The Shadow Stick立竿見影：圭表
The simplest sun clock. Its noon shadow is a calendar: shortest at the summer solstice, longest at the winter solstice. But its hour marks shift with the seasons.
最簡單的太陽時鐘。正午的影子就是日曆：夏至最短、冬至最長。但它的整點位置會隨季節移動。
Astronomy · Lesson 8 · 天文教育 第八課
How Did People Tell Time by the Sun?古人怎麼用太陽看時間？
Turn a stick into a clock, tilt it toward the North Star to make a sundial, and find out why a Changhua sundial can be 19 minutes off your watch.
把一根竿子變成時鐘，再讓它斜斜指向北極星做成日晷；看看彰化的日晷為什麼會和手錶差到 19 分鐘。
Big idea · 一句話看懂
As the Sun crosses the sky, a stick's shadow swings around, so a stick can be a clock. But sundial time and clock time drift apart during the year, by up to about 16 minutes.
太陽橫越天空，竿子的影子就跟著轉，所以一根竿子就能當時鐘。但日晷時間和時鐘時間在一年中會慢慢錯開，最多大約 16 分鐘。
3D Model · 3D 模型
A Shadow Clock in Changhua 彰化的影子時鐘
The Sun moves along its real path over Changhua for the chosen date. With the shadow stick, the white dots mark where the shadow's tip falls at each hour of sundial time; the colored curves show the same tip path on the solstices, so you can see the hour marks move with the seasons. Switch to the sundial: its gnomon points at the North Star, so the shadow turns 15 degrees every hour, all year round. On the right, compare the sundial with the clock, and press 3 days a second to watch the gap open and close through the year.
太陽沿著所選日期在彰化上空的真實路徑移動。看「立竿見影」時，白點是日晷每個整點時影子頂端落下的位置；彩色曲線是冬至、夏至同一條影子頂端的路徑——可以看到整點的位置會隨季節改變。切到「赤道式日晷」：晷針指向北極星，影子一年到頭都是每小時轉 15 度。右邊對照日晷和時鐘；按「每秒 3 天」，看兩者的差距在一年中怎麼拉開、又收回來。
Drag to turn · 拖曳旋轉 Scroll or pinch to zoom · 滾輪／雙指縮放
This 3D model needs WebGL, which this browser does not support. The clock comparison and the table below still work.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；時鐘對照與下方的表格一樣能用。
- Gold arc: the Sun's path across the sky on the chosen date
金色弧線：所選日期太陽在天上的路徑 - White dots: where the stick's shadow tip falls at each hour of sundial time (gold at noon)
白點：日晷每個整點時竿影頂端的位置（正午是金色） - Orange and blue curves: the same shadow-tip path on the summer and winter solstices
橘色、藍色曲線：夏至、冬至的竿影頂端路徑 - Sundial gnomon: tilted 24 degrees, pointing at the North Star
日晷的晷針：傾斜 24 度，指向北極星
The stick and sundial are drawn far bigger than the sky dome would allow; the Sun's path is drawn on a dome around them. The Sun's position, the dates, and the times are real for Changhua (24.08°N, 120.54°E).
竿子和日晷相對於天穹畫得很大；太陽的路徑畫在它們周圍的天穹上。太陽位置、日期與時刻都是彰化（北緯 24.08°、東經 120.54°）的真實數值。
Sun positions and the equation of time: low-precision solar formulas from Meeus, Astronomical Algorithms (the same calculations as Lessons 3 and 6), checked against published values: +16.4 minutes on November 3 and −14.2 minutes on February 11.
太陽位置與均時差：Meeus《天文演算法》的低精度太陽公式（與第三、六課同一套），已對照公認值：11 月 3 日 +16.4 分、2 月 11 日 −14.2 分。
Reading · 英文閱讀
8
Unit 8: How Did People Tell Time by the Sun?
Long before anyone owned a clock, the Sun was the clock. Push a stick straight into the ground on a sunny morning, and its shadow stretches far to the west. As the hours pass, the shadow swings around and shrinks, until around midday it is at its shortest and points due north. Then it grows again toward the east until sunset. An old Chinese saying, "set up a pole and see its shadow," still means getting results right away. With a stick and a few pebbles to mark the shadow, anyone can tell the time.
在大家擁有時鐘之前很久，太陽就是時鐘。晴朗的早晨把一根竿子直直插進地裡，它的影子會遠遠伸向西方。隨著時間過去，影子轉動、縮短，到了中午前後最短，指向正北；然後又往東邊越拉越長，直到日落。中國的成語「立竿見影」，到今天還是指馬上見到成效。只要一根竿子和幾顆小石頭標記影子，誰都能看出時間。
The shadow moves because Earth spins. Every hour, Earth turns 15 degrees, so the Sun appears to cross the sky from east to west, and the shadow always points away from the Sun. In the morning, when the Sun is low in the east, the shadow is long and points west. At noon, the Sun is highest in the south, and the shadow is shortest. In the evening, the Sun sinks in the west, and the shadow stretches long toward the east.
影子會動，是因為地球在自轉。地球每小時轉 15 度，所以太陽看起來從東往西橫越天空，而影子永遠指向背對太陽的方向。早上太陽低低地在東方，影子又長又指向西；中午太陽在南方最高處，影子最短；傍晚太陽在西方落下，影子往東拉得很長。
A plain stick, however, is not a very good clock. As you saw in Lesson 3, the Sun takes a high path in summer and a low path in winter, so the shadow at nine o'clock in June does not land where it lands at nine o'clock in December. The fix is to tilt the stick so that it points at the North Star, parallel to Earth's axis, as you saw in Lesson 6. In Changhua, that means tilting it 24 degrees above the northern horizon. Now the shadow turns evenly, 15 degrees every hour, all year round. This tilted pointer is called the gnomon, and the great equatorial sundial in front of the Hall of Supreme Harmony in Beijing's Forbidden City works exactly this way.
不過，一根普通的竿子並不是很好的時鐘。第三課說過，太陽夏天走得高、冬天走得低，所以六月早上九點的影子，和十二月早上九點的影子落在不同的地方。解決辦法是把竿子斜過來，讓它指向北極星，也就是和地軸平行——第六課看過的那條線。在彰化，就是斜到北方地平線上方 24 度。這樣影子就會均勻地轉動，一年到頭每小時都是 15 度。這根斜斜的指針叫做「晷針」；北京紫禁城太和殿前的赤道式日晷，就是這樣運作的。
The shadow's length is a calendar, too. At noon, the shadow is shortest at the summer solstice and longest at the winter solstice. Chinese astronomers measured it for thousands of years with a gnomon called a guibiao: a tall pole with a ruler lying north along the ground. In 1276, Guo Shoujing built one 40 chi tall, five times the usual height, and measured the length of the year as 365.2425 days, the same value our calendar uses today. In Changhua, the noon shadow almost disappears in June, because the Tropic of Cancer passes just to the south, through Chiayi.
影子的長度也是一本日曆。正午的影子在夏至最短、冬至最長。中國天文學家用一種叫「圭表」的工具量了幾千年：一根高高的「表」，加上一把平躺在地上、指向北方的尺「圭」。1276 年，郭守敬造了一座高 40 尺的高表，是傳統高度的五倍，量出一年是 365.2425 天——和今天全世界使用的曆法一模一樣。在彰化，六月正午的影子幾乎消失，因為北回歸線就在南邊不遠處，穿過嘉義。
If you check a sundial against your watch, you will notice they rarely agree. A clock ticks at the same rate all year, but the Sun does not keep perfect time. Earth's orbit is an oval, so Earth moves faster in January, when it is closest to the Sun, and its tilted axis adds another wobble. Together, they make sundial time run up to about 16 minutes ahead of clock time in early November and about 14 minutes behind in mid-February. Astronomers call this difference the equation of time.
如果拿日晷和手錶對時，會發現它們很少一致。時鐘一年到頭走得一樣快，太陽卻不是完美的報時員。地球的軌道是橢圓，一月離太陽最近時走得比較快；傾斜的地軸又再加上一層變化。兩者加起來，讓日晷時間在十一月初比時鐘快將近 16 分鐘，二月中又慢大約 14 分鐘。天文學家把這個差叫做「均時差」。
There is one more twist. All of Taiwan sets its clocks by the Sun's position at 120 degrees east, but Changhua lies a little farther east, so its sundials run about 2 minutes ahead. Add it all up, and a Changhua sundial is about 19 minutes fast in early November and about 12 minutes slow in mid-February. Before time zones, every town set its clocks by its own Sun. Railroads in the United States finally adopted standard time zones in 1883, so trains could keep one schedule. On the next sunny day, stand a pencil in the ground and see what time the Sun says it is.
還有一個轉折。全台灣的時鐘都以東經 120 度的太陽位置為準，但彰化稍微偏東一點，所以彰化的日晷又快了大約 2 分鐘。全部加起來，彰化的日晷在十一月初大約快 19 分鐘，二月中大約慢 12 分鐘。在有時區以前，每個城鎮都照自己的太陽對時；直到 1883 年，美國的鐵路才採用標準時區，讓火車能用同一張時刻表。下一個晴天，把一枝鉛筆插在地上，看看太陽說現在幾點。
Read aloud · 課文朗讀
Questions · 閱讀理解
Why does a stick's shadow move during the day?
Earth spins 15 degrees every hour, so the Sun moves across the sky, and the shadow always points away from the Sun.
Why should a sundial's gnomon point at the North Star?
Then it is parallel to Earth's axis, so the shadow turns evenly, 15 degrees every hour, in every season.
Give two reasons a Changhua sundial and a clock can disagree.
Earth's oval orbit and tilted axis make the Sun run up to about 16 minutes fast or 14 minutes slow (the equation of time), and Changhua lies east of 120 degrees east, which Taiwan's clocks follow, so its sundials run about 2 minutes ahead.
Words & Phrases · 生字及片語
shadow(n.)影子On a sunny afternoon, my shadow was twice as tall as me.晴朗的下午，我的影子有我的兩倍高。swing(v.)擺動；轉向The door swung open in the wind.門被風吹開了。dial(n.)刻度盤Turn the dial on the radio to find the station.轉動收音機的刻度盤找電台。parallel(adj.)平行的The two railroad tracks run parallel to each other.兩條鐵軌彼此平行。evenly(adv.)均勻地Spread the butter evenly on the toast.把奶油均勻地抹在吐司上。measure(v.)測量We measured the classroom with a tape measure.我們用捲尺量了教室。uneven(adj.)不均勻的；不平的The sidewalk is uneven, so watch your step.人行道不平，走路小心。ahead of(phr.)比……快；在……前面My watch is five minutes ahead of the school clock.我的手錶比學校的時鐘快五分鐘。
Quick Check · 小測驗
1. In the morning, which way does a stick's shadow point?
2. How many degrees does the Sun move across the sky each hour?
3. In Changhua, when is the noon shadow longest?
4. A sundial's gnomon should point toward...
5. Because of Earth's orbit and tilt, sundial time and clock time can differ by up to about...
Sun Clocks · 太陽的時鐘
From a stick to a sundial 從一根竿子到日晷
Each instrument fixes a problem with the one before: the stick tells time roughly, the tilted gnomon makes the hours even, and the clock makes every day the same length.
每一種儀器都解決了前一種的問題：竿子能大致看時間，斜放的晷針讓鐘點均勻，時鐘則讓每一天都一樣長。
The Equatorial Sundial赤道式日晷
The gnomon points at the North Star and the dial faces the equator. Read the top face from spring to autumn and the bottom face from autumn to spring.
晷針指向北極星，晷面和赤道平行。春分到秋分看上面，秋分到春分看下面。
The Clock on the Wall牆上的時鐘
A clock follows an imaginary Sun that moves at a perfectly even pace, set to 120 degrees east for all of Taiwan. The real Sun runs up to 19 minutes ahead in Changhua.
時鐘跟著一個「假想的、走得完全均勻的太陽」，全台灣都以東經 120 度為準。在彰化，真正的太陽最多會快 19 分鐘。
Today · 今天
Today's Sundial in Changhua 今天彰化的日晷
Calculated in your browser for today. When a sundial in Changhua shows each hour, this is what your clock will say.
依今天的日期在你的瀏覽器裡現算：彰化的日晷指到每個整點時，你的時鐘是幾點幾分。
Calculating… · 計算中…
East and West · 東西方的星空
Telling Time, East and West 東西方怎麼看時間
Many of the words we use for time were born from shadows and sundials.
我們談時間的許多說法，都是從影子和日晷來的。
圭表 · The Guibiao
Guo Shoujing's Giant Gnomon郭守敬的高表
At Dengfeng in Henan, Guo Shoujing built an observatory with a gnomon 40 chi tall. Its long shadow made noon measurements five times more precise, and his Shoushi calendar of 1281 set the year at 365.2425 days, the same length as the calendar used worldwide today, three centuries earlier.
郭守敬在河南登封建造觀星台，高表達 40 尺。更長的影子讓正午的測量精確了五倍；他 1281 年頒行的《授時曆》把一年定為 365.2425 天，和今天全世界使用的曆法相同，卻早了三百年。
日晷 · Forbidden City
The Emperor's Sundial太和殿前的日晷
In front of the Hall of Supreme Harmony stands a stone equatorial sundial, tilted to Beijing's latitude so its gnomon points at the North Star. Its place beside the throne hall showed that the emperor kept heaven's time.
太和殿前立著一座石造赤道式日晷，依北京的緯度傾斜，晷針指向北極星。它擺在大殿旁邊，象徵天子掌握天時。
a.m. · p.m. · o'clock
Words from the Sundial從日晷來的英文
The meridian is the north–south line the Sun crosses at noon. A.m. is Latin for "before the meridian," and p.m. means "after the meridian." O'clock is short for "of the clock," once used to tell clock time apart from sundial time.
子午線是太陽正午時經過的南北線。a.m. 是拉丁文「子午線之前」，p.m. 是「子午線之後」。o'clock 是 of the clock（照時鐘的）的縮寫，以前用來區分時鐘時間和日晷時間。
1883 · Railroad Time
Trains Invented Time Zones火車發明了時區
Before 1883, each American town kept its own sun time, so a railroad might juggle dozens of different noons. On November 18, 1883, the railroads switched to a few standard time zones. Taiwan's zone today is set by 120 degrees east, eight hours ahead of Greenwich.
1883 年以前，美國每個城鎮都用自己的太陽時，一條鐵路可能要應付幾十種不同的「中午」。1883 年 11 月 18 日，鐵路公司改用幾個標準時區。今天台灣的時區以東經 120 度為準，比格林威治快八小時。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思A sundial always matches the clock.日晷和時鐘永遠一致。
✓ Fact · 事實They agree only on a few days a year. In Changhua, a sundial runs about 19 minutes fast in early November and about 12 minutes slow in mid-February.一年只有少數幾天一致。在彰化，日晷十一月初大約快 19 分鐘，二月中大約慢 12 分鐘。
✗ Myth · 迷思At 12 o'clock, the Sun is straight overhead.中午 12 點，太陽就在頭頂正上方。
✓ Fact · 事實Solar noon rarely falls at 12:00 by the clock, and the Sun is straight overhead only between the tropics. In Changhua, the noon Sun is always at least a little to the south.太陽正午很少剛好在時鐘的 12:00，而且只有在南北回歸線之間，太陽才會到正頭頂。在彰化，正午的太陽永遠至少稍微偏南。
✗ Myth · 迷思Noon shadows always point north.正午的影子永遠朝北。
✓ Fact · 事實Not south of the Tropic of Cancer. In Tainan and Kaohsiung, the noon Sun passes overhead twice a year, and for a few weeks around June the noon shadow points south. In Changhua, just north of the line, it always points north.在北回歸線以南就不是。台南、高雄每年有兩次太陽正午到頭頂，六月前後有幾個星期，正午的影子朝南。彰化在北回歸線稍北，影子永遠朝北。
✗ Myth · 迷思A sundial works the same anywhere you put it.日晷放在哪裡都一樣準。
✓ Fact · 事實A sundial is built for one latitude: its gnomon must tilt at that latitude and point to true north, not magnetic north. A Changhua sundial tilts 24 degrees; one in Boston tilts 42.日晷是為某個緯度做的：晷針要依當地緯度傾斜，並指向真北（不是羅盤的磁北）。彰化的日晷斜 24 度，波士頓的要斜 42 度。
Remember It · 記憶口訣
Read the Sun 一句話讀懂日晷
The gnomon points at the North Star晷針指北極星
Tilt the pointer to your latitude, 24 degrees in Changhua, so it lies parallel to Earth's axis. Then every hour is the same 15 degrees.
把晷針斜到當地的緯度（彰化 24 度），和地軸平行，每個鐘點就都是 15 度。
Fifteen degrees an hour一小時 15 度
Earth turns 360 degrees in 24 hours, so the Sun and every shadow move 15 degrees an hour, about one and a half fists.
地球 24 小時轉 360 度，所以太陽和影子每小時移動 15 度，大約一個半拳頭。
Short in summer, long in winter夏至影短，冬至影長
The noon shadow is shortest at the summer solstice and longest at the winter solstice. That is how the guibiao found the solstices.
正午的影子夏至最短、冬至最長；圭表就是這樣找出二至的。
Fast in November, slow in February十一月快，二月慢
A Changhua sundial runs about 19 minutes ahead of the clock in early November and about 12 minutes behind in mid-February.
彰化的日晷十一月初比時鐘快大約 19 分鐘，二月中慢大約 12 分鐘。
Classroom Activity 1 · 課堂活動一
Find Solar Noon with a Stick 用一根竿子找太陽正午
You need · 準備材料
- A straight stick or pencil about 30 centimeters long, standing upright一根約 30 公分長的直竿或鉛筆，直立插好
- Chalk or small stones to mark the shadow粉筆或小石頭，用來標記影子
- A watch and the Today's Sundial table on this page一支手錶，以及本頁「今天彰化的日晷」表
Steps · 步驟
- On a sunny day, start at 11:15 by the clock. Stand the stick straight up on flat ground.晴天裡，從時鐘 11:15 開始。在平地上把竿子直直立好。
- Every 5 minutes, mark the tip of the shadow and write the time beside it.每 5 分鐘標一次影子頂端的位置，並在旁邊寫上時間。
- Keep going until about 12:30. Find the mark with the shortest shadow.一直做到大約 12:30，找出影子最短的那一點。
- The time of the shortest shadow is solar noon. Compare it with the solar noon on this page.影子最短的時刻就是太陽正午。和本頁算出的太陽正午比一比。
- A line from the stick to the shortest mark points true north. Check it against a compass, and notice that they differ a little.從竿子到最短那一點的連線，就是真北。拿羅盤對照，會發現兩者有一點差距。
Teaching tip: in October and November, solar noon in Changhua comes well before 12:00, around 11:41 to 11:48, which surprises most students.
教學提示：十月、十一月時，彰化的太陽正午大約在 11:41 到 11:48 之間，比 12:00 早不少，學生通常很驚訝。
Classroom Activity 2 · 課堂活動二
Make a Paper Sundial 做一個紙日晷
You need · 準備材料
- A paper plate or card circle, with a pencil pushed through the center一個紙盤或圓形卡紙，中心插一枝鉛筆
- A protractor and a marker量角器和麥克筆
- A wedge of cardboard or clay to hold the dial at an angle一塊紙板或黏土，用來把晷面撐出角度
Steps · 步驟
- Draw lines from the center every 15 degrees, like a clock face with 24 hours. Number the bottom line 12 and go around: 13, 14, 15... on one side and 11, 10, 9... on the other.從圓心每 15 度畫一條線，像 24 小時的鐘面。最下面那條標 12，一邊往 13、14、15……，另一邊往 11、10、9……。
- Push the pencil through the center so it sticks out on both sides. This is the gnomon.把鉛筆穿過圓心，兩面都露出來，這就是晷針。
- Outside, point the pencil toward true north and tilt it up 24 degrees, so the dial faces the sky at 66 degrees. Use the cardboard wedge to hold it steady.到戶外，讓鉛筆朝正北、往上斜 24 度，晷面就會以 66 度朝天。用紙板或黏土固定。
- Read the hour where the pencil's shadow falls. Then add or subtract the difference from the Today's Sundial table to get clock time.讀出鉛筆影子落在的鐘點，再依「今天彰化的日晷」表加減差距，換算成時鐘時間。
Teaching tip: between the March and September equinoxes the shadow falls on the top face; for the rest of the year, read the bottom face, just like the sundial in the 3D model.
教學提示：春分到秋分，影子落在晷面上面；其餘時間要看下面——和 3D 模型裡的日晷一樣。