Doyle scholars Jon Lellenberg and Daniel Stashower (both, I believe, acquaintances of my dad, "Corot") edited and annotated Conan Doyle's journal as 'Dangerous Work': Diary of an Arctic Adventure, published by the University of Chicago Press in 2012. Unsurprisingly, it's a good read; Doyle's turns of phrase, sense of humour, and essential compassion for humanity will be recognizeable to anyone familiar with the Sherlock Holmes stories.
'Dangerous Work' appealed to me both as a Holmesian and as someone with an interest in Arctic wildlife. So I was particularly intrigued by the entry for 16 April:
Jack Buchan shot a hawk in the evening which the Captain with his eagle eye discerned upon a hummock, and detected even at that great distance to be a hawk. About 18 inches high with beautifully speckled plumage.
The use of "speckled plumage" would seem to indicate that this was a white gyr. Consider this entry from 18 March, about a month earlier: "Captain saw a large speckled owl a couple of hundred yards from the ship, saw a few roaches [dovekies, Alle alle] and guillemots but we are too far from land to have many. We are considerably to the North of Jan Mayen now." Clearly at this latitude, what the captain reported was a snowy owl; if both the owl and the "hawk" were speckled, we might assume both shared black markings on a white background.
Later in the journal, however, Conan Doyle includes on a "Zoological List of Whaling Voyage" an "Iceland hawk (Falco Icelandicus)". At that time, taxonomists recognized several species of gyr, corresponding to what we now denote "colour morphs", and the Icelandic falcon was grey on the back and white underneath. A white gyr with black markings would be considered a Greenlandic falcon.
[Field guide illustration by Roger Tory Peterson. Peterson would have shunned the old-fashioned terminology, but the central bird represents the "Icelandic" type, and the right-hand bird the "Greenlandic".]
So, was Doyle's gyr white or grey? The young medical student turned whaler was not an ornithologist, and made no claim to be one, so it could be a mistake to rely too heavily on his identification of the bird as an "Iceland hawk" specifically. His drawing ("my idea of a hawk—had the Smallpox in its youth") makes no distinction between the back and underneath, showing instead a uniform spotting all over—but again, while some of his sketches are quite good, he had no pretentions of being an artist, either. The question could be easily settled if the collected specimen could be tracked down, but if I'm honest, I'm far too lazy a researcher to make the effort even if I knew for a fact that the specimen still existed.
[Conan Doyle's sketch, along with one by Captain John Gray.]
What is beyond question is that Conan Doyle's observation of a gyr perched on an ice floe far from land is consistent with a "discovery" made over a century later by Kurt Burnham of the High Arctic Institute, indicating that some gyrs actually spend a good portion of the year out at sea. As Doyle's most famous creation, Sherlock Holmes, proclaims in The Hound of the Baskervilles, "The world is full of obvious things which nobody by any chance ever observes."