Observations of some minor planets have indicated a variation of their apparent magnitudes. Frigga, discovered by Dr. Peters in 1862, was observed at the next opposition in 1864; but after this it could not be found till 1868, when it was picked up by Professor Tietjen. From the latter date its light seems again to have diminished, as all efforts to re-observe it were unsuccessful till 1879. According to Dr. Peters, the change in brightness during the period of observation in that year was greater than that due to its varying distance. No explanation of such changes has yet been offered. It has been justly remarked, however, that "the length of the period of the fluctuation does not allow of our connecting it with the rotation of the planet." 13. The Average Asteroid Orbit. At the meeting of the American Association for the Advancement of Science in 1884, Professor Mark W. Harrington, of Ann Arbor, Michigan, presented a paper in which the elements of the asteroid system were considered on the principle of averages. Two hundred and thirty orbits, all that had then been determined, were employed in the discussion. Professor Harrington supposes two planes to intersect the ecliptic at right angles; one passing through the equinoxes and the other through the solstices. These planes will intersect the asteroidal orbits, each in four points, and "the mean intersection at each solstice and equinox may be considered a point in the average orbit." In 1883 the Royal Academy of Denmark offered its gold medal for a statistical examination of the orbits of the small planets considered as parts of a ring around the sun. The prize was awarded in 1885 to M. Svedstrup, of Copenhagen. The results obtained by these astronomers severally are as follows: +-----------------------------+-------------+------------+ | | Harrington. | Svedstrup. | +-----------------------------+-------------+------------+ | Longitude of perihelion | 14° 39´ | 101° 48´ | | " of ascending node | 113 56 | 133 27 | | Inclination | 1 0 | 6 6 | | Eccentricity | 0.0448 | 0.0281 | | Mean distance | 2.7010 | 2.6435 | +-----------------------------+-------------+------------+ These elements, with the exception of the first, are in reasonable harmony. 14. The Relation of Short-Period Comets to the Zone of Asteroids.