牛顿于1686年6月20日致哈雷的信（前半部分）
在我之前的一篇博文中，我提到：牛顿在1686年6月20日致哈雷的一封信中，列举了在他之前对引力研究做出贡献的几位先驱。
此信的背景是：牛顿当时已完成他的著作《自然哲学的数学原理》的前二卷，正着手写作第三卷。胡克通过哈雷要求牛顿在其著作的前言中声明引力的平方反比律的思想源自胡克。这激怒了牛顿，于是牛顿给哈雷写了一封整整四页的长信，悉数发泄他对胡克多年积聚起来的怨气。 但同时，牛顿也在此信中列举了许多关于引力研究的史料。
此信是一份对理解和研究牛顿发现万有引力的历程至关重要的原始资料。据我通过网络搜索了解到，迄今为止此信仅有部分内容被译成了中文：例如，[美]理查德.韦斯特福尔著《牛顿传》(郭先林等译 ，1993) 第188、189页。这里我尝试翻译整信和对那段科学史感兴趣的人分享。
此信分为两部分，是牛顿在同一天的两个不同时段写成。以下是前半部分。
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先生，
为了让您了解我和胡克先生之间的情况，我将尽我记忆所能记述我和他之间的通信内容；因为这些信件已久远，我也不确定我最初看过之后是否还看过。根据种种迹象，我几乎可以肯定，我拜访克里斯蒂安·雷恩爵士时，雷恩爵士已经知道引力的平方反比关系；而胡克先生（通过他后来撰写的《彗星》一书）将会被证明是我们三人中知道平方反比关系的最后一位。我想在此信中让您全面了解情况；但这事有点似无聊琐事， 所以我简要地告诉你要点：我从未将平方反比关系的适用范围扩展到地球表面以下，而且在去年我发现某个确凿的证据之前，我一直怀疑它在地表以下的范围不够精确；因此，在抛射体理论框架内，我从未使用过平方反比关系，也从未考虑过天体的运动；因此，胡克先生无法从我关于抛射体以及此类落体下降到地心的信件推断我对天体理论一无所知。他告诉我的关于平方反比关系说法的是错误的，即引力从太阳一直延伸到地心。现在他却要求我公开承认我当时对天体引力的平方反比关系一无所知——他这样做是不诚实的；原因在于他当时仅仅是在用抛射体的例子来叙述平方反比关系，并因此错误地指责我无知。在我回复他的第一封信时，我试图拒绝与他进一步通信，告诉他我已经搁置了哲学，只寄给他一个关于抛射体实验的描述（只是摘要而非详细描述），以此作为礼貌，让我的回复显得更友好，希望不再收到他的后续信件；当我收到他的第二封信时，我几乎无法说服自己回复他，但我最终还是回复了他；当我收到他的第三封信时，我没有回复他，因为我当时确实在忙其他事情；除了他的信中提到的哲学问题之外，当时我没有再思考过其他哲学问题，因此您也可以理解：当时我并没有多么深刻地思考这类事情。既然他可以断定我对平方反比关系的其余部分一无所知，那么他也可以断定我对之前从他书中读到的那部分理论一无所知。在我十五年前（我记不清是哪一年了，但我肯定那是在我与奥尔登堡先生有任何通信之前）写的一篇论文中，我阐述了行星受太阳的引力与其距太阳的距离之间的平方反比关系，并计算了地球引力与月球“远离地心趋势”（conatus recedendi a centro terrae）之间的比例，尽管当时的计算精度尚显不足。当惠更斯出版《摆钟论》（Horologium Oscillatorium）并赠我一册时，我在给他的致谢信末尾特别赞扬了他书中的法则在自然哲学中的应用价值，并结合我前述的手稿，举例说明了这些法则的用途：例如比较月球受地球的引力与地球受太阳的引力，解决关于月相的问题，以及确定太阳视差的界限。这表明我当时已关注并理解了行星如作圆周运动时的引力的平方反比关系。因此，后来当胡克先生在其著作《试图证明地球运动》（Attempt to prove the Motion of the Earth）的结尾郑重提出这一问题时，即便我此前未曾知道平方反比关系，那时也定能推导出来。十到十一年前间，我在您的书中有一项假说记录在案，其中我暗示了指向地球、太阳及各行星的引力成因，以及天体运动对此的依赖关系；在该假说中（尽管当时为求简略未明确写出），一行星的中心到其表面的引力的衰减必然是两者之间距离的平方反比。我希望没人会强迫我公开承认我不理解这一由我本人提出的假说中显而易见的数学条件。即便退一步说，假设我是后来才从胡克先生那里获知引力的平方反比关系的，我对它的发现的权利也正如我对行星的椭圆轨道律的发现的权利一样正当。正如开普勒知道行星的轨道并非圆形并推测其为椭圆形那样，胡克先生在不了解我后来研究成果的情况下，所知的仅仅是：引力在天体的远离中心处“近似”符合平方反比关系——他虽准确猜到了这一点，却错误地将其推广至天体的中心，而开普勒对行星的椭圆轨道律的推测则是正确的。因此，胡克先生对平方反比关系的发现，远不如开普勒对行星的椭圆轨道律的发现那样确凿。针对平方反比关系的精确性从来存在着强有力的反驳意见；若没有我的证明——胡克先生对此证明尚很陌生——任何明智的哲学家都不会相信它在任何情况下是精确的。因此，在叙述这一问题时，我声称我对引力的平方反比关系所做的贡献，正如我对行星的椭圆轨道律所做的一样；正如我理应从开普勒那里获得关于行星的椭圆轨道律的认可一样，我也理应从胡克先生及所有人那里获得对于引力的平方反比关系的认可。正因如此，胡克先生至少应当收敛一下他对于引力的反比关系的发现所有权的声称。
我很满意您寄给我的我的著作的书样。我原计划全书由三卷构成；第二卷篇幅较短，已于去年夏天完成，目前仅需誊写并精细绘制插图。后来我又构思了一些新命题，不过这些命题不写也无妨。第三卷尚缺关于彗星理论的内容。去年秋天，我花了两个月时间进行计算，却因缺乏良法而徒劳无功；这促使我回过头来扩充第一卷，增补了若干命题——其中既有关于彗星的，也有关于其他事物的，皆为去年冬天所得。我现在打算放弃第三卷。自然哲学这位‘女士实在是个好惹是生非的主儿，与她打交道还不如去打官司呢。我早年便领教过这一点；如今刚一重拾旧业，她便又给我敲响了警钟。若缺了第三卷，前两卷便不太适合冠以《自然哲学的数学原理》（Philosophiae Naturalis Principia Mathematica）之名；因此我曾将其改为《物体运动论》（De Motu Corporum）两卷本。但转念一想，我还是保留了原先的书名。这有助于书籍的销售，既然书的版权已归您所有，我不应削减其销量。书中的某些条款（articles）篇幅较大；若您愿意，也可将其改称为“节”，但这无碍大局。以上便是目前的情况。
您挚爱的朋友与谦卑的仆人，
艾萨克·牛顿
Original in English sourced from: “Memoirs of the life writings, and discoveries of Sir Isaac Newton ” (by Sir David Brewster, 1860). pp. 401–403.
Sir,
In order to let you know the case between Mr. Hooke and me, I gave you an account of what passed between us in our letters, so far as I could remember ; for, 'tis long since they were written, and I do not know that I have seen them since. I am almost confident by circumstances that Sir Chr. Wren knew the duplicate proportion when I gave him a visit; and then Mr. Hooke (by his book Cometa written afterwards) will prove the last of us three that knew it. I intended in this letter to let you understand the case fully; but it being a frivolous business, I shall content myself to give you the heads of it in short, viz., that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it did not reach accurately enough down so low; and therefore in the doctrine of projectiles never used it nor considered the motions of the heavens; and consequently Mr. Hooke could not from my letters, which were about projectiles and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely, that it reached down from hence to the centre of the earth. That it is not candid to require me now to confess myself, in print, then ignorant of the duplicate proportion in the heavens; for no other reason, but because he had told it me in the case of projectiles, and so upon mistaken grounds accused me of that ignorance. That in my answer to his first letter I refused his correspondence, told him I had laid philosophy aside, sent him only the experiment of projectiles (rather shortly hinted than carefully described), in compliment to sweeten my answer, expected to hear no further from him; could scarce persuade myself to answer his second letter ; did not answer his third, was upon other things ; thought no further of philosophical matters than his letters put me upon it, and therefore maybe allowed not to have had my thoughts of that kind about me so well at that time. That by the same reason he concludes me then ignorant of the rest of the duplicate proportion, he may as well conclude me ignorant of the rest of that theory I had read before in his book. That in one of my papers writ (I cannot say in what year, but I am sure some time before I had any correspondence with Mr. Oldenburg, and that's) above fifteen years ago, the proportion of the forces of the planets from the sun, reciprocally duplicate of their distances from him, is expressed, and the proportion of our gravity to the moon's conatus recedendi a centro terrae is calculated, though not accurately enough. That when Hugenius put out his Horol. Oscil. , a copy being presented to me, in my letter of thanks to him, I gave those rules in the end thereof a particular commendation for their usefulness in Philosophy, and added out of my aforesaid paper an instance of their usefulness, in comparing the forces of the moon from the earth, and earth from the sun ; in determining a problem about the moon's phase, and putting a limit to the sun's parallax, which shows that I had then my eye upon comparing the forces of the planets arising from their circular motion, and understood it; so that a Avhile after, when Mr. Hooke propounded the problem solemnly, in the end of his Attempt to prove the Motion of the Earth, if I had not known the duplicate proportion before, I could not but have found it now. Between ten and eleven years ago, there was an hypothesis of mine registered in your books, wherein I hinted a cause of gravity towards the earth, sun, and planets, with the dependence of the celestial motions thereon; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity's sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre. And I hope I shall not be' urged to declare, in print, that I understood not the obvious mathematical conditions of my own hypothesis. But grant I received it afterwards from Mr. Hooke, yet have I as great a right to it as to the ellipsis. For as Kepler knew the orb to be not circular but oval, and guessed it to be elliptical, so Mr. Hooke, without knowing what I have found out since his letters to me, can know no more, but that the proportion was duplicate quam proxime at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre, whereas Kepler guessed right at the ellipsis. And so Mr. Hooke found less of the proportion than Kepler of the ellipsis. There is so strong an objection against the accurateness of this proportion, that without my demonstrations, to which Mr. Hooke is yet a stranger, it cannot be believed by a judicious philosopher to be any where accurate. And so, in stating this business, I do pretend to have done as much for the proportion as for the ellipsis, and to have as much right to the one from Mr. Hooke and all men, as to the other from Kepler; and therefore on this account also he must at least moderate his pretences.
The proof you sent me I like very well. I designed the whole to consist of three books ; the second was finished last summer being short, and only wants transcribing, and drawing the cuts fairly. Some new propositions I have since thought on, which I can as well let alone. The third wants the theory of comets. In autumn last I spent two months in calculations to no purpose for want of a good method, which made me afterwards return to the first book, and enlarge it with diverse propositions, some relating to comets, others to other things, found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious Lady, that a man had as good be engaged in lawsuits, as have to do with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning. The two first books, without the third, will not so well bear the title of Philosophiae Naturalis Principia Matheniatica; and therefore I had altered it to this, De Motu Corporum libri duo. But, upon second thoughts, I retain the former title. 'Twill help the sale of the book, which I ought not to diminish now 'tis yours. The articles are, with the largest, to be called by that name ; if you please you may change the word to sections, though it be not material ; which is all at present from
Your affectionate friend and humble servant,
Is. Newton.
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