only the so-called apparent rising and setting are practically observable. We have already seen that the sun every day drops nearly 4 minutes behind a certain star. Assuming that sun and star rise simultaneously on one day (true cosmic rising), then after a few days have passed--the period varying somewhat according to the latitude of the place of observation, the time of the year, the size and place of the star--there will come a day on which the star rises so early that it is visible in the morning twilight, immediately before the sun appears. This is the _heliacal_ or _morning rising_. From this day the star will rise earlier and earlier, and will therefore remain visible for a longer and longer period. In the course of half a year, commonly a little sooner or later, the time of rising will have been pushed so far back that it will take place in the evening twilight; when it is pushed still farther back the rays of the setting sun eclipse the star and its rising is no longer visible. The last visible rising of the star in the evening twilight is the _apparent acronychal_ or _evening rising_. After a few more days the star goes so far back that it rises at the very moment in which the sun sets--the true acronychal rising. The rising, which is advanced constantly further into the light of day, is no longer visible, but on the other hand we now see the setting of the star. If it is assumed that the star is situated on the western horizon, i. e. sets, when the sun is on the eastern horizon, i. e. rises--and incidentally it is to be noted that this position, when the star is not situated in the ecliptic, may be divided by an interval of a larger or smaller number of days from the opposite position, viz. star on the eastern, sun on the western horizon--this is the true cosmic setting. The star moves forward, i. e. its setting takes place earlier in the morning, and after a few days it will be noticed in the morning twilight immediately before it sets, and this is the first visible setting in the morning twilight, the _apparent cosmic_ or _morning setting_. From this day the setting moves further and further forward into the night and approaches the evening twilight. At length it will be so near sunset that the star no longer sets in the night but in the evening twilight. The last visible setting of the star in the evening twilight is the _heliacal_ or _evening setting_. After a few days the star has approached still nearer to the sun: both set at the same moment, the true cosmic setting. If the star stands in the ecliptic, the true cosmic setting coincides in date with the true cosmic rising, otherwise these are divided by a greater or smaller number of days (see above). As the star moves on, a heliacal rising follows again, and so on. Between the day of the heliacal setting and that of the heliacal rising the star is invisible, since it stands so near the sun that it is eclipsed by the sun’s rays. It has already