Happily, I may have found our William on a passenger list. Details fit, so perhaps someone in Australia will recognize them.
The *SS Euripides* sailed from London England on 22 May 1924, bound for Sydney Australia, most likely not arriving until the month of June.
According to the manifest, William BAIN was 15 years of age, with his home address listed as Mossbank School, Willerston and/or Willirston, Glasgow, Scotland. Listed occupation was 'Farming'.
Mossbank School was an industrial school [borstal] at the time. William was the only passenger with Mossbank listed as residence.
Toni ~ Ontario Canada