What is the instrument and the scale that is used to measure the magnitude of an earthquake called?

The instrument is called "seismometer."

The first sacle of measurment for earthquakes is called the richter magnitude scale after its inventor, Charles Richter (in 1935 ), which categorises them in terms obtained by calculating the logarithm of their amplitude.

This scale has been replaced in the 1970s, by the moment magnitude scale which measures the size of earthquakes in terms of the energy released.

The modern scale retains the familiar continuum of magnitude values defined by the older one.