412 OHM ON THE GALVANIC CIRCUIT. 



and 



A + A' + X" = L 



then according to the law just ascertained 



G F' is a fourth proportional to L, A and X 

 I H' a fourth proportional to L, A and xl 

 L K' a fourth proportional to L, A and x". 

 Draw the line F M through F parallel to A D, regard this line as 

 the axis of the abscissae, and erect at any given points X, X', X" 

 the ordinates XY, X'Y', X"Y", we obtain their respective 

 values, thus : 



In the first place Ave have, since A B = F F" 

 AB: GF' = FX:XY, 

 whence follows : 



-^_. FX.GF 



^^ - AB ' 



A . X 



or if we substitute for G F' its value -^ — 



^Y^A FX.x 



L AB • 



If now X represent a line such that 



A B : F X = X : a:, 

 then 



Secondly, since B C and F' X' are equal to the lines drawn 

 through I and Y' to G H parallel to A D 



B C : I H' = F' X' : F' H - X' Y', 

 whence 



T H' F' X' 

 "" — R C ^ '■^ 



or, since F' H = G H - G F' 



„, „, I H' . F X' ^ „, 

 - X'V = g-g + G F' - a. 



A . x' 

 If now for I H' and G F' we substitute their values — ^ 



— =^ — , we obtain 



and if by a?' we represent a line such that 



