180 Captain Owen on Circummeridian Altitudes. 
similar, but she would have had the greatest altitude (10") ten 
minutes before she came to the meridian, but the excess of the 
greatest altitude would be — 2’.5 likewise. 
Observe that the zenith moves to or from the object only by 
a quantity equal to the difference of latitude made by her true 
course and distance, and that the easting or westing, viz. the 
longitude, must be disregarded altogether in this problem, so far 
as it has yet been considered in this paper. 
Circummeridian or Proximeridian Altitudes considered with Refer- 
ence to this Problem. 
It is evident, on mere inspection of the diagram, that the apex 
of the celestial object’s path is the point to which all altitudes 
taken near the meridian must be reduced. The calculation is 
equally simple from the apex and from the meridian, and the prop- 
er motion in altitude, a, is precisely the same in both cases, or 
differs by an insensible quantity only, but the times by whose 
squares this quantity is to be multiplied must be reckoned from 
the apex, not from the meridian. Thus, in the first example, a= 
1”.5; when on the meridian at 3™ from the apex, the correction 
for 3" would have been 13”.5 as before shown by the analysis. 
Of equal Altitudes of the same Object, when the Motion in Dec- 
lination is a constant Quantily, or may be so esteemed. 
Equal altitudes can be demonstrated to be equally distant in 
arc and time from the apex, when the motive forces are constant, 
and not from the meridian, except when there is no motion equiv- 
