Time constants

From Glossary of Meteorology
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time constant

(Also called lag coefficient.) Generally, the time required for an instrument to indicate a given percentage of the final reading resulting from an input signal; the relaxation time of an instrument.

In the general case for instruments such as thermometers, with responses exponential in character to step changes in an applied signal, the time constant is equal to the time required for the instrument to indicate 63.2% of the total change, that is, the time to respond to all but 1/e of the original signal change.