166 Captain Owen on Circummeridian Altitudes. 
The mean sum of all the squares —Q, being multiplied by the 
prepared number a divided by 60, or 4{—=a’, the product will be 
the number of miles and decimal parts to be added to the mean 
of all the altitudes corrected for refraction, will give the greatest 
altitude, from which and the declination the latitude may be found 
as usual, and the direction of the apparent meridian, or of the 
greatest altitude, and the apparent variation of the needle will have 
been found by the operations directed. 
Remark. —If the observations were by the sun, or a star, or 
by a planet with no very sensible motion in declination, the fore- 
going results will not err sensibly from the truth. But when the 
object observed is the moon, a comet, or any other body having 
any considerable proper motion in declination and right ascension, 
it is of importance that the distance in time or azimuth from 
the meridian, as well as the excess of the greatest altitude over 
the meridian altitude, be applied, let d express the motion in 
declination, north or south, and z the motion of the zenith north 
or south by change of place, then 2+d—d’, and let a@ express 
the motion in altitude in (1™) one minute of time from the me- 
ridian, when ¢, the equation of the apex in time is required, and 
let Q’ express the motion in altitude for 1° of azimuth at the 
meridian, and d’ the motion of declination for 1° of azimuth near 
the meridian, when « the equation of the apex in azimuth is 
required, ¢ being the distance in time of the greatest altitude 
from the meridian, and =< its distance in are of azimuth, and 
r in all cases may express the excess of the greatest altitude 
d 
above the meridian altitude in seconds of arc, then ,.—e™, and 
2a7-— 
2. =e™; and e™ is always + to the middle time of equal alti- 
tudes, or to the time of the greatest altitude, when the object is 
receding from the observer’s zenith; and when advancing —, and 
