Equation-of-Time is in the gnomonical (not astronomical) convention (i.e. solar time to local mean time, rather than vice versa).
Solar to Civil Correction is the number of minutes to apply to Sundial Time in order to get Civil Time (i.e. that which one reads from a clock). It is the effect of both the Equation of Time & the Longitude Correction.
Accuracies quoted are by comparison with MICA version 2.2.2 of July 2011 by Astronomical Dept of US Naval Observatory, using more than 70,000 6-hourly computations using UT1 between 2000 and 2050, for a temperate latitude. Altitude & azimuth accuracy will degrade at very high latitudes.
The precision of these routines is FAR, FAR greater than that required by a gnomonist. However, computational shortcuts have NOT been made, so that the html code can be adapted for any other astronomical use. The code is free of copyright and is used at one's own risk!
Routines used are those described in Astronomical Algorithms 2nd Edition 1998 by Jean Meeus incorporating VSOP theory, nutation, aberration, parallax and refraction.
Delta T (the difference between Terrestrial & UT1 time) is derived by polynominal fitting of data from the aforementioned MICA .
The difference between the input Delta UT1 (the argument required for Earth rotational calculations) and UTC (Universal Time Coordinated) will never differ by no more than 0.9 secs of time. Its value is unpredicable.
The position of the mean sun (i.e. GMST) is not calculated by Meeus' method but by the more modern IAU-approved method described in USNO Circular 179 The IAU Resolutions on Astronomical Reference Systems, Time Scales and Earth Rotation Models - Eqns 2.11 & 2.12 by G.H. Kaplan.
Input values of Height (needed for parallax corrections), Pressure and Temperature (needed for refraction corrections) have very minor effect on the results. In almost all cases, the default values will surfice.