38 M. If. Fizeau on the Expansion of Solids by Heat* 



Quartz. (Rhombohedral.) 

 a. . . . . =0-00000781 

 a' . . . . =0-00001419 

 « lin . . . =0-00001206 

 «*.... =0-00001206 



Bismuth. (Rhombohedral.) 

 a . . . . =0-00001621 

 «'.... =0-00001208 



The third observation was made at right angles to a natural 

 face of the rhombohedron — that is, at an angle of 56° 24' with 

 the principal axis. The corresponding calculation was made by 

 means of formula (3) : 



Calculation . . . a = 0-00001334 

 Observation . . . a = 0*00001338 



Rhombic System. 



As the situation of the axes of expansion is always subordi- 

 nate to the crystalline structure, it must be admitted that to 

 identical directions, as regards symmetry of faces, there corre- 

 spond identical expansions — a principle which leads directly to 

 fixing the situation of the three axes of expansion in this system 

 parallel to the three crystal] ographical axes. 



Suppose, in fact, a rectangular parallelepipedon constructed on 

 the three crystallographic axes as edges; it will be at once seen 

 that during the expansion of this solid the displacement of any 

 point upon one of its faces can only take place parallel to the 

 edge at right angles to this face and without lateral deviation, 

 which is the character of the axial expansion ; for if it were other- 

 wise, and if the displacement took place along a certain inclined 

 direction, it would be sufficient to turn the crystal through 180° 

 in the plane of the face in question to find another direction in 

 which the crystallographical relations would be the same, and 

 along which, consequently, the same inclination would be pro- 

 duced. 



The same kind of considerations may be employed to deter- 

 mine the position of the first axis in the dimetric prism previously 

 considered, as well as in the hexagonal prism. For the case of the 

 rhombohedron an analogous conclusion is reached by attributing 

 to the crystal two successive rotations of 120°, 



A subsequent communication will be devoted to completing 

 the subject of the right rhomboidal system, and to considering 

 the oblique rhomboidal system. 



