I would be surprised if there wasn't some relationship here, but I don't think your William was a brother, perhaps a nephew since there was a big age range in her siblings. Here's what I've learned about this family since my original posting:

Cornelius Arn m. Karoline Wilhelmina Bossert in 1816 in Germany. They came to Canada in/about 1850.
Children:

Regina Barbara Arn (b. Dec 12, 1816)
Cornelius Arn (b. March 27, 1818)
Carolina Catherina Arn (b. March 27, 1818)
Cornelius Arn (b. June 26, 1821)
Wilhelmine Arn (b. Sept. 17, 1822)
Regina Barbara Arn (b. August 1, 1824)
Regina Barbara Arn (b. March 19, 1826)
Magdalena Arn (b. May 21, 1827)
Elias Arn (b. October 31, 1828)
Karl Friedrich Arn (b. June 2, 1833)
Philippine Arn (b. June 3, 1833)
Juliana Arn (b. August 31, 1834)
Philippina Arn (b. February 23, 1836)
Christian Arn (b. July 14, 1837)
Magdalena Arn (b. November 10, 1839)
Rosina Arn (b. March 11, 1841)
Magdalena Arn (b. December 6, 1842)

I don't have much more information on this family, especially the siblings. Seems like I might have some information on the son, Cornelius's family, but will have to look for it. I originally thought that my Magdalena was his son (and he has children older than her!). When was your William born?