Charles Darwin was very thorough in his explanation of natural selection as a prime driver for evolution. Just as importantly, Darwin also put forward the idea of gradualism. Understanding gradualism is very critical to Darwin's theory. Even in his own day, he noted that traits in livestock, especially cattle, sheep and dogs, were selected for artificially, and sometimes abruptly. However, he realized that in the natural world, trait selection also must occur, but much more slowly. Gradual change had to be a key, as most environments change only over many millions of years. It was already observed, too, in Darwin's day that geologic evidence suggested that the Earth was very ancient, indeed.
Charles Lyell, a geologist, befriended Darwin and the two corresponded about Lyell's theory called uniformitarianism. Uniformitarianism suggested that depositions, erosion and continual gradual change over the Earth was uniform. These natural processes stayed the same over time, thus natural laws were in effect. Accumulated change, not cataclysmic biblical floods, were the modern "truth" these men elaborated upon. Lyell, in addition to helping Darwin get his theory published, himself would publish a book in 1863 entitled "Geological Evidences of the Antiquity of Man."
The theory of gradualism was supported by the geologic and fossil record. However, evolution through natural selection does not disallow some relatively sudden changes being selected for when there are significant changes to the environment to which each organism must adapt. Still, it is the gradual modifications, or, as he called them, the "fine gradations" that prevail over all through time. In "The Origin of Species," Darwin wrote: " It is indeed manifest that multitudes of species are related in the closest manner to other species that still exist, or have lately existed; and it will hardly be maintained that such species have been developed in an abrupt or sudden manner. Nor should it be forgotten, when we look to the special parts of allied species, instead of to distinct species, that numerous and wonderfully fine gradations can be traced, connecting together widely different structures."
Darwin realized that so very many slight changes are evidence that life forms are related. The sheer number of uses of five appendages (or fingers) on a hand or paw, for example, is evidence supporting gradualism. The same basic "hand" can be seen in animals as diverse as whales, where the appendages slowly became streamlined fins. In the many species of bats, the same design gradually becomes webbed tips of wings. In dogs and cats, they manifest with fur and claws. In tree-climbing forms, they become very well adapted to holding branches. Darwin realized that all of these extreme and diverse adaptations are simply variations on a theme. They are realized in a multitude of organisms over immense time spans. And, as Darwin noted, such slow change continues even today.