Prof. Sylvester oji a linear MetJiod of 'Eliminating^ S^c. 425 



ultimate action of the chlorine all the bicarbonate of potash is 

 decomposed, the caHjonic acid entirely expelled, and a por- 

 tion of hypochloroiis acid remains free in solution. 



This formation of free hypochlorous acid does not occur 

 with carbonate of soda, owing to the much weaker affinity 

 which that base has for carbonic acid, and its forming a much 

 less stable bicarbonate than potash does. The free carbonic 

 acid cannot therefore react upon the hypochlorite of soda, 

 and liberate hypochlorous acid as the free carbonic acid does 

 upon the hypochlorite of potash. The same formation of 

 free hypochlorous acid occurs in a more striking degree when 

 chlorine is sent through a solution of acetate of potash ; that 

 solution, it is well known, absorbs a large quantity of gas, and 

 acquires the strong yellow colour, the odour, and all the other 

 properties of free hypochlorous acid. It is here evident, that 

 b)' the action of chlorine upon acetate of potash, chloride of 

 potassium is formed, with the binacetate of potash, free hypo- 

 chlorous acid, and the hypochlorite of potash. If the large 

 absorption of chlorine by carbonate of potash is due to car- 

 bonic acid, it follows that caustic potash should not absorb 

 any excess of chlorine, but that the property should be con- 

 fined to the carbonate. Accordingly, in two experiments, the 

 proportion of chlorine absorbed by caustic potash was found 

 to be as nearly as possible a single equivalent. In one ex- 

 periment 449" I chlorine, in the other 424'8 chlorine were 

 taken up, instead of 442*6 chlorine, by a single equivalent or 

 589*9 of potash. Caustic potash, therefore, dissolves no more 

 chlorine than caustic soda. There appears therefore to be 

 no reason to abandon the old theorj', that the bleaching solu- 

 tions of chlorine in alkalies and alkaline earths contain a chlo- 

 ride and hypochlorite, for these bleaching compounds certainly 

 do not correspond with metallic peroxides, as has been lately 

 maintained. 



LXIX. On a linear Method of Eliminating between double^ 

 treble, and other Si/stenis of Algebraic Equations. By J. J. 

 Sylvester, F.R.S., Fro/essor of Nattiral Philosophy i?i 

 University College, London. 



Part I. — Binary Systems. 

 T ET U and V be two integer complete homogeneous func- 

 ■'-^ tions of a' and ?/, one of the mih, the other of the ?ah de- 

 gree; and let it be required to express the condition of the 

 coexistence of the two equations U = V = by means of 

 the eriuation C = 0, where C is free from all appearances of 

 X or y. 



This equation, according to the system of notation de- 



