A book I’d read about the history of New Jersey mentioned something usable for a real-world-based problem in fraction manipulation, for a class which was trying to get students back up to speed on arithmetic on their way into algebra. It required some setup to be usable, though. The point is a property sale from the 17th century, from George Hutcheson to Anthony Woodhouse, transferring “1/32 of 3/90 of 90/100 shares” of land in the province of West Jersey. There were a hundred shares in the province, so, the natural question to build is: how much land was transferred?
The obvious question, to people who failed to pay attention to John T Cunningham’s This Is New Jersey in fourth grade, or who spent fourth grade not in New Jersey, or who didn’t encounter that one Isaac Asimov puzzle mystery (I won’t say which lest it spoil you), is: what’s West Jersey? That takes some historical context.
New Jersey as we know it was formed when the English occupied the Dutch colonies in New Amsterdam, by the expedient of sending an army bigger than the whole population of New Amsterdam and waiting for the Dutch population to count; besides what’s now New York and Albany, they also took the Dutch holdings between the North River (the Hudson) and the South River (the Delaware), including some former Swedish colonies and various Leni Lenape populations. It, along with New York, and various pieces of New England and Maritime Canada, was the domain of James, Duke of York, who’d go on to gain fame by making the Glorious Revolution possible.
The Duke of York, being aristocracy, was in debt, so he sold off New Jersey to Lord Berkeley of Stratton and to Sir George Carteret. From 1674 to 1702, New Jersey was split into East Jersey and West Jersey, with their own capitals and constitutions and an endless set of lawsuits regarding property rights, since among other things James didn’t seem to see much reason not to give or sell title to land in New Jersey just because Berkeley and Carteret were doing the same with the same land, at least until their debts forced them to sell off their rights to other groups (the Quakers, in West Jersey).
The division of New Jersey produced a lot of political problems, notably because James seems to have tried transferring sovereignty to his subjects, and the rights were ultimately placed in Boards of Proprietors for East and for West jersey, which is the sort of thing that gets governments all tense when they notice it. The Boards of Proprietors were eventually convinced to give up their governmental powers, although they retained ownership of unclaimed land within the province, later the state. These boards would become some of the longest-lasting corporations in the United States; the Board for East Jersey was in independent existence until 1998, when it was finally determined there wasn’t any more unclaimed land in what was formerly East Jersey. The West Jersey board still exists, the last time I checked, with meetings scheduled for the third Tuesday of May, in case you’re not doing anything that day.
So that’s what West Jersey was. The question is: how big is it? When I adapted this to a word problem I couldn’t find a simple answer. The division was, mostly, based on the Keith Line, a line starting near Little Egg Harbor township and running northwest. If you look at a map of New Jersey’s counties, you can see its traces as the straight line running to the east (mostly) of Burlington and Hunterdon counties. It’s even more obvious if you look at the map of municipalities. But the line doesn’t go all the way from the Atlantic to the Delaware river — as was tradition for this sort of thing, surveyor George Keith wasn’t able to finish his work before political conflicts made him stop, and there were other attempts at dividing the territory.
Even if we supposed the line divided New Jersey evenly — and there’s not much reason to think it would — we couldn’t just take the current area of New Jersey — according to Wikipedia 8,721 square miles — and divide that by two. As with every colonial charter the exact bounds are disputable; the declaration that New Jersey’s border should run along the Delaware “to the northward as far as the northward most branch … which is in latitude 41 degrees, 40 minutes” ran afoul of the Delaware river having no such branch. New Jersey maintained it should have the land up to the northernmost extent of the Delaware River, a good bit farther north than the current boundary. New York won that border squabble.
Worse, even if we were sure just how much land might be called New Jersey in the late 17th century, it’s not clear the Keith Line would be the whole story on the dividing point. The Keith Line only reached as far as the Raritan River; the rest of the division, the Coxe and Barclay line, follows an irregular pattern that to my untrained eye looks like it’s probably near where the highlands divide between rivers that flow to the Delaware and rivers that flow to the Atlantic directly.
At this point, since I wanted to use this for a problem, I needed some estimate of the area of West Jersey. The thing to really do would be to find out what the Board of Proprietors thought its area was. But there are some things the Internet just isn’t very good at, as a source: the Boards of Proprietors have barely any Internet presence, one consisting mostly of popularizations mentioning this little land-owning oddity; they don’t even rate their own Wikipedia entries.
So in writing this up I gave in and just divided the area of New Jersey, as it’s presently constituted, in half. But I did include the warning that “if the area of West Jersey was 2,421,120 acres”, which sadly does give the impression that this actually was the area. For the sake of the homework problem it’s not important, and the mathematical work would have been the same if we had been talking about the divisions of an imaginary land. But I knew, writing the question, that historians — people who try to come up with some meaningful answer to questions like “how many people died in the Thirty Years War” or “how much wealth was created by the McCormick Reaper” — would snort derisively at me if they ever suspected I existed.
Later research, I should say, came to my rescue: one Oscar McMurtrie Voorhees gave in 1906 a speech, which became a 21-page tome called The East And West Boundary Line Controversy. According to Voorhees’s work (I admit I skimmed), West Jersey received about 5,403 square miles, and East Jersey 2,392 square miles. This adds up to a total of 7,795 square miles, which Wikipedia disagrees with, so, again, I feel all the more sympathetic to historians trying to extract useful demographic and economic data from the record. I can’t even get the area of my home state sorted out.
In any case, taking Voorhees’s data, the implication is that West Jersey had about 3,457,920 acres to its name. That’s the important information needed to say how many square acres George Hutcheson transferred to Anthony Woodhouse.
Well, almost. The transfer was of 1/32 of 3/90 of 90/100 shares, and there were 100 shares in West Jersey. But, do we know that the shares were all the same size? To the modern perspective it may seem obvious that each share should be of equal size; but to the modern perspective, land is pretty much something to look at and maybe build a house on. To the 17th century perspective, though, land is more likely something to farm. A share, small in acreage but highly productive, might be worth as much as a vast acreage with lousy crop yields.
This isn’t my fantasy: England and Wales formerly used the “hundred” as a measure of area, and this was a spot of variable acreage, roughly (originally) enough land to sustain about a hundred households. (One of them, the Chiltern Hundreds, still has a shadowy existence as a way for members of Parliament to leave office without resigning, as they’re not permitted to resign from the House of Commons. They may instead apply to the Crown for appointment as Crown Steward for the Chiltern Hundreds, which is granted automatically, and the obligation to the crown thus assumed overrides the obligation to one’s constituents that they could not just walk away from.)
So, to get this problem exactly right, I would need to find out just which share George Hutcheson and Anthony Woodhouse were involved in, and whether the shares of West Jersey were of equal size after all.
For this class, though, I again swallowed my concern that I get this detail exactly right, and said, “if” the shares are all of the same size. I could only hope not too many people rely on a prealgebra homework question as a source for information about land distribution in colonial New Jersey.