability or training which enables them to apprehend a gene- 

 ralization when solely expressed in mathematical terms. The very 

 merits of Professor Miller's book as a scientific work renders it very 

 difficult to the average student, although it only involves the simplest 

 forms of algebra and trigonometry. 



Independence, breadth, accuracy, simplicity, humility, courtesy, are 



* Obituary Notices from the Proceedings of the Royal Society, No. 206, 

 1880, to which the writer has been indebted for several biographical details. 



