Final answer:
James Hutton and Charles Lyell influenced Charles Darwin's evolutionary theory by introducing the concepts of deep geological time and gradual change, which Darwin applied as a necessary condition and analogy for evolution by natural selection.
Step-by-step explanation:
James Hutton and Charles Lyell significantly impacted Charles Darwin's theory of evolution by providing the concept of deep geological time and the idea of gradual change through uniform processes. Hutton proposed that the Earth's geological features were the result of slow accumulations over a long period, which was a stark contrast to the prevailing notion of a young Earth shaped by catastrophic events. Lyell further popularized this idea and suggested the Earth was much older than previously thought, which implied that there was ample time for biological evolution to occur through gradual changes.
Darwin incorporated these principles into his own theory, understanding that the long time scales necessary for geological changes were also applicable to the evolutionary changes in species. This concept provided a plausible timeframe for his mechanism of evolution by natural selection. Furthermore, the gradual and continuous nature of geological processes suggested by Lyell and Hutton provided an analogy for the gradual and cumulative changes in biological traits that lead to evolution.