The present third and final posthumous edition, published in 1865, was the only edition that credited the maps debt to William Smith.

First published in 1819, four years after, and in response to, William Smith's seminal map on the same subject, and a key milestone in the history geology.

Greenough (1778-1855) was the first President of the Geological Society, and was later President of the Royal Geographical Society. The Geological Society was founded in 1807, but Smith never became a member, although his geological work that was the basis of the map was well underway by then. Greenough had actually been shown a copy of an early version of Smith's map by the surveyor John Farey in 1802, who later attacked Greenough in the press for his "unhandsome conduct" in the matter (Philosophical Magazine). There were probably two reasons for this: personally, Smith probably could not afford the membership fee; and professionally, he advocated a method of differentiating between strata using the fossils in each layer. This theory went against the prevailing scientific method of inductivist reasoning, and was viewed with suspicion by most of his contemporaries. Greenough and other Society members visited Smith to look at his collection of fossils and the progress of his stratigraphical map, and were unconvinced by Smith's method, his claims to have done the field work for the map himself, and probably unimpressed by his plain lodgings (Herries Davies).

Greenough decided (as he claimed later) that Smith did not have the resources to complete the project and initiated the production of an official map on behalf of the Geological Society. Greenough's map, with the financial backing of the Society, benefited from expert draughtsmanship and engraving, which Smith could not afford. Unlike Smith, however, Greenough did not conduct field work himself. Instead, he relied on the work of other geologists, including Smith - both he and the Society are on the list of subscribers to Smith's map - creating much debate as to the extent to which his map is derived from Smith's. It is clear that Greenough's work drew on Smith's method of delineating strata, and he does not credit Smith at all for this. There are, however, several stylistic differences between the two: Greenough uses a scale of 6 miles to the inch rather than 5; retains the topography whereas Smith removes it; and uses flat areas of colour rather than the fading watercolour washes employed by Smith.

Greenough's map, and its lack of fieldwork, was met with a scathing reception by some. The geologist Thomas Webster called it "so very defective and inaccurate that I was obliged to begin de novo" (Winchester). It sold, however, by virtue of being produced under the auspices of the Society and because it was cheaper than Smith's work, which has been suggested as a deliberate ploy on Greenough's part (Winchester). Greenough was forced to defend his actions later, arguing that the similarities between his and Smith's work came about because both works were correct. Eventually, the 1868 edition of Greenough's map credited Smith for the first time, but by then it was too late. Smith had died in 1839, heavily in debt.

Rare. OCLC records five institutional examples: Bristol University Library; The Natural History Museum; Nation Library of Scotland; Leeds University Library; and The British Library.