In 1835, the Maine Legislature passed a "Resolve in favor of certain Officers and Soldiers of the Revolutionary War, and the widows of the deceased Officers and Soldiers," granting 200 acres of land to those who had served three years while residents of Massachusetts or the District of Maine. The land would be taken from the "Indian Purchase" in Penobscot County and from unappropriated townships in Washington County. The applications for these bounty land grants have long been available from the Maine State Archives, and are among those indexed on its website. The images of these applications are now available at FamilySearch. (Edit: The collection is now searchable.)
Using the index previously linked, we can find those applications marked "Maine" by browsing the alphabetically arranged images here. (Those marked "Mass." will be found here.) My ancestor Moses Dunham's application should be toward the back of Box 5. Sure enough, his file begins here and includes ten images. Moses declared that he had served the requisite three years.
Statements of Jonathan Holmes and Malachi Bartlett—neighbors he had previously called on to confirm his service—were copied from his pension file. On March 29, 1836, he was granted Lot No. 95 in Township No. 3, Indian Purchase. Moses soon assigned the certificate to his son-in-law Calvin Gurney for $70.
These applications may seem duplicative to those who have viewed their ancestors' applications for federal pensions, but careful comparison will often reveal unique and valuable testimony. In any event, they provide added evidence of each veteran's service and of his financial state a half century after the Revolution.