5. Correct the observed altitude for index correction, dip, semidiameter, correction in altitude, and thus get a zenith distance. 6. From the versine of zenith distance subtract the natural number found as above. The remainder will be the versine of a meridian zenith distance, which find from the tables. 7. Under the meridian zenith distance put the declination, and proceed to find the latitude by one of the preceding rules for finding the latitude by a meridian altitude. NOTE.-If the latitude thus found differ much from the estimated latitude used in the question, the work should be corrected by using the last latitude found, in place of the former one. EXAMPLES. August 22, 1853, A.M., in latitude by account 50° 48′ N., and long. 1° 6' W., a chronometer showed 11h 50m 22s, error on Greenwich mean time being 40.2 fast, when the observed altitude of the sun's lower limb (in artificial horizon) was 101° 14′ 10′′ (Z. N.), index correction + 30", required the latitude. As this latitude differs from the estimated latitude, one part of the above operation should be repeated, using lat. 50° 47′ 49′′ instead of 50° 48', thus The same natural number as before, which shows that the erroneous latitude used in the first operation produced no practical error in the resulting latitude. The above example worked by formulæ, p. 134. (135.) May 10, 1853, A.M., in latitude by account 50° 50 N., and long. 2° 10′ W., a chronometer showed 11h 51m 58s, error on Greenwich mean time being 11m 31s fast, when the observed altitude of the sun's lower limb was 56° 19′ 30′′ (Z. N.), index correction 3' 20", and height of eye 18 feet, required the latitude. Ans., lat. 50° 51′ 34′′ N. (136.) Nov. 14, 1853, P.M., in lat. by account 87° 41' S. and long. 1° 0′ W., a chronometer showed Oh 25m 273, error on Greenwich mean time being fast 5m 56.7%, when the observed altitude of the sun's lower limb was 20° 26′ 20′′ (Z. S.), index correction - 2′ 20′′, and height of eye 10 feet, required the latitude. Ans., lat. 87° 42′ 15′′ S. (137) June 30, 1853, A.M., in lat. by account 63° 20′ N. and long. 23° 30′ W., a chronometer showed 11h 30m 15s, error on Greenwich mean time being 7m 32s fast, when the observed altitude of the sun's upper limb was 44° 20′ 22′′ (Z. N.), index correction + 2' 20", and height of eye 14 feet, required the latitude. Ans., lat. 63° 21' N. (138.) July 10, 1853, A.M. in lat. by account 57° 24′ N. and long. 3° 40′ W., a chronometer showed 11h 20m 153, error on Greenwich mean time being 30m 30s slow, when the observed altitude of the sun's lower limb was 54° 17′ 19′′ (Z. N.), index correction-2' 40", and height of eye 20 feet, required the latitude. Ans., lat. 57° 25′ 25′′ N. (139.) May 20, 1853, A.M., in lat. by account 79° 48′ N., and long. 44° 30′ E., a chronometer showed 11h 30m 0s, error on Greenwich mean time being 15m 20s slow, when the observed altitude of the sun's lower limb (in artificial horizon) was 54° 30′ 20′′ (Z. N.), index correction 4' 30", required the latitude. Ans., lat. 79° 48′ 30′′ N. (140.) June 16, 1853, P.M., in lat. by account 52° 25′ N., and long. 1o 6' W., a chronometer showed 1h 2m 98 error on Greenwich mean time being 40m 30s fast, when the observed altitude of the sun's lower limb was 60° 37′ 50′′ (Z. N.), index correction - 2′ 10′′, and height of eye 17 feet, required Ans., lat. 52° 24′ 15′′ N. the latitude. To find the latitude by Inman's rule for double altitude. The most general rule for finding the latitude by a double altitude of a heavenly body is the one selected by Dr. Inman : the labour of reducing the observations is somewhat greater than in the one known as Ivory's Rule, which follows: but the great advantage of the method adopted by Inman is that it may be applied to the same or different heavenly bodies, observed at the same instant or at different times: we will Z W N S y X E give examples of its application to all the cases that usually occur, referring the student for more complete information on the subject to the Appendix to "Inman's Navigation." Let p be the pole, z the zenith, x and y the same heavenly body observed at different times; or different heavenly bodies ob served at the same instant, or different heavenly bodies observed at different times. Let zx zy be their zenith distances. Then in the figure we know by observation z x and z y, and from the Nautical Almanac we can find the polar distances PX and Py; also by means of the elapsed time as measured by a watch, or from the right ascension of the bodies, or from both, we can compute the polar angle XPy; the colatitude Pz may then be computed in the following manner by the application of the common rules of spherical trigonometry. 1. In triangle Pyx are given two sides PX, Py and the included angle x Py to find xy, which call arc 1. 2. In triangle PXy are given three sides PX, Py and arc 1, to find angle Pxy, which call arc 2. 3. In triangle zxy are given three sides zx, zy and arc 1, to find angle z xy, which call arc 3. 4. Arc 2 arc 3 angle P XZ arc 4. But if the arc xy drawn through x and y pass when produced between P and W N P S E z the pole and the zenith, then it is evident by the annexed figure that the arc 2+ arc 3 = PXZ or arc 4. If the arc xy produced pass near z, the bodies x and y in such a position should not be observed. Lastly. In triangle PXZ are given the two sides PX and z x and arc 4 (namely, the in cluded angle PXz), to find Pz the colatitude, and thence the latitude. Correction for run. If the ship have moved in the interval between the observations, the second altitude will in general differ from what it would have been if both observations had been taken at the same place. On this account it is usual to apply to the first altitude a correction so as to reduce it to |