A compound sentence contains two or more independent clauses. The independent clauses are joined in one of the following ways to indicate that they form one sentence.
Organic chemists have gained substantial command over the synthesis of
small complex molecules, but the goal of constructing large
well-defined molecules has been more elusive.
--"Dendrimer Molecules," Scientific American (modified)
In John Conway's famous game of "Life", there is a finite grid filled with
cells. Either each cell is alive, or it
is dead.
--Kai Wu, "Artificial Life," SciTech Magazine (modified)
In 1931 Oppenheimer attempted to find an equation for the photon that would
be an analogue to Dirac's equation for the electron; he failed
in this effort.
By virtue of their prevalence alone, it is clear that mood disorders do not
necessarily breed genius; indeed, 1 percent of the general
population suffer from manic-depression and 5 percent from a major depression
during their lifetime.
--"Manic-Depressive Illness and Creativity," Scientific American (modified)
Do not attempt to form a compound sentence by joining the independent clauses with just a comma. Such a structure is called a comma splice.
The independent clauses that make up the compound sentence should be at least approximately equal in importance. If one clause is clearly less important than the other(s), make the less important clause a dependent clause by introducing it with a subordinating conjunction. The resulting sentence will then be complex rather than compound.
Jupiter has an enormous size and gravity [background]
and the Galileo probe steadily gained velocity as it approached the
planet [focus].
Because Jupiter has an enormous size and gravity
[background], the Galileo probe steadily gained velocity as it
approached the planet [focus].
--"Halo Nuclei," Scientific American (modified)