and on the Change of Crystalline Form by Heat. 263 



volume may be more correctly estimated in another class of 

 carbonates. 



The carbonates of zinc and magnesia, mesitine, the car- 

 bonates of iron and manganese, dolomite and calcareous spar, 

 are a group of bodies which possess both an analogous con- 

 stitution and an equivalent crystalline form. The crystalline 

 form of all of them is that of a rhombohedron, but the axes a 

 in them are unequal and the angle R different. If we adopt the 

 mean of the observations already given as the atomic volume 

 of each of these bodies, we find that the axis a of the rhom- 

 bohedron increases, that the angle R diminishes, whilst the 

 atomic volume increases. 



Axis a. 



Carbonate of zinc 0-80708 



Carbonate of magnesia 0-81165 



Mesitine 0-81498 



Carbonate of iron 0-81962 



Carbon, of manganese 0-82182 



Dolomite 0-83312 



Calcareous spar 0-85440 



We wish to establish a connexion between the length of the 

 axis a\ and the atomic volume of a body ; for this purpose it 

 is natural to assume the atomic volume as the volume or the 

 cubic capacity of its fundamental form. Accordingly, in the 

 group now considered, the atomic volume (V) must be pro- 

 portional to the length of the axis a ; hence we have 

 a = j/V. 



But another number is found for j/ in every body, and the 

 cause of this is obvious. It is supposed in this formula, that 

 the filling up of the space in the rhombohedral crystals is 

 equal on all sides ; but it is known by the optical characters 

 of these crystals that this is not the case. In order to dis- 

 cover a relation between a and V, let us suppose 

 a'' = i/ V. 



We seek x and y according to the method of the least 

 squares from the estimations of a and V of the seven different 

 substances, and we find 



x'= 4-739 y = 0-0020417. 



The relation between a and V is therefore 

 ^4.7 39 = 0-0020417 V. 



This formula coincides very exactly with the observations. 

 And as the greater part of the substances in their natural con- 

 dition are accompanied by impurities, the formula may be 



