The first appearance of THE HEART OF THE WORLD was as a serialized novel, published by PEARSON'S WEEKLY, August 1894 through January 1895. I have never seen this serialization.
McKay, Scott and Whatmore claim that Longmans, Green, and Company published the first edition in book-form in New York in May 1895. There are 13 Amy Sawyer illustrated plates in this edition. Ads at the end of the book are not dated.
McKay, Scott and Whatmore all claim March 27, 1896 as the publication date of the first British edition. This edition, purportedly composed of 10,000 copies, contains 15 Amy Sawyer illustrations, 2 more than the American edition. Ads at the end of the book are dated December 1895.