NOTES
The same effect will reshape the Ring – even though the gravity of the Sun at the surface of the Ring is quite small, the force toward the center of the Ring will tend to create a “hump” of soil and water. When I first realized that Ringworld would have this kind of curvature I thought I had found a way to navigate on the Ring – because an instrument like a sextant could be used to measure the local slope (by observing where the Arch was with respect to the stars) wherever you were on the Ring, telling you where you were. I also was concerned that this curvature would ruin the scene where one character can see both rim walls at once. However, when I did the calculations, the maximum slope turned out to be very small indeed (making use of a sextant problematical), and the rise in the middle was only 1.3 km, which would not interfere with seeing the 1000-mile-high Rim walls. However, this solar tide effect does affect the idea of “bobbing” the Ring for seasons. Here’s why.
P.S. Note that I didn’t calculate the effect of the gravity of the Ringworld floor material, or of the soil, rock, water, etc. on the Ring. It’s easy to see that the effect of each of these would be to increase the size of the hump, though.