In many of the cartoons, De la Beche takes on the theories of the (at that time) up-and-coming lawyer-turned-geologist Charles Lyell. The first volume of Lyell's hugely popular Principles of Geology, which would so inspire Darwin, had just been published in 1830. Principles would become one of the most influential geology texts ever written.
De la Beche was unimpressed.
Principles is often thought of as an early textbook, but it is better thought of as a persuasive argument in three volumes. Lyell was not simply laying out known facts, he was delivering a theoretical argument at the highest levels of the science. Principally he was arguing that the causes of change observable today have been the causes of change throughout all of geologic history, an idea called "uniformitarianism". Uniformitarianism is now taken for granted, but Lyell's version was far stricter than anything that would now be considered acceptable. As put by John McPhee, Lyell's commitment to uniformitarianism "out-Huttoned Hutton" -- Hutton having formulated the idea to begin with. However, his commitment to the principle was not born directly out of the data itself. It was an a priori conviction. Lyell's grandest hope was to do for geology what Newton's Principia had done for the universe at large: Create a clockwork planet that acted according to known, well-understood natural law.
It is not unusual in science for theory to precede facts, as much as we sometimes like to believe otherwise. De la Beche, however, viewed himself as a "Baconian" scientist, chiefly concerned with finding out facts through hard labor. Facts, and lots of them, always had to come first. He believed the field of geology was too young, and its data much too sparse, to be able to yet build large theories with lasting value. He had little patience for abstract theoretical models and "system-building". In fact, he considered them dangerous.
De la Beche would eventually come around to some of Lyell's views. In 1851, Roderick Murchison wrote a letter to him in which he regretted that De la Beche seemed to favor Lyell "more than of old", and that he hoped he had not "actually become an inch by inch geologist."
More information can be found especially in Rudwick, M. J. (1975). Caricature as a source for the history of science: De la Beche's anti-Lyellian sketches of 1831. Isis, 66(4), 534-560. Link [journals.uchicago.edu]
James Secord's introduction to the 1997 Penguin Books reprint of Principles of Geology is an excellent discussion of Lyell's goals and strategy in Principles, and its impact on Victorian Britain.
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