Info from Secretary of State's Site.
The first state capitol building in Jefferson City was built in the period of 1823-1826 and was destroyed by fire in 1837. A new capitol building had been approved at the time and was completed in 1840. The second capitol was destroyed by fire on February 5, 1911, when a bolt of lightning struck the dome. The present capitol was built in the period of 1913-1917 and stands upon the same spot as its predecessor, high atop a bluff overlooking the Missouri River.
Looking at these pictures one does not think about it, but as you will see as you scroll on through the pictures there is actually an internal dome and an external dome of the Capitol. The stained glass windows are on the internal dome, thus not visible from the outside and they do not get direct sunlight.