Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/447

The most important part of the method consists in measuring the resistance, not of the whole length of the conductor, but of the part between two marks on the conductor at some little distance from its ends.

The resistance which we wish to measure is that experienced by a current whose intensity is uniform in any section of the conductor, and which flows in a direction parallel to its axis. Now close to the extremities, when the current is introduced by means of electrodes, either soldered, amalgamated, or simply pressed to the ends of the conductor, there is generally a want of uniformity in the distribution of the current in the conductor. At a short distance from the extremities the current becomes sensibly uniform. The student may examine for himself the investigation and the diagrams of Art. 193, where a current is introduced into a strip of metal with parallel sides through one of the sides, but soon becomes itself parallel to the sides.

The resistance of the conductors between certain marks $S,\,S'$ and $TT'$ is to be compared.

The conductors are placed in series, and with connexions as perfectly conducting as possible, in a battery circuit of small resistance. A wire $SVT$ is made to touch the conductors at $S$ and $T$, and $S'V'T'$ is another wire touching them at $S'$ and $T'$.

The galvanometer wire connects the points $V$ and $V'$ of these wires.

The wires $SVT$ and $S'V'T'$ are of resistance so great that the resistance due to imperfect connexion at $S,\,T,\,S'$ or $T'$ may be neglected in comparison with the resistance of the wire, and $V,\,V'$ are taken so that the resistance in the branches of either wire leading to the two conductors are nearly in the ratio of the resistances of the two conductors.

Calling	$H$ and $F$ the resistances of the conductors $SS'$ and $TT'$.
"	$A$ and $C$ those of the branches $SV$ and $VT$.
"	$P$ and $R$ those of the branches $S'V'$ and $V'T'$.
"	$Q$ that of the connecting piece $S'T'$.
"	$B$ that of the battery and its connexions.
"	$G$ that of the galvanometer and its connexions.

The symmetry of the system may be understood from the skeleton diagram. Fig. 33.

The condition that $B$ the battery and $G$ the galvanometer may be conjugate conductors is, in this case,

${\frac {F}{C}}-{\frac {H}{A}}+\left({\frac {R}{C}}-{\frac {P}{A}}\right){\frac {Q}{P+Q+R}}=0.$