Page:Scientific Memoirs, Vol. 2 (1841).djvu/431

$u={\frac {u_{1}r}{r+R}}$.

The intensity of the electricity received by the body will, therefore, be the more nearly equal to that which the circuit possessed at the place of contact before being touched, the smaller $R$ is with respect to $r$; it will amount to the half when $R=r$, and become weaker, as $R$ becomes greater in comparison with $r$. Since these changes are merely dependent on the relative magnitude of the spaces $r$ and $R$, and not at all on the qualitative nature of the circuit, they are merely determined by the dimensions of the circuit, nay, even by foreign masses brought into conducting connexion with the circuit. If we connect this fact with the theory of the condensor, we arrive at an explanation of all the relations of the galvanic circuit to the condensor, noticed by Jäger^[1], which is perfectly surprising. I content myself with regard to this point to refer to the memoir itself, to give room here for the insertion of some new peculiarities of the galvanic circuit.

The mode of separation of the electricity, within a homogeneous part of the circuit, is determined by the magnitudes of the dips of the lines $FG$, $HI$, $KL$, (fig. 3,) and there again by the magnitudes of the ratios ${\frac {GF'}{AB}}$, ${\frac {IH'}{BC}}$, ${\frac {LK'}{CD}}$. But, as was already shown,

$GF'={\frac {A}{L}}\cdot \lambda ,\qquad IH'={\frac {A}{L}}\cdot \lambda ',\qquad LK'={\frac {A}{L}}\cdot \lambda ''$;

hence it may be seen, without much trouble, that the magnitude of the dip of the line corresponding to any part of the circuit, and representing the separation of the electricity, is obtained by multiplying the value ${\frac {A}{L}}$ by the ratio of the reduced to the actual length of the same part. If, therefore, $(\lambda )$ represent the reduced length of any homogeneous part of the circuit and $(l)$ its actual length, the magnitude of the dip of the straight line belonging to this part, and representing the separation of the electricity, is

${\frac {A}{L}}\centerdot {\frac {(\lambda )}{(l)}}$,

which expression, if we designate by $(\chi )$ the conductibility,

1. Gilbert's Annalen, vol. xiii.