12 EXPLANATION OF TABLES . 
= 
Thus, if the body bears S. 45° E. and the change in latitude is to the southward, the change in 
longitude will be to the westward; and, if the change in latitude is to the northward, the change in 
longitude will be to the eastward. 
The convenient application of the longitude factor in finding the intersection of position lines is 
explained under ‘‘Computing the intersection of position lines,” chapter XIV. 
TABLE 36.—THE LATITUDE FACTOR. 
The change in latitude due to a change of 1’ in the longitude, called the latitude factor, f, is 
given in this table at suitable intervals of latitude and azimuth. The quantities tabulated, being 
the reciprocals of the values of the longitude factor, are computed from the formula— 
he 1 
f F sec. Lat. X cot. Az. 
When an ex-meridian sight is solved with a longitude afterwards found to be in error, this table, 
by setting forth the number of minutes of latitude due to each 1’ of error in longitude, gives the 
means of finding the correction in the latitude for the amount of error in the longitude used in the 
calculation. 
Regarding the azimuth of the observed celestial body as less than 90° and as measured from 
either the North or the South point of the horizon toward East or West, the rule for determining 
whether the correction in latitude is to be applied to the northward or to the southward is as follows: 
» If the change in longitude is of the same name as the second letter of the bearing, the change in lati- 
tude is of the contrary name to the first letter, and vice versa. Thus, if the body bears S. 14° E. 
and the change in longitude is to the westward, the change in latitude will be to the southward, and, 
if the change in longitude is to the eastward, the change in latitude will be to the northward. 
=cos. Lat.Xtan. Az. 
TABLE 37.—NOON INTERVAL FACTOR. 
An important item in the day’s work is the proper setting of the watch to show the correct time 
of local apparent noon, or to find the interval of time from the morning sun observation to local 
apparent noon. The rate of change of longitude of the sun in its diurnal path from east to west is 
900’ per hour. If to this is added the hourly change in longitude of the vessel due to course and 
speed, combined with the current, when this change of longitude is to the eastward, or if to this is 
subtracted the hourly change in longitude when speed and current are to the westward, the result 
will be the rate of approach per hour of the meridian of the sun toward the meridian of the observer. 
Suppose at watch time 7» 59™ 43s (G. C. T. 12 12™ 508) the local observation of sun gave an easterly 
hour angle of 35 34™ 068 (3.5683), the vessel changes longitude 19’ every hour to the eastward due 
to course and speed, and that the current in longitude is 0’.6 eastward; then the interval to noon is 
3.5683X oe From the table for 19’.6, Easterly hourly change in longitude the factor found is 
-97869 and this number multiplied by the hour angle 34.5683 is the interval to noon. 
logarithm of .97869=9.99065 
logarithm of 3».5683=0.55246 
logarithm of interval=0.54311=34.4923—3h 29™ $28 
W.T. obs. 7» 59™ 438 Gale: Dofobss 2h a2 =550s 
Intv. to noon, 3 29 32 TInty. to noon, 3 20) BP 
W. T. of L. A. noon, 11 29 15 G. C. T. of L. A. noon, 15 42 22 
The declination for noon is found in the nautical almanac for G. C. T 15 42™ 22s, 
TABLE 38.—CONVERSION OF SIDEREAL INTO MEAN SOLAR TIME. 
TABLE 39.—CONVERSION OF MEAN SOLAR INTO SIDEREAL TIME. 
These tables give, respectively, the reductions necessary to convert intervals of sidereal time into 
those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for 
any interval is found by entering with the number of hours at the top and the number of minutes at 
the side, adding the reduction for seconds as given in the margin. 
The relations between mean solar and sidereal time intervals, and the methods of conversion of 
these times, are given in Chapter IX. 
TABLE 40.—CORRECTIONS TO BE APPLIED TO FIND THE TRUE ALTITUDE OF A 
STAR AND ALSO OF THE SUN FROM THE OBSERVED ALTITUDE ABOVE THE 
HORIZON. 
This is a consolidated table in which the tabulated correction for an observed altitude of a star 
combines the mean refraction, and that for an observed altitude of the sun’s lower limb combines 
the mean refraction, the parallax, and the mean semidiameter, which is taken as 16’. The addi- 
tional correction for the sun takes account of the variation of the sun’s semidiameter in the different 
months of the year. The auxiliary table for height of eye gives the additional corrections for dip. 
