The concept of a "nurse" historically was the person doing a lot of the palliative care- soothing, caring, changing dressings, bathing, administering medications, and assisting the doctor. Similar to today, but particularly in an historic context the doctor really was the man (because only men were allowed to attend university in Western Europe in nearly all cases until the 19th c) who diagnosed, prescribed, and performed procedures- then left the more mundane palliative care to someone else.
Without getting too deep into the history of doctors, apothecaries, chirurgeons, barbers, midwives, etc- everyday care was generally left to housewives (for their own families), servants, or in special cases, women/men religious at places for the sick and injured, eventually called "hospitals" from the same root as "hospitality". Obviously in wartime the gender divide was more pronounced, but more formal wounded care was only on home soil- women rarely traveled to the battleground unless they were camp followers, women in service (i.e. laundresses), or otherwise attached to the army, and were generally not expected to involve themselves in medical treatment.
In the early modern era, a lot of the male mendicant orders changed their priorities a bit and the staffing of hospitals became increasingly associated with women religious (and sometimes male orderlies for the heavy lifting). Combine this with a lot of wars between 1600-1800, advances in epidemiology and germ theory, technological improvements in military technology with high attrition rates, exploding Industrial Revolution-era populations, and you end up with an overwhelmed medical profession struggling to keep up with demands for improved care, better nutrition, hygiene, and increased survival rates. Many doctors also tried to preserve the mystery of their order by clinging to the arcana of previous centuries- keep the brotherhood small and elite, then prices and respect stay high.
Hence Crimea. And the hideous, filthy, disease-ridden conditions that killed a lot more soldiers than bullets did. So when Flo arrived, armed with a peculiarly abrasive brand of tenacity, she decided to do something about it- to the dismay of the men in charge. She was one of the first to combine the idea of women nurses (palliative care) with battlefield trauma care, and since a lot of the work involved housewifely things like cleaning, bathing, and changing linens she managed to establish a place for women in medicine. Then women graduated to assisting with operations, anesthesia, triage, and thus is born the modern "nurse".
There are a lot of feminists out there who say it became a woman's profession because nursing involved all the things male doctors didn't feel like doing- and history pretty much supports that. There was also a lot of 19th c moralizing about how women were inspirational, "angels of the battlefield", giving our dear boys the care their own mothers can't... which of course limited women to their "sphere" in medicine as in many other things during that period.
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