= Torsion balance zero drift
{title2=$\beta_{\mathrm{eq}}=\beta_0(t)+\tau_{\mathrm{ext}}/\kappa$}
<Torsion balance zero drift> is slow motion of the unloaded reference <angle> $\beta_0(t)$ during a measurement. If the <torsion constant> remains fixed, a constant applied <torque> gives $\beta_{\mathrm{eq}}=\beta_0(t)+\tau_{\mathrm{ext}}/\kappa$. For two equal and opposite applied <torques> measured at the same reference zero, their <equilibrium> <angles> differ by $2\tau_{\mathrm{ext}}/\kappa$. A stable offset cancels; a changing zero contributes $\beta_0(t_+)-\beta_0(t_-)$ and does not cancel automatically.
A simple symmetric sequence makes the limitation explicit. Let $b_1,b_2,b_3$ be settled <equilibrium> <angles> for applied <torques> $+\tau,-\tau,+\tau$ at equally spaced times $t_0-h,t_0,t_0+h$. If the unloaded zero is linear in <time>, $\beta_0(t)=u+vt$, and $\kappa$ and $\tau$ remain fixed, then
$$
\widehat\tau=\frac\kappa2\left(\frac{b_1+b_3}{2}-b_2\right)=\tau.
$$
The arithmetic average of the outer zero values equals the middle zero, so both the constant offset and linear drift cancel. Curved zero motion, unequal time spacing, changing <torsion constant>, changing signal strength, or unsettled <oscillations> violate these assumptions. This is an algebraic control example, not a claim that every <torsion balance> follows a linear drift law.
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