A scientific principle holding that planets with similar conditions tend to produce similar biology and societies, cited to explain the Roman-style civilisation of planet 892-IV.
Hodgkin's Law is stated in the Original Series episode Bread and Circuses. Arriving at the fourth planet of system 892, the Enterprise finds a world of twentieth-century technology on which the Roman Empire never fell, with televised gladiator fights and spoken English.
Kirk records that the planet is a striking example of the law of parallel planetary development. The idea is offered as the reason so many worlds visited by the ship resemble periods of Earth history.
The parallel extends to religion: the persecuted sun worshippers of the planet prove, as Uhura realises at the end, to be followers of the son of God. The law is one of several explanations the franchise has given for its humanoid galaxy, alongside the Preservers and the ancient humanoids of The Chase.