156 Intelligence and Miscellaneous Articles. 



of calc-spar for 1°, from to 100° (between which limits it expands 

 uniformly), to be 000001 8. From 17°-5 to 100° it expands there- 

 fore 82-5x0-000018=0001485, whence we have 



X X 3-00479=0-001485 and.r=0-0004942. 



Axis a expands by 00004942, 

 „ c „ 0-00049657. 



For 1° a expands by 0-00000599, 

 „ c ., 0-00000602. 



We arrive at these last values also if we indicate the expansion of 

 axis a for 1° by a;; w^e then have 



j-x 3-0121 792=0000018, &c. 



Bitter-spar (muricalcite) (hexagonal system). — The terminal di- 

 hedral angle of the principal rhomboid at the temperature 17°-5 is 

 106° 15' ; at 100° it becomes 4' 6" more acute, and measures there- 

 fore 106° 10' 54". In the first case the ratio of the axes is as 

 follows : — 



«:c=l-2016: 1 = 1 : 0-8322; 

 in the second, 



a: c=l-1993: 1 = 1 : 0-8338. 



Axis c therefore expands r00192 as much as a ; or for 1°, 0'012144 

 times as much. If the cubical expansion of bitter-spar be known, 

 the absolute expansions of a and c can be calculated as in the former 

 case. 



Arragonite (rhombic system). — At 17°-5 the acute angle of tlie 

 prism OD P (axisZ') = 63°48' 14"; the polar dihedral angle of the prism 



P co = 108° 27'. At 100° the first of these angles becomes 63° 44' 32" ; 

 the second, 108° 21' 31". Axes b and c have therefore expanded 

 more in proportion than axis a. The two temperatures in question 

 give the following proportions between the axes : — 



17°-5. 

 a:b:c=l: 1-60643:1-15754 

 = 0-62249 : 1 : 0-72056 

 = 0-86389 : 1-38780: 1 



100°. 



h:c=l : 1-60836: 1-16088 

 =0-62175 : 1 : 0-72177 

 =0-86142: 1-38547: 1 



Axis h therefore expands 1-001201 as much as a; axis c 1-19027 

 as much; and the latter 1-00167 as much as 6. For 1°, i 0-0121357 

 times, and c 0-0144275 times as much as a, c expanding 0-0121414 

 times as much as b. Kopp found the cubical expansion of Arra- 

 gonite for 1° to be 0-000065. The expansion in the direction of a 

 for 1° being called x, we have 



a: X 3-0265632=0-000065, 



.= Q-QQQQ^^ =0-00002147. 

 30265632 



The crystal expands therefore in the direction of — 

 a for 1°, 00000214 7 

 b „ 0-00002173 

 c „ 0-00002199 



