"Uniformitarianism" is based on the assumptions that 1) the laws of physics and chemistry haven't changed during earth's history and 2) past geological events occurred by natural processes similar to those that happen today. Lyell stressed the gradual nature of geological changes that occur through time, which later influenced Darwin's evolutionary theory, which was based on gradualism, or perpetual changes in animal's genetic makeup over time.
Work Step by Step
Lyell comes up with principle of uniformitarianism, stressing perpetual changes in nature. Later impacts Darwin's theory of evolution in animals.