This is a document, if it's a fragment. He's changed the title again on the motion of bodies in regularly yielding media. It's a fragment that consists of a series of definitions followed by a group of laws and followed by the first limits you saw before. And then it just stops.
It's a document written, and once again in Humphrey Newton's hand, but as you see with lots and lots of heavy changes by Newton. Craig Fox, a student who was in the course the last time it was taught at Tufts in 2011, who's done more work on this document than anybody ever has, has concluded there are four sequences of changes Newton came in.
There are five versions sitting here. There's the original version in Humphry Newton's hands, and there's four times Newton came in and revised it. Now that's a lot of hard work to reach that conclusion, and it's not a solid conclusion. That's not the point I'm going to be making about it.
The main point I wanna make about it is it's very heavily reworked. This is an inserted page that Harevel gets all wrong. He thinks it belongs in a separate manuscript. Whiteside corrected him. There's no issue. It belongs in this manuscript. We'll get to the inserted page after we do the rest.
This is more, I put the whole document here on the handout so you could see the whole thing. You can see how much reworking there is when Newton starts writing in margins, etc. This is not a simple matter. And we finally get up to the and that's where it stops.
And notice law six crossed out. Quick comment, cuz I'll be stressing this through much of the rest of the night. We'll go reasonably quickly, but it shouldn't surprise you. One can learn an enormous amount more from a document that's reworked from a document that's clean. Because one can see Newton changing his mind.
That doesn't mean you can always answer the question why did he change his mind, but at least you can see it, okay? So that's quite significant. All right, I'm starting discussion of this from the end of the definitions, where he explains why he puts the definitions in there.
Then I'm gonna skip around among the definitions, cuz this is available to you as part of the reading. The opening definitions are about absolute space, relative space in places like that. This is the last place we have where Newton talks about space and time as part of definitions.
In the Prinpcipia, they are not treated definitionally, they are treated separately. But here, he's still doing what he did in of having separate definitions for things like space and time. The aim of explaining all these things at length, that's the definitions, is that the reader may be free from certain vulgar prejudices and imbued with a distinct principles of mechanics, may agree in what follows to distinguish carefully from each other.
Which are both quantities, which are both absolute and relative. A thing very necessary since all phenomenon depend on absolute quantities. But ordinary people, who fail to abstract thought from sensible appearances, always speak of relative quantities so much so, that it would be absurd for wise men, or even prophets, to speak to them otherwise.
Hence, both the sacred writings and theological writings are always to be understood in terms of relative quantities. And he who would, on this account, bandy words with philosophers concerning the absolute motions of natural things, would be laboring under a gross misapprehension. All right, so, that's the point of the definitions.
Now the one I single out is the relative space, not so much for the relative space, but for the fact that he throws in here again this thing about being able to tell the Earth is moving. Relative space is that which is regarded as immobile in relation to any sensible thing, such as the space of our air in relation to the Earth.
However, these spaces are, in fact, distinguished from each other through the descent of heavy bodies. Which in absolute space seek the center directly, but in relative space, rotating absolutely, are deflected to one side. So he's back to that Coriolis test. That's not what I want to focus on, we'll worry about relative versus absolute space when we get to the Principia.
It's with this I start, and then it's gonna be a series of definitions. The motion of a body is it's translation from one place to another, and is consequently either absolute or relative according to the kind of place. But absolute motion is, in fact, distinguished from relative in circular motions by the endeavor to receive from the center, which in an entirely relative circular motion is zero.
But in a circular motion, that should be relative to bodies at rest, may be very large, as in the celestial bodies, which the Cartesians believe to be at rest, although, they endeavor to receive from the Sun. So far, all he's doing is attacking Descartes' account of motion, that you can tell whether a body is moving curvilinear by its endeavor to receive.
The fact that this endeavor is certain and determinant, determinant's a key word here. It's a quantity. To be a determinant quantity means it's got fixed ratios to other quantities. You'll hear me saying this next semester. Kline says no entity without identity. Newton would have said no quantity without fixed ratios to other quantities.
Determinate argues some certain and determinate quantity of real motion in individual bodies in no wise dependent on the relations between bodies, which are innumerable and make up as many relative motions. So if an object is spinning, the tells you it's spinning, and it has nothing to do with any other body.
If a body is in orbit and tends to recede, it has nothing to do with the motion of any other body. It has a determinant quantity, determinant, dictated by the level of its curvature, et cetera. You know, v square over r is the normal tendency to recede, it's got to be balanced by a force.
We know what the force is, it's v square over r. Okay, for example, that motion and rest absolutely speaking do not depend on the situation in relation to bodies between themselves is evident from the fact that these are never changed, except by force impressed on the body moved or at rest.
And are always changed after such a force. But the relative can be changed by forces impressed only on other bodies to which the relation belongs. And it does not change by a force impressed on both so that their relative situation is preserved. You see this idea in Descartes account of impact.
Determine what the situation is from the forces. So this is actually a Cartesian idea Newton is picking up on, but is going to be the central idea for distinguishing apparent motion from true motion. True motion is produced by forces. So if you can show a force is acting and that's, of course problematic, show of force is acting by giving a determinant measure, etc.
Then you've got true motion. If you can't show that a force is acting on a body and it appears to be moving, then you have to be suspicious the motion is only relative, as with dropping an object from a tower, etc. This is a series of definitions. Now being done with my translations only, not Harevels and I'm showing inserts in various places and deletions.
I'm not showing all the inserts and deletions. These are ones from a lecture I gave in Berlin last summer, and I'm being selective here. Later, I won't be selective. I'll show you all of them. So let's start. This is quantity of motion is that which arises from the velocity and the quantity of a body in translation jointly.
Moreover, the quantity of a body is to be reckoned from the amount copia of the corporeal matter, which is usually proportional to its gravity. The oscillations of two equal pendulums with bodies of equal heaviness are counted, and then amount of matter in each with be reciprocally as the number of oscillations made in the same time.
Newton has the word quantity, quantitous. It's a perfectly good Latin word. He has the word amount copia. In this stuff, he distinguishes between the two. Whether the distinction is meant to be anything, I don't know. But, of course, quantity meets quantity in the sense, and amount does not necessarily it can be a heap.
Definition 12, notice the Latin because Corey pressed on this last time, corporis V cencita en nata en ecentialis. The internal, innate, and the central force of a body. Now, of course, that's my translation, but the point is he has all three up there. And a central force of a body is the power by which it, crossed out or perseveres in its state.
So he was originally gonna say endeavor, then changed it. Perseveres in its state of rest, or of moving uniformly in a straight line. It is proportional to the quantity of the body. And is truly exercised proportionally to the change of state. And insofar as it is exercised, it can be said to be the exercised force of the body, of which one kind is the centrifugal force of rotating bodies.
Okay, that's all the force of the body. So the centrifugal force, the tendency that pull out is, of course, the resistance the body has to be taken off an inertial motion. That's what he's saying here. Definition 13 is cancelled, but is worth seeking. The force of a motion of a body from motion at its approach is that by which a body endeavors to preserve the total quantity of its motion.
It is commonly called impetus and is proportional to its motion. And according to it's kind, it's absolute or relative. So he's picturing here the resistance, when another body comes and the impetus it puts on that body, and he wants to relate it to the force in the body.
Then he decides this isn't clear and simply cancels the whole definition. And nothing like it quite appears again, but you'll see later next semester, what does. Definition 14, the force brought against and impressed on a body is that by which a body is urged to change his state of moving or rest and is of diverse kinds, such as impulse or pressure, percussion, continuous pressure, centrifugal force, resistance of a medium, etc.
And notice, that whole diverse cause, etc., is an insert in Newton's hand. The rest of it, whenever I don't show deletion signs, it means it's in Humphrey's hand. Definition 16, I call centripetal force, that by which a force is impelled or attracted towards a certain point regarded as the center of this kind is gravity tending towards the center of the Earth.
Magnetic force tending toward the center of a load stone. And the celestial force restraining the planets from going off along the tangents of their orbits. He is not identifying the celestial force with terrestrial gravity at this point. Whether he's being coy or whether he's simply hasn't decided they're one in the same is a perfectly good question.