At any rate, the questions are important. I wanna do two last things and then take a break. We may break early tonight. This is from part four. And as a further consequence of the theory, the vortex theory, but it doesn't naturally occur within the discussion of a visible universe, but instead in conjunction with the Earth.

It's the theory of the tides. So I'm not gonna read the whole thing, I'm gonna start where I've marked it off. Now if there were, picture first, one at the top, you saw a bigger version of that earlier, there's the moon sitting up, going in its orbit. The Earth is in the middle, it's driving a vortex.

You can see that the moon's orbit is not a circle but is shaped other than a circle. There's no sight of the sun in this case. But there's a vortex between the two. Now we're gonna get an account. Now if there were no moon in this vortex, point t, and I hope you can see t, t is the center of the earth.

Point t, which is the center of the earth, would be at point m, which is at the center of the vortex. But when the moon is situated near b, this center t must be between m and d, that is the earth has to be shifted slightly. Why? Because the moon is there, the vortex is trying to force its way between, and there's a constriction from the presence of the moon.

The moon of course is quite large compared to the Earth. No other satellite of anything in our system is remotely as large as the moon is in relation to the Earth. So he's not crazy here in thinking of the moon relatively large. That is going to create pressure which is going to move the earth a little.

Remember how Galileo had the two of them going about their common center of gravity? He had read that in Galileo. So he was in a perfectly good position to introduce the same thing. That's the start of the story. Since the heavenly matter of this vortex, that's the globules, is moved somewhat more rapidly than the moon or the Earth, which it carries along with it, if point t were not somewhat more distant from b than d, the presence of the moon would impede this heavenly matter from being able to flow as freely between b and d as between t an d.

And since the location of the Earth in this vortex is determined only by the equality of the forces of the heavenly matter flowing around it. It is evident that the Earth must therefore approach d ro some extent, that was just the account I gave you. And in the same way when the moon is at sea the center of the Earth will have to be between m and a and thusly the Earth will always recede slightly from the moon.

Further, in this way, not only is the space through which the heavenly matter flows through b and d made narrower by the moon it be, but so is the space through which the heavenly matter flows between t and d. Now why's that so important? We're simultaneously getting a speeding up of the matter between the Earth and the moon and on the opposite side.

How often do tides occur in a day? Twice a day. How often is the moon over head? Once a day. That's one of the mysteries of the tides. They correlate beautifully with the moon, but there are two of them a day, not one a day. He's giving an answer to that.

And the answer's about to come. It follows that this heavenly matter flows more rapidly in those spaces, therefore presses down more upon the surface of the air at six and eight and upon the surface of the water at two and four, than it would if the moon were not on diameter bd of the vortex.

And since the bodies of air and water are fluid and easily obey this pressure, those bodies must be less deep above the parts f and h of the earth than if the moon were not in the diameter b and d. And on the contrary they must be deeper at g and e so that the surfaces of the water and the air swell there.

So in other words he's saying directly overhead you're pressing down, that you're creating a low tide, 90 degrees away, two of them, two low tides. And 90 degrees away from that, two high tides. Now the only unfortunate thing is the high tide occurs a couple of hours after the moon is directly overhead.

That is, the timing doesn't work. There's another unfortunate thing that he doesn't know. The faster fluid goes, the lower pressure it exerts on anybody, not the higher it exerts. That's the basis for wings. That's why wings have a longer surface over the top than over the bottom, to create a pressure difference between the two.

So that's a principle Daniel discovered, this was 1738, his publication, I think. And there's no way he's gonna know that. He just doesn't, it's not there yet, the experiments that show it are not there. In fact, the experiments are in the Principia. Then he goes on to explain why water ascends in six and a fifth hours, and descends in six and a fifth hours.

And that's one of why isn't it exactly six hours? And there's a delay in the water. And finally, why are the ocean tides are greater when the moon is full or new? I don't remember what his explanation is there, but it isn't because of the link to the sun.

It's not the present answer. You can look up what this is, because you can go to the spots in the Principia. So there's one last thing about this and then we'll take a break. Why are the tides an astronomical phenomenon? Answer, they correlate with the moon. So the time it takes at any one place for the high tide to get back to midnight, midnight is a good choice, corresponds to full moon.

Okay, it's a monthly cycle. And that's very nice. So it's correlated to the moon. Second there's an annual variation. And that means it correlates with the Sun. So somehow, the tides has to be an astronomical phenomenon even though they're occurring on the Earth. Now, Galileo's account isn't quite astronomical.

It is, because it involves the motion of the Sun and the Moon. But it does not, like Kepler's, involve forces of the moon, and presumably the sun as well, acting, nor is it gonna be like Newton's when we get to it. And obviously, that's why I'm emphasizing this.

Because Newton, like Kepler, like Galileo, like Descartes, is gonna give an account of the tides. It's interesting, the four of the five people we're focusing on, who actually did work in orbital theory, all had a theory of the tides. Only Huygens never did any serious work in orbital theory, and I've given you the reason.

Because he was blinded by vortices of Descartes.