Luckily, Heilmann was much more successful with his work on the Equidae. He was able to transform the skull of Eohippus (extinct genus of horses, donkeys and zebras) to that of Equus (modern genus of horses, donkeys and zebras). Amongst the intermediate stages of this transformation he was able to recognise two of the forms as being similar to that of Mesohippus (an extinct genus of early horse) and Protohippus (extinct three-toed genus of horse) respectively. He also recognised, however, that Parahippus which had previously been believed to be in the direct line of descent of Eohippus and Equus did not appear to fit there and "must belong to another stem of the Equidae" Evidently this work highly impressed D'Arcy as he included it, accompanied by the drawings from Heilmann, in On Growth and Form. This is another example of how the transformation method could be used to make deductions about evolutionary paths. Heilmann believed that his success with Equus meant that the method worked. He also considered the physical implications of the work when he stated "we can not expect to find in nature quite the same equal and steady evolution of the single parts as in the constructed types; some parts putting on a faster speed and so keeping in advance of others".
Heilmann concluded his letter by stating that he would be continuing his reconstructions of Pro-Avis evidencing that he was still interested in using D'Arcy's method in his long term attempt at showing that birds did not descend directly from dinosaurs.
D'Arcy replied promptly (ms19143) to Heilmann's long letter on the 20th October 1915. Like Heilmann, he also recognised the difficulties with transforming the skulls of early humans but did not doubt the method. He believed that with a slight modification of the method, or by using different starting points, they could make it work. In fact, later on in this letter he suggested a different method for tackling this issue. He hoped that the method of transformations might lead to a skull of Pithecanthropus (java man) which appears more human like than the restoration carried out by Dubois. He was, however, very impressed with Heilmann's work on the Equidae and suggested that he write a paper on the topic which D'Arcy would then ensure was published by the Royal Society of Edinburgh. Clearly, D'Arcy recognised Heilmann's talents even though the scientific community in his own country did not. He realised the importance of Heilmann's work and how it would gain great interest within the scientific community of Britain. In fact, he suggested it would be a good idea to compare Equidae not only amongst themselves, but to other mammals as well.
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