Now we get to Horrocks. We know remarkably little about Jeremiah Horrocks. He died before he was 24 years old. We know he went to Cambridge from 1632 to 1635. He did not get a degree at Cambridge, he's what's called a sizar. So was Newton. He waited on tables of the fellows and did chores for the fellows to have enough money to be at Cambridge.
When I was an undergraduate, at Yale, it was called a bercer student. Waited on tables. But for whatever reason, he dropped out, returned to the Liverpool area. There's talk about his being a minister but we really don't know much about him. What we know comes from his astronomical writings.
And this table, which is from Curtis Wilson, I hope you can see it better than I can here, but you of course have it printed out. What he did was look at the five planets. Particularly he was looking at Venus at the time, and asking himself, well step one, he had read two works of Kepler's, the Epitome and the Rudolphine Tables.
In the Rudolphine Tables, Kepler makes clear that there was a reform needed on top of his, of get the correct parallax of the sun that Everything he had based it on was too large, but, remember, he didn't go back and change anything. So, the first thing Horrocks does is to say, I'm gonna institute his own proposal, go from three minutes of arc for the horizontal solar parallax to one minute of arc and see what it does.
Answer, it reduces the Earth's eccentricity from the number 0.018 that had been used by Kepler following Kico, half of Kico's, down to 0173. The correct number at that time was 0168 so he was much of the way there. What he didn't know was how wrong. The atmospheric reaction corrections were that Tycho had used.
When he gets it down to 0173, he then re-does Venus and discovers that Venus comes closer. Well, first of all, he gets a new eccentricity for Venus and its fairly dramatic difference. 072413 versus 072333. And he gets the period with high precision. And you notice the difference here between the Rudolphine Tables and his revision to the Rudolphine Tables.
He's getting a difference in predicted longitude that's non trivial in the case of Venus. That leads him to go back and ask the following question. He's getting closer to the three halves power rule, agreeing for Venus. If you got back to last week, it and Saturn were the two that were fairly far off.
That perfect three halves power rule. He goes back and it's much, much closer, now that he's made this change, and he then has the following thought. He says the actual mean distance, that's a tough inference to draw from observations. Why don't we take Kepler's three as power rule as exact.
We know the periods to many, many significant figures. From Ptolemy forward, let's infer the mean distances from the three as power rule, rather than measure them. And he puts that in there. That gives him the last place here, 72333. And he finds he's gotten a much more accurate orbit for Venus with the new elements that he's proposing, than the Rudolph.
Now notice when he's done here, he stayed totally within the framework of Kepler, he's pushing Kepler but he's saying Kepler himself warned me about this, why has nobody done it, I will do it. He does it, discovers he can make substantial improvements in the case of Venus, pushes even further with the 3-S.
So this is a real step forward. He starts doing the same thing for Saturn, and it proves messy. Okay? And you'll see why later in the course. Saturn and Jupiter interact. It's the largest inequality in our whole planetary system. It's called the great inequality. Their orbits are very, very poorly behaved for taking them to be fixed.
He had no way of knowing that. It took a long time for it to come out. Newton was proclaiming it when there was no evidence for it yet. All they knew, something weird was going on. But any rate, that at the time he died, we're not sure why he died natural causes, one of the other two died in the English Civil War which started in 1642.
I started to say I'm doing things up to 1642 because it's halfway to the time Newton starts on the Pergipia as well as the time that Galileo dies and Newton's next two are comments on other things Horrocks did. So this is I'm just gonna quote this from Curtis Wilson but it drives the point.
First of all look at the observations Horrocks made. We're not even certain he made these with a telescope or with lenses. But if you compare Horrocks to Kepler and then Horrocks to Tuckerman, all of Horrocks' observation occurs Wilson crossed checked against Tuckerman are within two minutes of arc.
None of Kepler's are within two minutes of arc. So it looks like he could do better observations than Rudolphine tables are based on, which is another step forward. All it's saying is Horrocks is being very careful. Because Horrocks is pushing Keplerian astronomy past the point that Kepler even tried.
And he's the only person doing that to Keplerian astronomy at the time. So now just great. Something of Horrocks' course of thought as well as his observations of Venus can be followed in the correspondence with Crabtree. The reform of the Keplerian parameters for Venus was closely tied up with the correction of Kepler's value for the eccentricity of the sun.
Now I've told you about that, you can read it on your own. Among the reasons he puts forward for this change are observations of Venus, again that's that table telling you how good they are. Halfway down now, or third of the way down. Further correction could be affected by reducing the size of the orbit of Venus, but apparently Horrocks had not yet considered this possibility.
A final three minutes of correction would be obtained by reducing the earth's eccentricity all the way to 1686, the value we find by using Newcomb's 1900 value, and rate of change to extrapolate back to 1640. But Horrocks had his reasons for choosing a 173. He knew that Keplerian value rested on etc., what I've again told you.
So he ends up perfecting this orbit in the manner described here, I'm laying this out so you can see it. I put the whole article on reserve by the way, and with it, I have put two articles by Van Helden on reserve. One on Galileo and the telescope, and the other on cosmic dimensions from this.
The one of Galileo and the telescope can help you with your papers. You don't have to do it, but if you're worried about whether you've got it straight was was going on at the time, that's an easy ready and can definitely help you. At any rate, what it comes down to is once he goes to this principle of the three halves power rule, he finally gets five significant figures for the eccentricity of Venus, and that gives him this enormous improvement.
All of this is him pushing very hard on Keplarian. He then goes on, and there's a transit of Venus that he observes, and writes just a remarkable 200 page monograph on his observations of the transit of Venus. This is of course an English translation of it. It's all in Latin.
But what he comes down to after seeing the size of Venuses across the sun and seeing the size of Mercury as it crossed the Sun, he decides that in effect, God had set it up where it's a progressive order of the size of Mercury, then the size of Venus, then the size of the Earth.
And if you do that, you conclude the horizontal silver parallax can not be more than 15 arch seconds. That's the first halfway decent number in history. It's 8.8 seconds. So we're actually in the ballpark now but of course it's not founded on any sensible principle. Okay so, when Newton sees that he dismisses it at first as you'll see later and goes for 20 arc seconds in the first edition of the Kernkipia, and then is told by Huygens he's wrong, that's a remarkable book though, before I jump to his theory of the moon and then basically ends tonight's class.
Horrocks died 1641, we know not what. Why was the work not lost? Well it was. Nobody was aware of it until 1661 when a Thomas Street published a book called Astronomia Carolina named for Charles II. It's in english by the way the book. It's the book from which Newton learned astronomy.
And in it street uses, Horrocks' infer the mean distances from the periods. And identifies Horrocks as the person, and all of a sudden people want to know who's this Horrocks? Well he's got these papers over in Liverpool. And so Hevelius a major astronomer publishes the transit across Venus in 1662.
And this one I'll pass around. In 1672, 1673 Horrocks collected papers are publish post humously. Newton owned that book I'm passing around. Newton owned. In fact, it's Bernard Cohen's copy that I inherited, and the marking in it are Bernard figuring out what Newton lifted out of it. This is a case where we had exactly one person in the world Who picked up Keplerian astronomy and started pushing it for all its worth.
He showed really substantial progress. He dies. Nobody else picks it up. He's the only one to really push to Keplarian astronomy rather than alternatives to it, until end of the 1670s, when his own work emerges. Okay, but it does reemerge. It doesn't disappear. And becomes a major influence in the 1670s.