Cassini,Roemer,Huygens comments and modifications

"..contain the inequality of the days or the true motion of the Sun [i.e. the inequality due to the eccentricity of the Earth's orbit], the eccentric motion of Jupiter [i.e. the inequality due to the eccentricity of the orbit of Jupiter] and this new, not previously detected, inequality [i.e. due to the finite speed of light]." Cassini

There is a confluence of a number of astronomical principles that meet at this historical period based on the Equation of Time and the Equation of light with specific interest in the former which Roemer used in concluding that the anomalous motion of Io was due to finite light speed. Having nobody to bounce these ideas off is perhaps the loneliest element of all this considering that I admire these dedicated historical astronomers even though they did not have the information available to 21st century observers.

The conception of the Equation of Time by Huygens is flawed in terms of the period across which the Equation is valid and by virtue that there cannot be a complete set of tables valid from one 4 year period to the next period -

" Here take notice, that the Sun or the Earth passeth the 12. Signes,or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49 min. or there about, and that those days, reckon'd from noon to noon,are of different lenghts; as is known to all that are vers'd in Astronomy" Huygens

http://adcs.home.xs4all.nl/Huygens/06/kort-E.html

The natural inequality in the noon cycle,as opposed to constant daily rotation, arises from a single source,in this case the uneven surface rotation in addition to and aside from constant daily rotation. The Equation of Time requires the return of the Sun to noon in order to equalize the variations to a 24 hour average and there are 1461 such natural noon cycles across 4 orbital circuits with Feb 29th as the noon cycle that returns the Earth roughly to the same orbital position that began on March 1st four years and orbital circuits earlier.

There is a tremendous amount of work at this juncture which sets out ,for the first time,the references for the 24 hour day,the calendar system and the dynamics which link the two. It doesn't beg vapid commentaries but rather an admiration for those astronomers who tried to understand observations at a time when telescopes and watches were emerging just as today modeling with computers has created huge difficulties in the wrong hands.