Part 1.
The image on the left is of Vitruvius's analemma.
As long as you know your latitude and have a protractor, you can draw this diagram without measuring shadow length, any day at any time of the year.
If you wish to follow in Vitruvius's foot steps the method below is to be used at midday at the equinox. That's tomorrow!
The work starts as the sun crosses the south axis of the meridian. Place a stick upright in the ground .
Using a rope as long as the post, draw a circle with it.
Now, draw a line from the shadow tip at C, through A and take it to the edge of the circle.
Call that place N.
This line represents the equator.
Next add the north-south line (line P Q) 90 degrees to the equator line NC.
Next the horizon (line E I ) . A horizontal line to represent the horizon, 90 degrees to the line AB.
The shadow tip C represents midday at the equinox.
The sun is on the equator.
At the solstices, the sun is at its maximum distance from the celestial equator.
The distance of the sun from the celestial equator is declination. It has a maximum value of 23.4 degrees, the axial tilt of the earth.
Now shadow points for the solstices are added.
Two lines are drawn 23.4 degrees from the equator line (C A).
Point T on the diagram at the top is where a long winter shadow will end at midday at the winter solstice, and point R is the shorter shadow in the summer.
These points are found by drawing a line at an angle of the obliquity of the ecliptic, to the equator line. So, draw line AT with an angle of 23.4 degrees with a protractor.
...But Virtuvius seems to have thought something like this:
The sun moves 15 degrees in one hour because 360 degrees divides by 15 degrees = 24. That is close enough to the obliquity, so why don't I just mark off one fifteenth of my circle at point F to G?
Virtuvius used Circumference = πd or, if he was a dunce at maths like me, would have laboriously dragged another rope all the way around the circle, measured it and divided it into 15 and used that length.
The ecliptic lines are extended and give points K and L on the diagram below.
End of part 1.
Link: http://myreckonings.com/wordpress/2007/10/28/12/
As long as you know your latitude and have a protractor, you can draw this diagram without measuring shadow length, any day at any time of the year.
If you wish to follow in Vitruvius's foot steps the method below is to be used at midday at the equinox. That's tomorrow!
The work starts as the sun crosses the south axis of the meridian. Place a stick upright in the ground .
Using a rope as long as the post, draw a circle with it.
- The center of the circle is A.
- The base of the post is B
- The tip of the shadow is C.
Now, draw a line from the shadow tip at C, through A and take it to the edge of the circle.
Call that place N.
This line represents the equator.
Next add the north-south line (line P Q) 90 degrees to the equator line NC.
Next the horizon (line E I ) . A horizontal line to represent the horizon, 90 degrees to the line AB.
The shadow tip C represents midday at the equinox.
The sun is on the equator.
At the solstices, the sun is at its maximum distance from the celestial equator.
The distance of the sun from the celestial equator is declination. It has a maximum value of 23.4 degrees, the axial tilt of the earth.
Now shadow points for the solstices are added.
Two lines are drawn 23.4 degrees from the equator line (C A).
Point T on the diagram at the top is where a long winter shadow will end at midday at the winter solstice, and point R is the shorter shadow in the summer.
These points are found by drawing a line at an angle of the obliquity of the ecliptic, to the equator line. So, draw line AT with an angle of 23.4 degrees with a protractor.
...But Virtuvius seems to have thought something like this:
The sun moves 15 degrees in one hour because 360 degrees divides by 15 degrees = 24. That is close enough to the obliquity, so why don't I just mark off one fifteenth of my circle at point F to G?
Virtuvius used Circumference = πd or, if he was a dunce at maths like me, would have laboriously dragged another rope all the way around the circle, measured it and divided it into 15 and used that length.
The ecliptic lines are extended and give points K and L on the diagram below.
End of part 1.
Link: http://myreckonings.com/wordpress/2007/10/28/12/
Comments
Post a Comment