In Nancy Drew: Treasure in the Royal Tower, you follow clues in the library to open a globe, then enter a combination above the fireplace, and reveal a secret study. Locate the globe in the right corner, and click towards the top of the globe. Change the compass arrow to point towards Wisconsin, which is at the 90 degrees West longitude. (This information can be found in the Atlas book over at the desk by the hole in the wall.) Pull the knob on top to open the globe compartment.
Read the note inside. The sketch is of a sextant, and the numbers you need to note are -15, 10, -5.
Close the globe and walk over to the fireplace. Examine the poem on the mantel. The sextant can be found behind it. Hover your cursor to the right or left in order to move the dial. The red button in the center is the reset button. The green button “enters” your selection. Move the dial to -15 and hit the green arrow, then 10 and -5, respectfully.
Successful entering will result in a loud creaking sound. Climb the spiral stairs, then turn left, and you will see the secret study.