New York Newtonianism
The following is Cadwallader Colden’s first published article following his arrival in North America. Colden was not the primary author of this article and so it is often overlooked. This article is about an activity he engaged in New York-New Jersey Governor William Burnet in 1723. Since his arrival to the Colonies in 1708, 15 years have elapsed and his professional focus has been in medicine and the practice and application of some scientific practices akin to the modern day practice of engineering. Following a brief stay in Philadelphia, Colden removed to New York City and begin his political life with Governor Burnet and James Alexander. Burnet’s desire was simply to document the location of Fort George located at the south end of Manhattan Island in terms of longitude and latitude measures. For Colden this was an important political and professional step towards entering the fields he wished to work or practice in.
Galileo Galilei (1564-1642)
The history of the mathematics underlying this activity is fairly substantial and quite impressive. A number of major changes in philosophy during this time led to what might otherwise appear to be a simple surveying activity. In 1610, Galileo Galilei (1564-1642) published an account of Jupiter’s moons entitled Sidereus Nuncius (The Starry Messenger) in which he detailed his observations of the four moons he same around the planet Jupiter, the presence of a cloud which has we now know as the Milky Way, the characteristic of the moon’s surface, and the tendency for celestial bodies to travel along different paths and direction due to their different placement in relation to one another. Over the next ten to twenty years he followed up on this work substantially, describing in detail numerous other celestial events that he witnessed. One of the primary claims his findings led him to make was in aggreement with that of Copernicus, which was that the solar system (and ultimately universe) was not geocentric, like Ptolemy claimed, meaning that the Earth as it was produced and created by God was not the centerpiece of the Creator’s Work of Art. From this point on, this meant that no one could contest the claims made by Copernicus, Galileo and others which stated that the earth and other planets travelled independently about the sun or helios, a theory that came to be called the heliocentric theory, and that many other systems out there in the universe appeared to be operating independent of the earth’s events.
The heliocentric theory alone was enough to bring about serious questioning of the beliefs and philosophies promoted by the Church. Galileo’s work led to a reinterpretation of the sunspots, tides, comets, and other natural events which had been given theological interpretations as to their cause. From 1616 to 1638, in spite of church attacks, with the support of Inquisitors Galileo was able to publish a number of writings about his discoveries and related theories. This set the stage for the next major set of events to happen due to the efforts of Isaac Newton.
Isaac Newton (1643-1727)
Isaac Newton’s major accomplishments relate to his skills as a mathematician. His contributions to mathematics include the development of the calculus method of analysis (independently accompanied by similar accomplishments made by Leibnitz), the study of the activity and behavior of light (focusing on refraction and the formation of discrete color bands, the creation or the theory of color, the “corpuscular” theory of light), the development of a way to study and analyze the attraction and movement of everything from exceptionally small objects to planetary bodies (the theory of gravitation). Newton’s philosophy on these universal energies were not only related to non-living processes, but also to the regular events that took place as a part of the life process.
In 1671, Newton wrote and essay entitled Methods of Fluxions. This study of fluxion or the flow and change of numbers as Newton inferred was actually his first attempt to define events using what would later be known as integral calculus. Thirteen years later, a similar writing called De Motu Corporum in Gyrum was produced, which he submitted in the form of a letter to Edmund Halley who then submitted it to the Royal Society, who soonafter published in their Register Book. Over the next three years, Newton expounded upon this work, resulting in publication of his famous writing on this subject in 1687, Philosophiae Naturalis Principia Mathematica. Even then, Newton was slow to promote his work publically in an aggressive manner.
Between 1687 and 1700, a number of events took place in the science community, including the application of Newton’s thinking in every way possible, ranging from simple calculations of the heavens to the use of these calculation methods to define reasons for recurring natural outcomes and to use this understanding to help explain the next cycling of similar events. Newton’s work also had influences upon how we interpreted energy and objects in relation to one another. The most important part of Galileo’s work that Newton and several of his predecessors help to expound upon pertained to the constant movement of matter and the continued presence of gravity as an energy form responsible for making everything happen.
The bulk of the evidence out there documenting Newton’s impacts on science pertained to the field of astronomy, but the basic methods of applying mathematical thinking to solving other equations in similar fashion helped to make Newton’s work applicable to more than just the stars and planets. Whereas calculus was being used to define the basic physics of the universe in a strictly non-medical scientific sense, the mathematics related to geometry and trigonometry made it possible for planetary behaviors related to cycles and orbits to become better understood and applied to anything and everything having to do with the motion of stars, planets and other stellar masses, and the phenomena related to these events.
When Colden arrived in Philadelphia around 1708, he was a physician and mathematician in search of a new life. His professional goals in Philadelphia lasted only a short time due to other political events taking place during the upcoming years. Through his work and contacts in Philadelphia he made an important connection with William Burnet, Governor of New Jersey and New York. This connection led Colden to move to New York City in order to take advantage of the advances in his career and professional services about to take place.
Governor Burnet was very much interested in the geography of New York City and its exact location. By this time natural theology had popularized the method of calculating locations based on distant planetary and solar behaviors. Both astro-theologians and astronomers believed there was a unique lay out of the solar system, but each one had his own theory. Governor Burnet took advantage of this perfected skill in the sciences to determine the location of the Fort in New York City. The application of Newton’s and Halley’s mathematics would be used to calculate and then document the exact location of this government setting. He made use of a centuries old trick known to skilled mathematicans engaged in the use of the stars and the planets to time particular events.
William Burnet invited James Alexander and Cadwallader Colden to participate in his goal of identifying the latitude and longitude of the fort in New York. Colden’s role in this task was two-fold. Aside from assisting in some of the basic techniques required to set up the apparati needed to register this astronomical event, he was to document the planetary processes taking place and the tome and place of Jupiter’s four moons. These four moons had extremely predictable orbit patters about Jupiter. With knowledge of their relative speeds and routes of travel, Colden should be able to estimate the speed at which the earth moved during this several minute process the eclipse took place between Jupiter, the Sun and the Earth and relate this to other well known periodic rotation processes involving the speed of the earth’s rotation with New York.
The event that Governor Burnet, Colden and Alexander were engaged in demonstrated the growing success of Newton’s approach to observing, documenting, calculating and even predicting natural events such as an astronomical event. They used this method to estimate the length of the distance of land surface travelled across the planet’s surface by the moon, per degree of longitude line that was passed during such a travel, in relation to the rotation and travels of the earth and sun in related to each of these celestial events. Although many of the events Newton was involved with up till now pertained to just the movement of the Sun, Earth, and Moon, or a number of activities focused on planetary moon behaviors, this activity was carried out with a specific goal in mind–to document their location precisely doen to minutes, degree and seconds. Due to the difficulty and complexity of such a measure, this type of mathematics required Colden to be more precise in his approach to taking these measures than if they were taken through the more common helio-lunar-terracentric measurement methods related to solar and lunar eclipses. Factors that had to be taken into count for this type of evaluation focused on the placement of Jupiter’s first moon (Io), its distance from Jupiter, the earth and the sun, and the geometric details about the actions of each of these moving bodies (Jupiter, moon, earth, sun) and their speeds about the sun and each other. It is even possible that Burnet, Colden and Alexander were also hoping to make their achievements stand out amongst the others performed each month in numerous places around the world.
The following is the article of this event in its entirety (Article II, pp. 162-165). Note that Colden is not an author in this work. Instead, his name appears as part of the team involved in this celestial process.
Follow-up research needed for:
Specific details about Methodology used.
“Mr. Pound’s tables”
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