of Prof. Encke's Ephemeris fo)- 1831. 179 



distant from the sun and the earth, and at a distance equal to 

 its mean one, or to its semi-axis major, should be taken as 

 unit}'. For the purpose of determining the longitude, the 

 stars which are on the parallel of the moon at the time of 

 the moon's transit over the meridian, have again been selected. 

 Agreeably to the wish of Professor Ai'gelander, the horary 

 motion of the moon in right ascension has always been added, 

 in order to facilitate to observers in other places the exact cal- 

 culation of the transit. The given horary motion of the moon 

 in right ascension, being multiplied by the difference of longi- 

 tude from Berlin, expressed in parts of an hour, taken nega- 

 tively if east, and the product being applied to the given right 

 ascension, the time of transit will be obtained with perfect ex- 

 actness, as the given horary motion is that belonging to a 

 lunar hour. The declination which is added has already for 

 the greater part been divested of the influence ox parallax, 

 at least for IBerliu, and may serve in our northern countries, 

 without any further correction, for pointing the instruments. 

 It may perhaps be doubtful whether, for observations of the 

 moon's second limb in the early hours of the morning, the ad- 

 dition of stars would be of essential service, as they must often, 

 for having the necessary light, be at a considerable distance 

 from the parallel of the moon. Considering the accuracy of 

 the principal stars, it aj^pears that the derivation of the right 

 ascension of the moon's second limb from all principal stars, 

 and the position of the instrument, would lead to results quite 

 as accurate as would be obtained by the observed difference 

 in right ascension, of stars which are at considerable distances 

 from the parallel of the moon. 



Tlie arrangement with regard to occultations of stars is 

 sufficiently explained by the paper on that subject (Phil. Mag. 

 ibr Nov. and Dec. 1829). The size of the page did not permit 

 me to add at once the declination of the stars, which is to be 

 taken from the list of occulted stars immediately following. 

 The calculation was made twice, in order to ensure exactness : 

 First, by the method explained in the preceding year's volume, 

 which, especially for several occultations on the same day, fa- 

 cilitates the decision as to their taking place, or not. Next, a 

 moment of time was chosen, which was as near tlie time of 

 tiie smallest distance, and as convenient for interpolation, as 

 possible; and lor this moment the values of ^;, y, 7/, </' were 

 calculated, and thence the innnersions and emersions were de- 

 duced. The year 1831 is distinguished by many considerable 

 occultations. Aldebaran will be occulted six times, llegulus 

 twite, and, besides, Jupiter and Saturn once. 



Although the tables next following will no more serve the 

 2 A '2 purpose 



