ROYAL ASTRONOMICAL SOCIETY 179 due to north or south position of the observer, is a factor to be considered. Writing generally, the effect of the earth's rotation is to shorten the duration of a transit because a place on the hemisphere of the earth which is towards the sun moves lineally in the direction opposite to that in which Venus moves, and therefore hastens her motion across the disc, and for two observers in the same hemisphere, the shortening is less for the one who is nearer the pole, because his linear movement is less. But a case to be specially considered is that of an observer in the Arctic or Antarctic circle, according as the northern or southern pole of the earth is towards the sun, who, though on the sunlit hemisphere, is carried by the earth's rotation in the same direction as the planet. To such an observer the duration of transit is lengthened, and at a December transit, if the planet is south of the sun's centre, this lengthening of the passage for a southern observer, which is already greater than that for a northern, will be an advantage ; but if the geocentric transit is north, its duration as seen by the southern observer, which is less than that seen by the northern, will again be lengthened, and this will make the difference of the observed times less than it would otherwise have been, and hence it will be disadvantageous to observe the phenomenon from a station within the Antarctic circle, which will be beyond the pole, so to speak, at mid-transit. A transit will happen in December, if Venus is at inferior conjunction and at the same time sufficiently near to the ascending node of her orbit. A transit will happen in June if similar circum- stances occur, the planet being then near the descending node ; in general, transits happen in pairs, the individuals of a pair being at the same time of the year and separated by an interval of eight years. At the first of a pair of December transits, Venus will have just passed the ascending node, and since the planet is then in north latitude the geocentric transit will be above the centre of the sun's disc. It will be found from consideration of the length of the synodic period of Venus, and her sidereal period, that the second transit of the pair at either node happens before her passage through the node, and the chord of geocentric transit will in this case be south of the centre of the disc. The southern observer in each case sees the planet displaced northward, but, as explained above, the advantage that can be gained by an observer in the Antarctic circle the southern pole of the earth being in the sunlit hemisphere in December cannot be maintained at the first of a pair of transits, since it lengthens the duration of the shorter transit, and hence shortens the difference. At the second of a pair of December transits, omitting the consequences of the earth's rotation, the
