Longitude 

1  Once on a Wednesday excursion when I was a little girl, my father bought me a beaded wire ball that I loved. At a touch, I could collapse the toy into a flat coil between my palms, or pop it open to make a hollow sphere. Rounded out, it resembled a tiny Earth, because its hinged wires traced the same pattern of intersecting circles that I had seen on the globe in my schoolroom – the thin black lines of latitude and longitude. The few colored beads slid along the wire paths haphazardly, like ships on the high seas.

2 My father strode up Fifth Avenue to Rockefeller Center with me on his shoulders, and we stopped to stare at the statue of Atlas, carrying Heaven and Earth on his.

3 The bronze orb that Atlas held aloft, like the wire toy in my hands, was a see-through world, defined by imaginary lines. The Equator. The Ecliptic. The Tropic of Cancer. The Tropic of Capricorn. The Arctic Circle. The prime meridian. Even then I could recognize, in the graph-paper grid imposed on the globe, a powerful symbol of all the real lands and waters on the planet.

4 Today, the latitude and longitude govern with more authority than I could have imagined 40-odd years ago, for they stay fixed as the world changes its configuration underneath them – with continents adrift across a widening sea, and national boundaries repeatedly redrawn by war and peace.

5  As a child, I learned the trick for remembering the difference between latitude and longitude. The latitude lines, the parallels, really do stay parallel to each other as they girdle the globe from the Equator to the poles in a series of shrinking concentric rings. The meridians of longitude go the other way: They loop from the North Pole to the South and back again in great circles of the same size, so they all converge at the ends of the Earth.

6   Lines of latitude and longitude began crisscrossing our world view in ancient times, at least three centuries before the birth of Christ. By AD 150, the cartographer and astronomer Ptolemy had plotted them on the 27 maps of his first world atlas. Also for this landmark volume, Ptolemy listed all the place names in an index, in alphabetical order, with the latitude and longitude of each – as well as he could gauge them from travelers’ reports. Ptolemy himself had only an armchair appreciation of the wider world. A common misconception of his day held that anyone living below the Equator would melt into deformity from the horrible heat.

7 The Equator marked the zero-degree parallel of latitude for Ptolemy. He did not choose arbitrarily but took it on higher authority from his predecessors, who had derived it from nature while observing the motions of the heavenly bodies. The sun, moon, and planets pass almost directly overhead at the Equator. Likewise the Tropic of Cancer and the Tropic of Capricorn, two other famous parallels, assume their positions at the sun’s command. They mark the northern and southern boundaries of the sun’s apparent motion over the course of the year.

8 Ptolemy was free, however, to lay his prime meridian, the zero- degree longitude line, wherever he liked. He chose to run it through the Fortunate Islands (now called the Canary & Madeira Islands) off the north-west coast of Africa. Later mapmakers moved the prime meridian to the Azores and to the Cape Verde Islands, as well as to Rome, Copenhagen, Jerusalem, St. Petersburg, Pisa, Paris, and Philadelphia, among other places, before it settled down at last in London. As the world turns, any line drawn from pole to pole may serve as well as any other for a starting line of reference. The placement of the prime meridian is a purely political decision.

9 Here lies the real, hard-core difference between latitude and longitude – beyond  the superficial difference in line direction that any child can see: The zero-degree parallel of latitude is fixed by the laws of nature, while the zero-degree meridian of longitude shifts like  the  sands of  time. This difference makes finding latitude child’s play, and turns the determination of longitude, especially at sea, into an adult dilemma – one that stumped the wisest minds of the world for the better part of human history.

10 Any sailor worth his salt can gauge his latitude well enough by the length of the day, or by the height of the sun or known guide stars above the horizon. Christopher Columbus followed a straight path across the Atlantic when he “sailed the parallel” on his 1492 journey, and the technique would doubtless have carried him to the Indies had not the Americas intervened.

11 The measurement of longitude meridians, in comparison, is tempered by time. To learn one’s longitude at sea, one needs to know what time it is aboard ship and also the time at the home port or another place of known longitude – at the very same moment. The two clock times enable the navigator to convert the hour difference into a geographical separation. Since the Earth takes 24 hours to complete one full revolution of 360 degrees, one hour marks 1/24 of a spin, or 15 degrees. And so each hour’s time difference between the ship and the starting point marks a progress of 15 degrees of longitude to the east or west. Every day at sea, when the navigator resets his ship’s clock to local noon when the sun reaches its highest point in the sky, and then consults the home port clock, every hour’s discrepancy between them translates into another 15 degrees of longitude.

12Those same 15 degrees of longitude also correspond to a distance traveled. At the Equator, where the girth of the Earth is greatest, 15 degrees stretch fully one thousand miles. North or south of that line, however, the mileage value  of  each  degree  decreases. One degree of longitude equals four minutes of time the world over, but in terms of distance, one degree shrinks from 68 miles at the Equator to virtually nothing at the Poles.

13 Precise knowledge of the hour in two different places at once – a longitude prerequisite so easily accessible today from any cheap pair of wristwatches – was utterly unattainable up to and including the era of pendulum clocks. On the deck of a rolling ship, such clocks would slow down, or speed up, or stop running altogether. Normal changes in temperature encountered en route from a cold country of origin to a tropical trade zone thinned or thickened a clock’s lubricating oil and made its metal parts expand or contract with equally disastrous results. A rise or fall in barometric pressure, or the subtle variations in the Earth’s gravity from one latitude to another, could also cause a clock to gain or lose time.

14  For lack of a practical method of determining longitude, every great sea captain in the Age of Exploration became lost at sea despite the best available charts and compasses. From Vasco da Gama to Vasco Nuñez de Balboa, from Ferdinand Magellan to Sir Francis Drake – they all got where they were going willy-nilly, by forces attributed to good luck or the grace of God.

Translation

经度

1      当我还是一个小女孩的时候，有个星期三外出远足，父亲给我买了一个带珠子的金属线球，我很喜欢。只要用手轻轻一碰，我就可以把球折成一个扁平的线圈，放在手掌之间；也可以一下子把它打开，变成一个空心球。如果撑圆了，它看起来就像一个小地球，因为上面的用铰链连接在一起的金属丝构成了一系列交叉的圆圈，跟我在教室里见到的地球仪上的那些圆圈——那些细细的黑色的经线和纬线——是同样的形状。几个彩色的珠子在圆球的金属丝上随意滑动，就像船在公海上航行一样。

2      那个时候父亲会把我扛在肩上，迈着大步从第五大道走到洛克菲勒中心。我们会停下来凝视那个顶着天空、举着地球的阿特拉斯雕塑。

3      阿特拉斯手中高举的那个青铜球和我手中的那个玩具一样，是空心的，一些想象中的线勾勒出其轮廓：赤道、黄道、北回归线、南回归线、北极圈、本初子午线。即使是在那个时候，我也能意识到，地球仪上的那些像绘图纸格子似的格子线是地球上所有真实存在的陆地和水域的强有力的象征。

4      今天，经度和纬度更加具有权威性，这是40多年前的我无法想象的。因为尽管世界形态在不断地变化——大陆在变得越来越宽的大洋上不停地漂移，战争与和平一次又一次地重新界定国土疆界——但是经度和纬度依然保持不变。

5      当我还是一个孩子的时候，我就学会了如何区别经线和纬线。纬线总是平行的，它们从赤道到两极一圈又一圈地环绕地球，是一连串越来越小的同心圆。经线则不同：它们从北极绕到南极，再从南极到北极，形成同样大小的大圆圈，所以所有的经线都在地球的两极会集。

6      在古代，至少在基督诞生前300年，经线和纬线就开始影响我们的世界观。到了公元150年，地图绘制家和天文学家托勒密在他绘制的第一本世界地图册中的27幅地图上都标上了经线和纬线。在这本具有里程碑意义的地图册上，托勒密把所有的地名按字母顺序列在一个索引中，并注明了每个地方的经度和纬度——有些是他从那些旅行者的游记中大致推测出来的。托勒密本人对广阔世界的知识大多是通过阅读等间接获得的。在他生活的那个时代，一个流传很广的误解是赤道以南的地区天气太热，所以生活在那里的人都会变成畸形。

7      对托勒密来说，赤道标志着零度纬线。他并不是随意选择零度纬线的位置，而是采纳那些更具权威的天文学先辈的意见。这些先辈们通过观测天体的运动，从大自然中得到答案。因为在赤道上， 太阳、月亮和其他行星几乎都是从我们头顶的正上方经过。另外两条著名的纬线——北回归线和南回归线也是依照太阳的位置来确定的。它们标志着太阳在一年中运动轨迹的南北界限。

8      但是，托勒密可以随意决定本初子午线，即零度经线的位置。他当时界定的本初子午线穿过位于非洲西北海岸附近的幸运群岛（即现在的加那利与马德拉群岛）。而后来的地图绘制者又先后将本初子午线移到了亚速尔群岛、佛得角群岛，以及罗马、哥本哈根、耶路撒冷、圣彼得堡、比萨、巴黎和费城等许多地方。本初子午线最终落户伦敦。其实随着地球的转动，任何一条通过两极之间的经线都可以作为起始参照经线，本初子午线的位置纯粹是一个政治决定。

9      除了连孩子都能看出来的方向上的不同之外，经线和纬线实际的核心区别在于：零度纬线是由自然规律确立的，而零度经线就像流逝的时光一样变化不定。这种差别让确定纬度像儿戏一样简单，而在人类历史上的大多数时候，确定经度——特别是在大海上——成了让人们抓耳挠腮的难题。世界上那些最聪明的人都对此束手无策。

10      任何一个称职的水手都可以通过白昼的长短、太阳的高度和天空中已知的那些导航星而足够精确地推测出纬度。在1492年的那次航行中，克里斯托夫·哥伦布就是沿着“与纬线平行的方向航行”，直线跨越大西洋。要不是半路杀出个美洲大陆的话，这种航海技术无疑能让他航行到西印度群岛。

11      相比之下，经线的测量则受时间的影响。在海上，要想知道自己所在位置的经度，你首先要知道船上的时间，同时要知道起航港或者另外一个已知经度的地方的时间——两个地点在同一时刻的时间。两个不同的时间能够让航行者把两个地方的时差转化成地理上的距离。因为地球每24小时完成一次360度的旋转，那么一个小时就是1/24圈，或者是15度，所以船上的时间和起航港的时间每差一个小时，就意味着船向东或向西航行了15度。在海上，每天正午领航员在太阳到达天空最高点时把船上的钟调到本地时间12点，然后再对照起航港的时间，每差一个小时就意味着船跨越了15 度的经度。

12     与此类似，15度的经度也对应一定的航行距离。在赤道，地球的周长最长，15度的经度代表长达1,000英里的航行距离。但是在赤道以北或赤道以南，经度每增加1度，就意味着航行的距离就相应地缩短一点。在地球上的任何地方，就时间而言，1度的经度相当于4分钟，但就距离而言，1度的经度所对应的距离是从赤道开始，向北、向南逐渐递减的。在赤道上，1度的经度相当于68英里的航行距离，但在两极，其对应的距离几乎为零。

13     现在任何便宜的腕表都可以精确地告诉人们两个不同地理位置的地点在同一时刻的时间，这是计算经度的先决条件。但这在人类使用摆钟以及之前的时代是根本不可能的。在一艘颠簸的船上， 这样的摆钟会走慢或走快，或者干脆就停了。船只在从一个寒冷的国家出发开往一个热带信风区的途中，气温的任何正常变化都会使钟表的润滑油变稀或者变稠，并且导致金属零件膨胀或收缩，这两种情况都会造成灾难性的后果。气压的升降，或者从一个纬度到另一纬度地球重力的细微变化， 都会使钟表走快或者走慢。

14     在地理大发现时代，尽管有当时最好的航线图和罗盘，但由于缺乏比较实用的确定经度的方法，每一位杰出的船长都曾在海上迷过路。从瓦斯科·达伽马到瓦斯科·努涅斯· 德·巴尔博亚，从费尔迪南德·麦哲伦到弗朗西斯·德雷克爵士——他们都好像是命中注定似的，靠运气或上帝的恩典到达了目的地。