Conductors like copper and tungsten have a large +ve Tempco (PTC) such that the R.hot=10x R.cold.

You know that when voltage is applied across 2 series connected R's , the resistor with the largest value sees the most voltage.

40W Bulbs have 50% lower resistance than 60W bulbs so they see 50% more voltage and thus due to the square law \$V^2/R=Pd\$ the rise in temperature accelerates the voltage divider so that the smallest power bulb starts brighter and ends up with 10x more power dissipation than the higher power rated bulb.

The same effect would occur with two identical rated bulbs but one +10% and the other -10%. It just occurs slower and a different power share.

The effect could also be called Thermal Runaway. So if you put two 100W bulbs rated for 120V and used 240V across, the smaller power larger R bulb burns hotter than rated.

Conclusion Verified by simulation.

Conductors like copper and tungsten have a large +ve Tempco (PTC) such that the R.hot=10x R.cold.

You know that when voltage is applied across 2 series connected R's , the resistor with the largest value sees the most voltage.

40W Bulbs have 50% higher resistance than 60W bulbs so they see 50% more voltage and thus due to the square law \$V^2/R=Pd\$ the rise in temperature accelerates the voltage divider so that the smallest power bulb starts brighter and ends up with 10x more power dissipation than the higher power rated bulb.

The same effect would occur with two identical rated bulbs but one +10% and the other -10%. It just occurs slower and a different power share.

The effect could also be called Thermal Runaway. So if you put two 100W bulbs rated for 120V and used 240V across, the smaller power larger R bulb burns hotter than rated.

Conclusion Verified by simulation.