The 1880s refers to the decade 1880-1890. By the 1880s... would refer to a situation that began to exist during that decade or before it, where the exact date is unknown or unknowable.
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soheil1Why not by the 1890?(or should it be by the 1889?)The phrase is usually used when you are discussing a situation that existed at a particular time, without being specific about the exact moment it came into effect. In the case of my example, we are describing the situation that existed during that decade: the population of the city was 200,000, or a li