Amongst the physical properties which point out the general relationship and classification of chemical substances, none has so deservedly obtained the confidence of chemists as isomorphism. The vanadium compounds have, however, proved a remarkable and unexplained exception to the conclusions which generally follow from well-ascertained identity of crystalline form. Rammelsberg, and afterwards, more completely, Schabus, pointed out the fact that the mineral vanadinite from several localities (a compound of lead vanadate and lead chloride) is isomorphous with apatite, pyromorphite, and mimetesite, minerals consisting of calcium phosphato-fluoride, lead phosphato-chloride, and lead arsenato-chloride, having the formulæ 3(Ca 3 P 2 O 8 ). Ca Fl 2 ; 3(Pb 3 P 2 O 8 ). Pb Cl 2 , and 3(Pb 3 As 2 O 8 ). Pb Cl 2 . The crystalline form of all these minerals is an hexagonal prism, terminated by 6-sided pyramids. The angle P: P (terminal) found by Rammelsberg for vanadinite, and by different observers for the other minerals, is as follows: (1) Vanadinite . 142° 30'; (3) Pyromorphite . 142° 15'; (2) Apatite . . 142° 2 0'; (4) Mimetesite . . 142° 7'; and the relation of the axes (1) 1:0·727; (3) 1:0·736; (2) 1:0·732; (4) 1:0·739.