To apply this to the point we are discussing. The moon in her orbital course across the heavens is continually passing before, or occulting, some of the stars that so thickly stud her apparent path. And when we see a star thus pass behind the lunar disc on one side and come out again on the other side, we are virtually observing the setting and rising of that star upon the moon. If, then, the moon had an atmosphere, it is clear, from analogy to the case of the earth, that the star must disappear later and reappear sooner than if it has no atmosphere: just as a star remains too short a time below the earth’s horizon, or behind the earth, in consequence of the terrestrial atmosphere, so would a star remain too short a time behind the moon if an atmosphere surrounded that body. The point is settled in this way:—The moon’s apparent diameter has been measured over and over again and is known with great accuracy; the rate of her motion across the sky is also known with perfect accuracy: hence it is easy to calculate how long the moon will take to travel across a part of the sky exactly equal in length to her own diameter. Supposing, then, that we observe a star pass behind the moon and out again, it is clear that, if there be no atmosphere, the interval of time during which it remains occulted ought to be exactly equal to the computed time which the moon would take to pass over the star. If, however, from the existence of a lunar atmosphere, the star disappears too late and reappears too soon, as we have seen it would, these two intervals will not agree; the computed time will be greater than the observed time, and the difference, if any there be, will represent the amount of refraction the star’s light has sustained or suffered, and hence the extent of atmosphere it has had to pass through.
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.