246 Prof. Daniell and Dr. Miller on the 



which equality of products of factors, takfen in opposite orders, 

 does 7iot in general hold good for quaternions {j i=z—ij) ; the 

 commutative character of ordinary multiplication is therefore in 

 general lost in passing to the new operation, and QQ' — Q'Q, 

 instead of being a symbol of zero^ comes to represent a pure 

 imaginary, but not (in general) an evanescent quantity. On 

 the other hand, for quaternions as for ordinary factors, we may 

 in general associate the factors among themselves,^ by groups, 

 in any manner which does not alter their order ; for example, 



Q.Q'Q".Q"'QIV^QQ/.Q^/QWQIV. 



this, therefore, which may be called the associative character 

 of the operation, is (like the distributive character) common 

 to the multiplication of quaternions, and to that of ordinary 

 quantities, real or imaginary. 



[To be continued.] 



XL. Additional Researches on the Electrolysis of Secondary 

 Compounds. By J. Frederic Daniell, Esq., D.C.L., 

 For. Sec. M.S., Prof, of Chem. in King's College, London, 

 and W. A. Miller, Esq., M.D., Dem. of Chem. in King's 

 College, London. 



[Continued from p. 188 and concluded.] 

 6. "X^T^E were purposing to follow up the examination of the 

 ▼ ▼ double salts by the electrolysis of other classes of 

 these compounds, when we were stopped by the occurrence 

 of a new order of phaenomena, which it was necessary to turn 

 aside and examine as affecting the very foundation of the pro- 

 cess which we were employing. In our examination of the 

 phosphates, our plan had been to transfer by electrolysis the 

 acid of the salt placed in the platinode cell into a solution of 

 potassa placed in the zincode cell for its reception, and then 

 to determine its quantity and its properties from those of the 

 salt which was formed by secondary combination. 



The arrangement which we now made was to place the salt 

 at the zincode with the view of passing its bases into an acid 

 at the platinode. We commenced our experiments with the 

 double sulphates with the view of comparing the different hy- 

 drates of the sulphuric acid with the hydrates of the phos- 

 phoric acid already examined, and throwing more light upon 

 the results of the electrolysis of the dilute acid. 



(s.) Some pure sulphate of potassa and copper (CuO, SOg, 

 + KO, SO3) was carefully prepared, and its solution placed 

 in the zincode and connecting cells of the diaphragm appara- 

 tus : the platinode cell was charged with dilute sulphuric acid, 

 the current of twenty cells of the battery was transmitted 



