Gilbert B Norman wrote:"Ex Libris" is a book "Passenger Trains and Terminals" by John Droege (NY, 1919) which, while describing Hudson Terminal, notes that a South Tunnel was "to be built".
I don't think it ever was, but am I mistaken?
Parts were. There is a postcard showing a dual portal at Hudson Terminal, despite the eastbound and westbound tubes coming in very far apart. The other half of the dual portal was for a link to connect Hudson Terminal direct to Erie (later Pavonia, now Newport). There are small sections of lined tunnel passing diagnonally underneath Tunnel E (WTC -> EXP). There is no access to them. There is (or was, haven't looked since the post-9/11 rebuild) a set of "barn doors" on the left side of Tunnel F (EXP -> WTC) which led into a short section of tunnel and muck-out, approximately under the old pier line.
You can see the Erie line as the white diagonal lines between the yellow (existing tunnels) lines in this picture:
That also explains why the Scribner's drawing shows a full X crossover on 2 levels at the caisson instead of what you can see now (there's a signal shack in the unused Erie portal - that's where you see the Christmas tree / American flag lights):
]
If this seems like a wasteful expense to simply duplicate existing service, you're looking at this with a modern mindset. Back then, the Pennsylvania Railroad (served by Exchange Place), the Erie (served by Newport), and the DL&W (served by Hoboken) were very independent. Talking Erie customers from Hudson Terminal to the Erie station via their competitor's basement (Exchange Place) was looked upon with disfavor by all parties. By the time anybody thought about building these (and other things, like extending to Grand Central, making the whole system 4-track instead of 2-track, etc.) all available capital was tied up in stock speculation (later leading to the crash and Great Depression) and the Hudson River Vehicular Tunnel (later named the Holland Tunnel after one of its deceased Chief Engineers) was well under construction.
Regarding building to the CRR terminal (now Liberty State Park), there were a number of options considered. The one you can still see today is at Grove Street - leaving Grove St. toward Journal Square, you can see a well-lit large set of electrical equipment to your right just after leaving the station. There's another one of those metal signal sheds in the portal that would have led to CRR. On the other side of the station, for many years there was a large dark opening, which they eventually covered up with plywood. Don't confuse either of these with the Y track lead at the east end of Grove St. westbound - that went up to a now-removed rail yard.
Another alternative, not shown on the above drawing, is conversion of the branch south of Newport, where trains go either to Exchange Place or to Journal Square, into a triple branch with a center route continuing south toward CRR. The only sign of this is a brief section of F track (GROVE -> EXP) which is in lined metal rings for strength - the rest of that part of F is cut-and-cover with concrete lining. Something similar was done where the NJ-bound tracks from 33rd Street split to Hoboken or Newport - a central branch was planned there to continue west toward Newark after joining the tracks from Erie - you can see that on the drawing.
At Liberty State Park, out in the (when I was there last many years ago) tick-infested fields of long un-cut grass and weeds, are some ring segments lying on the ground. I don't know if these were put there by the H&M, dumped there later, or how else they could have gotten there.