The clock running at a constant (say, a pendulum clock) rate _____

Local Apparent Solar Time is the hour angle of the Apparent Sun plus twelve hours. Local solar time is the time based on the position of the sun with respect to a particular location. It is also called local apparent time.
Solar time is the time measured by the Earth's rotation relative to the Sun. Apparent solar time is the time measured by direct observation of the Sun or by a sundial.
The apparent angular motion of the sun is not uniform. It moves faster when it is nearer to the earth and slower when it is away.

Related: Renewable Energy Practice Test: Measuring Solar Radiation