The Equation of Time may be displayed on or near a Sundial (or anywhere else) in a number of ways... For historical information - refer to The Equation of Time as shown on Sundials by John Davis BSS Bulletin Dec 2003 - which can be found at the bottom of this page.
... AS A TABLE
The table may have : Every day of the Year : Occasional Days : Every Day that the EoT changes by a minute or half minute
... AS A GRAPH
The Graph may be Rectilinear, Polar or Intrinsic
Intrinsic Graphs (in the cases illustrated) are explained below.
... AS AN ANALEMMA ... ON OBJECTS
The Analemma is a graph of the Equation of Time plotted against the Declination of the Sun. This portrayal is seen particularly in Noon Mark sundials. The analemma was also added to globes, as a illustration - (often to fill the large blue space occupied by the Pacific Ocean)..
... AS AN ANALEMMA ... IN THE SKY
But it is also interesting that the analemma can be 'seen' in the sky with time lapse photography. A sequence of photos of the sun is taken on different days from a single location and at a set Mean time
... AS A FIGURATIVE ILLUSTRATION
HOW TO DRAW AN INTRINSIC REPRESENTATION OF THE EOT
There are many Intrinsic forms, but the one used here is the easiest. The dependent variable (EoT in this case) is plotted along x-axis. The independent variable (a constant time interval of 1 day in this case) is plotted along the curve itself (not along the y-axis as in a cartesian curve)..
In the left figure above, both the Cartesian & Intrinsic methods are illustrated. The advantage of the Intrinsic method is shown on the right, the 2nd possible option for the last point is shown. This allows the curve to be folded at any point. This in turn can lead to a very compact representation of data, with no loss of information.
This compactness allows a fully readable, day-by-day representation of the equation of time to be placed on the face of a sundial, see below.
INTRINSIC CURVES AND THE BURY ST EDMUNDS DIAL
Bury St Edmunds is a small market down in East Anglia in the UK. In the Abbey Gardens, there is a dial, with its Intrinsic EoT Curve This is of much cultural, scientific and horological interest. It is believed to be the first sundial to acknowledge National Mean Time - rather than Local Mean Time. It is greatly in need of conservation. The following YouTube video was made by the author for the Friends of the Abbey Gardens to help their fundraising. I do not think they ever deployed the video and I understand that restoration efforts have come to nought.
For the historical background, republished by kind permission below are two papers by Dr John Davis:
1. © J. Davis: 'The Equation of Time on Sundials' BSS Bull., 16(iv), 135-144 (December 2003)
2. © J. Davis: 'More on The Equation of Time on Sundials' BSS Bull., 17(ii), 66-75 (June 2005)