C 87 3 
IV. A general Method of Calculating the Angles made hy any 
Planes of Crystals, and the Laws according to which they are 
formed. By the Rev. W. Whewell, F. R. S. Fellow of 
Trinity College, Cambridge. 
Read November 25, 1824. 
1. It has been usual to calculate the angles of crystals 
and their laws of decrement from one another, by methods 
which were different as the figure was differently related to 
its nucleus ; which were consequently incapable of any 
general expression or investigation, and which had no con- 
nexion with the notation by which the planes of the crystals 
were sometimes expressed. And the notation which has 
hitherto been employed, besides being merely a mode of 
registering the laws of decrement, without leading to any 
consequences, is in itself very inelegant and imperfect. The 
different modes of decrement are expressed by means of 
different- arbitrary symbols ; and these are combined in a 
manner which in some cases, as for instance in that of in- 
termediary decrements, is quite devoid both of simplicity 
and of uniformity, and indeed, it may be added, of precision. 
The object of the present paper is to propose a system which 
seems exempt from these inconveniences, and adapted to 
reduce the mathematical portion of crystallography to a 
small number of simple formulae of universal application. 
According to the method here explained, each plane of a 
