·6. ́ ́ COURSE AND DISTANCE BY MERCATOR'S SAILING.

1. For the True Difference of Latitude.-Latitudes of the same name, take their difference; Latitudes of different names, take their sum. The result will be the True Diff. Lat.; then multiply the degrees by 60, and add in the miles.

2. For the Meridional Difference of Latitude. From the Table take out the Meridional Parts corresponding to the two Latitudes; take their difference for Lats. of same name; take their sum for Lats. of different names. The result I will be the Mer. Diff. Lat.

(Mer. Parts Tab. III. of Norie; Tab. 6. of Raper; Tab. 3 of Rosser.)

3. For the Difference of Longitude.-Longitudes of same name, take their difference, Longitudes of different names, take their sum, and if this sum exceeds 180° subtract it from 360°. The result will be the Diff. Long.; then

multiply the degrees by 60, and add in the miles.

4. For the Course.-Under the Diff. Long. (in miles) write the Mer. Diff. Lat. from the Log. of Diff. Long. (index increased by 10) subtract the Log. of Mer. Diff. Lat.: the result will be the Log. Tangent of Course, which take out in degrees and minutes.

5. For the Distance.-Under the Course write the true Diff. Lat. ; to the Log. Secant of Course add the Log. of true Diff. Lat.: the sum (rejecting index 10) will be the Log. of Distance, which take out.

(1.) When both Lats. have same name, sailing from less to greater Lat. will give Course of same name as greater Lat.; but sailing from greater to less Lat. will give Course of different name from greater Lat. When Lats. have different names, sailing from N. to S, will give Course S., but sailing from 8. to N. will give Course N. Also, (2.) When both Long. have same name, sailing from less to greater Long. will give Course of same name as greater Long,: but sailing from greater to less Long, will give Course of different name from greater Long. When Long. have different names, sailing from E, to W. will give Course W., but sailing from W. to E. will give Course E., except when crossing the meridian of 180°, then Course will be E. if Long, from is E., but W. if Long. from is W. Hence

Course is named from N. or S. according to Diff. Lat., towards E. or W. according to Diff. Long.; thus N. or S., . . . E. or W.; dist.

miles.

7. TIME OF HIGH WATER BY ADMIRALTY TIDE TABLES. The work known as the "Admiralty Tide Tables" gives, in the first 97 pages, daily tide tables (i.e., morning and afternoon times of high water) for 24 of the chief ports of the United Kingdom, including Brest; these are recognised as Standard Ports,

At pp. 104 to 108 are also found a collection of Tidal Constants for 231 places on the coasts of the United Kingdom and of Europe; the constant for

a given port being applied according to its sign (+ or -) to the times belonging to the standar port to which it is referred, will give (approximately) the time of high water at that port.

A port other than the standard one being given, to find the A.M. and p.m. times of high water on a certain day, proceed as follows :—

1. Turn to the "Tidal Constants;" seek for the given port, take out the constant, and note its sign (+ or -) as well as the standard port for reference.

2. In the first part of the book, turn to the given month, seek out the standard port, and for the given day will be seen the morning and afternoon times of high water at that port. If a blank or dash occurs in either column, it indicates no high water, and consequently there is but one high water on that day. 3. In every case take out the tidal hour at standard port of reference, and under it write the tidal constant.

4.

When the constant is +, that is, additive to the tidal hours at standard port: (a) Both tides being given for the day at the standard port

If sum of morning tide and constant is less than 12h., it is the A.M. tide required. Then,

If sum of afternoon tide and constant is less than 12h., it is the P.M. tide required; but if sum is more than 12h., there is no P.M. tide.

Or,-If sum of morning tide and constant is more than 12h., reject 12h. and it is the P.M. tide required. Then,

To afternoon tide of previous day add constant, and if sum is less than 12h. there is no A.M. tide; but if sum is more than 12h., reject 12h., and it is the A.M. tide required.

(b) No morning tide being given at the standard port

To afternoon tide of previous day add constant; if sum is less than 12h. there is no A.M. tide; but if sum is more than 12h., reject 12h, and it is the A.M. time required. Then,

To afternoon tide of given day add constant, and the sum is the P.M. tide required.

(c) No afternoon tide being given at the standard port

If sum of morning tide and constant is less than 12h. it is the A.M. tide required, and there is no P.M. tide; but if the sum is more than 12h., reject 12h., and it is the P.M. tide required; in the latter case, to afternoon tide of previous day add constant, and if sum is less than 12h. there is no A.M. tide; but if sum is more than 12h., reject 12h., and it is the A.M. tide required.

5. When the constant is that is, to be subtracted from the tidal hours at standard port:

(d) Both tides being given for the day at the standard port, and constant less than both

From morning tide subtract constant, and remainder is the A.M. tide required. From afternoon tide subtract constant, and remainder is the P.M. tide required. (e) Both tides being given, and constant greater than morning tide, but less than afternoon tide

Disregard the morning tide at standard port as of no value; for there can be no A.M. tide at the place for which the tide is sought.

From afternoon tide subtract the constant, and remainder is the P.M. tide required.

(f) Both tides being given, and constant greater than both

Disregard the morning tide at standard port as of no value.

To afternoon tide add 12h. and subtract the constant; the remainder is the
A.M. tide required. Then,

If constant is less than morning tide of next day there is no P.M. tide; but
If constant is greater than morning tide of next day, add 12h. to the latter,
subtract the constant, and remainder is the P.M. tide required.

(g) No morning tide being given at the standard port

If constant is less than afternoon tide, there is no A.M. tide. Then,

From afternoon tide subtract constant, and remainder is the P.M. tide required. But, if constant is greater than aftern on tide, add 12h. to the latter, subtract constant, and remainder is the A.M. tide required. Then,

If constant is less than morning tide of next day, there is no P.M. tide; but If constant is greater than morning tide of next day, add 12h, to the latter, subtract constant, and remainder is the P.M. tide required.

(h) No afternoon tide being given at the standard port

From morning tide subtract constant, and the remainder is the A.M. tide required. Then,

If constant is less than morning tide of next day, there is no P.M. tide; but If constant is greater than morning tide of next day, add 12h. to the latter, subtract constant, and remainder is the P.M. tide required.

8. AMPLITUDE BY THE SUN,

TOGETHER WITH ERROR AND DEVIATION OF THE COMPASS.

1. For Greenwich Date.-Write down the Ship Date, month, day, hours, minutes, and seconds, expressed astronomically-that is, if question gives P.M., bring down the day and hours as they stand; but if question gives A.м., add 12 to the hours, and put the ship date 1 day back. (See p. 14 No. III.)

To the ship time add the Long. in time if W., but subtract Long. in time if E. The result will be Green. Date Apparent time. (See p. 14 No. IV.)

2. For the Declination.-From Naut. Alm. page I. of given month take out the Declination for the Green. Date, and correct it for Green. App. time. (See p. 14 No. V.)

3. For the True Amplitude.-Under the Latitude write the corrected Declination; to the Log. Secant of the Lat. add the Log. Sine of the Dec.; their sum (rejecting index 10) will be the Log. Sine of the True Amplitude, which take out in degrees and minutes, thus E. or W...° .. N. or S.

To be named from E. if question gives A.M., but from W. for P.M.
Towards N. for N. Dec., towards S. for S. Dec.

If the Dec. is 9, the True Amplitude is exactly East for A.M., exactly West
for P.M.; no computation is required. For Lat. 0, the Dec. is the True Amp.
4. For the Error of the Compass.-Under the True write the observed
Amplitude, reckoned from the same point as the true, E. or W. as the case may be.
If both are N., or both S., take their difference; if one is N. and the other
S., take their sum; the result in each case will be the Error of Compass.
Then, looking from the centre of the compass in the direction of the observed
Amplitude-

Name Error E. if true, is to right of observed, Amplitude.
Name Error W. if true, is to left of observed, Amplitude.

5. For the Deviation of the Compass.-Under the Error of Compass write the Variation as given in the question, then

Error and Var., both E. or both W., take their difference.

Error and Var., one E. and the other W., take their sum.

The resulting Deviation will be of the same name as the Error of Compass; unless the Error has been subtracted from the Variation, in which case the Deviation will be E. when Error is W., but W. when Error is E.

Also, with Error 0, Deviation is of the same amount as the Variation, but of the opposite name; with Variation 0, the Error is the Deviation.

9. LONGITUDE BY CHRONOMETER AND SUN'S ALTITUDE. In this problem two chronometric errors are given, which, by means of the elapsed time, will give a daily rate, hence proceed as follows:

1. Write down the Time by Chronometer, with the month and day before it; under this time write the second error in the question, adding it if slow, subtracting it if fast; the result will be the approximate Greenwich Date. 2. For the Daily Rate.-Write one error under the other, then— Both errors fast, or both slow, take their difference.

One error fast and the other slow, take their sum.

The sum or difference must be converted into seconds, and divided by the number of days elapsed between the dates of the two errors. The result will

be the Daily Rate, in seconds, or seconds and tenths, or perhaps tenths only.

3. For the Accumulated Rate.-Multiply the Daily Rate by the number of days elapsed between the date of the second error and the date by chronometer, allowing a proportion for the given hours. The product will be seconds, which, if above 60, reduce to minutes and seconds; the result will be the Accumulated Rate, and to know whether it has been a gaining or losing rate, note the following:

With 1st error fast, and 2nd error faster;
With 1st error slow, and 2nd error not so slow;
With 1st error slow, and 2nd error fast;

With 1st error slow, and 2nd error slower;
With 1st error fast, and 2nd error not so fast;
With 1st error fast, and 2nd error slow;

کم

Gaining rate.

Losing rate.

4. For the Greenwich Date, Mean Time.-To the approximate Green. Date apply the Accumulated Rate, subtracting it if gaining, but adding it if losing.

5. For the Declination.-Take the Declination from the Naut. Alm. p. II. of given month, and correct it for the Green. Date, mean time. (See p. 14 No. V.)

6. For the Polar Distance.-Subtract the corrected Declination from 90° when Lat. and Dec. are both N., or both S.; if Lat. and Dec. are one N. and other S., add 90° to the Declination. For Lat. 0, subtract Dec. from 90°.

7. For the True Altitude, correct the observed Altitude for Dip, Refraction, Semidiameter, and Parallax. (See p. 16 No. VI.)

8. For the Equation of Time.-For the given day take the Equation from Naut. Alm. p. II. of month; also, take "Var. in 1h." for same day from p. I. of month; multiply the "Var. in 1h." by the hours and tenths of Green. Time, marking off as many decimal places in the product as there are decimal places in the "Var." and Time together. This is the correction of EquationTo be added if Equation is increasing;

To be subtracted if Equation is decreasing.

Also, take special notice, on p. I. of Naut, Alm. of the day, when the Equation

changes; in the column it is marked by a strong dash

and at top

For the Apparent Time at Ship.-Add together the true Altitude, the Latitude, and the Polar Distance; divide the sum by 2, for the Half-sum; and subtract the Altitude from the Half-sum, which call Remainder.

Then, add together the Log. Secant of the Latitude, the Log. Cosecant of the Polar Distance (take Secant of Declination if Pol. Dist. is greater than 90°), the Log. Cosine of the Half-sum, and the Log. Sine of the Remainder. The sum of these four Logs. (rejecting index 30) will be the Log. of the Hour-Angle, that is, the time from the nearest noon, which take out in hours minutes, and seconds. N.B.-All Logs. to be taken out to seconds of arc.

Note: Hour-Angle Table XXXI. of Norie; Tab. 69 of Raper; Tab. 20 Rosser. If the question gives A.M. at ship, subtract the hour-angle from 24 hours, and before the remainder write the Ship Date, which will be 1 day less than the date in the question :—

If the question gives P.M. at ship, the hour-angle is the correct time, before which write the Ship Date unaltered :

And you have the Ship Date, Apparent Time. (See also p. 16 No. VII.)

10. For the Mean Time at Ship.-Under the App. Time at Ship write the Equation of Time, which is to be added or subtracted as directed in Naut. Alm. p. I. of given month. The result will be the Mean Time at Ship.

For the Longitude.—Under the Ship Date, Mean Time, write the Greenwich Date, Mean Time; take the less from the greater, remembering that the value of the days in each must be considered as well as the hours. The remainder will be the Longitude in time, which turn into . . .", and name

East if Green. Mean Time is less than Ship Mean Time.
West if Green. Mean Time is greater than Ship Mean Time.

10. AZIMUTH BY SUN'S ALTITUDE,

TOGETHER WITH ERROR AND DEVIATION OF THE COMPASS.

1. For Greenwich Date.-Write down the Ship Date, month, day, hours, minutes, and seconds, expressed astronomically; that is, if question gives P.M. bring down the day and hours as they stand; but if question gives A.M. add 12 to the hours, and put the ship date 1 day back. (See p. 14 No III.)

To the ship time add the Long. in time if W.; but subtract Long. in time if E.-The result will be Green. Date Mean Time, or Apparent Time, according to the question. (See p. 14 No. IV.)