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]
Figure 1.
Functional reconstruction of the water-bath comparison described by Charles-Édouard Guillaume, with movable rods and an instrument baseline that can drift
. Details.
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.

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