S¥) Sir W. Rowan Hamilton on Quaternions. 



Experiment to separate Phosphoric from Pijrophosphoric Acid. 



The different reaction of the phosphate and pyrophosphate 

 of soda towards a solution of sulphate of magnesia and am- 

 monia, led me to hope that it might form the basis of a method 

 of separating these two modifications of phosphoric acid. 



When pyrophosphate of soda is dissolved in a large amount 

 of water, and the solution is mixed with a very large quantity 

 of chloride of ammonium, no precipitate is produced on the 

 addition of sulphate of magnesia and solution of ammonia. 

 But at the end of a considerable period a precipitate falls, and 

 is deposited firmly upon the sides of the vessel. If, however, 

 the quantity of chloride of ammonium is very considerable, it 

 frequently does not appear for several days. 



1 '828 grm. of hydrated c-phosphate of soda, which had lost 

 a small quantity of its water of crystallization by efflorescence, 

 was dissolved in water with 1*521 grm. of the same salt, which 

 had been previously heaied to redness and furnished 0"611 

 grm. of pyrophosphate of soda. The solution was mixed with 

 100 grms. of chloride of ammonium, then diluted with 1600 

 grms. of water, and sulphate of magnesia and solution of am- 

 monia added. The precipitate was filtered ofFafter an interval 

 of two hours, then washed, first with water containing chloride 

 of ammonium, afterwards with water containing ammonia. 

 0-814- grm. of calcined phosphate of magnesia was obtained, 

 which contains 0*516 grm. of phosphoric acid. But the 1*828 

 grm. of phosphate of soda contains only 0*391 grm. of phos- 

 phoric acid : hence a considerable amount of pyrophosphoric 

 acid was precipitated with the phosphate of anmionia and mag- 

 nesia. This method of separation is consequently inapplicable. 



XLVII. On Qjiiaternions ; or on a New System of ImagiJiaries 

 in Algebra. By Sir William Rowan Hamilton, LL.D., 

 M.R.I. A. y F.R.A.S.y Corresponditig Member of the Insti- 

 tute of France, S^c, Andrews' Professor of Astronomy in the 

 University of Dublin, and Royal Astronomer of Ireland. 



[Continued from p. 297-] 

 68. ^T^HE equation of the ellipsoid (see Philosophical 

 JL Magazine for October 1847, or Proceedings of the 

 Royal Irish Academy for July 1846), 



T(»p-[-px)=x2-i^, eq. (9.), art. 38, 



which has so often presented itself in these researches, maybe 

 anew transformed as follows. Writing it thus, 



^(^+H(pO^^^(,„,)^ . . . (125.) 



