In parts III and IV, Descartes takes the principles of physics, which he has deduced from the nature of body and the laws of motion, which he has supposedly deduced from the immutability of God, and he applies these to observable phenomena. His goal is to demonstrate the explanatory power of his principles by showing that they alone can account for all of our observations. Part III focuses on the most universal phenomena of nature, the general structure of the entire visible world.
Chapter III reads like a checklist, with Descartes running through every astronomical observation of which he can think. In nearly every English translation of the Principles, most points on this checklist are omitted. However, the two most important discussions—the analysis of planetary motion and the analysis of the elements of the universe—are generally included.
Descartes' model of planetary motion is an odd cross between heliocentrism and a static earth theory. Descartes agrees that all of the planets, including earth, move around the sun. However, he maintains that none of the planets are really in motion. This way, Descartes gets to have it all: he can account for all the observations that seem best explained by heliocentrism, and he can also avoid the wrath of the Church. Nonetheless, Descartes is very careful to point out that his model is only a hypothesis and is not meant to necessarily reflect the way things really are.
Descartes' cagey model rests on his odd definition of motion. Remember that a body is only in motion if it changes its position relative to the bodies with which it is in immediate contact. The raisins in the twirling raisin bagel are not in motion because their position relative to the bready matter does not change. The planets, on Descartes' view, are much like raisins in a raisin bagel. Only instead of bread, they are suspended in a fluid body. This fluid body is the heavens. The fluid heavens move in a vortex around the sun (a vortex is like a whirlpool, swirling around a center), carrying all the planets with them. Within the celestial goop, however, the planets retain their position. Therefore, though they travel around the sun, they remain at rest.
Only the most die-hard Descartes scholars pay much attention to his scientific explanations of heavenly phenomena, since they are all consistently off target. (This explains the scarcity of English translations; there is currently only one full translation). However, Descartes' accomplishment should not be underestimated simply because he was dead wrong. It is fascinating to read through the explanations in Parts III and IV and see how each principle that he established in Parts I and II plays a role in some way.
Just to run through the more prominent examples from this section: First, why does Descartes' claim that the heavens are a fluid? This claim rests on two previous principles: the proof that space is a plenum and the proof of the nature of fluid bodies. Since there is no such thing as empty space, the plenums have to be some sort of body. In order to determine what sort of body they are, we must consider their behavior. One thing that can certainly be said about the heavens is that they are penetrable—they easily yield their place to other bodies. Comets zip through them, and planets take their place in their midst, etc. Looking back to the definition of II.54, we see that this means that the heavens must be fluid, since it is fluid bodies, composed of quickly moving particles, that are easily displaced by other bodies.
Next, we must ask, why does this heavenly fluid move in vortices, like a whirlpool. This claim rests on principle II.33, in which Descartes proves that all motion must be in the form of a continuous circuit. Since all of space is a plenum, in order for A to move to B's spot, B must move to C's spot and C to D's spot and so on. As each tiny body takes the other's spot in the quickly moving heavenly fluid, a vortex, swirling around the center, is formed.
Descartes is then able to use the physics of vortices to explain certain other observable phenomena, particularly the relative motion of the planets. Those planets that are positioned toward the center of the vortex naturally move around the sun the quickest, since in a vortex the middle swirls most rapidly. (Just imagine a whirlpool to understand why this is true).