1. Earth Dial Fundamentals with a Look at a New Digital Dial Robert L.Kellogg, PhD. December 2009 Horizontal Earth Dial E A R T H 2 0 0 4 T W O W O R L D S - O N E S U N Latitude: 38 Degrees 7 8 9 10 11 12 1 2 3 4 5

2. Irish Stone Pillar Dial with Reconstructed Gnomon [photo by Mario Arnaldi] Midday ix ninth vespers iii third terce

3. Place a Sphere on the End [photo by Mario Arnaldi] Midday ix ninth vespers iii third terce

4. Views of Pillar Dial with Sphere Gnomon Side View Gnomon Midday ix ninth vespers iii third terce Sunset Sunrise Gnomon Shadow Gnomon with Sphere on Top

5. Delineated Shadow of Gnomon Sphere Midday ix ninth vespers iii third terce 1 PM 2 PM 3 PM 4 PM 5 PM Sphere Shadow Winter Solstice Summer Solstice Equinox North Point

6. Horizontal Earth Dial Made on Same Principle Gnomon Shape (To Scale) Horizontal Earth Dial E A R T H 2 0 0 4 T W O W O R L D S - O N E S U N Latitude: 38 Degrees 7 8 9 10 11 12 1 2 3 4 5 Gnomon

7. Now look at shadow of a Flag instead of a Sphere Midday ix ninth vespers iii third terce Sunset Sunrise Flag Shadow Gnomon Shadow Flag Gnomon Side View Flag Added Gnomon Notice that flag has been set offset from vertical parallel to shadow

8. Shadow of a Flag Midday ix ninth vespers iii third terce 1 PM 2 PM 3 PM 4 PM 5 PM Flag Shadow Winter Solstice Summer Solstice Equinox Flag North Point

9. Shadow Plane two parallel plates replace the ancient gnomon and flag. A slit is etched in the front plate. Light shines through to the second plate Summer Slit twist angle is same for laying out hour angles: tan(  ) = cos(lat) tan(HA) forlat = 54° HA = 3 hours gives slit twist  = 30°.4 Equinox NP Winter Slit slit illumination at different seasons 

10. Alignment of Three Vertical Planes Opaque Plane with Slit Translucent Screen Hour Line Mask for 3 pm at 30.4° and extends from winter to summer solstice Generating Slit for 3 pm at 30.4° Sunbeam illumination through both slits onto translucent screen Gnomon Height Opaque Plane with Slit

11. Shadow Duration – Rectangular and Wedge Slits Gnomon Wedge Summer NP Winter w = wo +  ’ = width of slit  W=R  ’ that is a bit smaller than duration  R  ’+w+p shadow motion w = wo Summer NP Winter w = width of slit shadow motion  W+w+p W = width of mask opening R  Gnomon Slit

12. Time Error – Rectangular vs. Wedge Slits

13. Look at Both Planes Simultaneously S W Observer Looking South at Local NoonSide View Slits Number Mask

14. Detail of Typical Hour Number W =.05 -.15 mm 10-30 cm 5-25 cm Gap =.5 – 1.5 mm

15. Winter Shadows Movement Winter 1:00 PM

16. Winter Shadows Movement Winter 2:00 PM

17. Summer Shadows Movement Summer 1:00 PM

18. Summer Shadows Summer 2:00 PM