REPORT ON MINERALOGY. 
333 
faces being formed by given laws of decrement in the courses ol 
this sort of masonry. This doctrine was readily accepted, be¬ 
cause it pretended to offer to our curiosity the ultimate analysis 
of the constitution of bodies ; but by reason of this very boldness 
of promise, it was unlikely to bear the test of time and trial. At 
present this doctrine is probably not maintained, as a physical 
truth, by any one who has examined the subject; for though 
its assumptions may appear obvious a priori , they are not 
confirmed by observation. In order to support the theory 
of integrant and subtractive molecules, the facts of the case 
ought to be quite different from what they are. If indeed, in 
all minerals, the cleavage planes were such as to bound forms 
which would join so as to fill space, and if the forms of the cry¬ 
stals could always be referred to these planes w'ith greatnumerical 
simplicity, the theory would still be a good mode of grouping 
the facts. But it appeared very early that it could not claim 
this praise ; and when the author of it was driven (as in the 
case of fluor spar,) to conceive crystals made up of solids hang¬ 
ing together by their edges, we had an example of a theory in 
which difficulties were solved by suppositions directly contra¬ 
dicting the only reasons which could be assigned why the 
theory should be accepted. 
Any theoretical mode of representing in general the ultimate 
structure of crystals, as consisting of elementary particles, 
whether as an aggregate of plane-faced solids, spheres, or sphe¬ 
roids, will probably not be of great value to the science in its 
present stage. But it must be considered interesting to know 
how far that numerical simplicity in the relations of the faces 
of crystals which led to the hypothesis of decrements, is really 
found in nature. The greater part of the faces of the most 
usual crystals are expressible by laws of which the ratios are 
very remarkable for simplicity. But in not a few cases the 
numbers run considerably beyond what was supposed to be the 
admissible limit in the earlier stage of the study. Thus in 
arragonite we not only have the numbers 2, 3, 4, 5, but 7, 9, 
10, 19, occurring in the ratios. In carbonate of lead we have 
13, 19, 21, 28. In galena Naumann has 12012, and 36036, ac¬ 
cording to his notation. In certain crystals of gold from the 
Ural, Rose finds a face which is ( a, -yy, yy) in the notation of 
Weiss. It would be important if any one could decide whether 
there is any limit of magnitude or simplicity to such ratios. 
The most generally useful result which has followed from 
the modern methods of treating the subject of crystallometry, 
has been a great simplification in the mode of deducing the 
law's of formation of faces, when we find them on the crystal. 
