German physicist Gustav Theodor Fechner discovers that an increase in the intensity of a stimulus does not produce a one-to-one increase in the intensity of sensation. Instead, the sensation seems to increase as the logarithm of the excitation.

Mathematician Bernard Bolzano's Paradoxien des Unendlichen is published, two years after the Bolzano's death. It is the first work to use the word "set" in a modern mathematical sense, and also treats infinite sets.

In Über die bewegende Kraft der Wärme, mathematical physicist Rudolf Julius Emanuel Clausius articulates what comes to be known as the Second Law of Thermodynamics. The law states that heat can only be transferred from a warmer body to a colder body. In 1865, he'll restate the Law, saying that in the closed system entropy always increases.

"Bibless overalls" made of canvas are sold by the 20 year-old Levi Strauss in San Francisco. Within three years he will switch to denim and dye his pants indigo blue.

Mathematician Joseph Liouville demonstrates the existence of transcendental numbers (transcendentals are numbers that are not the solution to any algebraic equation).

Léon Foucault demonstrates that the Earth rotates using a pendulum, suspended from the ceiling of a church.

Physicist William Thomson proposes a concept of "absolute zero", at which the energy of molecules is zero. He draws on Charles' Law to show that such a condition would hold at -273 degrees Celsius.

Arithmometer: first commercially successful mechanical calculator launched

The fast-acting Collodion process invented by Frederick Scott Archer. Images require only two or three seconds of light exposure. Collodion process, mostly synonymous with the "collodion wet plate process", requires the photographic material to be coated, sensitized, exposed and developed within the span of about fifteen minutes, necessitating a portable darkroom for use in the field. Collodion is normally used in its wet form, but can also be used in humid ("preserved") or dry form, at the cost of greatly increased exposure time. The latter made the dry form unsuitable for the usual portraiture work of most professional photographers of the 19th century. The use of the dry form was therefore mostly confined to landscape photography and other special applications where minutes-long exposure times were tolerable.

Isaac Singer patents the continuous-stitch sewing machine.

The Erie Railroad, now controlled by Daniel Drew, becomes the first rail line connecting the Great Lakes with New York City, and begins to compete with the Erie Canal as a transportation route.

Albrecht von Kölliker publishes the first textbook of histology, Handbuch der Gewebelehre.

Hermann Ludwig von Helmholtz becomes the first to discover how fast a message travels along a nerve, measuring the speed of transmission in a frog nerve cell.

James Prescott Joule and William Thompson, later Lord Kelvin, establish that an expanding gas becomes cooler. This is now known as the Joule-Thompson effect.

In South Bend, Indiana, Clement and Henry Studebaker found Studebaker Brothers. Joined by a third brother, John, in 1858, the company will become the world's largest maker of wagons and carriages.

In Sweden, safety matches are patented by J. E. Lundstrom.

The brown paper bag is invented.

The elevator is invented, facilitating the future development of skyscrapers.

The U.S. state of Pennsylvania adopts a non-standard railroad gauge in order to prevent New York's Erie Railroad from establishing a route, through Pennsylvania, to Ohio.

Rudolph Albert von Kölliker discovers the cellular origin of spermatozoa, which were believed by some to originate from a fermentation process.

In Britain, vaccination against small pox is made compulsory.

Léon Foucault demonstrates that the velocity of light is lesson water than in air, tending to confirm the wave theory of light.

William John Macquorn Rankine introduces the concept of potential energy, or energy of position.

Potato chips are invented.

Mathematician George Boole, whose "Calculus of Logic," appeared in 1848, publishes An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities, which articulates a system of "symbolic logic".

Andr -Adolphe-Eug ne Disd ri credited with introduction of the carte de visite (English: visiting card or calling card) format for portraiture. Disd ri uses a camera with multiple lenses that can photograph eight different poses on one large negative. After printing on albumen paper, the images are cut apart and glued to calling-card-size mounts. Photographs had previously served as calling cards, but Disd ri's invention of the paper carte de visite (i.e. "visiting card") enabled the mass production of photographs. On 27 November 1854 he patented the system of printing ten photographs on a single sheet (although there is no evidence that a system printing more than eight actually materialized). Disd ri's's cartes de visite were 6 9 cm, about the size of conventional (nonphotographic) visiting cards of the time, and were made by a camera with four lenses and a sliding plate holder; a design inspired by the stereoscopic cameras. The novelty quickly spread throughout the world. According to a German visitor, Disd ri's studio became "really the Temple of Photography - a place unique in its luxury and elegance. Daily he sells three to four thousand francs worth of portraits". The fact that these photos could be reproduced inexpensively and in great quantity brought about the decline of the daguerreotype and ushered in a carte de visite craze as they became enormously popular throughout Europe and the United States. Disd ri also invented the twin-lens reflex camera.

Alfred Russel Wallace publishes "On the Law which has Regulated the Introduction of New Species," anticipating Darwin's theory of evolution by natural selection.

Rudolf Virchow states the principle that new cells come into being only by division of previously existing cells: Omnis cellula e cellula.

Recherches sur la putréfaction, by Louis Pasteur, is published. The book describes how fermentation is caused by microorganisms.

A mercury pump is developed by inventor Heinrich Geissler, to produce vacuum tubes. The first cathode rays will be observed in these tubes, after they are modified and improved by Sir William Crookes.

Engineer Frederick Taylor carries out "time-motion" studies of workers with the idea of making their labor more efficient. He will pioneer the "scientific management" of the workplace.

The remains of the first known example of what come to be known as the "Neanderthals" is found in a cave near Düsseldorf, in the Neander Valley. The discovery was made by limestone quarry miners and consists of a skullcap, two femora, the three right arm bones, two of the left arm bones, ilium, and fragments of a scapula and ribs. The fossils were given to Johann Carl Fuhlrott, a local teacher and amateur naturalist. The first description of the remains was made by anatomist Hermann Schaaffhausen and the find was announced jointly in 1857.In 1997, the specimen was the first to yield Neanderthal mitochondrial DNA fragments. The description of this discovery represents the beginning of paleoanthropology as a scientific discipline.

Louis Agassiz publishes Essay on Classification advocating a theory of multiple creations and contradicting both evolution and Noah's ark.

Gregor Mendel, a monk at the Augustinian monastery of St. Thomas in Brünn, Austria (now Brno, Czechoslovakia), begins breeding experiments with the garden pea, Pisum sativum.

Heinz Christian Pander describes conodonts — toothy microfossils that will puzzle paleontologists for many years.

A railway bridge spanning the Mississippi opens between Rockville, Illinois, and Davenport, Iowa. Abraham Lincoln, a lawyer, will defend the legality of the bridge before the Supreme Court, in response to a "right of way" suit brought by a steamship company.

During Easter vacation from London's Royal College of Chemistry, 18-year-old William Henry Perkin synthesized mauve, or aniline purple — the first synthetic dyestuff — from chemicals derived from coal tar. Mauve was enthusiastically adopted by the fashion industry in England and synthetic dyes quickly destroyed the market for natural substances derived from plants like indigo and madder. Perkin's creation was an accident — he was trying to synthesize quinine.

The "Bessemer process" for making inexpensive steel, which involves using blasts of cold air to decarbonize melted pig iron, is developed by inventor Henry Bessemer.

The 458-mile Wabash and Erie Canal opens after 24 years, and is the largest canal ever dug in the U.S. By 1860, however, sections will begin to be close, and, unable to compete for railroads, the entire Canal will be closed by 1874.

Über die Art der Bewegung, welche wir Wäe nennen (On the type of motion turned heat) by Rudolf Clausius is establishes his kinetic theory of heat of the mathematical basis. It also explains how evaporation occurs.

In Burrville, Connecticut, commercial production of Gail Borden's patented "condensed milk" begins. The product is made from skim milk, without any fat and without a number of nutrients found in cow's milk.

In California, Tokay, Zinfandel, and Shiraz grapes (all from Hungary) are first planted, and Italian honeybees are introduced. This is the beginning of the U.S. wine and honey industries. In North America, honey bees are an artificially introduced and invasive species.

Robert Wilhelm von Bunsen (along with Henry Roscoe) publish a design for a laboratory burner in Poggendorff's Annalen der Physik und Chemie, 100:84-85.

Rudolf Virchow finalizes the cell theory originally announced by Schleiden and Schwann 11 years earlier by declaring that cells are the basic units of all living things, and all cells are formed by the division of existing cells.

Alfred Russel Wallace sends to Darwin a manuscript — "On the Tendency of Varieties to Depart Indefinitely from the Original Type" — that shows clearly that Wallace has independently formulated a model of evolution by natural selection.

Darwin's and Wallace's ideas are jointly presented to the Linnaean Society of London.

The first relatively complete dinosaur skeleton, of Hadrosaurus foulkii, is found in New Jersey.

Physician Henry Gray publishes Anatomy of the Human Body, Descriptive and Surgical. Gray's Anatomy will be a standard textbook of anatomy for more than a century.

The concept of "bonds" is introduced by chemist Archibald Scott Couper, who believes that carbon atoms are the fundamental building blocks of organic compounds.

Julius Plücker shows that cathode rays bend under the influence of a magnet, suggesting they are connected in some way with charge. This is an early step along the path that will lead in 1897 to the discovery that cathode rays are composed of electrons.

J. Schweppe & Co. Ltd. patents a quinine tonic water that they will begin selling in 1880.

John Landis Mason patents a reusable glass jar.

Charles Darwin publishes On the Origin of Species.

An exceptionally well-preserved skeleton is discovered in Bavaria. Two years later, this bird-like, bipedal dinosaur will be named Compsognathus, meaning "dainty jaw."

Catholic priest Jean-Jacques Pouech describes fossil eggshell fragments. They will eventually prove to be the first described dinosaur eggs.

Matrix algebra begins, as mathematician Arthur Cayley discusses the matrix in the context of a theory of invariant transformations.

Gustav Kirchoff recognizes that sodium is found on the sun and discovers his black-body radiation law.

Physicist Gustav Robert Kirchhoff and chemist R. W. Bunsen explain that when light passes through a gas, or heated material, only certain wavelengths of the light are absorbed. Therefore, an analysis of the spectrum of the light can reveal the chemical makeup of the gas or material.

In Titusville, Pennsylvania, commercial production of petroleum begins, with drilling of the first well by Edwin Laurentine Drake. The well will produce approximately 400 gallons/day.

The first internal combustion engine is developed by Jean-Joseph-Etienne Lenoir. The engine uses coal gas.