412 



Art. XIX. — Astronomical and Nautical Collections. 

 No. IV. 



i. Remarks on the Calculation of Parallax for a Spheroid. 



It is not unusual to employ, in the calculation of eclipses, 

 instead of the true latitude, a latitude reduced according to a 

 table of Mayer, in order to determine the effect of the earth*s 

 ellipticity on the lunar parallax : and the same correction may, 

 in some cases, be thought necessary for the very accurate com- 

 putation of lunar distances, for the purpose of determining the 

 longitude. 



Professor Vince, in his valuable System of Astronomy, observes, 

 (vol. i. n. 173,) that " the most elegant and simple method of 

 finding the parallax in latitude and longitude on a spheroid, is 

 the following, given by Mayer. Subtract the angle [formed by 

 the vertical line with the earth's semidiameter] from the latitude 

 on the spheroid, and you get the . . latitude of the point re- 

 duced to a sphere. Also the horizontal parallax must be adapted 

 to the [corrected radius.] . . The latitude thus reduced, and 

 the horizontal parallax thus found, are to be employed in comput- 

 ing the moon's parallaxes in longitude, latitude, right ascension, 

 and declination, which will now be performed by the rule 

 founded on the hypothesis of the earth being a sphere." 



Thus, if the latitude of Greenwich is 51° 28' 40", we are to 

 deduct 14' 29", and employ 51° 14' 11", which, when the moon 

 is near the equinoctial, and on the meridian of the place, makes 

 alone a difference of about 8" in the parallax ; that is, taking 

 the ellipticity ^^^« which is a correction not wholly inconsi- 

 derable. 



But, supposing the moon, as may easily happen, to be con- 

 siderably to the north of the east or west, this correction will 

 be not merely superfluous, but absolutely erroneous, since in 

 truth a smaller correction of an opposite nature is required. 



When the moon is due east, or due west, her altitude is not 

 affected by the obliquity of the surface ; since the perpendicular 

 to the meridian is obviously parallel to the surface of the sphere: 



