M. H. Fizeau on the Expansion of Solids by Heat. 35 



to each other ; that is to say, 



« = «' = «"; 

 equation (1) then becomes 



D = a (cos 2 S + cos' 2 8' + cos 2 S"), 

 and, by equation (2), 



D = «; 

 that is to say, the expansion is constant, independent of the di- 

 rection in question, and always equal to that which takes place 

 along the axes, the position of which cannot be revealed by any 

 difference in the expansions, and which must be regarded as inde- 

 terminate. The following are some observations which refer to 

 crystals of this system. These numbers and the following re- 

 present the linear expansion for the unit of length for I degree 

 at the point = 40° of the thermometric scale. 



Fluor-spar. — Normal to a face of octahedral cleavage, 



« = O00001911, 



a = 0-00001910; 

 on a face of the cube (another crystal), 



u = 0-00001 910; 

 on a face cut at an angle of 5° to a face of the cube (another 

 crystal), * = 0-00001915. 



Galena. — At right angles to a face of cubic cleavage, 



a = 0-00002014 ; 

 on a cut octahedral face, 



« = 0-00002014. 

 Cubic pyrites.— At right angles to a natural face of the cube, 



a = 0-00000907; 

 on a face cut in a group of Peruvian crystals without any com- 

 mon direction, u _ O00000908. 



Suboxide of Copper. — At right angles to a face of the rhom- 

 boidal dodecahedron, 



a = 0-00000093; 



on a face situated at 90° from the foregoing, 



a = 0-00000093; 

 on a face cut in a group of crystals without any common di- 

 rection, « = 0-00000093. 



Dimetric and Hexagonal or Rhombohedric Systems. 

 These two systems, distinct in crystallographic relations, merge 

 into each other in their optical phenomena, their conductivity for 



D2 



