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Indeed it was misleading. "The basis for vaccination began in 1796 when an English doctor named Edward Jenner observed that milkmaids who had gotten cowpox did not show any symptoms of smallpox after variolation. The first experiment to test this theory involved milkmaid Sarah Nelmes and James Phipps, the 9 year-old son of Jenner’s gardener. Dr. Jenner took material from a cowpox sore on Nelmes’ hand and inoculated it into Phipps’ arm. Months later, Jenner exposed Phipps a number of times to variola virus, but Phipps never developed smallpox." from https://www.cdc.gov/smallpox/history/history.html