129) “To quote William Carpenter, “Why, in the name of common sense, should observers have to fix their telescopes on solid stone bases so that they should not move a hair's-breadth, - if the Earth on which they fix them moves at the rate of nineteen miles in a second?”

Mr Dubay would be well advised not to make this point, because it highlights a piece of evidence that destroys his flat earth argument; astronomical telescopes need motorised equatorial mounts, 

otherwise they drift off their targets as the earth rotates. Anyone with a telescope can confirm this, by simple experiment, and it could not happen within the motionlessness flat disk world Mr Dubay imagines. See more at the end of this point.

So, on his "Why stone bases" question:

The lateral motion of the earth is too small to have an effect in the time that a telescope is used.   Because the distances between stars are almost unimaginably huge compared to the motion of the Earth round the sun, and of the Sun around the Galaxy, this makes little difference.

However, two other effects do make a difference:

a) Simple wobble - if you have ever tried to use a telscope on a wobbly tripod, you will understand this one:

b) The rotation of the earth on its axis, which changes the angle oe of view, rather than moving the telescope a little sideways) 

In half a year, the earth move roughly 186 million miles around the sun. Sounds a long way? Yes, but the distance to the nearest star, Proxima Centauri, is 4.243 light years. One light year is 5.88 trillion miles . So the distance to the nearest star is 2494884000 million miles! Or 13413355 times the distance the earth moves from one edge of it’s orbit to the other. See why that little motion is too tiny to disturb a telescope’s aim?

What does make a difference is the rotation of the earth on its axis. That introduces a large shift in the angle of view – which is just what we see. Again, the appearance of things matches what we’d expect in a scientifically sound universe.

The need for an equatorial mount shows that we live on a rotating world.

Here's why talking about telescope mounts destroys a flat earth perspective.

If astronomers really put their telescopes on a flat, fixed base, they have to keep realigning them every few minutes or seconds, depending on how far away the object they are studying is. I’ve seen this myself when using a telescope on a fixed mount.

The green equatorially mounted telescope rotates at the same rate as the earth but in the opposite direction, while the red telescope is not driven.
https://en.wikipedia.org/wiki/Equatorial_mount

That’s why modern astronomical  telescopes all have equatorial mounts, like this:

http://www.telescope.com/Mounts-Tripods/Equatorial-Mounts-Tripods/pc/2/34.uts

https://en.wikipedia.org/wiki/Equatorial_mount

Videos on why we need equatorial mounts 

And how amateur astronomers set them up:

These line up with the axis around which the Earth rotates, and a precise motor keeps them lined up. Although that wasn’t the intention, the fact that equatorial mounts are both necessary and effective is a strong piece of evidence for a rotating round earth. A big own goal here, Dubay and Carpenter!