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486 SCIENCE PROGRESS. 



established facts, or dismissed as mere fanciful speculations, 

 by readers who have not had occasion to follow the growth 

 and development of the theories upon which they are based. 

 They are, as we shall see, neither the one nor the other. 



THE LATTICE THEORY. 

 Omitting- the somewhat crude theories of earlier investi- 



o 



gators, the first serious attempt to grapple with the theory 

 of crystal structure is the work of the French mathematician, 

 Bravais (6). His classic memoir on Systems of Regularly 

 Distributed Points is an investigation of all the possible 

 forms of space-gratings (Reseaux). 



The reader may get a fair idea of what is meant by 

 a space "grating," or "lattice," or (as I have previously 

 termed it) (7) a "space-network," by imagining a hail- 

 storm to become suddenly rigid, each hailstone being 

 . arrested at a given instant, and fixed at the point of space 

 which it occupies at that moment. Imagine also that the 

 hailstones were descending at perfectly regular intervals, so 

 that when the whole set becomes fixed the hailstones lie at 

 equal intervals upon parallel straight lines like beads strung 

 upon straight wires ; if there is no wind these lines are 

 vertical. 



Suppose, further, that the lines of descending hailstones 

 are separated by certain regular intervals in such a way 

 that they lie in planes, that all the lines lying in one vertical 

 plane are equidistant, and that in all parallel planes the 

 distance between adjacent lines is the same. It will now 

 be clear that the hailstones not only lie in vertical lines and 

 planes, but also in horizontal or transversely inclined lines 

 and planes ; such that along all parallel lines the particles 

 lie at equal intervals, and in all parallel planes the lines 

 which run in the same direction are separated by equal 

 intervals. 



A hailstorm of this nature, supposed to become rigid, 

 constitutes a space-lattice or network of particles of the sort 

 investigated by Bravais. 



The lattice-structure is one which may very reasonably 



