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正方案

郭守敬的天文儀器之一，有一放置在西貢天文公園內

direction determining table, aka horizontal gnomon


其貌不揚, 但古人在建築房屋, 街道, 城牆等, 非常注重要對正東南西北方向, 考工記亦有題及正四方，水平。簡儀基架也有架設一正方案，以正南北


功能: 記錄日出日沒的晷影

: 定子午線南北方向, 及東西方向(正四方)




若用來測量緯度,需要準確垂直(how?)豎立在子午線平面上,  似乎有點複雜:





1.測定緯度時,在正方案中心畫 兩條正交直線,分別代表天極 及天赤道方向。

2.再按黃赤交角, 在赤道上下各繪一平行線, 與規圈各相交於兩點,每點分別 代表夏、冬二至時太陽的方向。

把正方案垂直懸掛在平行 子午面,並於冬至或夏至中午時,在案中心及規圈相交點 各插一小棒。

3.以案中心為軸心 轉動正方案,使三棒的影子重疊。北極線的高度便是當地 緯度。

NB 此方法是要首先知道黃赤交角的角度（23.44度）。


在元史中根本不是這樣記載：

又测用之法，先测定所在北极出地度，即自案地平以上度，如其数下对南极入地度，以墨斜经中心界之，又横截中心斜界为十字，即天腹赤道斜势也。” 

解释：用倾斜墨线经正方案中心，测量出天空中北极星（南极星）出地角度，又在对应出地角度倾斜墨线上横截中心得出来的十字交叉，得到的就是天球赤道面的倾斜度。






或用此公式(邱紀良）

φ = 90° –（a1+ a2）÷2

φ ： 緯度 latitude 

a1,a2 ： 冬至，夏至的太陽離地面的角度，或叫太陽仰角 sun elevation angle


Btw，PBS用" 2 stick quadrant", 就簡單易明得多了



Reference

baidu 

元史

Zhihu 

日晷百變


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