454 



CRYSTALLOGRAPHY. 



Theory. 



General 

 rules for 

 under- 

 standing 

 the sym. 

 bo!s. 



dicated by it. In the second case, the zero indicates 

 that the angle or edge to which it exclusively relates 

 undergoes no decrement whatever. Thus, in the sym- 



I 2 2 -O 



bol D e E PB/i, B expresses a decrement by one 



1 2 1 



range, which takes place only on the edges conti- 

 guous to the superior summit A (Fig. 32.) ; b indi- 



2 



cates a decrement by two ranges, which only takes 

 place en the edges contiguous to the inferior summit. 



2 2.0 



The quantities e and E ought likewise to be consider- 

 ed independent of each other. The first indicating a 

 decrement of two ranges on the angles e only, and the 

 second indicating that no decrement whatever takes 

 place upon the angles E, opposite to the preceding. 



The preceding observations have been given in con- 

 siderable detail, in order to put our readers completely 

 in possession of the method, and to enable them to 

 make a figure of a secondary crystal, merely from the 

 symbol representing the laws of its formation. But to 

 enable any person to read these symbols, and to under- 

 hand them, much briefer directions would have sufficed. 

 We shall subjoin the following rules, which will be suf- 

 ficient for that purpose, and which will serve as a kind 

 of epitome of the preceding observations : 



1 . Every vowel employed in the symbol of a crystal 

 indicates a sobd angle, marked with the same letter in 

 the figure which represents the nucleus. Every con- 

 sonant indicates the edge which has the same letter in 

 the figure. 



2. Each vowel and consonant is accompanied by a 

 figure, the value and position of which indicates the 

 law of decrement which the coi-responding angle or 

 edge undergoes. We must except the three consonants 

 P, M, T ; each of which, when it appears in the sym- 

 bol of a crystal, indicates that the crystal has faces pa- 

 rallel to those faces which have the same letters on the 

 figure of the nucleus. 



3. Each letter contained in the symbol of a crystal, 

 is understood, with the figure belonging to it, to apply 

 to all the angles or edges which have the same function 

 as it in the figure, and is marked with the same letter. 



4. Every number joined to a letter indicates a de- 

 crement, setting out from the angle or the edge denoted 

 by that letter. If the number is a whole number, it 

 indicates how many ranges in breadth are subtracted, 

 supposing each plate to have only the thickness of one 

 molecule. If the number is a fraction, the numerator 

 indicates the number of ranges subtracted in breadth, 

 and the denominator the number of ranges subtracted 

 in height. 



5. According as the number is placed below or above 

 the letter which it accompanies, it indicates that the 

 decrement descends or ascends, setting out from the 

 angle or edge marked by the letter. If it is placed to- 

 wards the top, and either on the right or the left side of 

 the letter, it indicates a decrement in a lateral direc- 

 tion, either to the right or to the left of the angle or 

 edge marked by the letter. 



6. When a letter is twice repeated, with the same 

 number placed on *\vo different sides, as 2 G G' 2 or G i 2 G, 

 ■A A 2 or A 2 2 A, the two edges, or the two angles which 

 it marks, ought to be considered on the figure in tlie 

 same relative positions ; that is to say, for example, that 

 in the symbol *G G 2 , the quantity 2 G indicates the ef- 

 fect of decrement on the edge G situated at the left, 

 and the quantity G 2 the effect of decrement upon the 

 edge situated at the right. 



7. When a letter has the same number both on the 



left and the right side, as 3 G ? , it applies equally to all Gcmiome. 

 the edges G. The same thing holds with the letters ters - 

 which belong to the angles. """" Y""""' ' 



8. The parenthesis, as for example (OD l F a ), indi- 

 cates an intermediate decrement. The letter O indi- 

 cates, in the first place, that the decrement take.* place 

 by three ranges on the angle O, and that its effect is 

 ascending. D 1 F 2 indicate, that for one molecule sub- 

 tracted along the edge D, there are two molecules sub- 

 tracted along the edge F. 



9. Every small letter occurring in the symbol of a 

 crystal, indicates the angle or the edge diametrically 

 opposite to that which lias the capital letter of the same 

 name in the figure, where the small letter is omitted as 

 superfluous. We must except the letter e, which is al- 

 ways employed in the rhomboid, and which indicates, 

 according to the principle, the angle opposite to that 

 which bears the letter E. 



10. When a symbol contains two letters of the same 

 name, the one large the other small, with different 

 numbers attached to them, the two opposite edges or 

 angles to which these letters belong, are conceived to 

 undergo each exclusively the law of decrement indica- 

 ted by the number attached to the letter. 



11. Every letter, whether large or small, marked by 

 a number having a zero following it, indicates that the 

 decrement denoted by that number does not take place 

 on the particular edge or angle denoted by the letter. 



As the whole theory of crystallization depends upon 

 the knowledge of the angles which the different faces 

 of the crystal make with one another, it is necessary 

 to be in possession of instruments for measuring these 

 angles. Such instruments are known by the name of 

 Goniometers. The goniometer first employed is ex- 

 hibited in Fig. 34. The way in which it is used must 

 be obvious without much description. It consists of a 

 semicircle of brass, divided into degrees. At its centre 

 c is fixed a pin, upon which slide the two arms AB 

 and GF. The last of these GF, by means of a screw, 

 may be fixed in any position, so that the distance be- 

 tween the end G and the centre, may correspond with 

 the face of the crystal to be measured. The other arm 

 AB is drawn up, till the distance between B and the 

 centre corresponds as nearly as possible with the size 

 of the other face of the crystal. It is then turned 

 round, till the angle of the crj'stal to be measured cor- 

 responds exactly with the angle BcG; the arm AB 

 then cuts the semicircle in the angle which corresponds 

 with that of the crystal. There is a hinge upon the 

 middle of the brass semicircle, which is not seen in the 

 figure. By means of it, one-half of the semicircle may 

 be thrown back, when the crystal to be examined hap- 

 pens to be so situated in a group, that the arms could 

 not otherwise come at it. 



This was the only goniometer used by Rome de 

 Lisle, and Hauy, when he published his Treatise on 

 Mineralogy, in 1801. It can scarcely be depended on 

 nearer than two or three degrees ; or when the faces of 

 the crystals are large and very smooth, perhaps a very 

 steady hand, accustomed to handle the instrument, may 

 come within one degree. On that account, the surpri- 

 zing accuracy of many of Hauy's measurements reflects 

 the greatest credit both on his care and his sagacity. It 

 is true, indeed, that all his measurements are ultimately 

 fixed by the application of his mathematical theory. 

 But the original data of that theory itself are derived 

 from the goniometrical measurement of angles. We 



Goniome- 

 ters for 

 measuring 

 the anglts 

 of crystals. 



Plate 



ccxxiii. 



Fig. 34. 



Rome" de 

 I,isle*» and 

 H.-tuy's go- 

 niometers. 



