M. H. Fizeau on the Expansion of Solids by Heat. 37 



octahedron suitably arranged ; but in the present case this octa- 

 hedron of mean expansion must be conceived as having one axis 

 coinciding with the principal axis of the crystal, while the two 

 others may be arranged in any manner whatever. 



To make this decisive comparison between experiment and the 

 result deduced from theory, three expansions must evidently be 

 measured, a, a', a m , in the three following directions : the first 

 parallel, and the second perpendicular to the principal crystallo- 

 graphical axis, the third making an angle of 54° 44' with this 

 axis ; while the two latter directions may be in any azimuth what- 

 ever around the same axis. 



Under these circumstances the cubical expansion will be 

 a cub _ a + 2« f i 



the mean linear expansion, 



« - 3 , 



and the theory will only be satisfied provided this latter value 

 coincide with the value found directly for « m — that is, if we have 



a m_ ft lin _ 



The following are the results of these observations :— 

 a is the expansion along the principal crystallographic axis. 

 a.' along the normal to this same axis. 



a lin the mean linear expansion deduced from a and from a'. 

 a m the expansion in the direction of the angle 54° 44', with a 

 possible error of 5' to 10' in the cutting of the crystal*. 



Siberian Zircon, (Prism with square base.) 

 a . . . . =0-00000443 



x 1 . . 



, 





= 0-00000233 



« lin 



, 





•=0-00000303 



a m . . 



. 





= 0-00000304 



Emerald 



{Beryl) 



(Hexagonal.) 



OL 



, 



= 



-0-00000106 



a' . . 



, 



= 



0-00000137 



a lin 



, 



= 



0-00000056 



« m . . 



. 



= 



0-00000057 



Iceland Spar 





(Rhombohedral). 



u 



, 



= 



0-00002621 



a' . . 



. 



= 



-0-00000540 



a lin 



, 



= 



0-00000514 



a m 



, 



=5 



0-00000507 



* I must here render fresh testimony to the remarkable skill and the in- 

 telligent zeal with which M. Henri Soleil has cut the crystals used in 

 these researches. 



