This is not a common idiom in modern English.
Grandfather clocks were often powered by weights. As the weights descend they provide the energy to drive the clock mechanism. Sometimes a separate weight was used to provide energy for the chime. The descent of the weights could give rise to a local or dialect expression "I heard the time drop". I've not found any direct evidence for this, but it is possible.
Much of the language we use for time now existed in the 1880s. Digital time was not known, so people would say "Quarter to three" instead of "two forty-five". In the 1880s word like "to-day" were still often hyphenated. Accurate clocks in the home were rarer. In villages most people would depend on the church clock. Only the relatively wealthy could afford a house clock or a watch. Farms would still run to the sun.