= ABBA measurement sequence
{c}
{title2=$\widehat{B-A}=(y_1+y_2-y_0-y_3)/2$}
Alternating sample and reference readings can suppress instrument drift. In this original four-reading model, measure objects $A,B,B,A$ at equally spaced times $0,\Delta t,2\Delta t,3\Delta t$. Assume the objects are stable during that short sequence and each reading is its object's <length> plus the same <affine function> of time, $a+bt$. Then
$$
\widehat{B-A}=\frac{y_1+y_2-y_0-y_3}{2}=L_B-L_A,
$$
because both pairs have mean time $3\Delta t/2$. The constant offset and linear drift cancel. With a further drift term $ct^2$, direct substitution instead leaves bias $-2c\Delta t^2$. A shorter sequence reduces that term, but neither this ordering nor averaging corrects unequal <temperatures>, sample changes or reference <measurement uncertainty>. This is a modern illustrative protocol; the historical account below establishes alternation, without attributing this particular four-reading sequence to <Charles-Édouard Guillaume>.
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