288 On Mr. Daniell's Theory of Crystallization. [April, 



The specific gravity of the latter solid must, therefore, be greater 

 than the specific gravity of the former." 



In the first sentence Mr. Daniell must either suppose that 

 specific gravity depends on surface, or that solid content depends 

 on surface : by proceeding a few lines further, we find " the 

 number of atoms in a given space " mentioned, which proves (as 

 well as the obscurity of the passage allows me to judge) that Mr. 

 D. does not understand specific gravity to depend on surface, 

 but on bulk ; and further proves that our author has fallen into 

 the other error of supposing bulk to depend on surface ; this is 

 evident from Mr. D.'s asserting that the surface of the octohe- 

 dron, because it is double of the surface of the tetrahedron will 

 contain a double quantity of matter. 



An actual demonstration that solid content does not depend 

 on surface, is surely as unnecessary as to prove that specific 

 gravity does not depend on surface. 



We may now, therefore, proceed to examine the mode which 

 Mr. D. uses to find the content of the solids, viz. the summa- 

 tion of the sphericles composing each. 



Having an octohedron and a tetrahedron whose linear edges are 

 equal, i. e. composed of the same number of particles, the geome- 

 trical mode of measurement would have given the content of the 

 former to be four times as great as the latter; but by Mr. Daniell's 

 M elegant process of counting the balls in the two piles," * 



Content of octohedron : content of tetrahedron :: 44 : 20. 

 How shall we account for this modern discovery which portends 

 the instant overthrow of all our faith in geometry ? the truth is, 

 that this mode of finding the content of a regular body is never 

 correct until the magnitude of the sphericles is diminished, and 

 their number increased sine limite. To make this matter more 

 plain, and to show that the two modes, when properly managed, 

 do not produce different residts, let a tetrahedron and an octohe- 

 dron be taken whose linear edges consist of the same number, 

 viz. of («) particles, or spheres. 



The number in the tetrahedron = {1 + 3 +6 + 10 + 



( 2 + r=-i). 2} 



ii + 1 . n + 2 



1.2.3 



and supposing the octohedron to consist of two pyramids, 

 the number in the first pyramid = {l 2 + 2 2 + 3°- + 4* + 

 + »*} 



n . n + 1 . 2 n + 1 

 " 1.2.3 



* Jnnah, Feb. p. 102. 



