Emma Sophia Petersen
Her name is listed as "Emma Sophia Petersen" on FamilySearch. The surname is spelled "Peterson" on the manifest of the ship Thornton, the Deseret News roster of the Willie Company, and the Josiah Rogerson account published in the Salt Lake Herald.
The 1860 Utah census lists the surname of the children as "Smith."
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Emma Sophia Petersen (1850 - 1900) Profile