S62 NEW VAPvIETT OF CARBOXATE OF LIMB. 



if we suppose the intermediate decrement to be made hy a 

 single row, the hypothetical nucleus would become a rhom- 

 boid extremely flattened, in which the great angle of the 

 rhombus would be 119° instead of 114" IS'', and the great- 

 est angle of incidence between the faces 160° 26' instead of 

 134° 23' : and besides, on this supposition the values of the 

 , angles of the dodecaedron would differ very sensibly from 

 those that give the law of -|, which agree with observation. 



Measures of its The following are the measures of the saliant angles. 



aj)gles. Between ^ and g, 134^ 23' 38"; s and /', 118° 29' 4",* 



*and^, or 5" and g', 143° 32' 39"; s and *, 115° lM4''j 

 s and s', 142° 24' 6". 



Numerical car- I give this variety the name of numerical carbonate of 

 ""^lime, on account of the properties of the numbers that ex- 

 press its form ; the sum of the exponent of B, which is 2, 

 and of the exponent of D, which is 3, being equal to the 

 numeraitor of the exponent of E, which is 5, and their 

 product being equal to its denominator, G. 



I have likewise investigated the law that would govern 

 the dodecaedron, if the hypothetical ntscleus were substi- 

 tuted for the true; and I have found, that in this case tho 



symbol of the dodecaedron would h$ p^ a quantity the 



exponent of v.hich is double that of E in the preceding 

 case. 

 Possibilit)' of In my Treatise on Mineralogy, vol. ii, p. 15 and follow- 



substitutiiig a iug^ J }i^YQ developed the theory respecting the possibility 

 to the primitive of thus Substituting a secondary form to the primitive one, 

 *^"^- so as to derive any other secondary form from it by the laws 



of decrement. This view gives an infinite scope, if I may. 

 , ^ be allowed the expression, to the results of that branch of 



geometry, which arises from the study of the laws, to which 

 the wisdom and power of the supreme Being has subjected 

 the formation of the regular bodies, that people the subter- 

 ranean world; and our admiration increases, when we see 

 this immensity of results end in one common term, the in- 

 variable form of the particle shown hy the dissection of cry- 

 Tin:^ variety stals. I Ought to say here in particular, that none of th* 

 easily disicctccl. ya^j,jg^jg5 ^f carbonate of lime exhibit the rhomboid of 

 101° 30' by the help of mechanical division with more fa- 

 cilityj and more neatly, than that which has been described^ 



