
Brian B. answered 08/22/19
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The first part of your question is easy; the second is tricky and also quite interesting.
Alcoholism was, in the general view, very much a no-no for women. Drinking was what you did in bars ("saloons"), and saloons were for men. The alcohol-banning or "temperance" movement was, unlike many political movements of the time, largely led by women. The temperance movement, a very important and frequently successful one that passed many county and state laws, was in large part motivated by family trauma. Too many men earned a household's primary income, but then spent most of that income drinking at taverns so that their wives and children stayed desperately poor.
"Did women become alcoholics at the same extent to which men did?" feels like an easy "no", then, right? Not so fast. This was also the era of "patent medicines", where magazine ads and traveling "physicians" (not to be mistaken for real doctors) would pitch "medicinal" liquids that, they promised, would prevent or cure all sorts of ailments, from cancer to cholera to colic to "female complaints" to scarlet fever, tuberculosis, venereal diseases, and simple depression. Frequently, the "medicines" would contain around 20% alcohol (40 proof), as well as, perhaps, opium or morphine or cocaine, all of which were legal at the time. They weren't regulated prior to the Pure Food & Drug Act of 1906.
The result, then, is that while we suspect that more men than women were alcoholics in the 19th century, we don't have enough reliable data to say for sure. The only difference we're sure about is that most women alcoholics wouldn't have known that they were alcoholics. And some of them would have been completely sincere supporters of laws banning the sale of alcohol!