CLOCKS THAT READ SOLAR TIME
The use of mean time (some kind of man-made idea) - compared with solar time (God's or true time) - was only slowly accepted in the 17th/18th C. (Bear in mind that Aristotelian natural philosophy was still being widely accepted and taught in the 18th C - notwithstanding the birth of modern science in the Enlightenment.) As a result, there are rare examples of Clocks whose pendulum length was varied with an Equation mechanism, so that the clock directly read solar time.
Letter from Joseph Williamson claiming to have invented variable length Pendulum Clocks
TABLES TO CORRECT CLOCKS TO READ SOLAR TIME
the author is grateful to Prof Frederick W. Sawyer III for the information in this section.
The same lack of acceptance of mean time, together with the introduction of clocks, led to the publication of a number of works by John Smith C.M. on the Equation of Time. The last of these, published in 1694, elucidated the 10 Rectifying Days of the year on which one would need to adjust one's pendulum clock so that the clock would always indicate the time within 3½ minutes of Solar time. The title page of his book contains .... "With TABLES of EQUATION, and Newer and Better RULES than any yet extant, how thereby precisely to adjust ROYAL PENDULUMS, and keep them afterwards, as near as possible to the apparent (= Solar) Time,
John Smith's Book and the output obtained, viz that one's clock, properly rectified, would always be within 3½ mins of Solar Time. But there were some mathematical problems with his method. 
Recent re-working of John Smith's ideas by Fred Sawyer give a slightly better picture - in Gregorian dates. On Jan 1st, one sets the clock to equal Solar Time and then offsets it back by 7min 9 secs, etc.
The clock will always be with 3 mins and 30 secs of Solar Time
EQUATION CLOCKS
The first pendulum clock was introduced by Christian Huygens in 1656. It was a great improvement over the verge and foliet mechanisms of the mediaeval days - but it suffered from a lot of friction in its escapement and required an over-wide pendulum swing. Early pendulum clocks had an accuracy of about a minute per day. But improvement in escapements was very rapid. By the beginning of the 18th Century, ownership of accurate clocks were beginning to be commonplace amongst rich people. But such clocks had to be set. 
If there was a nearby navigator or astronomer, you could set your clock by comparison with their astronomical  measurements. Thus in large cities and seaports, one could access accurate time. by the noon cannons (? 18th C) and noon balls (19thC )  - which were introduced to broadcast astronomically measured  time. The people of Edinburgh joke that the noon cannon fired each day from the castle is so accurate that it always hits the noon ball at the observatory on the other side of town. It was of course the noon ball that triggered the firing of the gun.
But in the absence of such time signals, the only way to set a clock was with a sundial. Thus to types of clock were developed. First and simply, there were those that displayed the equation of time. Secondly and more complex were those which combined the pendulum's mean time (for daily use) with the equation to give solar time (used to set the clock from the sundial)..
Left to Right : Click to Enlarge (i) Daniel Quare's Equation Clock : ca 1696 : British Museum (ii) Equation face showing both date and Equation of Time o the golden sun hand (iii) Cam mechanism driving the Equation hand (iv) Equation Clock By Enderlin, pre 1820
The Demise of the Equation Clock
The introduction of commercial  telegraph systems (independently patented in 1936 by Vale/Morse in the US and Cooke/Wheatstone in the UK) allowed astronomically measure time to be broadcast across a nation. This spelt the demise of the Equation Clock.
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