Instead of a diameter of three thousand miles he proved to have one of thirty-four hundred, making his volume nearly half as large again as had been credited him. These measures bore intrinsic evidence of their trustworthiness in an interesting manner, and at the same time produced internal testimony that accounted for the smallness of previous determinations. Measures heretofore had been made, usually if not invariably, either when the planet transited the Sun or when it exhibited a pronounced phase. Now in both these cases the planet looks smaller than it is. In the first case this is due to irradiation, the surrounding disk of the Sun encroaching both to the eye and to the camera upon the silhouette of Mercury. And this inevitable effect had not been allowed for in the measures. In the second case the horns of the planet never seem to extend quite to their true position. This was rendered evident by the Flagstaff series of measures, which began when the planet was a half-moon and continued till it was almost full. As it did so, the values for the diameter steadily increased, even after irradiation was allowed for, although this against the brilliant background of the noonday sky must have been exceeding small, and tended in part to be diminished as the planet attained the full, because of its consequent nearing of the Sun. The measures thus explained themselves and vouched for their own accuracy.[3] Then came a curious bit of unexpected proof to corroborate them. In his “Astronomical Constants,”[4] published but a short time before, Newcomb had detected a systematic error in the right ascensions of Mercury which he was not able to explain. By diligent mousing that eminent computer had discovered that Mercury was registered by observers too far from the Sun on whichever side of him it happened to be, and in proportion roughly not to its distance off but to the phase the planet exhibited. When the disk was a crescent the discrepancy between observation and theory was large, and thence decreased as the planet passed to the full. He suspected the cause, and would have found it had he not considered the diametral measures of the planet too well assured to permit of doubt. As it was, he neglected a factor which has vitiated almost all the observations made on the planets up to within a few years, the correction for irradiation. This was the case here. The received measures, beginning with Bradley and ending with Todd, had almost without exception been made in transit, and, as no regard had been paid to the contracting effect of irradiation, had been invalidated in consequence. The new method supplied almost exactly the amount needed to explain the right ascensions, a second of arc, and in precise accordance with the place which the discrepancy demanded. [3] New Observations of the Planet Mercury, _Memoirs Amer. Acad._ 1897. Vol. XII, No. 4. [4] “Astronomical Constants,” 1895, pp. 67, 68.