This extraordinary movement can safely be attributed to Joseph Williamson, ?1669-1725. Williamson claimed to have been the inventor of the equation clock or at least all the clocks to have been made by English makers up until 1719. Indeed he wrote a letter to this effect which was published in the Philosophical Transactions, November-December, 1719. In it he disputes an entry in a French publication wherein the author had given himself the honour of making the first equation movement (the author's name was not given). Williamson goes on to mention other clocks that he (Williamson) had earlier made for other important clockmakers.
'...... I made others for Mr. Quare which showed Apparent Time by lengthening and shorting the pendulum, in lifting it up and letting it down again, by a Rowler in the form of a ellipsis, through a slit in a piece of brass, which the Spring at the Top of the Pendulum went through..For one of those, and not the first, made with the rising and setting of the sun, Mr. Quare sold to the late King William and it was set up at Hampton Court in his lifetime, where it hath been ever since...So that I think that I may justly claim the greatest right to this contrivance of making clocks to go with Apparent time; and I have never heard of any such clock sold in England but that was of my own making, though I have made them so long.