From East Tennessee
New Market, Feb. 18.
--The work of re-enlisting goes bravely on — nearly all the troops having given unmistakable evidence that they are in for the war. Hampton's Legion have re-enlisted.
Privates Issue Morgan, of the 50th, and W. F. Gunoon, of the 24th Georgia regiment, were shot to-day, in the presence of their brigade, for desertion.