XVI.] ON EQUIVALENT VOLUMES. 435 



in the state of ice, with the addition of the bases, the acid 

 being excluded.* In reality, the equivalent volume of alum 

 is to that of the rhombic phosphate as 270 :235; and 24 HO 

 crystallizing in the monometric system would have the same 

 volume as alum, with a specific gravity of about .8, giving for 

 HO, 11.25 instead of 9.8. 



What are called the atomic volumes of crystallized species 

 are the comparative volumes of their crystals. In the rhom- 

 bohedral system, the length, of the vertical axis being constant, 

 the volume varies with the length of the lateral axes, or, in 

 other words, increases as the rhombohedron becomes obtuse, 

 and diminishes as it becomes acute, the cube being the limit 

 between the two. So in the dimetric and trimetric systems, 

 the length of the vertical axis being unity, the volume dimin- 

 ishes as the base of the prism, the specific gravity increasing. 

 Monoclinic and triclinic crystals may be calculated as if deriva- 

 tives of the trimetric system, with which they will be found to 

 correspond in volume, t 



It is now necessary to determine what equivalent corresponds 

 to a given specific gravity in any crystalline solid, or, in other 

 words, what is the value of the condensation which takes place 

 in the change from the gaseous to the solid state ; and here a 

 degree of uncertainty is met with, because the equivalent of a 

 crystallized species may often be a multiple of that deduced 

 from those chemical changes which only commence with the 

 destruction of its crystalline individuality. The simplest for- 

 mula deducible for alum is KO S0 3 , A1 2 3 3 S0 3 , 24 HO, or 

 S 4 Kal 3 16 , 12H 2 2 , and, hydrogen being unity, its equivalent 

 is at least 474.6, which, with a specific gravity of 1.75, gives a 

 volume of about 270. Again, grape-sugar is not less than 

 C24H 2 40 2 4, if we regard its combination with common salt as 

 corresponding to one equivalent of each ; and the ferrocyanides 

 in the same way are represented by C 12 , etc. There are rea- 

 sons for believing that the equivalents of these species in the 



* Chemical Society, Quarterly Journal, I. page 139. 



[t The conclusions in this paragraph may be liable to correction, but I leave 

 them as they were printed twenty-one years since.] 



