The first image comes from page 222 of the 1920 expanded edition of Marshall Gardner's hollow earth book Journey to the Earth's Interior, or Have the Poles Really Been Discovered?.
The second image is from page 637 of James William Buel's 1884 The World's Wonders As Seen by the Great Tropical and Polar Explorers...
Neither book gives the name of their artist. The title page of Buel's book tells us that it contains "beautiful engravings from designs by the explorers themselves," but I have been unable to determine who the explorer is that Buel's illustration refers to. Buel's illustration appears above an account of the discovery and recovery of the Adams/Schumachoff mammoth (Gardner's appears above a blockquote of that same section of Buel's).
I'm not aware of any illustrations attached to Adams' report (he published French, German, and English versions; I've only been able to locate the English account). As it was a scientific report, I think it's safe to say that, if he had commissioned illustrations, he would have made them of anatomical details of the mammoth and not a romantic representation of his eyes meeting the mammoth's across a crowded room.
Buel places his retelling of the Adams/Schumachoff mammoth inside a larger discussion of John Cleves Symmes' hollow earth theory. This may be one reason why Gardner chose Buel's account to quote rather than one of the dozens of other tellings available to him. The main telling of Symmes' hollow earth theory was a novel called Symzonia: Voyage of Discovery by Capn. Adam Seaborn (probably a pseudonym for Symmes). The book has no illustrations--or mammoths, for that matter--so it isn't the source of Buel's illustration.
We may never know the original source of the illustration, but it's clear that Gardner's illustration is based on Buel's. The main elements of each are the mammoth in the glacier face and the explorer, with his dog team in the background. The Buel illustration is more detailed, better composed, and better executed. In making his illustration wider, Gardner stretched the elements and changed their size. The most obvious change is that Gardner's explorer stands further away from the mammoth and further back in the picture. He smaller than Buel's explorer, making the that much relatively larger.
However, Gardner's changes are based on more than a bad eye for art. Gardner was trying to sell his hollow earth concept. In his version of the hollow earth theory, the inner earth could be reached through polar openings several hundred miles across. The Arctic ice pack was just a ring surrounding the hole. Because the inner earth was lit by a tiny sun at its center, we, on the outer skin of the earth, could see its light shining out of the polar opening. We call that light the auroras. Mammoths enter the story by straying too close to the hole where our cold air freezes them and they drift in icebergs over the edge and onto the coast of Siberia.
Gardner's image illustrates these concepts. In spreading the image, Gardner shows the the unobstructed path to the pole. He has removed a range of hills in the background of the Buel image to show us that the mammoth has come directly out of the sea. The light of the inner sun streams out of the polar hole just over the horizon. The picture might look crappy to us, but it told the story Gardner wanted it to tell.
Stealing an image is even easier today than it was in Buel and Gardner's day--and it was easy then. Sometimes, it's hard not to steal. The above image is on a dozen or so websites. I would love to credit the artist, but none of the sites I've checked say who the artist was.
* A case could be made that Steller's sea cow was the first extinct animal to provide soft tissue for examination. Georg Wilhelm Steller was the naturalist assigned to Bering's second expedition in 1741. While in Alaska, he was the first European to describe several plants and animals, including the lovely blue jay that bears his name. On the way back to Russia, the expedition was shipwrecked in the Comandorski Islands. Bering and about half the crew died during the winter that they were stranded there. Steller didn't allow this to interrupt his work; he explored the island and wrote detailed descriptions of the flora and fauna. One of the animals he discovered was a large, slow moving sirenian unique to the islands. Within thirty years of Steller's return, whalers and trappers on their way to Alaska hunted Steller's sea cow into extinction. Technically, the sailor who butchered the last Steller sea cow was also conducting the first disection of an extinct species.