Captain Owen on Circummeridian Altitudes. 167 
‘=r’ always —to the greatest altitude. So, also, @*°—rv, and, 
4a\\ 
for azimuth, “ =e«°--as before, and = —r", the excess of altitude. 
Now in the example of circummeridian altitudes on the 20th 
May, the sun’s motion in declination was 0’.5 for one minute of 
time, or 0”.9 for degree of azimuth—d, and Q—3".2 then 4—= 
2° = 0".08 or 4°.8=¢ and r—0".02 for time. For an observation 
by azimuth, d=0".9 in 1° of azimuth, and @=—9".9 2—% — 
0°.45 = 0°.2'.7 and r=0".02 for azimuth. 
Remark. — This equation of 0°.2'.7 in azimuth at the meridian 
in very common cases of the sun’s azimuths may account for some 
of the diurnal and annual fluctuations sometimes attributed to the 
magnetic needle, where the true meridian may have been deter- 
mined by equal altitudes, and may be important in the art of 
dialling ; this equation (here 0°.2'.7)—¢ is + to the instrumental 
azimuth of the meridian, if the (lunar) object be receding in de- 
clination from the observer’s zenith, otherwise —. 
It may be remarked, also, that it is desirable that a system of 
practical geographical astronomy for determining positions of places, 
and times and measures on the surface, &c., should be developed, 
in which the azimuths may enter as an element, either as a sub- 
stitute for time as used at sea, or in combination with it, specifi- 
cally for shore practice. 
There is, however, no method given in the usual treatises on 
navigation or practical astronomy for converting an arc of time 
into are of azimuth, and all the ephemeral elements are necessa- 
rily given for certain times, because they are uniform in motion. 
This, at the meridian, is simply done, as follows: when we 
found the a, either for motion in time or azimuth, we used the 
log. cosines or secants of approximate latitude, declination, and of 
the meridian zenith distance (which, in all cases, must either be 
