This is pretty simple, but rather than damage anything delicate by actually 
thinking, I thought I'd just ask.
 
 In the summer, obviously I lose the morning and evening hours on my direct 
south vertical dials.
 
 How far back would I have to recline a direct south dial to pick up 6 am and 6 
pm at the summer solstice if I live at 37.72 N? How about 5 am / 5 pm?
 
 If there is a way to think to think about this without doing spherical 
geometry, I would like to know it.
 
 Thanks!
 John
 
  
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