Carleton then launched his own offensive intended to reach the Hudson River, whose navigable length begins south of Lake Champlain and extends down to New York City. Control of the upper Hudson would enable the British to link their forces in Quebec with those in New York, recently captured in the New York campaign by Major General William Howe. This strategy would separate the American colonies of New England from those farther south and potentially quash the rebellion. Lake Champlain, a long and relatively narrow lake formed by the action of glaciers during the last ice age, separates the Green Mountains of Vermont from the Adirondack Mountains of New York. Its length and maximum width creates more than of shoreline, with many bays, inlets, and promontories. More than 70 islands dot the surface, although during periods of low and high water, these numbers can change. The lake is relatively shallow, with an average depth of . Running roughly from south to north, the lake's waters empty into the Richelieu River, where waterfalls at Saint-Jean in Quebec mark the northernmost point of navigation.