M. F. Wohler on Cryptolite. 31 



proposed lines a, a! are rectangular, we may write the fol- 

 lowing equation of perpendicularity, 



S. aa' = 0; or aa' + a'a = 0. 



To express that two lines are similar or opposite in direction, 

 we may write the following equation qfcoaxality, or of paral- 

 lelism, 



V. aa' = 0; or aa) — a'a = 0. 



And to express that three lines are in or parallel to one 

 common plane, we may write the equation oj 'coplanarity, 



S. aa'a" = ; or a a 'a" — a" a' a = ; 



either because the volume of the parallelepipedon under the 

 three lines then vanishes, or because one of the three vectors 

 is then perpendicular to the vector part of the product of the 

 other two. 



[To be continued.] 



VII. On Cryptolite. By F. Wohler*. 



THE new substance for which, from the hidden manner in 

 which it occurs, I propose the name of cryptolite, is, 

 phosphate of the oxide of cerium. It has only been found as 

 yet imperceptibly disseminated in the massive greenish or 

 reddish apatite of Arendal in Norway. It becomes apparent 

 when the apatite is placed in large pieces in dilute nitric acid, 

 appearing, as the apatite dissolves, in the form of fine, pa- 

 rallel, crystalline needles of about a line in length. The apa- 

 tite from which I obtained it, contained not more than 2 or 3 

 per cent. ; it neither occurred in all the varieties, nor was it 

 equally disseminated throughout the mass, but appeared 

 chiefly confined to those parts having a red colour. 



A complete description of cryptolite can only be given when 

 it shall be found in distinct isolated specimens. For the pre- 

 sent it can only be stated, that it crystallizes in transparent, 

 apparently six-sided prisms of a very pale wine colour. Spe- 

 cific gravity about = 4*6. At a moderate red heat it under- 

 goes no change. 



Finding it to contain nothing but phosphoric acid and prot- 

 oxide of cerium, with a mere trace of protoxide of iron, it 

 was analysed by means of strong hot sulphuric acid, which 

 acts upon it in the same manner as upon cerite. 



* Translated from PoggendorfF's /Innalen, No. 3, 1846, and communi. 

 cated by Dr. E. llonalds. 



