Comparisons of these two intervals of time have been repeatedly made, the most recent and most extensive was executed under the direction of the Astronomer-Royal several years ago, and it was based upon no less than 296 occultation observations. In this determination the measured or telescopic semidiameter of the moon was compared with the semidiameter deduced from the occultations, upon the above principle, and it was found that the telescopic semidiameter was greater than the occultation semidiameter by two seconds of angular measurement or by about a thousandth part of the whole diameter of the moon. Sir George Airy, commenting on this result, says that it appears to him that the origin of this difference is to be sought in one of two causes. “Either it is due to irradiation[3] of the telescopic semidiameter, and I do not doubt that a part at least of the two seconds is to be ascribed to that cause; or it may be due to refraction by the moon’s atmosphere. If the whole two seconds were caused by atmospheric refraction this would imply a horizontal refraction of one second, which is only 1/2000 part of the earth’s horizontal refraction. It is possible that an atmosphere competent to produce this refraction would not make itself visible in any other way.” This result accords well, considering the relative accuracy of the means employed, with that obtained a century ago by the French astronomer Du Séjour, who made a rigorous examination of the subject founded on observations of the solar eclipse of 1764. He concluded that the horizontal refraction produced by a possible lunar atmosphere amounted to 1″·5—a second and a half—or about 1/1400 of that produced by the earth’s atmosphere. The greater weight is of course to be allowed to the more recent determination in consideration of the large number of accurate observations upon which it was based. But an atmosphere 2,000 times rarer than our air can scarcely be regarded as an atmosphere at all. The contents of an air-pump receiver can seldom be rarefied to a greater extent than to about 1/1000 of the density of air at the earth’s surface, with the best of pneumatic machines; and the lunar atmosphere, if it exist at all, is thus proved to be twice as attenuated as what we are accustomed to recognise as a vacuum. In discussing the physical phenomena of the lunar surface, we are, therefore, perfectly justified in omitting all considerations of an atmosphere, and adapting our arguments to the non-existence of such an appendage.