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A liquid-in-glass thermometer has a bulb connected to a narrow graduated capillary. Thermal expansion of its liquid relative to the glass raises or lowers the column. A simple linear model iswith capillary area $A$ and volumetric expansion coefficients $\beta$.

For the historical Celsius graduation, establish an ice point in an equilibrium mixture of pure ice and water, and a steam point in saturated steam at standard atmospheric pressure, here a barometer height of $760\mathrm{mm}$. Mark $0^{\circ }\mathrm{C}$ and $100^{\circ }\mathrm{C}$, then divide the interval into one hundred equal parts. This is a historical two-fixed-point instrument calibration, not the modern definition of the kelvin or of Celsius temperature. Nonuniform capillary area and nonlinear expansion limit exactness.

Bulb contraction raises the column and makes the reading too high; retained expansion makes it too low. Glass volume changes with age and thermal history; heating can cause temporary zero-point depression followed by slow recovery. Rechecking the ice point detects a shifted zero, although it does not diagnose every scale error.^[ref]