Goldstein's Experiement: Discovery of vacuum pumps led many to experiment with gas discharge tubes (vacuum tubes filled with very small quantities of inert gases, subjected to high electric voltages). This led, first to the discovery of cathode rays (1870s) and later to the discovery anode rays (1886).
A ray seemed to emerge from the cathode (negative electrode) that travelled in straight line, reaching the anode. It carried momentum and so overshot the anode and struck the tube wall. This made the tube glow. These were named cathode rays by Eugene Goldstein. Application of magnetic field made it bend and it was shown to carry a negative charge. Later this cathode ray particles will be identified as electrons by J.J. Thompson.
Goldstein modified the gas discharge tube to have a perforated cathode. When potential difference of several kilo-volts were applied between the electrodes, Goldstein observed fain glow extending from the perforations of cathode. By applying magnetic field it was shown to carry a positive charge. Goldstein called it canal rays. Later this will be shown to be protons by Ernst Rutherford.
Chadwick's Experiement: In 1930 it was found that when Beryllium was bombarded with alpha particles it emitted a stream of highly energetic radiation. It was charge neutral. So it was believed to be high energy gamma ray photons. However when this radiation was incident on proton rich material such as paraffin, it was found to knock protons off with high kinetic energies.
In 1932, James Chadwick reasoned out that massless gamma ray photons cannot impart such high kinetic energies on protons and concluded that this radiation is made of particles that have mass. Using momentum conservation principle Chadwick was able to show that the mass of these neutral particles are very close to the proton mass. Thus he discovered neutrons which was kind of predicted to exist by Rutherford. Rutherford speculated the existence of electrically neutral tightly bound electron-proton pairs. But neutrons were particles by themselves and not the Rutherford electron-proton pairs.