David Dobson has done a ton of research over the years about Scottish immigration to the Americas.
"The Scottish participation in the settlement of America dates from the early seventeenth century, and from that time until the American Revolution probably around 150,000 Scots emigrated to the New World. During the seventeenth century many Scots settled within the English, Dutch and French colonies, while others attempted to establish independent colonies in Nova Scotia, New Jersey, South Carolina, and at Darien (Note: Darien is the Scots' name for Panama. --GB). After the political union of Scotland and England in 1707 the Scots had unrestricted access to the English plantations in America. Emigration expanded slowly but steadily until 1736 when a combination of factors in Scotland and America stimulated emigration, especially from the Highlands. Although Scots could be found throughout the American colonies from Barbados to Rupert's LAnd, areas such as Georgia, the Carolinas, upper New York, Nova Scotia and Jamaica had the greatest concentration of Scottish immigrants. This then was the general pattern of Scottish immigration and settlement in colonial America."
Source - "The Original Scots Colonists of Early America"1612-1783, David Dobson
I highly recommend reading any of his publications though be prepared for lists, and lots of them. I am currently reading "The Scottish Surnames of Colonial America."
I have the Arthur surname in my family and here's what the book says - Arthur. Probably from the Gaelic "Artair", also MacArthur, from "MacArtair". Their traditional lands were in Lorne in Argyll. Isabel Arthur, from Edinburgh, emigrated to Philadelphia in 1775, and Duncan McArthur from Jura settled in North Carolina in 1754. Linked with the Clan Campbell or the ClanMacArthur."
If you have Scottish Quakers in your lineage then check out "Scottish Quakers and Early America, 1650-1700." Very interesting.
One of his newest releases is "Genealogy at a Glance: Scottish Genealogy Research" a 4 page laminated resource for conducting research. It includes tips, publications and in-line resources. (where would most of us be nowadays in our research without on-line resources.) I'm looking forward to getting my own copy and trying it out.