On Crystallography. 455 



trix, in which they seem to be more or less fastened, so 

 that it l)ehnv'js ai^ observer to complete, in his imagination, 

 each of ihtf-o partial lorms. 



(n short, I have been more ihan once surprised to see 

 with what Facility vonng mineralogists, who have joined to 

 a tasic tor the science an aptitude for geometrical con- 

 ceptions, have referred every thing to its right place in 

 crystals the faces of which were the most deranged, or 

 have profited from the trifling part of a crystal sunk in 

 its matrix, fn order to guess at the rest. It would even 

 seem thai there is a peculiar satisfactiou attached to the 

 solution of these small problems : every person is pleased 

 uith giving proofs of sagacity, and with understanding 

 Mature as if by half a word. 



In order to determine the mut«al incidences of the faces 

 of a crystal, or of its salient angles, an instrument is used 

 which was invented bv M. Carangeau. This instrument, 

 which strongly rcsenibles the graphometer, is composed of 

 a semicircle MTN (<ig. 77)j <>t brass or silver, divided 

 into degrees, and which has f.vo arms A B, FG, one of 

 which V Cy is slit from u to R, excepting at K, where a 

 small piece is left unslit in order to give more solidity to 

 the instrument. This arm is attached at R and at c to a 

 brass rule situated behind, and winch is of a piece with the 

 semicircle. The junction of the arm with this rule is 

 produced by means of two screws which are inserted into 

 the slit. The other arm A B is slit in the same manner 

 from X to c, where it is attached abo /c the former by 

 means of the screw at this place, and which traverses the 

 two slits. On loosening the screws, we can shorten at plea- 

 sure the parts c G, c B, of the two arms, as circumstances 

 require. 



The arm AB having only a single point of attachincr at 

 c, where the centre ot" the circle is, has a movement around 

 this centre, while the arm G F remains constantly in the 

 direction of the diameter which passes by the points zero 

 and 180°. 



It may be useful to remark, that the upper part of the 

 arm A B ought to be bevilled ofl* towards its edge sz^ the 

 direction of which being prolonged bciow, pa-ises by the 

 centre c of the instruiiient. The reason of this is, that this 

 edge is what is called Hie index line ^ i. e. that which indi- 

 cates on the Q;raduated circund'-'renee the measurement of 

 the angle wanted. 



Let us now suppose that we wish to measure on a crystal 

 jthe angle formed by twoadioining plants. \Vc know that 



F f 4 ^ thi$ 



