594 DR MACVICAR ON THE LAW OF VOLUMES OF AERIFORMS 



shown by the very small percentages sometimes occurring in the analysis of 

 minerals. It is indeed usual to regard these small percentages as accidental 

 ingredients. But that will not do. Thus, prase is represented as quartz, with 

 about 2,9 per cent, of protoxide of iron as an accidental ingredient. But on 

 constructing that molecule, which seems to be the most prevalent in the crystal- 

 line world, viz., the compound dodecatom with marked poles, which, to show all 

 its constituents, may be expanded on the paper thus : — 



X (X),,X(X (X\,X),,X (X\,X, 



29 per cent, of protoxide of iron just gives four atoms, one to differentiate each of 

 the two poles of the two polar dodecatoms, that is, to take the place of the sepa- 

 rate atoms of X in the above formula, 



FlSX^F (S (S),,SX/ (s)i2F. 



Nay, half this quantity, or 1-5 per cent, might enter into the symmetry of the 

 molecule. And so it may possibly be with Ti in rose quartz, as found by Fuchs. 

 But let us look to the grand products of nature. 



The quartz molecule will tend to be differentiated more effectually than by an 

 element of its own kind on each pole of the dodecatom. And more especially, 

 we may expect ^ and K, or Na, or both performing this function and giving, 



Kii( S)i.2iK, or (See Type ^) 

 K S a{ S )jo l S K. (See Type 6) 



Felspar^ ..■'....'.. ^ ^ [ =K202.A1^0g.l2Si02. 



which last is the formula for orthoclase, in Watt's Chemical Dictionary (the 

 atomic weights of and of Si being here halved.) (See Art. Felsjyar). But both 

 the ratios of ingredients and the specific gravities show that, in order to explain 

 nature, we must rise from the simple dodecatom to the compound dodecatom. 

 Thus, the purest felspar or adularia gives, 



G= ^^5iii#i^ = 2-59. Expt.2-53 . . . 2-58. 

 8AQ 



Theory. Berthier. 

 C144Si02 4320 645 64-20 ) 



Adularia-^ 24AI2O3 1248 18-6 t8 40 I from St Gothard. 



( 24KO J.148 16-8 1695 j 



G= 8x324 )67r6(2'59. Expt.2-53 . . . 2-58. 



But in order to show the substitutions which take place during further differ- 

 entiation and development, the above formula requires to be written out, 



Ki(s)i.,IvK(Ki^(sX2^K),oKi(S)j2i^K. 



Thus, let us substitute Na for K, in the polar dodecatoms, and we obtain,— 



Nal^SX^'^^^^C^ ^ ^ '^)i2^ k)^oNaii( S )^2 '^ Na. 



