168 Captain Owen on Circummeridian Altitudes. 
the sum or difference of the latitude and declination) with a con- 
stant quantity. Using the same elements in part, we shall find 
the value in arc of azimuth of 1™ of time at and near the merid- 
ian, and consequently the value of 1° of azimuth in time, viz. for 
example, 
Meridian true distance, 24° 20/ cosecant, 0.385 
Declination, 20 6 cosine, 9.973 
1™. log. sine, 7.640 
Azimuthal are, 34*.2 log. sine, 7.998 
for 1™- of time at meridian, 
and 34’.2)60(1".79 = 1".47°.4—the value of one degree of azi- 
muth, at the meridian, in time, and the same analogy will apply 
at every other altitude, to convert time into azimuth, or azimuth 
to time. These values might be deduced from a and a for 
3.2)9.862(3.08 = square of the time corresponding to 1° of azi- 
muth, and 4/3.08 =1".76 = 1".46* nearly as before. 
Having the value of 1° of azimuth in time, we can easily find 
from the ephemeris the motion (d) in declination in that time, 
which, in our example, is—0.’90=d, and in example a 
— 0°.046 = « = 2'.76 for the azimuthal deviation from the meridian, 
S55 5 d O!.0414 
and the excess of greatest above the meridian altitude = 3 —e 
= 0.021. 
For surveying on shore, and for geographers who desire to use 
theodolites, a ready rule for converting arcs of time into corre- 
sponding arc of azimuth will be convenient at other parts of the 
sun’s (or other object’s) diurnal path, as well as at the meridian. 
The following was given to me, and demonstrated some years 
ago, by Lieutenant Raper, R. N., the author of a Treatise on Navi- 
gation, ViZ.: 
Given two altitudes of a known heavenly body, and the interval 
in time (limited) between them, to find thence the difference of 
azimuth in the same interval. 
