ANDERSEN: PROPERTIES OF PYROPHOSPHATES 323 



angle is, however, so large that most of the grains observed under 

 the microscope allow no conclusion whatever as to the optical 

 character, the dark bar being apparently straight. Only a few 

 favorable grains rendered the determination certain, these gi'ains 

 showing a bar with a slight though distinct curvatm*e. 



Attempts to determine the axial angle under the microscope 

 failed on account of the difficulty in finding grains with proper 

 orientation. Owing to the good cleavage most of the grains 

 were oriented along a cleavage face not showing any optic axis, 

 and in the few cases of an optic axis appearing in the field it was 

 in a position not favorable for satisfactory measurements (e.g., 

 too near the center of the field). It may, however, be concluded 

 from the curvature of the dark bar that the axial angle is not 

 much less than 90? A probable estimation is 2V = about 80? 

 The optical orientation is as follows: Bxa = 7 forming approxi- 

 mately 20° with a-axis in obtuste angle ^; 13 parallel to 6-axis. 

 Bxo = a forming approximately 4° with c-axis in acute angle /3. 

 The plane of symmetry is thus the plane of optic axes and sec- 

 tions parallel to this plane have an extinction angle of about 4° 

 in acute angle i3 against cleavage lines. 



Thick cleavage pieces show faint pleochroism: a light pink; 

 /3, 7 nearly colorless with a faint yellowish tinge. 



A comparison of the properties of the two compounds described 

 in the preceding pages shows that they are isomorphous; a com- 

 parison with other crystals proves that they belong to a new 

 group of isomorphous substances not hitherto described.^ As 

 .to the crystallography of the other members of this group (prob- 

 ably the pyrophosphates of different bivalent metals) nothing is 

 known. 



The isomorphism^ of the two compounds is here established 

 on the basis of similarity of chemical constitution, crystal form 



* The only anhydrous pyrophosphate whose crystal lographic properties are 

 known, the Thallopyrophosphate TI4P2O7 has an entirely different axial ratio. 

 Lamy and Des Cloizeaux, Ann. Chim. Phys. (4) 17: 325. 1869. See Groth's 

 Chem. Cryst. 



^ For an exhaustive discussion of the different meanings of the term isomor- 

 phism see Hlawatsch, Zs. Kryst. 51: 417. 1912. 



