Dr. Griffith oh the Ammo?iio-magnesian Phosphates oftheUrine. 373 

 whence there followed, 



m=-(q-i-q-*)-^=+q ] (q l -q 2 )- 1 , 



l<=- m <={q- qo )-K 

 Hence 



^=t¥i(9i+c) +mf 2 (q?+c), T>,= l'q'\(q ] + e)+mff $ {g 9 +e) ; 



and making, for conciseness, 



„ = fr'afe + c) _ , \<h+± u -.r 



q\^h+c) qi + c 



it was found that 



u = f~Yc= ^ = l+mv * - -g2(gi-g 2 )~ 1 + gi(gi-g2)" 1 ^ 

 Thus 



" +fyi= ( gl -y- 1 (l-^,) =:(1 " r ' ) " 1(ryi "^ ; 

 ^ + f/2 = »,. ( 1 - « r ) -H?,- ? 2 ) ; 

 and finally, 



_* — i^ = v 



M .r + <7l 



as before. 



And because in no one stage of the foregoing process has the 

 commutative principle of multiplication been employed, the 

 results hold good for quaternions, and admit of interesting in- 

 terpretations. 



Observatory, March 20, 1852. 



[To be continued.] 



LIU: On the Triple or Ammonio-magnesian Phosphates occurring 

 in the Urine and other Animal Fluids. By J. W. Griffith, 

 M.D., F.L.S., Member of the Royal College of Physicians*. 



TWO forms of the so-called triple or ammonio-magnesian 

 phosphates have long been considered to occur in animal 

 fluids. One of these is composed of microscopic stelL-c with 

 mostly six foliaccous rays, and is readily obtained by adding 

 excess of solution of ammonia to urine; this is commonly known 

 as the bibasic phosphate. The other exists in the form of micro- 

 scopic prisms, most of which are trilateral, frequently with one 

 of tin- edges truncated, the terminal facets being single and 

 oblique] these arc in reality hemihedric crystals. This salt is 

 well known as being almost constantly found in putrid urine j 

 * Communicated by the Author. 



