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Frank,

I read the paper, and it mostly confirms what I wrote before.

1. Horrocks Lunar theory was written in 1638 in a letter to a friend.
After his death, all his writings were collected as Opera Posthuma, and privately sent to
Newton, Flamsteed, Wallis and others. Later this was published, and now avaiable on Internet:


https://books.google.com/books?hl=en&lr=&id=xVQ_AAAAcAAJ&oi=fnd&pg=PA1&ots=cW8RsSOQB6&sig=pKMPRH4syyb3EPNAQIQ3wIQZNRw#v=onepage&q&f=false

In Latin, of course.

2. He himself considered this Lunar theory his greatest achievement. 
It was the most precise available
predictive Lunar theory before Mayer.

3.  Newton saw his first task is deriving this theory from his law of gravitation
(and mechanics), that is to do what he did to Kepler's laws. He failed.
 
That is he failed a) to produce a predictive theory more powerful than that of Horrocks,
and b) in mathematically deducing Horrocks's theory from the law of gravitation. 

Euler also started with Horrocks's theory and
"found it suggestive in leading to his invention of the method of variation of 
orbital parameters, so fruitful
in the celestial mechanics of Lagrange and Laplace."

The 18 page  paper of Wilson which contains all this information, and a 
readable description of Horrocks's Lunar theory in English
is available here:

https://journals.sagepub.com/doi/abs/10.1177/002182868701800201?journalCode=jhaa

for $2.50. I downloaded my copy from my university library, so I will not post it here,
but I can send a copy to the private e-mail address of anyone who will ask, since sharing 
a library material for research/educational purposes is considered a "fair use", and is permitted.

It is not known exactly how Horrocks derived his theory, and the main purpose of Wilson's paper
is a discussion of this.

Alex.

 

   

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