William's parents are listed as Hans Parsons and Christina Olson, with his birthplace listed as Ystad, Sweden in 1841. Genealogists have searched Ystad birth records, to no avail. Caroline Bjorkander's family was from Orebro.
In the 1880 New York City census, the Parsons are listed as living in Manhattan, 155 E. 26th Street, with him being listed as in "mining." His age here is given as 10 years older...born 1831/32.
That same year, a "William J. Parsons" that we believe to be the same individual is listed in the New York City Voters' list living on the same street.
Three years later, William Parsons is listed as "farmer" on his Swedish father-in-law's estate inventory, leading a researcher to wonder if he changed professions and was no longer living in New York City proper, as NYC directory analyses are somewhat inconclusive because there were a number of William Parsons and several were "brokers." Some can be ruled out, but others perhaps not identifiable as William remain. The Parsons [at least his widow] seem to have changed addresses fairly frequently.]
We do not know if William had siblings, but presume so. There are no family documents about this either way.
In either December, 1885 or 1886, a child believed to be that of William and Caroline, "Marie Louise Parsons," was born. The birth certificate has not been found,but the birth date has been extrapolated from other documents. There is an anomaly about MLP's birth date because it is given as 1880 in the 1900 NYC census. That NYC census lists "Carrie Parsons," "Mary Parsons," and Charles Burgunder [Bjorkander] as living together.
William does not appear in the NYC Death Index, as far as we can tell [unless his name is extremely misspelled], nor in the 1885-1891 deaths for Manhattan, as hand searched by a New York genealogist. New York State deaths were searched for the same time period, and none recognizable as our William Parsons is listed there. No Manhattan probate records for him appear either.
By the 1893 New York City directory publication, Caroline is listed as widow of William, and still a dressmaker. Thus we believe he had died by then, though divorce is a possibility, given the lack of a death certificate for William.
At the moment, everything else about William Parsons is a mystery.