Go left, pass two rooms. You will come to the rotating room. Go forward and click the pink egg in the wall. Talk with Thomas Jeffersant - he is in need of goose's feather. Look at the declaration and at the seals: purple, dark green and yellow.
Leave the rotating room and go right, pass three rooms. You will come to the place with cannon.
Click the yellow cover. There is a puzzle. You have two hints: from Lincoln and Jeffersant. Click the top seal 3 times - it becomes purple, click the middle once - becomes dark green and 4 times the bottom seal - it becomes yellow. Now click the upper arrow twice, the middle 3 times, and the bottom once - just as Lincoln said. Push the red button. The solution is on the screenshot below.
The cannon will fire and the ball will hit the bird. Take a feather and give it to Jeffersant (go back left).