Although other researchers before Coulomb had suggested the 1/r2 law, we refer to this relationship as Coulomb’s Law in honor of Coulomb’s independent results gained through the evidence provided by his torsional measuring. In other words, Coulomb provided convincing quantitative results for what was, up to 1785, just a good guess.
One version of Coulomb’s torsion balance contains a metal and a non-metal ball attached to an insulating rod. The rod is suspended at its middle by a nonconducting filament or fiber. To measure the electrostatic force, the metal ball is charged. A third ball with similar charge is placed near the charged ball of the balance, causing the ball on the balance to be repelled. This repulsion causes the fiber to twist. If we measure how much force is required to twist the wire by the same angle of rotation, we can estimate the degree of force caused by the charged sphere. In other words, the fiber acts as a very sensitive spring that supplies a force proportional to the angle of twist.
SEE ALSO Von Guericke’s Electrostatic Generator (1660), Battery (1800), Maxwell’s Equations (1861), Electron (1897).
Charles-Augustin de Coulomb’s torsion balance, from his Mémoires sur l’électricité et le magnétisme (1785–1789).
1797
Fundamental Theorem of Algebra • Clifford A. Pickover
Johann Carl Friedrich Gauss (1777–1855)
The Fundamental Theorem of Algebra (FTA) is stated in several forms, one of which is that every polynomial of degree n ≥ 1, with real or complex coefficients, has n real or complex roots. In other words, a polynomial P(x) of degree n has n values xi (some of which are possibly repeated) for which P(xi) = 0. As background, polynomial equations of degree n are of the form P(x) = anxn + an−1xn−1 + . . . + a1x + a0 = 0 where an ≠0.
As an example, consider the quadratic polynomial f(x) = x2 − 4. When plotted, the curve is a parabola with its minimum at f(x) = −4. The polynomial has two distinct real roots (x = 2 and x = −2), which are graphically seen as points where the parabola intersects the x-axis. .
This theorem is notable, in part, because of the sheer number of attempts at proving it through history. German mathematician Carl Friedrich Gauss is usually credited with the first proof of the FTA, discovered in 1797. In his doctoral thesis, published in 1799, he presented his first proof, which focused on polynomials with real coefficients, and also on his objections to the other previous attempts at proofs. By today’s standards, Gauss’s proof was not rigorously complete, because he relied on the continuity of certain curves, but it was a significant improvement over all previous attempts at a proof.
Gauss considered the FTA to have great importance, as evidenced by his returning to the problem repeatedly. His fourth proof was in the last paper he ever wrote, which appeared in 1849, exactly 50 years after his dissertation. Note that Jean-Robert Argand (1768–1822) published a rigorous proof of the Fundamental Theorem of Algebra in 1806 for polynomials with complex coefficients. The FTA arises in many areas of mathematics, and the various proofs span fields that range from abstract algebra and complex analysis to topology.
SEE ALSO al-Khwarizmi’s Algebra (830), Development of Modern Calculus (1665), Fractals (1975).
Greg Fowler’s depiction of the three solutions to z3 − 1 = 0. These roots (or zeros) are 1, −0.5 + 0.86603i, and −0.5 − 0.86603i, and are located at the center of the three large bull’s-eyes in this Newton’s method rendition of the solutions.
1798
Smallpox Vaccine • Clifford A. Pickover
Edward Anthony Jenner (1749–1823)
“Smallpox is a disease that terrified people for thousands of years,” writes medical historian Robert Mulcahy. “During the 1700s, this disease took approximately 400,000 lives each year in Europe alone and left hundreds of thousands more living with scarred and disfigured faces. The smallpox virus could spread through a town like wildfire, bringing high fever and a blistering rash to everyone who caught it. Half of those who contracted the disease would die within weeks—and there was no cure.”
Smallpox is a contagious viral disease that has devastated populations since the dawn of humanity. Smallpox skin lesions have even been found on the faces of ancient Egyptian mummies (c. 1100 BCE). When Europeans introduced the disease to the New World, smallpox became instrumental in the fall of the Aztec and Incan empires.
For many years, English physician Edward Jenner had heard tales that dairymaids were protected from smallpox after they had been afflicted with cowpox, a similar disease that affects cows but is not fatal for humans. In 1796, he removed material from a dairymaid’s cowpox lesions and transferred it into two scratches he made in the skin of an eight-year-old boy. The boy developed a minor fever and discomfort but soon was completely recovered. Later, Jenner inoculated the boy with material from a smallpox lesion, and no disease developed in the boy. In 1798, Jenner published additional findings in An Inquiry into the Causes and Effects of the Variolae Vaccinae. He called the procedure vaccination—which stems from vacca, the Latin word for cow—and began to send cowpox vaccine samples to anyone who requested them.
Jenner was not the first to vaccinate against smallpox. However, his work is considered among the first scientific attempts to control infectious disease. Physician Stefan Riedel writes that it was Jenner’s “relentless promotion and devoted research of vaccination that changed the way medicine was practiced.” Eventually, the smallpox vaccination was used throughout the world. By 1979 the world was essentially free of smallpox, and routine vaccination was no longer needed.
SEE ALSO Germ Theory of Disease (1862), Discovery of Viruses (1892), Structure of Antibodies (1959).
An 1802 cartoon by British satirist James Gillray, depicting the early controversy surrounding Jenner’s vaccination theory. Note the cows emerging from the people’s bodies.
1800
Battery • Clifford A. Pickover
Luigi Galvani (1737–1798), Alessandro Volta (1745–1827), Gaston Planté (1834–1889)
Batteries have played an invaluable role in the history of physics, chemistry, and industry. As batteries evolved in power and sophistication, they facilitated important advances in electrical applications, from the emergence of telegraph communication systems to their use in vehicles, cameras, computers, and phones.
Around 1780, physiologist Luigi Galvani experimented with frogs’ legs that he could cause to jerk when in contact with metal. Science-journalist Michael Guillen writes, “During his sensational public lectures, Galvani showed people how dozens of frogs’ legs twitched uncontrollably when hung on copper hooks from an iron wire, like so much wet laundry strung out on a clothesline. Orthodox science cringed at his theories, but the spectacle of that chorus line of flexing frog legs guaranteed Galvani sell-out crowds in auditoriums the world over.” Galvani ascribed the leg movement to “animal electricity.” However, Italian physicist and friend Alessandro Volta believed that the phenomenon had more to do with the different metals Galvani employed, which were joined by a moist connecting substance. In 1800, Volta invented what has been traditionally considered to be the first electric battery when he stacked several pairs of alternating copper and zinc discs separated by cloth soaked in salt water. When the top and bottom of this voltaic pile were connected by a wire, an electric current began to flow. To determine that current was flowing, Volta could touch its two terminals to his tongue and experience a tingly sensation.
“A battery is essentially a can full of chemicals that produce electrons,” write authors Marshall Brain and Charles Bryant. If a wire is connected between the negative and positive terminals, the electrons produced by chemical reactions flow from one terminal to the other.
In 1859, physicist Gaston Planté invented the rechargeable battery. By forcing a current through it “backwards,” he could recharge his lead-acid battery. In the 1880s, scientists invented commercially successful dry cell batteries, which made use of pastes instead of liquid electrolytes (substances containing free ions that make the substances electrically co
nductive).
SEE ALSO Von Guericke’s Electrostatic Generator (1660), Power Grid (1878), Electron (1897).
As batteries evolved, they facilitated important advances in electrical applications, ranging from the emergence of telegraph communication systems to their use in vehicles, cameras, computers, and phones.
1800
High-Pressure Steam Engine • Marshall Brain
Richard Trevithick (1771–1833)
There was a time in history when the human body was the only way to power things. Then we learned to harness horses and oxen. Then we figured out how to use water for power with waterwheels. But all these sources of power have their limitations. You cannot create a locomotive or a cruise ship like the Titanic with any of these power sources. And while you can create a power plant or a factory powered by water, you are severely limited as to where you can locate them. The world needed a better source of power.
The steam engine provided the transition to the industrial age. The first high-pressure steam engine was introduced in 1800 by British engineer Richard Trevithick. By 1850, engineers had incrementally improved steam engines and the Corliss steam engine became the state of the art for large stationary power needs. It was efficient and reliable, as well as large and heavy, making it a good engine for powering factories. The San Francisco cable car system used steam engines of this type.
The engine used to power the Centennial Exhibition in Philadelphia in 1876 is an example: a two-cylinder steam engine producing 1,400 horsepower (one million watts). Pistons more than a yard (one meter) in diameter moved 10 feet (3 meters) in their cylinders to spin a flywheel 30 feet (9 meters) across.
The Titanic used the next generation of steam engine, in which multiple cylinders captured energy from successive expansions of the same steam.
A key element for any high-pressure steam engine is the boiler, where boiling water creates the steam pressure. The problem with boilers is that, being under high pressure, they had some probability of exploding. One of the most horrific boiler explosions occurred aboard a steam-powered ship named the Sultana in 1865. It had four boilers, one of which had started leaking and had been hastily repaired. With roughly 2,000 people on board, the repaired area presumably failed, causing an immense boiler explosion that killed a total of about 1,800 people. Today engineers spec steam turbines instead. You find them in nearly every power plant.
SEE ALSO Carnot Engine (1824), Steam Turbine (1890), Internal Combustion Engine (1908).
President Ulysses S. Grant and Don Pedro starting the Corliss engine at the Centennial celebration, Philadelphia, 1876.
1801
Wave Nature of Light • Clifford A. Pickover
Christiaan Huygens (1629–1695), Isaac Newton (1642–1727), Thomas Young (1773–1829)
“What is light?” is a question that has intrigued scientists for centuries. In 1675, the famous English scientist Isaac Newton proposed that light was a stream of tiny particles. His rival, the Dutch physicist Christiaan Huygens, suggested that light consisted of waves, but Newton’s theories often dominated, partly due to Newton’s prestige.
Around 1800, the English researcher Thomas Young—also famous for his work on deciphering the Rosetta Stone—began a series of experiments that provided support for Huygens’ wave theory. In a modern version of Young’s experiment, a laser equally illuminates two parallel slits in an opaque surface. The pattern that the light makes as it passes through the two slits is observed on a distant screen. Young used geometrical arguments to show that the superposition of light waves from the two slits explains the observed series of equally spaced bands (fringes) of light and dark regions, representing constructive and destructive interference, respectively. You can think of these patterns of light as being similar to the tossing of two stones into a lake and watching the waves running into one another and sometimes canceling each other out or building up to form even larger waves.
If we carry out the same experiment with a beam of electrons instead of light, the resulting interference pattern is similar. This observation is intriguing, because if the electrons behaved only as particles, one might expect to simply see two bright spots corresponding to the two slits.
Today, we know that the behavior of light and subatomic particles can be even more mysterious. When single electrons are sent through the slits one at a time, an interference pattern is produced that is similar to that produced for waves passing through both holes at once. This behavior applies to all subatomic particles, not just photons (light particles) and electrons, and suggests that light and other subatomic particles have a mysterious combination of particle and wavelike behavior, which is just one aspect of the quantum mechanics revolution in physics.
SEE ALSO Maxwell’s Equations (1861), Electromagnetic Spectrum (1864), Electron (1897), Photoelectric Effect (1905), De Broglie Relation (1924), Schrödinger’s Wave Equation (1926), Complementarity Principle (1927).
Simulation of the interference between two point sources. Young showed that the superposition of light waves from two slits explains the observed series of bands of light and dark regions, representing constructive and destructive interference, respectively.
1807
Fourier Series • Clifford A. Pickover
Jean Baptiste Joseph Fourier (1768–1830)
Fourier series are useful in countless applications today, ranging from vibration analysis to image processing—virtually any field in which a frequency analysis is important. For example, Fourier series help scientists characterize and better understand the chemical composition of stars or how the vocal tract produces speech.
Before French mathematician Joseph Fourier discovered his famous series, he accompanied Napoleon on his 1789 expedition of Egypt, where Fourier spent several years studying Egyptian artifacts. Fourier’s research on the mathematical theory of heat began around 1804 when he was back in France, and in 1807 he had completed his important memoir On the Propagation of Heat in Solid Bodies. One of his interests was heat diffusion in different shapes. For these problems, researchers are usually given the temperatures at points on the surface, as well as at its edges, at time t = 0. Fourier introduced a series with sine and cosine terms in order to find solutions to these kinds of problems. More generally, he found that any differentiable function can be represented to arbitrary accuracy by a sum of sine and cosine functions, no matter how bizarre the function may look when graphed.
Biographers Jerome Ravetz and I. Grattan-Guinness note, “Fourier’s achievement can be understood by [considering] the powerful mathematical tools he invented for the solutions of the equations, which yielded a long series of descendants and raised problems in mathematical analysis that motivated much of the leading work in that field for the rest of the century and beyond.” British physicist Sir James Jeans (1877–1946) remarked, “Fourier’s theorem tells us that every curve, no matter what its nature may be, or in what way it was originally obtained, can be exactly reproduced by superposing a sufficient number of simple harmonic curves—in brief, every curve can be built up by piling up waves.”
SEE ALSO Development of Modern Calculus (1665), Wave Nature of Light (1801), Schrödinger’s Wave Equation (1926).
Molecular model of human growth hormone. Fourier series and corresponding Fourier synthesis methods are used to determine molecular structures from X-ray diffraction data.
1808
Atomic Theory • Clifford A. Pickover
John Dalton (1766–1844)
John Dalton attained his professional success in spite of several hardships: He grew up in a family with little money; he was a poor speaker; he was severely color blind; and he was also considered to be a fairly crude or simple experimentalist. Perhaps some of these challenges would have presented an insurmountable barrier to any budding chemist of his time, but Dalton persevered and made exceptional contributions to the development of atomic theory, which states that all matter is composed of atoms of differing weights that combine in simple ratios in atomic comp
ounds. During Dalton’s time, atomic theory also suggested that these atoms were indestructible and that, for a particular element, all atoms were alike and had the same atomic weight.
He also formulated the Law of Multiple Proportions, which stated that whenever two elements can combine to form different compounds, the masses of one element that combine with a fixed mass of the other are in a ratio of small integers, such as 1:2. These simple ratios provided evidence that atoms were the building blocks of compounds.
Dalton encountered resistance to atomic theory. For example, the British chemist Sir Henry Enfield Roscoe (1833–1915) mocked Dalton in 1887, saying, “Atoms are round bits of wood invented by Mr. Dalton.” Perhaps Roscoe was referring to the wood models that some scientists used in order to represent atoms of different sizes. Nonetheless, by 1850, the atomic theory of matter was accepted among a significant number of chemists, and most opposition disappeared.
The idea that matter was composed of tiny, indivisible particles was considered by the philosopher Democritus in Greece in the fifth century BCE, but this was not generally accepted until after Dalton’s 1808 publication of A New System of Chemical Philosophy. Today, we understand that atoms are divisible into smaller particles, such as protons, neutrons, and electrons. Quarks are even smaller particles that combine to form other subatomic particles such as protons and neutrons.
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