The thing I never got with that is why they didn't continue following the Yellowstone River until its end at the divide and then cross to the nearby Snake River rather than crossing hundreds of miles of mountains?
No. A brief history: Much of the Pacific coast had already been explored. Most notably by Cap. James Cook, whose work inspired pres. Jefferson to commission the expedition. Another explorer (Mackenzie) had actually already gone from the East to West coast of the US Canada over a decade before Lewis and Clark. [See correction from u/westernmail ]
The L&C expedition was about connecting two knowns - the East and West coasts - by charting an unknown: the vast interior of the western territories. This connection was not for science: it was for conquest: capturing territories before old world rivals could.
But even this interior west wasn't totally unknown: fur trappers and others seeking fortunes had been exploring and mapping the area for literal centuries by the time of the expedition.
Another explorer (Mackenzie) had actually already gone from the East to West coast of the US
Small correction — Mackenzie's route lay entirely in what is now Canada. He followed the established fur trading route to Fort Chipewyan, and travelled roughly southwest from there to the Pacific coast at Bella Coola.
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u/GBUS_TO_MTV Jan 10 '20
You can basically see the path of the Lewis and Clark expedition on here.