I'm working backwards on the William Harper (1844) line, so you might find some of this info useful. I don't know if this would be David or William's son though, as the previous posters pointed out. The Canada 1870 migration would seem to fit better with David, but the Christening date might be better with William. Let me know if you find out other details further back.
"William M. Harper was born in Campsie Glen, Scotland, Aug. 29. 1844. In 1868 he came to the United States, locating first at Lynn, Mass., where he married Mary Martin Tweed, a native of Glascow, Scotland. Later, they removed to Toronto, Canada, where they lived for ten years, and in 1880 came to Erie, Pa., where Mr. Harper became connected with the old Stearns Manufacturing Company and later engaged in the insurance business, in which he has ben actively engaged since 1890. He is still a very active man in his profession. Mr. and Mrs. Harper were the parents of six children, as follows: William Rae, an instructor in the public schools of New York City; James L., died in Chicago in 1892, but is buried in Erie; David W., the subject of this sketch; Margaret Martin, the wife of Milton Rowley, a manufacturer, lives in Erie; Eva Hay, married Jay D. Cudney, lives at Houston, Tex.; and Ruth D., married Robert Lee Sale, president of the Sale Lithograph Company, Buffalo, N.Y. Mrs Harper died Feb 15, 1898, at the age of 52 years, and is buried in Erie."
Source: History of Erie County, Pennsylvania
