= Guillaume thermal expansion experiment
{c}
<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.<Nobel Lectures, Physics 1901–1921/Invar and Elinvar by Charles-Édouard Guillaume>[Nobel Lectures, Physics 1901–1921; Invar and elinvar, lecture 11 December 1920, pp. 444–448: motivation and comparator; pp. 451–453: composition, treatment and temperature limits]{ref}
\Image[/guillaume-expansion-comparator.png]
{title=Functional reconstruction of the water-bath comparison described by <Charles-Édouard Guillaume>, with movable rods and an instrument baseline that can drift}
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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