皮埃尔·布格Pierre Bouguer

皮埃尔·布格的父亲Jean Bouguer是皇家水文学教授。Jean Bouguer教他的儿子布格数学和水文学，而布格结果证明是一个出色的学生。作为一个真正的神童，他在十五岁时就对数学和科学有了深刻的理解。

然后发生了一件了不起的事。Jean Boutroux在布格十五岁时去世，因此他的水文学教授职位空缺了。布格申请了他父亲的教授职位，他是一个如此杰出的年轻人，既才华横溢又知识渊博，因此被任命了。

人们可能会认为，如此早的才华和成就将导致他过着平淡无奇的生活。然而，这与事实相去甚远，因为他的成就变得更加令人印象深刻。1727年，他因提交关于船桅的论文而赢得了Académie Royale des Sciences的大奖。两年后，他再次赢得大奖，这次是一篇关于在海上观测恒星高度的论文，然后，在1731年，他因在海上观测磁偏角的工作而第三次赢得Académie的大奖。

Académie Royale des Sciences进一步表彰了布格，他于1731年当选为数学部的通讯成员，随后于1735年当选为正式成员。1732年，布格研究了追踪曲线，并就此写了一篇论文，该论文[1]：-

……是若干篇展示他相当高数学能力的论文之一。

1735年4月，布格出发参加由Académie Royale des Sciences组织的远征，前往秘鲁测量赤道处子午线一度的长度。夏尔·马里·德·拉孔达米纳是同一远征队的成员，其第三位科学成员是远征队队长路易·戈丹。三人沿不同路线完成前往目的地的旅程，布格和戈丹乘船前往基多，而拉夏尔·马里·德·拉孔达米纳则从曼塔经陆路前往。三位科学家在基多会合。

三人很快陷入了分歧。Godin开始独自工作，而布格与夏尔·马里·德·拉孔达米纳合作。布格是第一个尝试利用山体引力导致的铅垂线偏转来测量地球密度的人。他与夏尔·马里·德·拉孔达米纳一起，于1740年在秘鲁进行了测量，并在La Figure de la terre Ⓣ（地球的形状）（1749年）中发表了他的结果。天文学家内维尔·马斯基林在1774年更成功地使用了同样的方法，将密度置于4.5到5之间。

1741年，布格发现了他与夏尔·马里·德·拉孔达米纳共同进行的测量中存在一个小错误，该测量旨在确定子午线一度的长度。两人就他们是否应重新检查结果发生了争执。三人各自独立进行了测量，工作于1743年完成。三人经由不同路线返回。

布格撰写了关于海军机动和导航的著作，并在船舶设计方面推导出了计算稳心半径（衡量船舶稳性的一个量）的公式。然而，他对一个他多年来视为业余爱好的科学领域做出了杰出贡献。这就是他在光度学方面的工作，这为他赢得了“光度学之父”的称号。

从1721年开始，他进行了一些最早的天文光度测量。1725年11月23日，他将月球的视亮度与标准烛焰的视亮度进行了比较。他的想法是，尽管人眼作为光度计很差，但它非常擅长判断两个物体是否具有相同的亮度。通过移动蜡烛并使用约翰内斯·开普勒的平方反比定律，他能够测量亮度。他于1729年在Essai d'optique sur la gradation de la lumièreⓉ（《论光的等级的光学论文》）中发表了这一方法。这部著作包含布格关于光的第二大发现，即布格定律。该定律表达了辐射能吸收与吸收介质之间的关系[1]：-

在均匀透明的介质中，准直光束中剩余的光是光在介质中路径长度的指数函数。

Pierre Bouguer's father, Jean Bouguer, was Royal Professor of Hydrography. Jean Bouguer taught his son Pierre both mathematics and hydrography, and Pierre turned out to be an outstanding pupil. A real child prodigy, he had a deep understanding of mathematics and science by the age of fifteen years.

Then a remarkable thing happened. Jean Boutroux died when Pierre was fifteen years old and so his professorship of hydrography became vacant. Pierre applied for his father's professorship and he was such a remarkable young man, both brilliant and knowledgeable, that he was appointed.

One might think that such early brilliance and achievement would lead to him leading an unexciting life. However, this is far from the truth for his achievements became still more impressive. In 1727 he won the Grand Prix of the Académie Royale des Sciences for his submission on masts of ships. Two years later he again won the grand prize, this time with an essay on observing the altitudes of stars at sea then, in 1731, he won his third Grand Prix from the Académie for his work on the observation of the magnetic declination at sea.

The Académie Royale des Sciences further honoured Bouguer when he was elected as an associate in the mathematics section in 1731 and then, in 1735, he was elected to full membership. In 1732 Bouguer studied pursuit curves writing a paper on them which [1]:-

... was one of several that display his considerable mathematical ability.

In April 1735 Bouguer set out on an expedition, organised by the Académie Royale des Sciences, to Peru to measure the length of a degree of meridian at the equator. La Condamine was a member of the same expedition and its third scientific member was the leader of the expedition Louis Godin. The three finished their journey to their destination by different routes, Bouguer and Godin sailing to Quito, while La Condamine went overland from Manta. The three scientists met up at Quito.

The three were soon involved in disagreements. Godin began to work on his own while Bouguer worked with La Condamine. Bouguer was the first to attempt to measure the density of the Earth using the deflection of a plumb line due to the attraction of a mountain. Together with La Condamine, he made measurements in Peru in 1740 publishing his results in La Figure de la terre Ⓣ (1749). A more successful use of the same method was made by the astronomer Maskelyne in 1774, placing the density between 4.5 and 5.

In 1741 Bouguer discovered a small error in the joint measurements made with La Condamine to determine the length of a degree of meridian. These two now fell out over whether they should recheck their results. All three made independent measurements, the work being completed in 1743. The three returned by different routes.

Bouguer wrote on naval manoeuvres and navigation and, in ship design, derived a formula for calculating the metacentric radius (a measure of ship stability). However, he made an outstanding contribution to an area of science which he treated as a hobby for many years. This was his work on photometry which has earned for him the title of "father of photometry".

Starting in 1721 he made some of the earliest measurements in astronomical photometry. He compared the apparent brightness of the moon to that of a standard candle flame on 23 November 1725. His idea was that although the human eye was poor as a light meter it was very good at telling whether two objects were the same brightness. By moving the candle and using Kepler's inverse square law he was able to measure brightness. He published this method in Essai d'optique sur la gradation de la lumière Ⓣ in 1729. This work contains Bouguer's second great discovery relating to light, namely Bouguer's law. This law expresses the relationship between the absorption of radiant energy and the absorbing medium [1]:-

In a medium of uniform transparency the light remaining in a collimated beam is an exponential function of the length of the path in the medium.