DISTANCE, SIZE,, AND MASS. 29

creased by the effects of irradiation. When themoon’s diameter is deduced from observations madeduring solar eclipses (at which time irradiation tendsto reduce her apparent diameter, because she is thenseen as a dark body on a light ground), the valuedepends partly on the telescope employed. Withinstruments of average power it is about 30' 55", or1,855". From a careful discussion of the occultationsof stars by the moon, as observed at Greenwich andat Cambridge, the Astronomer Eoyal has inferred thatthe length of the moon’s mean apparent diameter is31' 5" - l, or 1,865"T.* This is the value assumedthroughout the present work. (It is a useful aid tothe memory to notice that the number of seconds ofarc in this value gives the number of the year inwhich the Astronomer Eoyal announced his results.)

* As inconvenience is often experienced from the absence of allexplanations of estimates such as these, I here state how the abovevalue has been inferred ; for I am unable to point to any passage inwhich the Astronomer Eoyal has distinctly stated it. In Madler’s“ Der Mond” it is stated, in § 14, that Burckhardt assigns as themoon’s semi-diameter 15' 31"‘95. In the Monthly Notices of theAstronomical Society for 1864^65, the Astronomer Eoyal assigns2" as the excess of the telescopic diameter of the moon over thatinferred from stellar occultations ; and speaking of the eclipse of1833, he says that the observations of the moon gave — 4" - 2 as thecorrection on Burckhardt’s semi-diameter, and — 6"'8 as the correc-tion on the telescopic semi-diameter. It follows that the telescopicsemi-diameter exceeds Burckhardt’s by 2"’6, and therefore thatBurckhardt’s estimate is less than Airy’s estimate from occulta-tions by 0"'6. Hence Airy’s estimate from occultations (nowherestated, in his paper) must be 15' 32"’55, corresponding to an apparentmean diameter of 31' 5"’ 1.