3-ii 



CATALOGUE. ASTRONOMY, CELESTIAL APPEARANCES. 



be 



303ii 



id 



id 

 3U3(/ — 3953 d — 13'"'(i — 14 

 I4A 



; whence d zz 



13A 



meiit apparens des corps celestes. 2 v. 4. 

 Par. 1786. . . R. S, 

 j—^; andif rf is less than 13, h being negative, the Euler on the degrees of light of the heavenly 



place of low water itiust be immediately below the lumi- 

 nary. 



, . \3h 14/1 



and d:z or 



h+3 fe+a 



The same conclusion may be obtained by very different 

 means ; considering the tide, in comparison with the sur- 

 face of the spheroid ot equilibrium, as a wave, which is 10 

 produce by its propagation, a sufficient velocity of ascent 

 and descent, for the actual motion of the tide upon a sphere. 

 Thus, if d were 52, the height of the tide would be 6= feet, 

 that is li feet above the spheroid ; and such a wave being 

 naturally propagated with a velocity twice as great as that 

 of the tide, the water would ascend or descend, with a velo- 

 city sufficient for its propagation with a velocity twice as 

 great as the velocity of rotation, and, since it is actually ex- 

 posed to the same force, for a time twice as great, a qua- 

 druple velocity will be generated, which will be equal to the 

 relocity of ascent, or descent, required for the tide of 6| feet, 

 which is four times as much elevated as the supposed wave. 



It appears, therefore, that for any given magnitude of the 

 elevation h, there are two values of rf, accordingly as we sup- 

 pose the time of high water, or of low water to coincide with 

 that of the moon's southing : thus, if /i^a, d must be either 

 gl or 3i ; and it is difficult to determine for the open ocean 

 whether the time of high or of low water, is nearest to 

 the transit of the luminary. For a sea 4000 miles broad, 

 the depth must exceed S miles, in order that the time of 

 high water may coincide with that of the greatest elevation 

 of the horizon ; and, if it be less than this, the time of high 

 water must be that of the greatest depression, that is, on the 

 eastern shore, about 5 hours after the moon's southing ; on 

 the western, about 7 ; and, if the sea were narrower, these 

 times might vary from the fifth to the third, and from the 

 seventh to the ninth hours, respectively. The effects of re- 

 sistance will also accelerate the tides of the latter kind, and 

 in this manner, tlie theory may be perfectly reconciled with 

 observation. 



Celestial Appearances in general, 

 with reference to the Earth. 



Baxter's matho. 



Hugeuii cosiiiotheoios, 4. Hag. I69B. 



Foiitaielle sur la pluralite des mondes. 12. 



1686. ParLalande. 1800. 

 Diunh du SejourTTa'iic analiiiqiie des motive- 



bodies. A.Berl. 1750.280. 



Makes the light of the sun equal to that of 6560 candles 

 at 1 foot distance, liiat of the moon to a candle at 71 feet, of 

 Venus, to a candle at 421 feet, and of Jupiter to a candle at 

 1620 feet : partly from Bouguer's experiments. Hence the 

 sun would appear like Jupiter, if removed to 131 000 times 

 his present distance. 



Appearances of the Stars. 



Twinkling. See Fixed Stars. 

 Bradley on a newly discovered motion of the 

 fixed stars. Ph. tr. 1728. XXV. 637. 



The aberration. It was observed by Flamstead, but not 

 understood. 



Lalande on the change of latitude of the 

 stars. A. P. 1758. 339- H. 87- 



Lagrange on the variations of the earth's or- 

 bit. A. P. 1774.97. H. 39. 



On the changes of latitude and longitude of the stars, p. 

 164. The change of obliquity affects the right ascension 

 a little, but not the declination. 



Appearances of the Sun. 



Seasons, Day and Night, Twilight. 

 La Caille on the length of twilight at the 



Cape. A. P. 1751. 544. H. 158. 

 Bergmann on twilight. Schw. Abh. 1760. 



237. Opusc. V. 331. VL 1. 

 Lambert Photomelria. §. 987. 



The limit of visible twilight is when the sun is a"i belovr 

 the horizon. In order to find the time when the twilight is 

 shortest, as Rad : Sin. X.at : ; S. 6° is" : S. Sun's declina- 

 tion, south. 



Appearances of the Primary 

 Planets. 



Halley on the appearance of Venus in the 

 daytime. Ph.tr. 1716. XXIX. 466. 



Godin on the apparent motions of the planets 

 in epicycloids. A. P. 1733. 285. H. 67. 



