Hi Maureen
Thanks for such a rapid response!
Arthur (Anton Martinus Nielsen) left Denmark as a young man and emigrated to Australia. I found a number of 'possible' members of his family in Denmark in the IGI - parents and three brothers all born in Aarhus.
Then I found a genealogy website in Denmark which seemed to indicate that there were three sisters born to this same couple (who had the four boys) but the girls, who were also all born in Aarhus, have the surname Andersen not Nielsen.
From that website it would appear that Arthur's father dies and his mother remarries. Frederikke Frandsen b. 1869 is the child of his mother's second marriage and his half sister. And given that I have found a record of a Frederikke Frandsen arriving in New York in 1890, it seemed plausible that she might have married a Mr Matson/Madsen and become the lady living in Richmond Valley, Stratton Island who Arthur travelled all the way from Australia to visit.
Mrs Matson may also have lived in Philadephia. The death notice for Arthur's wife, who dies in Sydney in 1943, says that she has been to New York and Philadelphia.
In 1928 Arthur arrives in Seattle/Vancouver and Victoria and is then said to be traveling on to New York. I guess the boat journey from Sydney via Auckland, Suva and Honolulu took him to the west coast.
Cheers
Mumfy