Since this is right in the Cowgirl's backyard, I thought I'd share this and try to explain what's different, as well as expound on some of the more picayune aspects of New York City history.
First, the old map. Along the left edge runs the Hudson River, and along the right edge, the Harlem (it even says, "Harlem River". The squiggly shaded bit connecting them is the original flow of the creek. Light portions below it are Manhattan, above are the Bronx.
The "Scene of the Disaster" is an artifact of the image, and beyond the scope of our needs. The image comes from an article on a rail disaster there in the late nineteenth century.
What was done, a bit over a hundred years ago, is actually pretty simple. Follow the river with your eyes from the Hudson to the Harlem.
See that peninsula jutting down from the Bronx? That was cleaved right about at the three-way intersection, forming two tidal mudflats where the river used to be, and the cliff where the famous Columbia "C" is painted.
See how on the next, larger peninsula jutting north of Manhattan, there are two narrow inlets on either side? Well, they cut through there to connect them, and then filled in the part of the creek the flowed up north of there. This is the area known as Marble Hill, in "The Bronx" but technically part of Manhattan.
You can sort of make out Marble Hill from the following Google Earth snapshot:
Marble Hill today.
On the north side of the river, left of the bridge, that neighborhood that's sort of bounded in a circle? That's Marble Hill. Technically it's part of Manhattan and residents there serve Jury Duty in Manhattan (seriously: the judge will say "residents of Manhattan and [zip code of Marble Hill]").
And that's that. The goal was to create a shipping canal so that vessels could go from the Hudson to Long Island Sound without the trouble of heading around the Battery.
And that, as they say, is that. It's a good bet that the Cowgirl and friends could have taken the old route down to Hell Gate and back, and it might have been more interesting. All the same, we're happy for the modern route. After all, how else would we get to practice dodging Circle Line and Classic Harbor Line vessels?