292 Mr.AFv Qockle on the Themyxf Equations. 



(t^il shallow vessels to the rays of the sun, or to a current of dry 

 or hot air. When dry it forms a friable mass, which, wh^fl 

 slightly rubbed, crumbles into a very fine powder. The quan- 

 tity of lime required to precipitate the phosphoric acid from 

 urine is by no means great, and the only difficulty experienced 

 in the whole process is in the filtration, which proceeds much 

 more slowly than could be wished, though I have no doubt 

 that a little practice would suggest the means of greatly, dimi-? 

 fiishing, if not of wholly obviating this impediment,jj{f, g.^ ^^ 

 Glasgow, August 26, 1 845, , ,y -^oqrnoosb ii 



\*"KS. Since the above was written, I have aiSdfe'rtkined that 

 /tl|e difficulty in filtering and drying the precipitate, to which 

 reference has more than once been made, may be greatly obvi- 

 atetl by intimately mixing a small quantity of finely-powdered 

 wood-charcoal with the precipitate, after the great bulk of tWe 

 water has been drawn off by means of a siphon or otherwise. 

 The quantity of charcoal which is necessary for this purpose, 

 is by no means considerable; it has the effect of rendering the 

 precipitate tolerably porous, and thus greatly facilitating its 

 being filtered and dried. If the charcoal-powder, before being 

 mixed with the precipitate, has had a considerable quantity of 

 putrid urine filtered through it, it becomes strongly charged 

 with ammonia, and is thus rendered much more valuable as a 

 manure. The urine which has been used to impregnate the 

 charcoal can, of course, be run into the tank, and the phos- 

 phoric acid it contains be prepipitated with lime in the way 

 already describ^^,,,,,- ^„^ „| M^^Xboqums'^ oi ^ML 



XLV. Supplementary 'Remarks on 'Elimination^ and on the 

 ii.nTheory of Equations. By James Cockle, M.A.^ of Trinity 

 -IV College, Cambridge; Special Pleader^. 



^i(5' TN the development ofj^^(10.)tj l«it the coefficient of 

 -■- Zp Zq Zr be denoted by {p q r\ with the exception of 

 ^that of ^^ ^hichwe shall represent by «i, and let 



\o cit^Xciio^ vti— sv 't si-KY • 's.^ i'o ■^ t* it) znoiJonifi 



,f)Iqioanq ziih lo anoianoixo 2u tfivdo oih lo zatxom vS .V = 'V 



subject to the condition that, when m of the quantities p, q, r 

 become equal, the last terms of (11.) and (12»)-are to bedi- 

 vided by ?;z (tw— 1 ) . . 2 . 1, then, if 'ijgiJaavni sesdjt Wb ni 



^,^.» Communicated by T. S. Davies, Esq., F.R.S., F.S.A., &c. " 

 " "f See my paper in this (August) Number of the Phil. Mag. p. 126, line 3. 



