Robert Bunsen (1811 - 1899)
Gustav Kirchoff (1824 - 1887)

Bunsen (left) and Kirchoff (right)
Flame tests

sodium, potassium, lithium
Spectroscope

Each element emitted its unique pattern of spectral lines.
If a gas emitted certain wavelengths of light, it would absorb those same wavelengths when white light was passed through it.
Bunsen and Kirchoff discovered rubidium and cesium using the spectroscope.