This may be a long shot, but the names all match. I have a William C. Jakeway (also Jaques Jaquay, etc) born in 1770, his son Varnum was born 1796, who had his first son William around 1817 in NY. I do not have any more information regarding this William or of his middle name; however, it is possible that he was named after his grandfather and had a middle initial C. Also, this William's step-mother was Julia Ann Case Jakeways.
When I read your message, both the William C. and Julia names seemed to fit in directly with this family. If your Julia was born 1845, this William, son of Varnum, would have been about 28 at the time, so the time-frame also fits to have possibly been her father.
However, I admit that William seems to have been quite a popular name among the Jaquays, Jaques, Jakeways, and many other spellings of the name.
If I can provide anymore information please let me know. As your message is a few years old, I don't even know whether you will read this, but I would be interested in any of the other Jakeway names of the family or history you might have.