13* DESCRIPTION OF THE GRAPHOMETER. 



When the angle which we meafure exceeds 90 degrees, we 



return the quadrantal arc T M to its former fituation, in order 



to afcertain its dimenfions. 

 The precife The utility of the goniometer will be very apparent to every 



meafure of angles one w ^ CO nfiders how interesting it is in defcriptions of cry f- 



tals, to know the angles which their faces form with each 



defcription of a 

 cryitel. 



Without this 



they cannot be 

 diftinguifhed. 



Inilances. 



Other cafes, 



other. Thefe indications render the defcription appropriate, 

 by diftinftive and truly charafteriftic traits : without them it 

 can be nothing more than a rude and imperfect fketch, that 

 may apply to a variety of different objects. 



Thus we do not give a determinate notion of the dodeca- 

 hedral zircon, when we merely fay that it is a prifm of four 

 fides, terminated by fummits with four rhombufes attached to 

 the longitudinal edges. This defcription applies equally to the 

 Harmotome (cruciform hyacinth) to the itilbite, to oxided tin, 

 &c. ; but if we add, that the fides form right angles with each 

 other, and that the faces of the fummit are inclined towards 

 each other in an angle of 124° 12', we confine the defcription 

 to the zircon. If we fay that the inclination is 121? 5T ', we 

 defcribe the harmotome ; if we fay that there are two different 

 inclinations, the one of 123° 32', and the other of 112° 14', 

 we defcribe the flilbite. 



And ftill farther : Several varieties of the fame fubftance 

 may prefent fimilar forms, differing only in the meafures of 

 their angles. Such are, on the one hand, the fix rhomboides, 

 and on the other the two decahedrons with rhombic faces, 

 which are found in the carbonates of lime. How (hall we 

 defcribe with accuracy all thofe varieties, which differ only 

 in the more or lefs, unlefs we give the differences with pre- 

 cifion ? There are even cafes in which the ufe of the goni- 

 ometer is the only means of avoiding an error, which other- 

 wife would not fail to infinuate itfelf into the defcription. 

 Thus the calcareous rhomboid, the angles of which differ only 

 by about 2° 18' from the right angle, was at firft taken for a 

 cube, and we fhould have continued to denominate it cubic 

 calcareous fpar, if geometrical meafurement had not reclined 

 this denomination, which is faulty in two refpecls, both in it- 

 felf, and with reference to the theory, which demonflrates that 

 the exigence of the cube cannot in this inftance be reconciled 

 iwitb any of the fymetric laws of diminution. . 



XI.— letter 



