496 Dr. E. J. Mills on Cumulative Resolution. 



2»N,H 8 S-(n-l){(2nH s )H4=N 2 , +s H 8B+ ,S a «. . (2) 



3=,[N 2 H 8 S 2 ], 

 J)=v 2 [N 2 H 8 S 4 ], 



&G. &C. 



S=v»[SJ. 



Of this series, the ratios in the first, fourth, fifth, and seventh 

 cumulates are known. The decompositions themselves, how- 

 ever, admit of various modes of representation, according to 

 the starting-point selected. 



4. Manganic Oxides. — The derivatives of manganic dioxide 

 can be represented as follows, — 



2n Mn0 2 -0 - l)0 2 = Mn 2w 2n+2 . 



Known ratios of Mn to correspond to the following values 

 of n ; viz. *5, 1, 1'2, 2, 3, and oc. 



Ferric Oxychlorides. — When ferric chloride is treated 

 with water, it decomposes, eventually producing a body whose 

 composition is very near to that of ferric oxide. Its formula 

 shows that there must be six distinct stages in this continuous 

 process. These are united, for the first time, in the equations 



n Fe 2 Cl 6 . 3H 2 0-(n-l) HCl = Fe 2n C1 5W+1 H 5W+1 3 „, 



T)=v[Fe 2 Cl 5 H 5 3 ], 



T) = , 2 [Fe 2 Cl 4 H 4 3 ], 



&c. <fec. 



T)=/[Fe 2 3 ]. 



Ferric compounds of the above nature are somewhat repul- 

 sive to analysts ; and hardly an attempt at their formulae appears 

 in systematic works. 



5. Bismuthic Nitrates. — The action of water on normal 

 bismuthic nitrate is necessarily represented as containing three 

 distinct continuous stages: — 



n Bi 2 3 . 3N 2 5 -(>- 1)N 2 5 = Bi 2 „ 3 „ . N 4n+2 O 10 „ +5 . 



3=v[Bi 2 O 3 .N 4 O 10 ], 



2)=v 2 [Bi 2 3 .N 2 5 ], 

 jT) =v 3 [Bi 2 3 ]. 



In the first stage, ratios are known for n = *l and 1 ; for the 

 second, n=2 ; for the third, n = f, f, f, 1, and oc. 



6. Silicates. — A large number of silicates are derivable 



