数学家传记
亨丽爱塔·勒维特是一位美国天文学家,发现了造父变星的亮度和周期之间的关系。这是测量遥远星系距离的关键一步。
亨丽爱塔·勒维特的父母是George Roswell 勒维特(1838-1911)和勒维特 勒维特 Kendrick(1844-1922)。George Roswell 勒维特是一位公理会牧师,出生于马萨诸塞州洛厄尔,曾在威廉姆斯学院学习,之后从安多弗神学院获得神学博士学位。他的父亲是Erasmus Darwin 勒维特,一位商人,而George Roswell 勒维特的一个兄弟也叫Erasmus Darwin 勒维特。勒维特的这位叔叔是一位工程师,因设计勒维特泵发动机而闻名。他是美国机械工程师学会的第二任主席,并当选为美国艺术与科学院会士。George Roswell 勒维特于1866年10月2日与勒维特 勒维特 Kendrick结婚,她是马萨诸塞州剑桥的Henry Kendrick的女儿。勒维特,即本传记的主人公,是她父母七个孩子中最年长的,其他孩子是Roswell Harvey Leavitt(生于1871年10月4日,幼年去世)、Martha Almira 勒维特(生于1873年8月1日)、George William(生于1875年9月2日)、Mira Fay 勒维特(生于1878年9月20日,2岁时去世)、Caroline Reed 勒维特(生于1880年5月16日)和Darwin Ashley 勒维特(生于1882年6月15日)。
在1870年人口普查时,勒维特两岁,住在马萨诸塞州米德尔塞克斯县洛厄尔她祖父的家中。户主是Erasmus Darwin 勒维特(老),当时60岁,已退休,房子由他57岁的妻子Almira管理。至少有另外十人住在这所房子里(都姓勒维特),包括当时34岁的Erasmus Darwin 勒维特(小),以及勒维特的母亲和父亲。
勒维特成为马萨诸塞州米德尔塞克斯县剑桥市朝圣者公理会的牧师,到1871年他的第二个孩子出生时,全家已住在剑桥。1880年的人口普查让我们看到勒维特一家住在沃兰德街9号,靠近乔治担任牧师的教堂。乔治被列为户主,妻子“操持家务”。他们的七个孩子中有五个在家,最大的两个,勒维特和玛莎,在上学。同住的还有勒维特的姑妈玛丽·肯德里克,以及25岁的仆人凯瑟琳·麦克唐纳。住在隔壁沃兰德街11号的,是勒维特的祖父伊拉斯谟斯·达尔文勒维特,与妻子阿尔米拉和女儿阿尔米拉(记录显示她患有脊柱疾病)。伊拉斯谟斯有一名22岁的仆人艾达·L·马斯顿。
勒维特一家搬到俄亥俄州克利夫兰,1885年勒维特进入奥柏林学院。这所学院成立于1833年,自建校起就实行男女同校,是美国最早的男女同校学院。她在1885-86学年学习预科课程,然后在1886-88两年进行本科学习。完成课程后她回到剑桥,并于1888年申请进入拉德克利夫学院。严格说来这并不准确,因为拉德克利夫学院直到1894年才如此命名。哈佛大学的一些教授在1870年代开始以非正式安排教授女性,这于1879年成为女性大学教育促进会。在被录取之前,她接受了古典文学知识的测试,必须写一篇短文,接受了拉丁语、希腊语和德语语言技能的测试,接受了历史以及数学、物理和天文学知识的测试。除历史外,她成功通过了所有这些测试,但获准在课程期间“弥补这一不足”。
勒维特在女性大学教育促进会所修的课程非常偏重文科,科学内容很少。她修了拉丁语、希腊语、英语、德语、法语和意大利语的语言课程。她还学习了美术、哲学、入门物理和数学。这门课程涵盖解析几何和微分,她因此获得A,但在最后一年修的天文学课程中她获得A-。她于1892年6月毕业,获得一份证书,上面写明如果她是男性,就有资格获得文学学士学位。
她最后一年的天文学课程是在哈佛天文台修的,毕业后她提出免费在天文台工作。当时天文台的负责人是爱德华·查尔斯·皮克林,他曾在麻省理工学院任物理学教授,1876年被任命为哈佛天文台台长。他认为天文台的任务是尽可能多地收集恒星数据,以便帮助他人进行理论工作。他的目标是尽可能多地列出恒星的位置、颜色和星等。他很高兴能得到勒维特的协助而无需付她报酬,便给她布置了研究照相底片的任务,她必须从中记录所需数据。然而,已知许多恒星的亮度会变化,所以勒维特的任务之一就是留意这类变星。1896年间,她写成了自己发现的手稿草稿。
1896年9月,勒维特申请了出国护照。此时她住在剑桥波特,该地如今是剑桥的一部分,但当时是紧邻剑桥的一个独立城镇。申请是为了让她出国并“在大约两年内”返回。申请中给出了勒维特的体貌特征:年龄——28岁,身高——5英尺8英寸,前额——高,眼睛——灰色,鼻子——长,嘴——中等,下巴——长,头发——黑色,肤色——浅,脸型——长。她从波士顿乘船前往欧洲。返回后,勒维特前往哈佛与皮克林讨论她的工作。皮克林就她如何改进手稿提出了一些建议,随后勒维特动身前往威斯康星州贝洛伊特的罗克,她的父亲当时在那里担任公理会牧师。1900年人口普查记录这家人住在贝洛伊特查芬街1263号;勒维特的父母和他们五个在世的孩子都在这个地址。此时她自称教师,并在贝洛伊特学院教授艺术。然而,她渴望重返天文学工作,但正如她在1902年5月13日写给皮克林的信中所解释的,她面临各种困难。她写道:——
我回来后的那个冬天被意外的操劳占满了。当我终于有空重拾工作时,我的眼睛严重困扰着我,使我无法如此近距离地使用它们。
她一直在做的工作需要非常仔细、紧张地检视照相底片上的图像,这导致她眼睛出问题,一点也不奇怪。然而,她的眼睛现在已康复,她希望皮克林把她完成1896年一直在做的手稿所需的材料寄给她。她的信继续写道:——
我无比遗憾地告诉你,我如此欣喜地承担、并怀着极大乐趣推进到一定程度的这项工作,竟被搁置未完成。我非常真诚地为这么久没有就此事写信而道歉。我的听力有些问题,有点奇怪地担心,观星可能会使它更糟。我的朋友们说,我也认识到这是事实,当我全神贯注于天文工作时,我的听力远不如平时好。寒冷的天气似乎加重了我的状况。显然,我无法在任何学校或学院教授天文学,因为那样我就得在寒冷的冬夜带班级外出。我的耳科医生禁止任何这样的暴露。你认为我有可能在某个天文台或冬季气候温和的学校找到工作吗?除了你自己之外,还有我可以申请的人吗?
皮克林立即回信,向她提供了一个全职职位:——
考虑到你的工作质量,我愿意为此支付每小时三十美分,尽管在此类情况下我们通常的价格是每小时二十五美分。如果你无法搬迁,我会支付你到剑桥短期访问的路费。你可以在那里工作,以便把工作带回家乡贝洛伊特。我不知道有哪个位于温暖气候的天文台可以雇用你从事类似工作,而且也很难为你提供大量你可以在其他地方进行的工作。无论如何,我怀疑天文学与你的听力状况有什么关系,除非有优秀的耳科医生向你确认情况确实如此。
勒维特回复道:-
亲爱的⟦N2⟧教授,我已设法安排好这里的事务,以便下个月能前往剑桥并留在那里直到工作完成。你提出的每小时三十美分的非常慷慨的报酬将使我能够做到这一点。
为了在七月底前到岗,勒维特出发前往剑桥,但在俄亥俄州停留探望一位亲戚时,她发现这位亲戚生病了,于是她花时间帮忙照料。这使得到达剑桥的时间推迟到了八月底。
她没工作多久就去度冬假了,并于1903年1月1日申请了护照。她的体貌特征描述与1896年早先申请时的描述完全相同,只是现在她把头发描述为“深色”而非“黑色”。她要求将护照寄往意大利那不勒斯的美国领事馆,因此她一定是前往那不勒斯。她肯定在S S Commonwealth上,因为她在1月3日从该船寄出了一封信。在欧洲逗留一段时间后,她于7月29日从英格兰利物浦出发,乘坐S S Ivernia,于8月6日抵达波士顿。从波士顿她乘火车前往伯洛伊特,然后返回剑桥,再次担任天文台的固定职位。她与叔叔、工程师勒维特一起住在他建在剑桥花园街的一栋大别墅里,距离天文台只有很短的步行路程。
1904年春天,她在检查阿雷基帕天文台拍摄的小麦哲伦云底片时,发现了变星。小麦哲伦云和大麦哲伦云是靠近银河系的星系。为了对距离有个概念,小麦哲伦云的直径约为7,000光年,距离银河系约190,000光年。大麦哲伦云的直径约为14,000光年,距离银河系160,000光年。银河系本身的直径约为140,000光年。两个麦哲伦云都只能从南半球看到。1891年阿雷基帕天文台在秘鲁建立后,南天恒星的底片被送往哈佛天文台。勒维特正在处理的正是这些底片,测量恒星的星等和位置。她开始发现“数量异常多”的变星——这是她自己的话。
1908年,勒维特在21页的论文1777 Variables in the Magellanic Clouds中完整叙述了她的工作。论文开头如下:-
1904年春天,用24英寸布鲁斯望远镜[在阿雷基帕天文台]拍摄的两张小麦哲伦云照片的比对,导致发现了若干暗弱变星。由于该区域似乎很有趣,又检查了其他底片,尽管其中大多数底片的质量低于后来底片通常的高标准,仍发现了57颗新变星,并在第79号通函中宣布。为了提供确定其周期的材料,次年秋天用布鲁斯望远镜拍摄了16张曝光时间从两到四小时的底片系列。当它们于1905年1月抵达剑桥时,将其中一张与早期底片比对,立即发现了异常数量的新变星。还发现,相隔两三天拍摄的底片可以比对,结果同样有趣,表明许多变星的周期很短。迄今为止这样发现的数量为969颗。加上此前已知的23颗,该区域变星总数为992颗。还用24英寸布鲁斯望远镜拍摄的18张照片检查了大麦哲伦云,发现了808颗新变星,其中152颗在第82号通函中宣布。由于讨论这些变星需要大量时间,下面准备了临时星表。
在论文末尾,她给出了16颗变星的列表,显示了它们的周期和星等。然后她作出了重要陈述:-
值得注意的是,较亮的变星具有较长的周期。
让我们注意,由于当时还不知道距离尺度,银河系中变星的绝对星等无法从其视亮度估计。然而,小麦哲伦云中的恒星,由于距离地球至少大致相同,其绝对星等可以从视星等相当准确地推断出来。这使得勒维特能够做出极其重要的观察,即变星的周期与其绝对星等相关。然而,尽管结果令人信服,它们仅基于十六颗恒星的样本。勒维特需要继续进一步测量。然而,这项工作因她生病而中断。
到1908年12月,勒维特在波士顿住院。出院后,她去了贝洛伊特,与父母和两个未婚兄弟同住:乔治William Leavitt,现在是传教士,以及达尔文·阿什利勒维特,现在是公理会牧师。1909年的大部分时间她都在贝洛伊特的家中度过,打算秋天恢复天文台的工作。然而,“小病”使她无法实现这一目标。皮克林热切希望她回来,但不是从事变星项目,而是从事他最喜欢的项目,即获取靠近北极星的96颗恒星的精确数据。最终,当她仍然身体不够好,无法来剑桥时,皮克林把材料寄给她在贝洛伊特工作。她处理了这些底片,将数据送回哈佛天文台,直到1910年5月她身体足够好,可以恢复在剑桥的工作。
随后她的工作又多次中断,例如1911年3月她的父亲去世,她再次回到位于Beloit的家中。她再次收到用于研究96颗近北极星恒星的底片,并在Beloit期间继续研究这些。1911年秋天她回到剑桥,除了其他工作外,她能够继续研究小麦哲伦云中的变星。她的工作报道在1912年的一份哈佛通告中,她在其中写道:-
这些变星的亮度与其周期长度之间的显著关系将会被注意到。[在1908年的论文中]曾提请注意较亮的变星具有较长周期的事实,但当时认为数量太少,不足以得出一般结论。然而,此后确定的8颗额外变星的周期符合相同的规律。这种关系以图形显示……得到的曲线,一条为极大值,一条为极小值,异常平滑,且形式非凡。……在对应于极大值和极小值的两组点中,可以轻松地画出一条直线,从而表明变星的亮度与其周期之间存在简单关系。周期每增加一个星等亮度,周期的对数增加约0.48……由于这些变星可能距离地球几乎相同,它们的周期显然与其实际发光量相关,这由其质量、密度和表面亮度决定。
勒维特没有将这些变星称为造父变星,但今天它们以该名称闻名,源于1784年由弗瑞兹·约翰 Goodricke发现的第一颗此类恒星。勒维特的发现使得宇宙的尺度得以确定,尽管还需要更多工作,因为她发现的关系只能确定相对距离,而需要其他技术来确定至少一颗此类变星的距离以校准尺度。勒维特没有机会参与这项工作,因为Pickering将她的技能用于其他项目。
在接下来的四年里,勒维特在哈佛天文台工作,除了1913年上半年因胃部手术而中断了三个月。她完成了关于北极星附近96颗恒星的工作并发表了结果,这是一项非凡的工作,她和利用来自13台不同望远镜拍摄的299张底片的数据进行了反复核对。
哈罗·沙普利正在研究银河系的大小,他于1917年8月联系Pickering,向勒维特询问关于球状星团中变星的问题。他在信中写道:-
我相信,她发现周期与亮度的关系,注定会成为恒星天文学最重要的成果之一。
直到1918年7月再次写信后,哈罗·沙普利才收到皮克林的回复,说勒维特有底片可以研究他的问题。1920年她亲自与哈罗·沙普利通信,询问她应该将研究重点放在什么上,他回复时再次建议研究球状星团中的变星。1921年3月,哈罗·沙普利成为哈佛天文台台长,此时勒维特是恒星测光部门的负责人。然而,到1921年11月,她已因胃癌病重,像此前一段时间那样,与母亲住在剑桥的林奈街。一位朋友于12月6日探望了她,并写道:-
去看望可怜的勒维特,她正因恶性胃病而垂危。如此消瘦,变化如此之大。非常、非常令人悲伤。
勒维特于12月12日晚上10点30分去世,她的葬礼于12月14日在第一公理会教堂的小礼拜堂举行。她被安葬在剑桥公墓。我们注意到,她的母亲并没有比她多活多久,因为母亲于1922年去世。尽管勒维特去世时没有立遗嘱,但她拥有伯洛伊特两处相邻房产的一部分,她去世后,她的份额归了她的兄弟们(因为她的母亲在此事解决之前已经去世)。
还有一点必须补充。1925年,约斯塔·米塔格-莱弗勒写信到哈佛天文台给勒维特,并不知道她已经去世。他写道:-
勒维特,我的朋友兼同事、乌普萨拉的冯·蔡佩尔教授告诉我,你令人钦佩地发现了小麦哲伦云中S造父变星的星等与周期长度之间关系的经验定律,这给我留下了如此深刻的印象,以至于我认真倾向于提名你为1926年诺贝尔物理学奖候选人……
这封信被交给了Shapely,他告知了约斯塔·米塔格-莱弗勒勒维特的死讯。然而,他的回复并不光彩,因为很明显他试图将勒维特的发现的大部分功劳归于自己,可能是希望约斯塔·米塔格-莱弗勒能提名他获得诺贝尔奖!
Henrietta Swan Leavitt's parents were George Roswell Leavitt (1838-1911) and Henrietta Swan Kendrick (1844-1922). George Roswell Leavitt was a Congregationalist minister, born in Lowell, Massachusetts, who had studied at Williams College before being awarded a doctorate in divinity from the Andover Theological Seminary. His father was Erasmus Darwin Leavitt, a merchant, while one of George Roswell Leavitt's brothers was also named Erasmus Darwin Leavitt. This uncle of Henrietta's was an engineer who gained fame designing the Leavitt pumping engine. He was the second president of the American Society of Mechanical Engineers and was elected a fellow of the American Academy of Arts and Sciences. George Roswell Leavitt married Henrietta Swan Kendrick, a daughter of Henry Kendrick of Cambridge, Massachusetts, on 2 October 1866. Henrietta, the subject of this biography, was the oldest of her parents' seven children, the others being Roswell Harvey Leavitt (born 4 October 1871 and died an infant), Martha Almira Leavitt (born 1 August 1873), George William (born 2 September 1875), Mira Fay Leavitt (born 20 September 1878 and died aged 2), Caroline Reed Leavitt (born 16 May 1880) and Darwin Ashley Leavitt (born 15 June 1882).
At the time of the 1870 census, Henrietta was two years old and living in her grandfather's home in Lowell, Middlesex, Massachusetts. The head of the household was Erasmus Darwin Leavitt (Sr.), at that time 60 years old and retired, and the house was run by his wife Almira who was 57. At least ten others were living in the house (all named Leavitt), including Erasmus Darwin Leavitt (Jr.), at that time 34 years old, and Henrietta's mother and father.
George Roswell Leavitt became pastor at the Pilgrim Congregational Church in Cambridge, Middlesex, Massachusetts and, by the time that his second child was born in 1871, the family were living in Cambridge. The 1880 census gives us a picture of the Leavitt family living at 9 Warland Street, close to the church where George was the pastor. George is listed at head of the house with his wife "keeping house". Five of their seven children are there, with the two eldest, Henrietta and Martha, being at school. Also living with them is Mary Kendrick, Henrietta's aunt, and a 25 year old servant Catherine McDonald. Living next door, at 11 Warland Street, is Erasamus Darwin Leavitt, Henrietta's grandfather, with his wife Almira and daughter Almira (who is recorded as having spinal difficulties). Erasamus has a 22 year old servant Ada L Marston.
The Leavitt family moved to Cleveland, Ohio and in 1885 Henrietta Leavitt enrolled at Oberlin College. This College, founded in 1833, was coeducational from its founding and was the earliest coeducational college in the United States. She studied the preparatory course in the academic year 1885-86, then spent two years 1886-88 on undergraduate studies. After completing the course she returned to Cambridge and, in 1888, she applied to enter Radcliffe College. This is not strictly accurate since Radcliffe College was not so named until 1894. Some professors from Harvard University had begun teaching women in informal arrangements in the 1870s and this became the Society for the Collegiate Instruction of Women in 1879. Before being accepted, she was tested on her knowledge of classic literature, she had to write a short composition, was tested on her language skills in Latin, Greek and German, was tested on her knowledge of history and of mathematics, physics and astronomy. She passed all these tests successfully except for history but she was allowed to "rectify this deficiency" during her course.
The course that Leavitt took at the Society for the Collegiate Instruction of Women was very arts based and contained little science. She took language courses on Latin, Greek, English, German, French, and Italian. She also studied fine arts, philosophy, introductory physics and mathematics. This course covered analytic geometry and differential calculus and she was awarded an A for this but for an astronomy course that she took in her final year she was awarded A-. She graduated in June 1892 receiving a certificate which stated that, if she had been a man, she would have qualified for a B.A.
Her final year astronomy course had been taken at the Harvard Observatory and, after graduating, she offered to work at the Observatory for free. The head of the Observatory at this time was Edward Charles Pickering who had been a professor of physics at the Massachusetts Institute of Technology before being appointed director of the Harvard Observatory in 1876. He believed that the task of the Observatory was to collect as much data as possible on the stars so that others might be helped in theoretical work. He aimed to tabulate the position, colour and magnitude of as many stars as possible. Delighted to have Leavitt's assistance without having to pay her, he set her the task of studying photographic plates from which she had to record the required data. However, it was known that many stars changed in brightness so one of Leavitt's tasks was to look out for such variable stars. During 1896 she wrote up a draft manuscript of her findings.
In September 1896 Leavitt applied for a passport to travel abroad. At this time she was living in Cambridgeport which today is part of Cambridge but at that time was a separate town close to Cambridge. The application was to allow her to go abroad and return "in about two years." The application gives a physical description of Leavitt: Age - 28, Stature - 5 ft 8 ins, Forehead - High, Eyes - Gray, Nose - Long, Mouth - Medium, Chin - Long, Hair - Black, Complexion - Light, Face - Long. She sailed from Boston to Europe. On her return, Leavitt went to Harvard to discuss her work with Pickering. He made some suggestions on how she might make some improvements to her manuscript and then Leavitt set off for Beloit, Rock, Wisconsin where her father was now the Congregational Minister. The 1900 census records the family living at 1263 Chafin Street in Beloit; Leavitt's parents and their five surviving children are all at this address. At this time she described herself as a teacher and she taught art in Beloit College. However, she longed to return to her work on astronomy but, as she explained in a letter to Pickering dated 13 May 1902, she had various difficulties. She wrote:-
The winter after my return was occupied with unexpected cares. When, at last, I had leisure to take up the work, my eyes troubled me so seriously as to prevent my using them so closely.
It is not at all surprising that the work she had been doing, requiring very careful intense inspection of images on photographic plates, had caused her eyes trouble. However, her eyes now having recovered she wanted Pickering to send her the materials that she needed to complete the manuscript she had been working on in 1896. Her letter continues:-
I am more sorry than I can tell you that the work I undertook with such delight, and carried to a certain point with such keen pleasure, should be left uncompleted. I apologise most sincerely for not writing concerning the matter long ago. I am having some trouble with my hearing, worrying, a little oddly, that stargazing might make it worse. My friends say, and I recognise the truth of it, that my hearing is not nearly as good when absorbed in astronomical work. Cold weather seems to aggravate my condition. It is evident that I cannot teach astronomy in any school or college where I should have to be out with classes on cold winter nights. My aurist forbids any such exposure. Do you think it is likely that I could find employment either in an observatory or in a school where there is a mild winter climate? Is there anyone besides yourself to whom I might apply?
Pickering replied immediately offering her a full-time position:-
For this I should be willing to pay thirty cents an hour in view of the quality of your work, although our usual price, in such cases, is twenty-five cents an hour. If it was not possible for you to relocate, I would pay your fare for a short visit to Cambridge. You could get work in order to take home to Beloit. I do not know of any observatory in a warm climate, where you could be employed on similar work and it would be difficult to furnish you with a large amount of work that you could carry on elsewhere. In any case, I should doubt if astronomy had anything to do with the condition of your hearing, unless you have been assured that this is the case by a good aurist.
Leavitt replied:-
My dear Prof. Pickering, it has proved possible for me to arrange my affairs here so that I can go to Cambridge next month and remain until the work is completed. Your very liberal offer of thirty cents an hour will enable me to do this.
Aiming to take up her position by the end of July, Leavitt set out for Cambridge but, stopping to visit a relative in Ohio, she discovered the relative was ill and so she spent time helping out. This delayed her arrival in Cambridge until the end of August.
She did not work too long before taking a winter break and applied for a passport on 1 January 1903. Her physical description is identical to the one on the earlier application in 1896 except she now describes her hair as "dark" rather than "black." She asked for the passport to be sent to the U S Consul in Naples, Italy, so she must have been travelling to Naples. Certainly she was on the S S Commonwealth since she sent a letter from that ship on 3 January. After spending time in Europe she returned to Boston from Liverpool, England, on the S S Ivernia, leaving Liverpool on 29 July and arriving in Boston on 6 August. From Boston she went by train to Beloit, then returned to Cambridge to again take up her permanent position at the Observatory. She lived with her uncle Erasmus Darwin Leavitt, the engineer, in a large villa he had built on Garden Street in Cambridge, only a short walk from the Observatory.
In spring 1904, while examining plates taken of the Small Magellanic Cloud by the Arequipa Observatory, she discovered variable stars. The Small Magellanic Cloud and the Large Magellanic Cloud are galaxies close to Milky Way. To get an idea of distances, the Small Magellanic Cloud is about 7,000 light years in diameter, and lies about 190,000 light years from the Milky Way. The Large Magellanic Cloud is about 14,000 light years in diameter and 160,000 light years from the Milky Way. The Milky Way itself is about 140,000 light years in diameter. Both Magellanic Clouds are only visible from the Southern Hemisphere. After the Arequipa Observatory was established in Peru in 1891, plates of southern stars were sent to the Harvard Observatory. It was these plates that Leavitt was working on, measuring magnitudes and position of stars. She began to find "an extraordinary number" of variables - these were her own words.
In 1908 Leavitt published a full account of her work in the 21-page paper 1777 Variables in the Magellanic Clouds. The paper begins as follows:-
In the spring of 1904, a comparison of two photographs of the Small Magellanic Cloud, taken with the 24-inch Bruce Telescope [at the Arequipa Observatory], led to the discovery of a number of faint variable stars. As the region appeared to be interesting, other plates were examined, and although the quality of most of these was below the usual high standard of excellence of later plates, 57 new variables were found, and announced in Circular 79. In order to furnish material for determining their periods, a series of sixteen plates, having exposures from two to four hours, was taken with the Bruce Telescope the following autumn. When they arrived in Cambridge, in January 1905, a comparison of one of them with an early plate led immediately to the discovery of an extraordinary number of new variable stars. It was found, also, that plates taken within two or three days of each other, could be compared with equally interesting results, showing that the periods of many of the variables are short. The number thus discovered, up to the present time, is 969. Adding to these 23 previously known, the total number of variables in this region is 992. The Large Magellanic Cloud has also been examined on 18 photographs taken with the 24-inch Bruce Telescope, and 808 new variables have been found, of which 152 were announced in Circular 82. As much time will be required for the discussion of these variables, the provisional catalogues given below have been prepared.
At the end of the paper she gave a list of sixteen variable stars, showing their periods and magnitudes. She then made the important statement:-
It is worthy of notice that the brighter variables have the longer periods.
Let us note that since no distance scale was known at this time, the absolute magnitude of variables in the Milky Way could not be estimated from their apparent brightness. However, the absolute magnitude of stars in the Small Magellanic Cloud, being at least approximately the same distance away from the Earth, could be fairly accurately deduced from their apparent magnitude. This allowed Leavitt to make the vitally important observation that the periods of the variables was related to their absolute magnitudes. However, although the results were convincing they were only based on a sample of sixteen stars. Leavitt needed to continue to work on making further measurements. However, this work was interrupted when she fell ill.
By December 1908 Leavitt was in hospital in Boston. On her release she went to Beloit to stay with her parents and two unmarried brothers, George William Leavitt, now a missionary, and Darwin Ashley Leavitt, now a Congregationalist minister. She spent much of the year 1909 at the family home in Beloit, intending to resume work at the Observatory in the autumn. However a "slight illness" prevented her from carrying out this aim. Pickering was keen that she return, but not to work on the variable stars project, but rather to work on his favourite project of obtaining accurate data on 96 stars close to Polaris. Eventually, when she still was not well enough to come to Cambridge, Pickering sent her material to work on at Beloit. She carried out work on these plates, returning data to the Harvard Observatory, until May 1910 when she was well enough to resume her work in Cambridge.
Further interruptions to her work followed, for example in March 1911 her father died and again she returned to the family home at Beloit. She was again sent plates for the 96 near Polaris stars and worked on these while in Beloit. She was back in Cambridge by the autumn of 1911 when, in addition to other work, she was able to continue to work on the variable stars in the Small Magellanic Cloud. Her work is reported on in a Harvard Circular of 1912 where she wrote:-
A remarkable relation between the brightness of these variables and the lengths of their periods will be noticed. [In the 1908 paper] attention was called to the fact that the brighter variables have longer periods, but at that time it was felt that the number was too small to warrant the drawing of general conclusions. The periods of 8 additional variables which have been determined since that time, however, conform to the same law. The relation is shown graphically ... The resulting curves, one for maxima and one for minima, are surprisingly smooth, and of remarkable form. ... A straight line can readily be drawn among each of the two series of points corresponding to maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods. The logarithm of the period increases by about 0.48 for each increase of one magnitude in brightness ... Since the variables are probably at nearly the same distance from the Earth their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness.
Leavitt did not refer to these variable stars as Cepheid variables, but they are known today by that name after the first such star discovered in 1784 by John Goodricke. Leavitt's discovery allowed the scale of the universe to be determined, although more work was required since the relation that she discovered only allowed relative distances to be determined while other techniques were required to determine the distance to at least one such variable star to calibrate the scale. Leavitt was not given the chance to participate in this as Pickering used her skills on other projects.
For the next four years Leavitt worked at the Harvard Observatory, except for a break of three months in the first half of 1913 when she had surgery to her stomach. She completed work on the 96 near Polaris stars and published the results, a remarkable piece of work which she and checked and rechecked using data from 299 plates produced by 13 different telescopes.
Harlow Shapley was working on the size of the Milky Way galaxy and he contacted Pickering in August 1917 with questions for Leavitt concerning variables in globular clusters. He wrote in his letter:-
Her discovery of the relation of period to brightness is destined to be one of the most significant results of stellar astronomy, I believe.
Only after writing again in July 1918 did Shapley receive a response from Pickering saying that Leavitt had plates to investigate his question. She corresponded with Shapley herself in 1920, asking advice on what she should focus her research and he replied, again suggesting variables in globular clusters. In March 1921 Shapley became Director of the Harvard Observatory and by this time Leavitt was Head of Stellar Photometry. However, by November 1921 she was serious ill with stomach cancer, living as she had done for some time, with her mother on Linnean Street, Cambridge. A friend visited her on 6 December and wrote:-
Went to see poor Henrietta Leavitt, dying with a malignant stomach trouble. So thin and changed. Very, very, sad.
Leavitt died at 10.30 p.m. on 12 December, and her funeral was held at the Chapel of the 1st Congregational Church on 14 December. She was buried in Cambridge Cemetery. We note that her mother did not outlive her daughter by much for she died in 1922. Although Leavitt died without making a will, she owned a share of two adjacent properties in Beloit and her share went, after her death, to her brothers (since her mother had died before this was settled).
There is a postscript that we must add. In 1925 Gösta Mittag-Leffler wrote to Leavitt at the Harvard Observatory, not being aware that she had died. He wrote:-
Honoured Miss Leavitt, What my friend and colleague Professor von Zeipel of Uppsala has told me about your admirable discovery of the empirical law touching the connection between magnitude and period-length for the S Cepheid-variables of the Little Magellan's cloud, has impressed me so deeply that I feel seriously inclined to nominate you to the Nobel prize in physics for 1926 ...
The letter was given to Shapely who informed Mittag-Leffler of Leavitt's death. However, his reply does him no credit for it is clear that he was trying to take much of the credit for Leavitt's discovery, probably in the hope that Mittag-Leffler would nominate him for a Nobel prize!
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