How do scientists measure the increase or decrease of carbon dioxide in the atmosphere ...?

Question

atmosphere over long periods of time (say, from hundreds or thousands of years ago)?

Please cite a sourceee.

Answer 1

Hope this helps....Search the internet using "carbon dioxide measurement method" and you will get lots of hits:

Carbon Dioxide Research Group, Scripps Institution of Oceanography, University of California, La Jolla, California 92093-0444, U.S.A.
Period of Record
1958-2004


Methods
Air samples at Mauna Loa are collected continuously from air intakes at the top of four 7-m towers and one 27-m tower. Four air samples are collected each hour for the purpose of determining the CO2 concentration. Determinations of CO2 are made by using a Siemens Ultramat 3 nondispersive infrared gas analyzer with a water vapor freeze trap. This analyzer registers the concentration of CO2 in a stream of air flowing at ~0.5 L/min. Every 30 minutes, the flow is replaced by a stream of calibrating gas or "working reference gas". In December 1983, CO2-in-N2 calibration gases were replaced with the currently used CO2-in-air calibration gases. These calibration gases and other reference gases are compared periodically to determine the instrument sensitivity and to check for possible contamination in the air-handling system. These reference gases are themselves calibrated against specific standard gases whose CO2 concentrations are determined manometrically. Greater details about the sampling methods at Mauna Loa are given in Keeling et al. (1982) and Keeling et al. (2002).

Answer 2

Do your own homework.