In continuation of researches communicated to the Royal Society of Edinburgh, 1880 (February 16), in which I gave the probable position of an ultra-Neptunian planet, I have now to inform the Society that I have detected the existence of perturbations in the motion of Uranus, agreeing remarkably in character and period with those which would be produced by the new planet. These results are obtained from observations of Uranus extending over more than a century. The position of the planet, from this point of view, is found, from the first rough examination, to be the same as that given by me in my former memoir. This gives a means of determining the mass of the new planet.