The strong presumption that the law of gravitation would prove truly universal has been fully borne out by investigations of stellar orbits. Binary stars circulate, it can be unhesitatingly asserted, under the influence of the identical force by which the sun sways the movements of the planets, the earth the movements of the moon. It is true that this does not admit of mathematical demonstration, but the overwhelming improbability of any other supposition amounts practically to the same thing. The revolutions of the stars are hence calculable, because conducted on familiar principles; their velocities have the same relation to mass, their perturbations may lead to similar inferences as in the solar system.

Observations, however, must precede calculations; and they are rendered arduous in double stars by the extreme minuteness of the intervals to be measured. Many revolving pairs never separate to the apparent extent of a single second of arc; yet this fraction of a second may represent, in abridgment, a span of some thousands of millions of miles. Infinitesimal errors, magnified in this proportion, become of enormous importance, and often impenetrably disguise the real aspect of the facts.

For determining the relative situations of adjacent stars, two kinds of measurement are evidently needed. The first gives their distance apart, the second the direction of the line joining them as regards some fixed line of reference.