Newton's Interests

December 2, 2024 5 minutes • 1040 words

When he was attending a meeting of the Royal Society in June 1682, the conversation fell upon the subject of the

M. Picard, a French Astronomer, measured a degree of the meridian in 1679.

Newton took notes of the result and computed from it the earth’s diameter.

This allowed him to resume his 1666 calculation.

He had grasped the master-fact: the law of falling bodies at the earth’s surface was finally identified with that which guided the moon in her orbit.

For 16 years, his Great Thought had loomed up in dim, gigantic outline.

It now stood forth

He then extended the law that he obtained.

He wrote a series of around 12 propositions on the motion of the primary planets about the sun.

These were sent to London, and communicated to the Royal Society around the end of 1683.

At this time, other philosophers like Sir Christopher Wren, Dr. Halley, and Dr. Hooke, were engaged in investigating the same subject but with no definite results.

Dr. Halley saw Newton’s propositions. So he went in August 1684 to Cambridge to consult with him on the subject.

Newton assured him that he had brought the demonstration to perfection.

In November, Dr. Halley received a copy of the work. In December he announced it to the Royal Society, with Newton’s promise to enter it on their Register.

Newton transmitted the manuscript of the first book to London, entitled Philosophiæ Naturalis Principia Mathematica presented to the Royal Society on April 28, 1685.

The highest encomiums were passed upon it.

The council resolved, on May 19, to print it at the expense of the Society, and under the direction of Dr. Halley.

The latter, a few days afterward, communicated these steps to Newton, who, in a reply, dated the 20th of June, holds the following language:

“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 calculation to no purpose for want of a good method, which made me afterward 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 law-suits as have to do with her, I found it so formerly, and now I can no sooner come near her again, but she gives me warning.

The first two books without the third will not so well bear the title of Philosophiæ Naturalis Principia Mathematicia; and thereupon I had altered it to this, De Motu Corporum Libri duo. But after second thought I retain the former title. It will help the sale of the book, which I ought not to diminish now ’tis yours.”

This “warning” arose from some pretensions put forth by Dr. Hooke.

Newton gave minute and positive refutations of such claims. To reconcile all differences, he added to Prop. 4, Cor. 6, Book 1, a Scholium.

In it, he admits that Wren, Hooke and Halley independently deduced the law of gravity from the second law of Kepler.

The suppression of the third book Dr. Halley could not endure to see.

“I must again beg you” says he, “not to let your resentments run so high as to deprive us of your third book, where in your applications of your mathematical doctrine to the theory of comets, and several curious experiments, which, as I guess by what you write ought to compose it, will undoubtedly render it acceptable to those who will call themselves philosophers without mathematics, which are much the greater number,”

To these solicitations Newton yielded. There were no “resentments,” however, as we conceive, in his “design to suppress.” He sought peace; for he loved and valued it above all applause. But, in spite of his efforts for tranquillity’s sake, his course of discovery was all along molested by ignorance or presumptuous rivalry.

The second book was sent to the Society, and presented on March 2.

The third on April 6.

The whole was completed and published in May 1686.

In the second Lemma of the second book, the fundamental principle of his fluxionary calculus was, for the first time, given to the world; but its algorithm or notation did not appear till published in the second volume of Dr. Wallis’s works, in 1693.

Principia consists of 3 books:

The first two, Of The Motion Of Bodies, are occupied with the laws and conditions of motions and forces.

These have many scholia treating of the best established points in philosophy, such as:

the density and resistance of bodies
spaces void of matter
the motion of sound and light.

From these principles, Book 3 is deduced as Of the System of the World written in a popular style.

“I had composed the third Book in a popular method, that it might be read by many.

But afterwards, considering that such as had not sufficently entered into the principles could not easily discover the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent disputes which might be raised upon such accounts, I chose to reduce the substance of this Book into the form of Propositions (in the mathematical way), which should be read by those only who had first made themselves masters of the principles established in the preceding Books: not that I would advise any one to the previous study of every Proposition of those Books."—“It is enough it one carefully reads the Definitions, the Laws of Motion, and the three first Sections of the first Book. He may then pass on to this Book, and consult such of the remaining Propositions of the first two Books, as the references in this, and his occasions shall require.” So that “The System of the World” is composed both “in a popular method,” and in the form of mathematical Propositions.