228 MINERALOGY 



nearly alike. Their crystals when pure are nearly of the same 

 angle. Compounds which replace each other are usually alike 

 chemically in that they are salts of the same acid, as carbonates, 

 sulphates, or phosphates ; but this is not always true, since sodium 

 nitrate, NaNO 3 , crystallizes in the same forms and nearly the same 

 angles as calcite, CaCO 3 . Elements or compounds which replace 

 each other in the crystalline molecule in all proportions are said to 

 be isomorphous. Formerly they were thought to be of exactly 

 the same form and angles, but at the present time it is thought 

 that it is only necessary for the angles and molecular volume to be 

 of nearly the same value. This is well illustrated in the isomor- 

 phous group of natural carbonates: 



FAT MOLECULAR VOLUME 



Calcite CaCO 3 74 55' 36.8 



Magnesite MgCO 3 72 36' 27.8 



Siderite FeCO 3 73 00' 30.3 



Rhodochrosite MnCO 3 73 00' 31.9 



Smithsonite ZnCO 3 72 20' 28.0 



The molecular volume or volume of the unit of the space lattice 

 is found by dividing the molecular weight by the specific gravity 

 of the substance. If the molecular weights of crystalline sub- 

 stances were the same and they differed in specific gravity, then the 

 same volume of the denser substance would contain more molecules 

 per volume than the less dense substance, and the molecular vol- 

 ume or the relative size of the space-lattice units will vary inversely 

 as the specific gravity. 



Topic parameters represent the relative distances or the ratios 

 of the distances between centers of the simple structural units of 

 the space- point-system, measured along the three axial directions. 

 The topic parameters are functions of the molecular volumes and 

 the axial ratio of a compound. 



The crystalline angles will vary directly with the composition ; 

 in pure calcite, with a rhombohedral angle of 74 55', as an end mem- 

 ber of a series in which pure smithsonite, with a rhombohedral angle 

 of 72 20', is the other end member, every molecule of zinc carbonate 

 crystallizing with the calcium carbonate will have the effect of 

 proportionally decreasing the angles of the calcium carbonate. 

 The amount of decrease in the angles will be directly proportional 

 to the percentage of zinc carbonate present. If there is no car- 

 bonate present, other than zinc carbonate and calcium carbonate, 

 in the crystal, their percentage proportion could be calculated from 



