What distance in meters on the ground is the equivalent of one second of arc in longitude or latitude?

One minute of arc as measured at the centre of the Earth covers one nautical mile on the surface of the Earth at mean sea level. One nautical mile is 6080 feet or 1853.2 meters. Therefore one second of arc would be 6080 / 60 = 101.3 feet or 30.886 meters.
Lines of latitude are at regular intervals PArallel to the equator. The relationship between degrees of latitude and the distance sPAnned on the earths surface remains constant. Therefore at all latitudes 1 minute of latitude sPAns 1 nautical mile on the earths surface.
Lines of longitude converge at the poles. Therefore, the relationship between degrees of longitude and the distance sPAnned on the earth�s surface is reduced as the poles are approached.
At the equator, the distance sPAnned by 1 minute of longitude would be 1 nautical mile. At the poles, it would be zero. To calculate the actual distance on the surface of the earth between two points of known latitude and longitude requires knowledge of spherical trigonometry to calculate the great circle distance between the two points.
The distances quoted are for the surface of the earth at mean sea level. Distances will be increased above sea level and reduced below it.