Notice that a solid object placed inside a discharge tube casts a shadow on the glowing glass wall opposite the cathode.
William Crookes improves the vacuum and proposes the rays are a fourth state of matter — charged particles streaming from the cathode.
Heinrich Hertz finds no deflection in an early electric-field test (residual gas ions in his tube mask the effect) and wrongly concludes the rays are waves, not particles.
Using a better vacuum, Thomson deflects the rays with both electric and magnetic fields, proves they are negative particles, and measures their charge-to-mass ratio — over 1000× lighter than a hydrogen ion.
Thomson calls the particle a "corpuscle"; the name electron (coined earlier by Stoney for a unit of charge) sticks. The atom is no longer indivisible.