Experimental facts
Laws tying the facts together
Hypothesis
Test of the hypothesis against past facts
Prediction of new facts
Further tests
Theory
Elaboration and application
In fact, no such set pattern has been realized in the evolution of any theory in physical science, but elements of the pattern can be discerned throughout the history of science. Near the end of the sixteenth century, for example, Tycho de Brahe made accurate observations of the positions of the planets in the sky. These proved to be vital experimental facts in the evolution of the theory of mechanics. Brahe’s assistant, Johannes Kepler, discovered the laws of planetary motion that neatly summarized the myriad individual observations of his master, without in any way “explaining” those observations. The fact that Kepler’s laws tied the facts together made further progress possible. Some decades later Isaac Newton drew upon Kepler’s work as well as contributions to mechanics by Galileo and by Robert Hooke, coupled with his own inspired hypothesis of universal gravitation, and created the theory of mechanics.
Newton’s theory at once accounted for the past observations summarized by Kepler and led to the prediction of new observations. It passed its most crucial test in 1846 when astronomers pointed their telescopes at a certain point in the sky and discovered the new planet Neptune where it was predicted to be. Elaborated by mathematicians and applied by astronomers and by practical people, mechanics evolved and still stands today as a comprehensive theory embracing the subject of motion of material objects over a wide range (but, as we now know, less than the infinite range once imagined for it).
More often, theory and experiment have developed side by side through mutual cross-fertilization. The experimenter without ideas can discover an endless sequence of useless facts. The theorist unbridled by the limitations of experiment can produce a stream of fanciful ideas that have nothing to do with nature.
1 A scaled-down version of this list, beginning with Hypothesis, is commonly used in school science fairs.