Physics: Newtonian physics, now more than a century old, is well established. As a result, the idea of a “clockwork universe” governed by deterministic laws is widely accepted.
Astronomy: Astronomy has risen to prominence. Herschel discovered the planet Uranus in the 1780’s. It is the first new planet to be discovered since the dawn of history. Asteroids are beginning to be discovered. The first four are discovered between 1801 and 1807.
Geology: Geologists have started making geological maps. James Hutton presented his paper Theory of the Earth in 1785, wherein he argued that the Earth was much older than typically supposed. In the 1800s, geology would focus largely on determining the age of the earth. Estimates ranged from hundreds of thousands to billions of years.
Thermodynamics: Sadi Carnot, “the father of thermodynamics” does his groundbreaking work in the 1820s. The field will mature over the course of this century. By the 1870s James Clerk Maxwell and Ludwig Boltzmann have developed the atomic theory of thermodynamics (statistical thermodynamics), as well as a formal definition of entropy.
Atomic Theory: John Dalton proposes that matter consists of indestructible spherical particles known as atoms. These atoms come in various types called elements. Throughout this century, chemists were divided between “atomists” such as Dalton and Boltzmann, and its opponents such as Ernst Mach. The matter wasn’t fully resolved until the early 20th century.
Astrophysics: Lord Kelvin and Hermann von Helmholtz apply Newtonian physics to the sun, and calculate how long it could burn due to gravitational contraction. They get a value of about 20 million years.
Evolutionary Biology: Gregor Mendel’s work on inheritance occurs in the middle of this century, and Charles Darwin’s groundbreaking work On the Origin of the Species is published in 1859.
On The Distant Horizon: Quantum Theory, DNA, General Relativity, and the list goes on.
A lot can happen in 200 years.