256 FELIX savart's researches ok the 



planes perpendicular to the preceding and passing through the axis, 

 although it be different in the latter from what it is in the former ; lastly, 

 it was necessary to verify whether the plates cut parallel to the faces a X 6, 

 e Xf, cXd of the pyramid were really susceptible of assuming the same 

 modes of division, and whether these modes Avere different from those 

 of the three plates cut parallel to the faces bXc, dXe, a X/, these latter 

 being besides similar to each other. Experiment having shown the 

 affirmative of these positions, it is evident that all the series of plates 

 perpendicular to a plane normal to any two parallel faces of the prism, 

 and passing through its axis, ought to present identical phaenomena for 

 the same degrees of inclination, and that the same ought to be the case 

 for the sei'ies of plates perpendicular to any plane passing through two 

 opposite edges of the hexahedron. All the plates we have employed 

 are 23 or 27 lines in diameter and 1 line in thickness ; they have 

 been cut with great care and are polished, in order that the phaenomena 

 they exhibit with respect to light might be compared with those they 

 present relative to sonorous vibrations. Lastly, although they have 

 been taken from five or six different crystals and from different coun- 

 tries, it may be supposed that they belong to the same piece of quartz, 

 because, whenever it was necessary to pass from one crystal to another, 

 the precaution was taken of causing to be cut in the new specimen a 

 certain number of plates, for the sole purpose of repeating the experi- 

 ments already made ; and by this process we may assure ourselves 

 that crj'stals of very different appearance, such as those of Madagascar 

 and of Dauphiny, do not however present remarkable differences in 

 their structure. 



Before proceeding to the description of the phaenomena which are 

 related to each series of plates, we shall observe, that in all the figures 

 the line x y represents the axis itself of the crj'^stal when it is contained 

 in the plane of the plate, or its projection in the contrary case, and that 

 the position of this axis has been determined with great care, for each 

 plate individually, by means of polarized light ; so that with this datum 

 and the details into which we shall enter, the position occupied by any 

 plate within the mass of the crystal may easily be represented to the mind. 



First Series. Plates parallel to the Axis of the Hexahedron. 



If we consider first the plates i., v., ix., fig. 2. and 2, bis, which are 

 parallel to the faces of the hexahedron, we see that they assume ex- 

 actly the same modes of division : one of these modes, that which is 

 represented by dutted lines, consists of two nodal lines, which cross 

 each other rectangularly, whilst the other resembles the two branches 

 of a hypei'bola, to which the two preceding lines serve as axes. The 

 sound of the first system being F, that of the second is the D JJ of the 



