 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 120 @-@ mile ( 190 km ) length and 12 @-@ mile ( 19 km ) maximum width creates more than 550 miles ( 890 km ) of shoreline , with many bays , inlets and promontories . More than 70 islands dot the 435 @-@ square @-@ mile ( 1 @,@ 130 km2 ) surface , although during periods of low and high water , these numbers can change . The lake is relatively shallow , with an average depth of 64 feet ( 20 m ) . 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 . 
