Investigation of the question of a possible trans-Neptunian planet was undertaken by the writer in 1877. As Neptune requires 164 years to travel completely round the sun, and the period during which it has been carefully observed embraces only half that interval, clearly its orbit cannot be regarded as very well known. Any possible deviations from the mathematical orbit could not therefore be traced to the action of a possible unknown planet outside. But the case was different with Uranus, which showed very slight disturbances, and these were assumed to be due to a possible planet exterior to both Uranus and Neptune. As a position for this body in the heavens was indicated by the writer's investigation, that region of the sky was searched by him with great care in 1877-1878 with the twenty-six-inch telescope at Washington; and photographs of the same region were afterward taken by others, though only with negative results. In 1880, Forbes of Edinburgh published his investigation of the problem from an entirely independent angle. Families of comets have long been recognized whose aphelion distances correspond so nearly with the distances of the planets that these comet families are now recognized as having been created by the several planets, which have reduced the high original velocities possessed by the comets on first entering the solar system. Their orbits have ever since been ellipses with their aphelia in groups corresponding to the distances of the planets concerned. Jupiter has a large group of such comets, also Saturn. Uranus and Neptune likewise have their families of comets, and Forbes found two groups with average distances far outside of Neptune; from which he drew the inference that there are two trans-Neptunian planets. The position he assigned to the inner one agreed fairly well with the writer's planet as indicated by unexplained deviations of Uranus. The theoretical problem of a trans-Neptunian planet has since been taken up by Gaillot and Lau of Paris, the late Percival Lowell, and W. H. Pickering of Harvard. The photographic method of search will, it is expected, ultimately lead to its discovery. On account of the probable faintness of the planet, at least the twelfth or thirteenth magnitude, Metcalf's method of search is well adapted to this practical problem. When near its opposition the motion of Neptune retrograding among the stars amounts to five seconds of arc in an hour; while the trans-Neptunian planet would move but three seconds. By shifting the plate this amount hourly during exposure, the suspected object would readily be detected on the photographic plate as a minute and nearly circular disk, all the adjacent stars being represented by short trails.