Final answer:
Darwin's observations of fossils and landscape changes provided evidence supporting Lyell's theory of an ancient Earth shaped by gradual geological processes, thereby giving credence to the sufficient time needed for evolution by natural selection.
Step-by-step explanation:
Charles Darwin's observations during his voyage on the HMS Beagle provided support for Charles Lyell's theory of an ancient Earth undergoing continual geologic change. Lyell proposed that geological change occurred gradually over long periods of time through processes still operating today, as opposed to sudden, catastrophic events. In light of Lyell's concepts, Darwin's discovery of sea life fossils high in the mountains indicated that the Earth's landscape had been reshaped over millions of years, which was compatible with his theory of evolution through natural selection. This slow and continuous change in geology suggested by Lyell allowed Darwin to consider that similarly gradual biological processes could lead to the evolution of species.
Darwin's reasoning, influenced by Lyell, was threefold: he recognized that species could change over time; he acknowledged the ancient Earth allowing sufficient time for evolution, given the diversity of life; and he saw the implication of a 'struggle for existence' from population pressures. Lyell's ideas, alongside the likes of Lamarck and Malthus, provided key frameworks for Darwin to propel his own evolutionary theories forward.