Tiz a "water dust-up":
Bring your water resistant field books.
DG
This could be a long & interesting case. My initial look at maps would lead me to favor the clammer, but the quality of lawyers & research will make a big difference. Also, getting a judge versed in the appropriate law could make a difference.
Best Evidence Would Be The Sand Hole Warrant
If the western boundary is The Sound, the New York State limit stands and the larger claim by Oyster Bay is disputed.
Paul in PA
This is going to become even more interesting after the boundary dispute is resolved. Whoever "loses" will probably persue litigation (punitive damages, loss of income, etc.) and all the attorneys will become wealthier!;-)
Headland to Headland
It seems like they are both using the Headland Method, just from different points.
As I recall (and I would have to review the books), there is a distance factor with the jurisdiction of municipalities and the definition of embayments.