2 Mr Whewell on the use of Notation 



termine its form, and the other circumstances of its geome- 

 try. And conversely, from the angles made by its faces, or 

 from other considerations, we may obtain the laws of derivation 

 by .which its faces are produced, as has also been shown in va- 

 rious cases by Mr Levy. 



But the fact is, that it is possible to obtain, in almost all 

 cases, the laws of crystalline derivation more simply. That is, 

 not by knowing the magnitude of the angles which the faces 

 make with one another, but by certain properties of the form, 

 as the parallelism of some of the edges, the figure of some of 

 the planes, Sec. ; and these considerations supersede the ne- 

 cessity of measuring the angles themselves almost entirely. 



Now, in order to make these deductions, it is most conve- 

 nient not to suppose all faces derived from one general law, un- 

 der which the indices only make the difference, as is the case 

 in Weiss's system, and in mine ; but to conceive the forms de- 

 rived by two or three laws, more simple, and less general ; 

 laws so selected, that such properties as are mentioned in the 

 last paragraph may be found arranged in classes, and may 

 thus enable us to make our inferences by reference to a small 

 number of principles. This is the important and beautiful 

 simplification which has been established by Mohs. 



In order to facilitate our reasonings of this kind, it becomes 

 proper to have a notation, declaring by means of which of the, 

 laws so classified our forms are obtained, and expressing also 

 the primary or fundamental form from which the derivation is 

 made. And this is the object of the notation which I shall 

 propose, and which is different from that of Mohs in several 

 respects, but subservient to his system. 



The following instance is produced as a specimen of the 

 reasonings above mentioned. And it will perhaps illustrate, 

 more clearly than language can describe, how, with such a 

 system, and such a notation, the determination of the laws by 

 which crystalline faces are derived, becomes simple and easy. 

 The requisite steps for this determination are these : The laws 

 of derivation being explained, a few propositions are establish- 

 ed as consequences of them, with respect to relations of the 

 edges and faces. And by reference to these propositions, we 

 are able, for each face, to trace the law by which it is dedu- 



