Isaac Newton in Principia Law II says:

"the change of motion is proportional to the motive force impressed, and takes place following the straight line in which that force is impressed". "If some force should generate any motion you please, a double will generate a double....whether it has been impressed all at once, or gradually and successively".

The textbooks often say that "the modern formulation is $F=ma$". But change of motion is $\Delta (mv)$, and the force impressed is over time. Would it be fair to say that what Newton is stating is the modern equation of Impulse, not Force?


2 Answers 2


Yes, I think that if the phrase 'motive force' had been removed and a blank space substituted, a present-day physicist would fill in "impulse". On the other hand, Newton might not have objected if someone had suggested that he add the words "and to the length of time for which it acts" after "the change of motion is proportional to the motive force impressed", in which case 'motive force' would mean just that. We shall never know.


Would it be fair to say that what Newton is stating is the modern equation of Impulse, not Force?


This response is just to further support the answer that was provided by Philip Wood. I was recently confused by Newton's use of "impressed forces", particularly in regards to Corollary 1 of the Laws. But after some digging around, I stumbled across a book written by James C. Maxwell titled "Motion and Matter" in which Maxwell clarifies Newton's meaning:

Article XLIV. - The Second Law of Motion.

Law II. - Change of motion is proportional to the impressed force, and takes place in the direction in which the force is impressed.

By motion Newton means what in modern scientific language is called momentum, in which the quantity of matter moved is taken into account as well as the rate at which it travels.

By impressed force he means what is now called Impulse, in which the time during which the force acts is taken into account as well as the intensity of the force.

Maxwell, later on, rephrases Newton's 2nd Law:

Article LII. - Statement of the Second Law of Motion in Terms of Impulse and Momentum.

The change of momentum of a body is numerically equal to the impulse which produces it, and is in the same direction.

Here is the text for reference: http://strangebeautiful.com/other-texts/maxwell-matter-motion.pdf

  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Jun 7, 2022 at 5:54
  • $\begingroup$ That's extraordinary. Thanks, Andrew! As a mere amateur, I battled with understanding Newton's exact words. It is fascinating to find Maxwell re-stating exactly that. $\endgroup$
    – Anthony
    Jun 8, 2022 at 17:52
  • $\begingroup$ Glad to have made an impact (no pun intended). On a related note, I recently made a post that's relevant to your question, and a user named terry-s made a very interesting response that cited a paper that suggests that perhaps Newton intended for both interpretations. Unfortuntely, I haven't been able to obtain the paper yet... hsm.stackexchange.com/questions/14492/… $\endgroup$
    – Andrew R.
    Jun 9, 2022 at 2:48

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