262 Dr. H. Kopp on Atomic Volumes, 



crystalline forms of isomorphous substances are identical, the 

 more nearly will their atomic volumes be the same. The 

 crystalline condition and atomic volume stand, however, in a 

 certain dependence on one another, which I will endeavour 

 to prove by several groups which have been more closely ex- 

 amined. It may be proper to remark, that the crystallographic 

 notation employed in the following remarks is that of M. 

 Naumann. 



It is said that witherite, strontianite, carbonate of lead, 

 and arragonite are isomorphous. They all crystallize in rhom- 

 boids, but the dimensions of their angles respectively are not 

 perfectly equal. If we consider the correct atomic volume 

 from each of these bodies as that deduced from the mean of 

 the views already stated, and compare these atomic volumes 

 with the proportions between the axes, the following is found 

 to be the case : — Atomic volume. 



Ba O, C 0.2 : a : b : c = 0-7413 : 1 : 0*5950 286-72 



SrO, CO2 0-7237:1:0-6096 255-53 



PbO, COg 0-7236: 1 : 0-6100 259-50 



CaO, CO2 0-7205:1:0-6215 213-48 



Or we may also compare the atomic volumes with the indivi- 

 dual angles, for example with the declinations oc P and P 00 : 



Atomic volume. 

 Ba O, C O2 : 00 P = 1 18° 30' P 00 = 286-72 



SrO, CO2: 117 16 108° 12' 255-53 



PbO, COg: 117 14 108 13 259-50 



CaO, COg: 116 16 108 27 213-48 



From these comparisons it is shown that the carbonates of 

 lead and strontia are perfectly isomorphous : their atomic 

 volumes also approximate very closely. Again, it is seen that 

 the two other bodies are neither isomorphous with one another 

 nor to the former minerals : hence we find that their atomic 

 volumes also differ. 



But it is also apparent that an increase of atomic volume 

 for this group must be followed by an increase of the axis a, 

 and a decrease of the axis c; or according to the augmenta- 

 tion in the atomic volume^ the declination 00 P must become 

 more, and the declination P co less obtuse. 



If one of these crystals (of arragonite for example) be heated, 

 its density becomes less, and in consequence of this its atomic 

 volume greater. The consequence of this jnust be that the 

 declination so P must be more and that of P 00 less obtuse; 

 and this has been long since observed to be really the case. 



But the relation between the crystalline form and the atomic 



