This equation is often written using the material derivative Dv / Dt, making it more apparent that this is a statement of Newton's second law:

It is referenced in the 2006 film Amazing Grace, which highlights Newton's influence on the leading British abolitionist William Wilberforce.

Waterhouse confronts Newton over his increasingly unstable behavior and his fruitless attempts to derive a " theory of everything " under the enabling influence of Newton's close friend Fatio.

Irrespective of historical influence, however, The Wealth of Nations represented a clear shift in the field of economics, similar to Sir Isaac Newton's Principia Mathematica for physics, Antoine Lavoisier's Traité élémentaire de chimie for chemistry, or Charles Darwin's On the Origin of Species for biology.

This is a seeming violation of Newton's law of cooling but in reality it is due to non-linear effects that influence the freezing process.

Newton's drag force theory was finally proved incorrect.

Some eight decades later, Isaac Newton proved that relationships like Kepler's would apply exactly under certain ideal conditions that are to a good approximation fulfilled in the solar system, as consequences of Newton's own laws of motion and law of universal gravitation.

Hubert A. Newton's more thorough historical work led to a refined prediction of 1866, which proved to be correct.

He also proved the correctness of Isaac Newton's classification of cubics.

Newton's chemical and mathematical knowledge proved of great use in carrying out this Great Recoinage of 1696, a process that was completed in about two years.

It is named for Isaac Newton, who first discovered it and proved that it was a harmonic function in the special case of three variables, where it served as the fundamental gravitational potential in Newton's law of universal gravitation.

The idea of absolute space has proved particularly controversial from Newton's time to the present.

Newton's father made plans for him to work at a sugar plantation in Jamaica.

Early in 1748 he was rescued by a sea captain who had been asked by Newton's father to search for him, he made it to freedom.

In 1686, when the first book of Newton's ' Principia ' was presented to the Royal Society, Hooke claimed that Newton had obtained from him the " notion " of " the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center ".

It seems that Bentley then realised that the editorship was technically too difficult for him, and with Newton's consent he appointed Roger Cotes, Plumian professor of astronomy at Trinity, to undertake the editorship for him as a kind of deputy ( but Bentley still made the publishing arrangements and had the financial responsibility and profit ).

In 1686, when the first book of Newton's ' Principia ' was presented to the Royal Society, Hooke claimed that Newton had had from him the " notion " of " the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center ".

Albert Einstein praised him in the 1931 foreword to an edition of Newton's Opticks.

Isaac Newton's theories about white light being composed of a spectrum of colors led him to the conclusion that uneven refraction of light caused chromatic aberration ( leading him to build the first reflecting telescope, his Newtonian telescope, in 1668 ).

This led him into conflict with members of the academic establishment who rejected Leibniz's theory, believing it inconsistent with Sir Isaac Newton's conservation of momentum.

He also translated Newton's Opticks, for which the author presented him with £ 500.

Newton's scientific work may have been of lesser personal importance to him, as he placed emphasis on rediscovering the occult wisdom of the ancients.

This discovery was communicated by him to Edmund Halley in 1700, but was not published, or communicated to the Royal Society, till after Newton's death, when a description of it was found among his papers.

During the period in which he wrote Cryptonomicon, Stephenson read George Dyson's Darwin Amongst the Machines, which led him to Gottfried Leibniz's interest in a computing machine, the Leibniz – Newton feud, and Newton's work at the Royal Treasury.

Dr Edleston, in his preface to Newton's correspondence with Cotes, justly remarks: " If Flamsteed the Astronomer-Royal had cordially co-operated with him in the humble capacity of an observer in the way that Newton pointed out and requested Of him ... the lunar theory would, if its creator did not overrate his own powers, have been completely investigated, so far as he could do it, in the first few months of 1695, and a second edition of the Principia would probably have followed the execution of the task at no long interval.

At the next meeting of the Society, on May 19, 1686, some dissatisfaction seems to have been expressed at the delay, as it was ordered " that Mr Newton's work should be printed forthwith in quarto, and that a letter should be written to him to signify the Society's resolutions, and to desire his opinion as to the print, volume, cuts and so forth.

He admitted the imperfection of his data on stars, noting that Flamsteed had refused to assist him, but he vaunted his coverage of astronomy, especially his full coverage of Newton's theories of the moon and of comets.

Newton's defection to Melbourne and Reynoldson's threats of legal action over the club refusing to play him in the fifteen games required to trigger his fourth contract year saw the club's reputation dragged through the mud.

Newton's own account in an interview for The Golden Age of Chicago Children's Television has him quitting the show and suggesting Thomas contact the Chicago Academy of Fine Arts for a replacement.

Aside from the lack of absolute certainty as to identification, Air Vice Marshal Bill Bostock, Air Officer Commanding RAAF Command, contended that naming him would change the impact of the news upon Newton's fellow No. 22 Squadron members " from the impersonal to the closely personal " and hence " seriously affect morale ".

Although he became a starter at left guard in 1987, Newton's breakout came with the arrival of Jimmy Johnson as the Cowboys coach in 1989, who eventually moved him to the starting right tackle position.

State papers on the case in the Public Records Office, released to the public in the 1970s, provide no information on the prince's involvement other than Newton's threat to implicate him.

Later, in 1686, when Newton's ' Principia ' had been presented to the Royal Society, Hooke claimed from this correspondence the credit for some of Newton's content in the ' Principia ', and said Newton owed the idea of an inverse-square law of attraction to him – although at the same time, Hooke disclaimed any credit for the curves and trajectories that Newton had demonstrated on the basis of the inverse square law.

The hymns were written for use in Newton's rural parish which was made up of relatively poor and uneducated followers.

It is not in the record, but he must have galloped his horse at Peach Tree Creek when he brought up Ward's guns to save Newton's crumbling line.

Common meter hymns were interchangeable with a variety of tunes ; more than twenty musical settings of " Amazing Grace " circulated with varying popularity until 1835 when William Walker assigned Newton's words to a traditional song named " New Britain ", which was itself an amalgamation of two melodies (" Gallaher " and " St. Mary ") first published in the Columbian Harmony by Charles H. Spilman and Benjamin Shaw ( Cincinnati, 1829 ).

" Wretch " also represents a period in Newton's life when he saw himself outcast and miserable, as he was when he was enslaved in Sierra Leone ; his own arrogance was matched by how far he had fallen in his life.

By starting with an inertial frame, where Newton's laws of motion hold, and keeping track of how the time derivatives of a position vector change when transforming to a rotating reference frame, the various fictitious forces and their forms can be identified.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and ( following Newton's first law of motion ), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly — that is, in a straight line and at constant speed.

Newton's notation for the derivative of acceleration can also be used, especially when " surge " or " lurch " is used instead of " jerk " or " jolt ".

In order to explain refraction, Newton's Opticks ( 1704 ) postulated an " Aethereal Medium " transmitting vibrations faster than light, by which light, when overtaken, is put into " Fits of easy Reflexion and easy Transmission ", which caused refraction and diffraction.

However, a century later, Young and Fresnel revived the wave theory of light when they pointed out that light could be a transverse wave rather than a longitudinal wave — the polarization of a transverse wave ( like Newton's " sides " of light ) could explain birefringence, and in the wake of a series of experiments on diffraction the particle model of Newton was finally abandoned.

* when the boat is traveling across the wind, the air coming in from the side is redirected toward the rear ; according to Newton's Third law, the air is accelerated towards the rear of the boat and the sails experience a force in the opposite direction.

Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets.

His account tells of Isaac Newton's absorption in his studies, how he sometimes forgot his food, or his sleep, or the state of his clothes, and how when he took a walk in his garden he would sometimes rush back to his room with some new thought, not even waiting to sit before beginning to write it down.

The standard Newton's method fails to converge when applied to the system ; Nash uses smoothing operators defined by convolution to make the Newton iteration converge: this is Newton's method with postconditioning.

While this might lessen the accuracy of the decomposition, it can be very favorable for other reasons ; for example, when performing Newton's method in optimization, adding a diagonal matrix can improve stability when far from the optimum.

Isaac Newton's law of gravity is popularly attributed to a creative leap he experienced when observing a falling apple.

The Fizeau experiment to measure the speed of light in water has been viewed as " driving the last nail in the coffin " of Newton's corpuscle theory of light when it showed that light travels more slowly through water than through air.

For larger matrices, the expressions for the coefficients c < sub > k </ sub > of the characteristic polynomial in terms of the matrix components become increasingly complicated ; but they can also be expressed in terms of traces of powers of the matrix A, using Newton's identities ( at least when the ring contains the rational numbers ), thus resulting in more compact expressions ( but which involve divisions by certain integers ).

Newton's growing reputation as a fashion photographer was rewarded when he secured a commission to illustrate fashions in a special Australian supplement for Vogue magazine, published in January 1956.

All three had been photography students at The Art Center College of Design in Pasadena, California in 1979 when they became Newton's longtime assistants, and all three went on to independent careers.

* Kepler's laws of planetary motion, which can be mathematically derived from Newton's laws, hold strictly only in describing the motion of two gravitating bodies, in the absence of non-gravitational forces, or approximately when the gravity of a single massive body like the Sun dominates other effects: