36 THE. H. J. BEOOKE ON THE OEOTVIETEICAL ISOMOEPHISH OE CRYSTALS. 
attended with little difficulty ; but in the cases of the prismatic, obhque, and anorthic 
systems it is far from definite. 
Having determined the system to which the ciystal belongs, the next operation is to 
measure the angles between the several faces, and to select from among these the angle 
which is to be regarded as elementary. And as the faces themselves afford no assistance 
in fixing upon a proper angle, the selection is left to the arbitrar}" choice of the obsen'er. 
After having fixed upon the elementary angle, the s^unbols of the faces which at their 
intersection produce that angle are determined, and from these and the known angles 
between other faces, other symbols and angles may be found. 
It is usual to measure as large a number of angles as the crystals in our possession will 
allow. Arrd when the observed angles between apparently similar pahs of faces are 
slightly different, these slight differences have been hitherto ascribed to the imperfection 
of the measured faces, and a mean of the measured angles has in this case been 
assrrmed as the probable angle between the faces. But as it seldom if ever happens that 
the mean of any number of measured angles agrees exactly with the geometric angle 
corresponding to the assumed symbols of the faces yielding that angle, it is usual to 
adjust, as it is termed, the symbols and angles in question, by increasing or diminishing 
the .value of the measured arrgles, and by altering, if necessary, the indices irntil both the 
arrgles and indices are in conformity with the elementary faces and angles of the crystals. 
This process of adjustment is the element of disagreement above alluded to, and is 
really the adapting or fitting to a particular primary form the angles and symbols of the 
other faces of the crystal, so that if a new primary form has to be assumed, the new 
symbols may become expressible in only very high numbers, and a readjustment of angles 
and symbols has then to take place. This process will, however, be goverrred by the 
number arrd greater or less degree of perfection of the observed faces, and by the care 
with which the angles have been measured. 
Irr nearly all the hitherto published works on mineralogy the faces of crj'stals have, for 
the convenience of writing and printing, been distinguished by letters. But it appears 
to the writer that the use ofWHEWELL’s symbols for this pru’pose instead of letters, is so 
much to be preferred, on account of its presenting at once to the eye the geometrical 
relations of the several faces, as to more than counterbalance the incorrvenierrce of hawrrg 
three or more figures to ’write instead of one letter ; and particidariy as these letters are 
frequently accompanied by one or more conventional marks of distinction wiiich are 
troublesome both to 'write and to remember. 
Construction of Tables . — We have now to explain the construction of the accompany- 
ing Tables, to consider the facts they present, and theh results. 
These Tables do not contain all the observed angles of the crystals belonging to the 
different minerals, but only such as have been, or might have been used in each case as 
elementary angles, these being sufficient for the pm'poses of this paper. 
No table is given of the cubic system, as that system consists of only a smgle strictly 
isoinorphous group. 
