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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, $a+bt$. Thenbecause both pairs have mean time $3\Delta t/2$. The constant offset and linear drift cancel. With a further drift term $c{t}^2$, 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.

A physicist.^[ref]

Charles-Édouard Guillaume sought affordable, stable length standards. His 1920 lecture describes two micrometer microscopes on stone supports sighting marks on a rod immersed in water. Their separation was not fixed: one method alternated the sample with a reference in a second trough at nearly constant temperature. His relative method compared sample and platinum–iridium reference in the same bath, adding the reference's known expansion to the measured difference. Composition and treatment affected the nickel–iron alloys; low expansion held over a limited temperature range.^[ref]

The differential length comparator calculation explains why a calibrated reference is needed even when its expansion is larger than the sample's. Keeping both rods in the same bath targets one source of systematic error; allowing for changes in the instrument baseline targets another. Discovering a low-expansion alloy and demonstrating its dimensional stability are connected experimental tasks.

Awarded to Charles-Édouard Guillaume for precision measurement through anomalous properties of nickel–steel alloys. The Guillaume thermal expansion experiment explains how a reference comparison reveals low thermal expansion.^[ref]