in 1889, Lieutenant Murray reported placing a heliograph station at a point in the Pinal Mountains in preparation for a series of Army heliograph exercises . From this location, he recorded visibility to several other stations in the network, including Lookout Peak, San Carlos, Saddle Mountain, Table Mountain, and Graham Mountain
This report allows us to analyze his location using modern geospatial methods. By modeling visibility from each of those distant stations, we can determine the overlapping areas from which all five would have been visible — effectively solving for Murray’s heliograph site. Terrain models derived from digital elevation data were used to calculate line-of-sight visibility. These calculations incorporated not only the rugged relief of and around the Pinal Mountains but also the curvature of the Earth and the refractive effects of the atmosphere—factors that become critical over the long distances these heliographs spanned.
Using a Digital Elevation Model (DEM), visibility diagrams were created for each of the known stations Murray listed. In these diagrams, every raster cell visible from a given station was assigned a value of 1, and non-visible cells were assigned a value of 0
For example, a visibility surface generated from Lookout Peak (today’s Aztec Peak) highlights all the terrain visible from that location. The same process was repeated for San Carlos, Saddle Mountain, Table Mountain, and Graham Mountain.
Using a Digital Elevation Model (DEM), visibility diagrams were created for each of the known stations Murray listed. In these diagrams, every raster cell visible from a given station was assigned a value of 1, and non-visible cells were assigned a value of 0
For example, a visibility surface generated from Lookout Peak (today’s Aztec Peak) highlights all the terrain visible from that location. The same process was repeated for San Carlos, Saddle Mountain, Table Mountain, and Graham Mountain.
Source: Lieutenants and Light
San Carlos, Saddle, Table, and the Graham Mountains could be seen” — can be expressed as a logical equation:
Areas visible to all listed stations = L ∧ SC ∧ S ∧ T ∧ G
By multiplying the rasters together (a Boolean algebra "AND"), we identify only those cells where all five stations are simultaneously visible. The result is a refined area that matches Murray’s described location.
Areas visible to all listed stations = L ∧ SC ∧ S ∧ T ∧ G
By multiplying the rasters together (a Boolean algebra "AND"), we identify only those cells where all five stations are simultaneously visible. The result is a refined area that matches Murray’s described location.
Source: Lieutenants and Light
The final raster highlights the overlapping visibility zones. This not only provides a likely placement for Murray’s heliograph station but also demonstrates how historical military records can be combined with modern GIS to recreate field conditions and confirm positions