There are two different kinds of double star. In the case where two stars are only apparently close to each other, but which are in fact separated by a great distance are known as optical doubles or optical binaries. In the vast majority of cases, however, the two stars are actually gravitationally bound and orbit each other; this is known as a binary star and is considered separately.
Optical doubles are distinguished from binary stars by observing them for a long period of time, usually years. If the relative motion looks linear it may be safely assumed that the motion is due to proper motion alone and that they are an optical double. Position angle changes progressively and distance oscillates between a maximum and minimum in the case of a binary.
The first recorded discovery of a double star was by G.B. Riccioli in 1650 when Zeta Ursae Majoris was announced to be a double star. Since that time the search for double stars has been carried out very thoroughly and every star down to the 10th stellar magnitude has been carefully examined. At least 1 in every 18 stars in the northern half of the sky which are as bright as 9.0 magnitude is a close double star visible with a 36-inch refractor telescope.