Captain Owen on Circummeridian Altitudes. 175 
Let the are AT or Aé in time =E, the equation of the apex, 
or apicial equation, and let AT’O or AZéR represent an arc in 
time equal to any given time from the apex A or from the meridian 
T, within certain limits. 
If the object were stationary with respect to the pole and zenith, 
viz. had no motion in declination, and the zenith also stationary as 
regards the object, then the points A and T would coincide, and 
the meridian altitude would also be the greatest altitude, and the 
point of meridian transit would be the apex of the apparent celes- 
tial track. But when the object has motion in declination, or the 
observer has motion in terrestrial latitude, under every such circum- 
stance the greatest altitude is always greater than the meridian 
altitude ; for suppose the object (the moon for example) to appear 
at O in her track about five minutes before her meridian passage, 
and that her declination moved towards the zenith at the rate of 
9 miles an hour, or 9” per minute; if the moon had not this mo- 
tion in declination, and had attained to T in the meridian, she would 
there have had no motion in altitude, and from that point she 
would have commenced her downward course, but her motion 
of 9” in 1™ of time towards the zenith must cause her to rise 
through the meridian precisely at that rate. Again, at 1™ after 
her transit, she will have risen 9”, and would have fallen (assuming 
a quantity =a) 1”.5, the difference would be 7”.5 by which amount 
the moon would have had a greater altitude 1™ after she had passed 
the meridian, than her meridian altitude; at the second minute 
after her meridian passage, she would have fallen 6” (= 1.5 X 2’); 
in the same time she has risen 18” by her motion in declination, 
the difference 12” by which amount her altitude at two minutes 
after her passage would be higher than her meridian altitude; at 
3™ she would have fallen 13”.5 and risen 27”, or 13”.5 higher; at 
