= Solution
For <Ørsted's experiment>, place a long straight conducting wire close to and parallel with a freely moving horizontal compass needle. With no <electric current>, the needle follows the horizontal terrestrial <magnetic field>. Closing the circuit deflects it; reversing the <electric current> reverses the deflection, and moving the wire from above to below the needle also reverses the effect. For a long straight wire, the modern idealization is
$$
B_{\rm wire}=\frac{\mu_0 I}{2\pi r},
$$
with the circular direction given by the <right-hand rule>. These controls distinguish a magnetic action of the current from a fixed magnetized piece of wire or a mechanical disturbance.
<Nobili's astatic galvanometer> increases sensitivity in two ways. A coil with many turns multiplies the magnetic action of a given <electric current>. Two nearly equal magnetized needles are rigidly connected with opposite <magnetic dipole moments> and suspended by a fine thread. Their torques in the approximately uniform terrestrial field nearly cancel. In a common arrangement one needle lies inside the coil and the other above it, outside its strongest field, so the coil retains a substantial torque while the terrestrial restoring torque is reduced. A weak residual magnetic or suspension torque still provides a reproducible equilibrium; “astatic” means nearly cancelled terrestrial torque, not magnetic shielding. A museum instrument dated 1840 has many turns of fine wire and is identified with measurements of muscle currents.<Astatic Galvanometer, Nobili Pattern by Museo Galileo>[Inventory 1417: construction and muscle-current provenance]{ref}
For weak physiological sources, use \b[a long fine-wire winding with many turns], rather than the short thick winding appropriate to a low-resistance thermoelectric source. The physiological source commonly has a large effective <internal resistance>; a moderate added coil resistance is then outweighed by the gain in turns. This is a source-and-detector matching argument, not a claim that arbitrarily much wire always improves sensitivity.
For example, at fixed mean turn length and fixed copper winding volume, $R_{\rm coil}=aN^2$. For source <electromotive force> $\mathcal E$ and resistance $R_s$, the small-angle driving torque is proportional to
$$
\frac{N\mathcal E}{R_s+aN^2}.
$$
Differentiation gives its maximum at $\boxed{R_{\rm coil}=R_s}$. This simple <optimal turn count for fixed winding volume> model explains why high-source-resistance work favors more turns, while also exposing the limit. Actual instruments additionally trade response time, damping, geometry and source loading against their steady deflection.
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