It was on this day in 1853 that the rotation of the Sun began to be measured using the Carrington Rotational Numbers.
CRN is defined as the number of rotations which the Sun has completed as seen from the Earth based on a mean rotation period of sunposts of 27.2753 days (ie the mean period for a single rotation of the Sun is 27.2753 days), and starting with rotation number one on November 9, 1853.
As the solar rotation is variable with latitude, depth and time, any measuring system is necessarily arbitrary and only makes comparison meaningful over moderate periods of time.
Differential rotation is when different latitudes rotate at different rates and it applies to all fluid bodies including all stars and the surface of gas giant planets. Solar rotation is arbitrarily taken to be 27.2753 days for the purpose of Carrington rotations. Each rotation of the Sun under this scheme is given a unique number called the Carrington Rotation Number.
Richard Christopher Carrington determined the solar rotation rate from low latitude sunposts in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured in relation to the stars, but because the Earth is orbiting the Sun, we see this period as 27. 2753 days.
Rotations are counted from that time with the central median longitude decreasing fom 360 to 0 during each rotation as the central meridian point rotates under the Earth. Traditionally, the start and stop times of the Carrington Rotations are derived assuming that the solar rotation period as viewed from the Earth is a constant. This assumption is perfectly adequate for most studies.
It is possible to construct a diagram with the longitude of sunposts horizontally and time vertically. The longitude is measured by the time of crossing the central meridian and based on the Carrington rotations. In each rotation, plotted under the preceding ones, most sunspots or other phenomena will reappear directly below the same phenomenon on the previous rotation. There may be slight drifts to the left or the right over longer periods of time.
Carrington Coordinates are heliographic (sun centered) and measure latitude and longitude in the rotating frame. Carrington Time is the rotation number and the longitude of the point on the sun that is at the sub-terrestrial point. Sorting out regular time, Carrington Time and Carrington longitude can sometimes be problematic.