264 Dr. H. Kopp on Atomic Volumes. 



employed to calculate their specific weight from their crystal- 

 line form. If we suppose that the axes of the bodies already 

 examined are' given, we deduce the atomic volume, and from 

 it the specific gravity. 



Atomic volume. Spec, gravity. 



Carbonate of zinc J77-37 4-3956 



Carbonate of magnesia... 182-18 2'9355 



Mesitine 185-75 3-3658 



Carbonate of iron 190-41 3-7585 



Carbonate of manganese 193-26 3-7377 



Dolomite 210-28 2-7755 



Calcareous spar 232-36 2-7220 



From the differences occurring between the specific weight 

 observed and calculated, we can conclude whether the sub- 

 stances found in their natural condition are rendered impure 

 by substances specifically heavier or lighter; but with those 

 minerals which occur in a state of purity, the specific gravities 

 ascertained by observation and calculation approximate very 

 closely. In the case of dolomite the specific weight obtained 

 by experiment is always greater than it is found to be by cal- 

 culation ; but analysis shows that it is always rendered impure 

 by the oxides of iron and manganese. The carbonate of 

 manganese is, on the other hand, less than the calculated re- 

 sult, but it is always mixed with carbonate of lime. 



From what has now been brought forward, it must be evi- 

 dent that an increase of atomic volume is dependent upon an 

 increase of the axis a. The application of heat to one of these 

 crystals must decrease its density, and the axis a must be en- 

 larged, whilst the angle R will be rendered less obtuse. 



This has long since been discovered by Mitscherlich. This 

 chemist has accurately determined the diminution of density 

 on the application of heat to calcareous spar. He found that 

 by a heat of 1 00° C. ( 1 80° F.) its specific gravity was decreased 

 in the proportion of 1 : t ooTtfttt- ^^ ^"^^ above the spe- 

 cific weight of calcareous spar, when its axis a = 085440 

 and its angle R = 105° 5' is 2-7220. By heating it for 

 100° C, therefore, it will be equal to 2-71675, or its atomic 

 volume passes from 232-36 to 232-80. If we determine the 

 length of the axis a by means of the formula already given, 

 we find it = 0-85672, corresponding to an angle R of 104° 

 57' 22". According to this calculation the change in the angle 

 R by 100° C = 7' 37", a result which coincides sufficiently 

 with that found directly by Mitscherlich (8' 34"), when we 

 consider the difficulties which necessarily accompany the di- 

 rect measurement of the dilatation and change of the angles. 



