How did he get away with it for so long before wife #1 caught on?
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It didn’t. Emma knew about polygamy after the second or third wife (her best friend Eliza Snow). She had gone to visit her parents and returned to find a pregnant Eliza in her house in her robe. She pushed Eliza down the stairs according to her report.
The revelation on polygamy specifically tells Emma to obey Joseph. She gave in at least once, but had a change of heart a few hours later.
He did most of it on the sly. There is a very sad account, of Emma at a Relief Society (women’s aux) where she is giving a speech on monogamy and the importance of it, not knowing that at least 1/3 of the women in the audience (including Eliza Snow at that point) were ‘married’ and had had sex with her husband.
History has recorded how Emma felt about Eliza; but I wonder how ELIZA felt about EMMA?