312 Irhprovements on Brunner^s process for Potassium. 



m-^-n - m+w - . z 



VI. The fluent of z^z' is z^'z- X ratio 



z- 



m+n ^ 



z . 



n 



When the fluxion arises from the product of two or more variable 



quantities its fluent is found in the following manner. Suppose the 



fluxion to be Sy^x^x'-^-bx^y'^y. Taking the termSy^x^x-, the 



XX X 



value of n IS 2+1=3, hence — =jr~» 2LVia'Sy"^x^x'y.^—=x^ii^ 

 ' ' nx' 3a;'' -^ 3a.- -^ 



the fluent of Sy^x'^x'. Taking the term bx^y'^y, the value of n is 



X V V 



4 + 1 = 5, hence — = r~, and 5x^y'^yX-r~ =x^y^ the fluent of 

 nx' oy •' '' oy ^ 



bx^y'^y. The s\im2x^y^ divided by 2 the number of parts, is 



2yxx'—Sx^y 

 x^y^ the fluent required. To find the fluent of 1 — — = 



2y~^xx' — ox^y~*y. Taking 2y~^xx- the value of n is 1 + 1=2, 



XX X • 



hence — :=^.j and 2y~^xx' X-^,=x^y~^ the fluent of 2y~^xx- 



X 



Taking — Sx^y^y the value of w is= — 4 + 1= — 3, hence — ; = — 



y y 



^, and —3x^y-'iyx-^,=x^y-^ the fluent of —Sx'^y-^y. 



The sum 2x^y-^ divided by the number of parts, which is 2, be- 



x^ 

 comes x^y ^=z — , the fluent required. 



To be continued. 



Art. XII. — On some improvements on Brunner^s process for Po- 

 tassium, and in the means of preserving that metal ; by R. Hare, 

 M. D., Professor of Chemistry in the University of Pennsylvania. 



When I first went through Brunner's process for potassium, as 

 modified and described by Berzelius, I conceived the idea of sub^ 

 stituting, for the piece of a gun barrel between the iron bottle and 

 receiver, an iron cylinder much larger in bore, and using an iron 

 vessel without naphtha, instead of that recommended by the great 

 chemist last mentioned. From the employment of this, much in- 

 convenience was experienced ; as in consequence of reiterated ex- 

 plosions, every one present was more or less bespattered with naph- 

 tha. Subsequently I found that in both of my conceptions I had 



