When the relative positions of the stars are compared at considerable intervals of time, they are in many cases found to have undergone small, but unmistakable changes of a seemingly capricious character. These are termed ‘proper motions,’ to distinguish them from merely nominal shiftings due to the slow variation of the points of reference which serve to define the places of all the heavenly bodies as seen projected on the inner surface of an imaginary concave sphere. Proper motions are by no means easy to get at. Only from the most delicate observations, and with stringent precautions for bringing those at distant dates under precisely similar conditions, can they be elicited with satisfactory accuracy. Otherwise, some trifling systematic discrepancies in the compared catalogues, or accidental errors of computation, might pass for genuine effects of movement, with disastrous influence upon sidereal investigations. Hence, proper motions cannot generally be regarded as established unless, in addition to the terminal observations showing a sufficiently marked change of place in the course of thirty, fifty, or one hundred years, at least one intermediate observation is at hand to prove that the suspected motion has proceeded uniformly in the same direction, and is accordingly not the creation of personal or instrumental inaccuracy.

Although not one of the millions of telescopic stars can, with any show of reason, be supposed at rest, less than five thousand of the stellar army are at present securely credited with measurable and progressive displacements.