After receiving the letter from Shufeldt, D'Arcy did not wait long before acting on it. On 29th December 1914 he reached out to Heilmann, sending him a copy of his paper on Hesperornis. In return he asked for Heilmann's work on this extinct bird and also expressed interest in his publications on the topic of origin of birds (ms19133).
The following correspondence was fast-paced. This is surprising especially considering that D'Arcy was located in Dundee, Scotland whilst Heilmann was living in Copenhagen, Denmark and the First World War was raging. Heilmann's first response to D'Arcy was written on 22nd January 1915, and in this letter (ms19134) he thanked D'Arcy for his copy of On the Systematic Position of Hesperornis. He also stressed the different goals of his own work and D'Arcy's. Whilst D'Arcy focused on the anatomy and finding similarities between Hesperornis and other bird-like dinosaurs, Heilmann says himself that "writing in a popular form for quite unscientific readers, it was my aim to make the bird live before their eyes". His talent for art allowed him to achieve this, but he already hinted at his struggles within the Danish scientific community. At the end of the letter he stated "I am an artist and only an incipient amateur in science" and clearly communicated his bewilderment at Shufeldt recommending him to D'Arcy. Whilst it is not said explicitly, Heilmann's respect for D'Arcy and his feeling of inadequacy ooze out of the letter. This provides a strong contrast to the amount of scientific information he included in his letter -- the reader can clearly see that Heilmann was a lot more capable than he thought himself to be.
Heilmann also mentioned that he hoped to compare the skull of Hesperornis to that of a reptile in order to prove his theory that birds did not come from dinosaurs. This shows that he was thinking of very similar problems as D'Arcy but he lacked the formal method to test his theories. D'Arcy's work was therefore very useful for Heilmann. However, this also shows that D'Arcy was not alone in his thinking. His network of contacts was so wide that no matter the topic he was able to find someone to discuss ideas with.
Following on from the previous letter, D'Arcy sent his response (ms19135) on 28th January 1915, less than a week after Heilmann sent his previous letter. He highlighted Heilmann's interest in the anatomy of Hesperornis which D'Arcy explored in his own paper. D'Arcy also stated that he did not read Danish well - yet he was able to read Heilmann's work on Hesperornis. No doubt this talent for languages helped his scientific learning considerably. To further Heilmann's curiosity, he introduced him to the method of "deformation". It is the main building block of the last - and most influential - chapter of D'Arcy's On Growth and Form. As D'Arcy explained in this letter
Differences between one animal and another are not so complicated as people think. [...] One does not need to draw in full the skull or other parts of a large series of animals. If you draw one of them only and draw the empty networks which correspond to the others, then the outline of these can be filled in at any time."Hence D'Arcy presented the field of morphology (the study of the shape, or structure, of organisms) to Heilmann and it sparked his interest in finding connections between animals and hence showing that they are related.
D'Arcy also included "a little puzzle" for Heilmann -- he described it as a human skull drawn inside a network and an empty network to which Heilmann was expected to re-draw the shape of the skull. This is a very practical and impressive demonstration of the method D'Arcy offered to Heilmann.
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