Any equatorial dial or other construction that gives equiangular hour lines can easily be converted to a civil time dial simply by rotating the hour and minute graduations by an amount proportional to the Equation of Time and Longitude correction on the day in question. This is commonly done using Pilkington's method.
The Day of Zero EoT on the Time Zone meridian (e.g. no Longitude Correction)
Zero EoT - Longitude Correction only
Maximum EoT + Longitude Correction
Minimum EoT + Longitude Correction
This shows how Pilkington's method works. The outer ring has evenly spaced calendar lines. The rotating inner ring with the hour and minute graduations has a similar scale, but each day is adjusted to the Equation of Time & Longitude Correction by 1/4° per minutes. Corresponding Dates on inner & outer scales are lined up - see black arrows.
Left hand figure shows the day with zero EoT and for a dial on the Time-Zone meridian.
Remaining three figure show the effect of a 20° longitude correction for the days of zero, max & min EoT 
Here is the background paper by Gordon Taylor on Equiangular Sundials
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