264 FELIX SAVART S RESEARCHES ON THE 



the first and the last, was rectangular, whilst in rock crystal this mode 

 of division may establish itself. 



Summary, 



1st. The elasticity of all the diameters of any plane perpendicular to 

 the axis of a prism of rock crystal, may be considered as being sensibly 

 the same. 



2nd. All the planes parallel to the axis are far from possessing the 

 same elastic state ; but if any three of these planes be taken, restricting 

 ourselves only to this condition, that the angles which they form with 

 each other are equal, tlien their elastic state is the same. 



3rd. The transformations of the nodal lines of a series of plates cut 

 round one of the edges of the base of the prism are perfectly analo- 

 gous to those which are observed in a series of plates cut round the 

 intermediate axis in bodies which possess three unequal and rectangu- 

 lar axes of elasticity. 



4th. The transformations of a series of plates perpendicular to any 

 one of the three planes which pass through two opposite edges of the 

 hexahedron are, in general, analogous to those of a series of plates cut 

 round a line which divides into two equal parts the plane angle in- 

 cluded between two of the three axes of elasticity in bodies where 

 these axes are unequal and rectangular. 



5th. By means of the acoustic figures of a plate cut in a prism of 

 rock crystal, nearly parallel to the axis, and not parallel to the two 

 faces of the hexahedron, we can always distinguish which are the faces 

 of the pyramid susceptible of cleavage. The same result may be 

 obtained by the disposition of the modes of division of a plate taken 

 nearly parallel to one of the faces of the pyramids. 



6tli. Whatever be the direction of the plates, the optical axis, or its 

 projection on their plane, always occupies a position on them which is in- 

 timately connected with the arrangement of the acoustic lines : thus, 

 for example, in all the plates cut round one of the edges of the base of 

 the prism, the optical axis, or its projection, invariably corresponds with 

 one of the two straight lines which compose the nodal system formed 

 of two lines which intersect each other rectangularly. 



Although there is doubtless a great analogy between the phsenoniena 

 which rock ciystal has just presented to us, and those we have obser\'ed 

 in bodies in which the elasticity is different according to three direc- 

 tions perpendicular to each other, nevertheless we are forced to acknow- 

 ledge that, with respect to the mode of experiment we have employed 

 in tliese researches, rock crystal cannot be placed in the number of 

 substances with three rectangular and unequal axes of elasticity, and 

 still less in the number of those all the parts of which are symmetri- 

 cally arranged round a single straight line. For the same phaenomena 



