Since this fragment and all lands bordering it are now part of the White Mountain National Forest, this historical peculiarity no longer has any practical consequences. The curving northwestern border of the township follows the height of land between the drainage of the East Branch of the Pemigewasset River to the west and the headwaters of the Sawyer River and the Swift River to the east. Important summits along the border (from northeast to southwest) include Mount Bemis, at above sea level; Mount Lowell, at ; Mount Carrigain, the highest point in Livermore at ; Mount Kancamagus, at ; and Mount Osceola, at . Two roads cross the township of Livermore, although neither one is close to the site of Livermore village. The Kancamagus Highway (New Hampshire Route 112) crosses Kancamagus Pass () on the Lincoln/Livermore boundary and passes through several miles of the southeastern part of Livermore to a point just west of Sabbaday Falls. The Tripoli Road (not usually maintained for winter travel), which runs from the northern tip of Thornton through Thornton Gap to Waterville Valley, crosses the southwest corner of the township. As of the census of 2010, there were no people living in the township. Historical census figures are shown in the adjacent table. As a logging town where most of the actual logging was done in the winter by transient men hired for the season only, ascertaining the actual population of Livermore at any given time would have been problematic, and these census figures may have been influenced by how these transients were counted. Diatomaceous earth—also called tripolite—was once mined in Little East Pond and processed in a mill located in the southwestern part of Livermore township. The Tripoli Road received its name from this mill. The USFS Little East Pond Trail follows for some distance the grade of the old railroad that served the mill, and the ruins of the mill can still be found by following the line of the railroad grade into the woods for a short distance. However, this mill was far from the village of Livermore and was historically more identified with Thornton.