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Equation of Time 時間的等式
看過愛彼錶 (Audemars Piguet) 的 時間等式錶Equation of Time 的人,除了驚嘆讚賞之外,可能有不少人心中會泛起一絲疑問,何謂時間等式,又為什麼錶圈上刻有Taipei 11h 56' 的符號呢?

其實,時間等式 (更正確地説是時間差,或天文時差) equation of time 指的是鐘錶時間 (即平均太陽時間 mean solar time) 和真正太陽時間 (true solar time)之間的差距。在進一步說明之前,我們先來上一點天文學和人類計時的歷史回顧吧!


more....


AP Equation of Time made for Taipei



一如眾所周知的,古人計算時間分為陰曆和陽曆,前者以月亮、後者以太陽為依據。辜不論何者為優,現今的文明社會是立基於太陽曆。然而,地球繞太陽一圈並非正圓形,地球亦非以軸心正對太陽公轉。因此,我們所熟知的一天24小時,其實真正是大約23小時56分又4秒,因此會有閏年的發生。而且,您手錶上指示的正午十二點也不是太陽真正「日正當中」的時候。做個小試驗便知道:先調校準確您手腕上的手錶,12點的時候,走到戶外有陽光的地方,如果太陽剛好在正上方,那麼鐘錶時間剛好是真正的太陽時間;如果太陽位在您的東方,那麼equation of time是負(negative) 的;反之,若在西方則equation of time是正 (positive) 的。當然很容易猜到您看到真的「日正當中」的機會不高,因為一年中僅有四月十五、六月十四、九月一日和十二月二十四日四天,平均太陽時間和真正太陽時間是一致的。其餘的時候,誤差可大到二月十一日的正 (快) 14分22秒到十一月四日的負 (慢) 16分23秒。



Sundial at Market Harborough, Leicestershire, England



平均太陽時間 和真正太陽時間之間的差距,可經由天文學的計算得出一個公式,即 E = 9.84*sin(2B)-7.53*cos(B)-1.5*sin(B);其中 B= 360*(N-81)/365,而N 指的是日數,即一月一日 N=1,其餘類推。這樣會得出來一個像不等邊8字形的曲線公式,稱為Analemma


鐘錶史上針對天文太陽時間差做研究,其實很早,最早約可推估到十七世紀,Nicholas Mercator 的所製作的時間等式時鐘。畢竟古人的生活對太陽運行的依賴,遠比今日就算是黑夜燈火依舊通明的現代,來得要緊很多。在十八及十九世紀,重要的製錶大師如Ferdinand and Louis Berthoud 和 Breguet等人也都製作過時間等式的時計。


Breguet Equation of Time Pocket Watch made in 1828Patek Philippe Equation of Time Pocket Watch made in 1890
Equation of Time Pocket Watches: Brequet vs Patek Philippe




Patek Philippe Caliber 89



最早出現的時間等式懷錶則是寶璣大師 Abraham-Louis Breguet 的 Marie-Antoinette 以及百達斐麗 Patek Philippe 的 Caliber 89 (後來因而衍生出Star Caliber 2000 的機芯)。在當代手錶方面,寶璣則領先於1991年推出第一只時間等式萬年曆月相手錶,以指針在1 和2 點鐘方向的扇型指示出太陽時間差,不但獲得大獎獎勵,也不負寶璣大師傳承下來的創新技藝。



Breguet Equation of Time



受到一只現今存於愛彼博物館的1925年製時間等式懷錶的啟發,Audemars Piguet於公元2000年推出了全世界第一只同時具有顯示萬年曆、日出和日落時間和天文時間差的腕錶 (Sunrise and Sunset Equation of Time)。其天文時間差指針裝配於錶盤的中軸線飾有小太陽標誌,錶圈上則刻有正負15-10-5-0的刻度,可以確切地顯示每天時間差的變化,而當手錶的分針和天文時間差指針重合時,即表示真正的正午。


而由於太陽極點時間與天文時間差會隨著城市所在的經度不同而不同,因此愛彼的時間等式腕錶必須為佩戴者量身訂造,錶圈上刻劃的城市與時間 (如TAIPEI 11h 56' 或GENEVE 12 h 36' 等等),其時間就是該城市當地的太陽極點時間。而為了精準讓佩戴者不需查看天文曆或借助計算機,就能得知即時的太陽極點時間,愛彼必須製作一個一年才旋轉一圈,絕對精準定形、製作和完工的一個腎形時間等式凸輪,才能達成這樣精準的鐘錶與天文學的要求。



Audemars Piguet Sunrise and Sunset Equation of Time



相對於太陽極點時間會隨著城市所在的經度不同而不同,日出和日落的時間則不僅取決於經度,也同時決定於緯度。在赤道上,晝夜一年四季等長,離赤道越遠季節變化愈大,而在北極和南極的夏至或冬至的時候,太陽甚至不升起或不降落(永晝永夜)。愛彼錶以9點鐘 (LEVER DU SOLEIL法文, 即英文SUNRISE之意)和3點鐘 (COUCHER DU SOLEIL, 即SUNSET) 處的兩個小錶盤來顯示每天的日出日落時間,每個小錶盤的指針都由其自身的凸輪控制,這兩個凸輪同樣也必須依城市量身訂做,更須精密的加工和調整製作,才不會因為失之毫釐而在小小的日出日落時間錶盤上差之千里。
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