Globe brightness in series circuit
Assuming the lights are identical within a small tolerance, one has a very slightly higher resistance than the others.
With the same current in each, (as must be true in a series circuit) the higher resistance one will dissipate more power and heat up more : this further increases its resistance, heating it up further, increasing its resistance. Finally it may have twice or more the resistance of the other relatively cool bulbs, dissipating twice the power and glowing much brighter.
Measure the resistance of each bulb when cold.
Measure the voltage across each bulb when hot.
Compare the ratio of these voltages to the ratio of resistances when cold.