Oblique will be found particularly useful in going along shore, and Sailing. in surveying coasts and harbours.

Ex. 1.-At 11 A.M. the Girdle Ness bore W.N.W., and at 2 P.M. it bore N.W. by N.; the course during the interval S. by W. five knots an hour; required the distance of the ship from the Ness at

each station.

N

F.

By Construction.-Describe the circle NESW (fig. 39), and draw the diameters NS, EW at right angles to each other. From the centre C, which represents the first station, draw the W.N.W. line CF; and from the same point draw CH, S. by W., and equal to 15 miles, the distance sailed. From H draw HF in a N.W. by N. direction, and the point F will represent the Girdle Ness. Then the distances CF, HF will measure 19.1 and 26.5 miles respectively.

W

By Calculation

L sin CFH...........
Log. FH...........................

To find the distance FH.

Log. CD
L sin ADC..

= 1.17609

4 pts. = 9.84948

4.02557 3 pts.-9.74474 ..19.07 m. =

L sin CAC.

= L sin 7

Log. AC...........

Ex. 2.-Running up Channel E. by S. per compass at the rate of 5 knots an hour. At 11 A.M. the Eddystone Lighthouse bore N. by E.E., and the Start Point N.E. by E.E.; and at 4 P.M. the Eddystone bore N.W. by N., and the Start N.E.; required the distance and bearing of the Start from the Eddystone, the variation being 2 points W.

By Construction.-Let the point C (fig. 40) represent the first station, from which draw the N. by E.E. line CA, the N.E. by E.E. line CB, and the E. by S. line CD, which make equal to 25 miles, the distance run in the elapsed N time. Then from D draw the N.W. by N. line DA, intersecting CA in A, which represents the Eddystone; and from the same point draw the N.E. line DB, cutting CB in B, which therefore represents the Start. Now the distance AB applied to the scale will measure 22.9, and the bearing per compass BAF will measure 7310.

HS Fig. 39.

15 m. = 1-17609 9 pts.

= 9.99157

""

11.16766 -9.74474 1.42292

3 pts. 26.48 m.

1-28083

F

Fig. 40.

44 pts. 23.86 m.

25 m. = 1.39794 4 pts. = 9.84948

B

11-24742 =-9.86979 1.37763

B Fig. 41.

CHAP. IX.-OF CURRENT SAILING.

The computations in the preceding chapters have been performed upon the assumption that the water has no motion. This may no doubt answer tolerably well in those places where the ebbings and flowings are regular, as then the effect of the tide will be nearly counterbalanced. But in places where there is a constant current or setting of the sea towards the same point, an allowance for the change of the ship's place arising therefrom must be made. And the method of resolving these problems in which the effect of a current or heave of the sea is taken into consideration is called current sciling

Current

In a calm, it is evident a ship will be carried in the direcSailing. tion and with the velocity of the current. Hence if a ship sails in the direction of the current, her rate will be augmented by the rate of the current; but if sailing directly against it, the distance made good will be equal to the difference between the ship's rate as given by the log and that of the current. And the absolute motion of the ship will be ahead if her rate exceeds that of the current; but if less, the ship will make sternway. If the ship's course be oblique to the current, the distance made good in a given time will be represented by the third side of a triangle, whereof the distance given by the log, and the drift of the current in the same time, are the other sides; and the true course will be the angle contained between the meridian and the line actually described by the ship.

It is evident from the above observations that we may consider the direction of the current in the light of a separate course; and by multiplying the rate of the current per hour by the number of hours it has been running, and treating this as a distance, we may estimate the ship's real place by any of the rules for compound courses.

D

B

current setting N.W. by N., and by account is in latitude 38° 42′ N., having made 44 miles of easting; 38° 58' N.; required the course and but the latitude by observation is distance made good, and the drift of

the current.

By Construction.-Make CE (fig. 43) equal to 22 miles, the difference of latitude by dead reckoning, and EA=44 miles, the departure, and join CA; make CD=38 miles, the difference of latitude by observation. Draw the parallel of latitude

Fig. 43.

DB, and from A draw the N.W. by N. line AB, intersecting DB in B, and AB will be the drift of the current in 24 hours: CB being joined, will be the distance made good, and the angle DCB the true course. Now AB and CB applied to the scale will measure 19-2 and 50.5 respectively, and the angle DCB will be 4110.

E

Distance.

.....

19.3 51

Log. distance.... ....... 50.5 m.

= .70354

By Traverse Table.-Taking the current course first, true difference of latitude 16, and course N.W. by N., we find in the traverse table the corresponding distance 19.3, and departure 10-7.

Again, for second course, we have true difference of latitude 38, and departure 44-10.7-33.3 E.

= 3 pts. = 16 miles.

33.4 +10=11.52244 38 = 1.57978 N. 41°14′E. = 9.94266

N.

= 1.20412 10 0.08015

= 1.28427

16 38

41° 14' E.-10= 0·12376 .38 = 1.57978

= 1.20412 10 9.82489 1.02901

Diff. of Latitude.

S.

Departure.

E.

...

33.3

W.

10.7

Whence the course and distance are found as above.

Or, from the traverse table to nearest degree and minute, we find in the columns of distance and angle, opposite to difference of latitude 38.5, and departure 35·5-distance 51, and angle 41°.

CHAP. X.-OF THE DAY'S WORK AND SHIP'S JOURNAL.

The most usual application of the principles laid down in the preceding chapters, is to ascertain from the several courses and distances run by a ship in the interval between the noons of two successive days, the ship's place at the noon of the latter day,―i.e., its latitude and longitude; its latitude and longitude being given for the noon of the preceding day. This constitutes a day's work; and the ship's place deduced therefrom is called her place by account or dead reckoning. The day aboard ship, like the astronomical day, commences at noon; and the ship's position is always calculated at every noon. In the Royal Navy, the log is hove once in every hour; but in most trading-vessels only once in every two hours. A record of the knots, and tenths of knots, run every hour or every two hours, the course, the direction of the wind, the leeway, and everything which affects the ship's place, is kept in the journal, which, for this purpose, is usually divided into six or seven columns. The first column on the left hand contains the hours

D

Day's from oon to noon; the second and third, the knots and Work and tenths of knots sailed every hour, or every two hours; the Ship's fourth contains the courses steered; the fifth, the direction Journal. of the wind; and the sixth, when there are seven columns, contains the leeway; and the last contains general remarks, including phenomena, variation, &c., &c.

The mode of forming a table showing the deviation of the compass for the several positions of the ship's head, has already been given.

The courses steered, as entered in the log-book, must be corrected for variation, deviation, and leeway. The setting and drift of current, and the heave of the sea, are to be marked down. These are to be corrected for variation only. In the day's work, it is usual to treat a current as an independent course and distance. If the ship does not sail from a place whose latitude and longitude are known (which rarely happens), the bearing of some known place is to be observed, and its distance found, which is usually done by estimation. The ship is then supposed to have taken her departure from this place, in a course exactly opposite to the observed bearing, and to have run the estimated distance on it. If there be any reason to suspect the correctness of the estimated distance, it will be easy to obtain the true distance as follows:-Let the bearing be observed of the place from which the departure is to be taken; and the ship having run a certain distance on a direct course, the bearing of the same place is again to be observed. We shall then have a triangle, all of whose angles are known from the observed bearings, and one of its sides, viz., the distance the ship has sailed. The other two sides, viz., the distance of the ship from the place of departure at each of the observations, can be immediately found, as in problem 1 on "Oblique Sailing." The distances for each course may be obtained by adding together the hourly distances. The courses being thus corrected, and the distances found, the latitude and longitude in may be found by any of the methods explained in chap. iv. As he differences of latitude are not usually great, the traverse table may generally be made use of for finding the latitude in; and having found the middle latitude, the longitude may be obtained by the middle latitude method.

The following example will enable the reader to apply the directions we have just given :

Dist...... Enter these in a table as under :

Course.

N.W. W. S.W.W.

N.E.6N.

S.E.6S.

S.E. by SE. N.W. by W.IN.

........

Distance.

Lat. from......64° 20' S. T. D. Lat...... 0 23 S. Lat. in.........64 43 S. Log. departure L sec mid. lat Log. diff. long...

4

Long from..... Diff. long........ Long. in..

pts. 0 qrs. left of N.

2

3

3

2

11

7 pts. 0 qrs. left of N.

1

2

0

3

46.2

1

3

34 7.

15.

2 pts. 0 qrs. right of N.

1

2

left.

0

3

right.

0

1

3

0

20.8.

5

15 46.2 34.7 29.1 31.4

20.8

14

3

0

1

1 pt. 0 qrs. right of S.

1

2

left.

6.6

446

2

2

0

2 14.

2

Diff. Eat. N. S.

8.9

right, or N.W.W.

4 pts. 0 qrs. left of N.

1

27-4

...

right.

right of N., or

N.E. by N.

left of S. left. right.

99

left of S. or S.E. by S.

..

left of N. or

N.W. by W. W.

59° 40' E.

0 26 W. 59 14 E.

Departure.

194 25.8 17.2 16.2 13.3

68.4 49.9 61.2 446 49.9 True diff. lat. S. 23-8 Dep. W. 11:3

...

W.

12:0 369

Lat. from......64° 20' S. Half... 0 12 S. Mid. Lat........64 32 S. 11.3 = 1.05308 64° 32'-10= 0.36654 26.2 = 1·41962

12.3

In this example the true differences of latitude and departures are taken by inspection from the traverse table.

When a ship is bound for a distant port, the bearing and distance of the port must be found. This may be done by calculation or by a chart. If islands, capes, or headlands intervene, it will be necessary to find the several courses and distances between each successively. The true course between the places must be reduced to the compass course

Sea Charts, by making the requisite allowances for variation and deviation, as already explained.

In hard blowing weather, with a contrary wind and a high sea, it is impossible to gain any advantage by sailing. In such cases, therefore, the object is to avoid as much as possible being driven back. With this intention it is usual to lie to under no more sail than is sufficient to prevent the violent rolling to which the vessel would be otherwise subjected, to the endangering of her masts and straining her timbers, &c. When a ship is brought to, the tiller or wheel is put down over to the leeward, which brings her head round to the wind. The wind having then little power over the sails, the ship loses her way through the water; and the action of the water on the rudder ceasing, her head falls off from the wind, the sail which she has set fills, and gives her fresh way through the water, which, acting on the rudder, brings her head again to the wind. Thus the ship has a kind of oscillating motion, coming up to the wind and falling off from it again alternately. The middle point between those upon which she comes up and falls off is taken for her apparent course; and the leeway, variation, and deviation are to be allowed from this to find the true course.

It is generally found that the latitude by account does not agree with that by observation. On considering the imperfections of the common log-line, and the uncertainty with regard to variation, an exact agreement of latitudes cannot be expected. When the difference of longitude is to be found by dead reckoning, and the latitudes by account and observation disagree, several writers on navigation have proposed to apply a conjectural correction to the departure or difference of longitude. Thus, if the course is near the meridian, the error is wholly attributed to the distance, and the departure is to be increased or diminished accordingly; if near the parallel, the course only is supposed to be erroneous; and if the course is towards the middle of the quadrant, the course and distance are both assumed to be in error. This last correction will, according to different authors, place the ship upon opposite sides of her meridian by account. As these corrections, therefore, are no better than guessing, they should be absolutely rejected.

If the latitudes do not agree, the navigator should examine his log-line and half-minute glass, and correct the distance accordingly. He is then to consider if the variation and leeway have been properly ascertained; if not, the courses are to be again corrected, and no other alteration whatever is to be made in them. He is next to observe if the ship's place has been affected by a current or heave of the sea, and to allow for them according to the best of his judgment. By applying these corrections, the latitudes will generally be found to agree tolerably well; and the longitude may be corrected in the same way.

It will be proper for the navigator to determine the longitude of the ship by observation as often as possible, and the reckoning is to be carried forward in the usual manner from the last good observation; yet it will perhaps be very satisfactory to keep a separate account of the longitude by dead reckoning. The modes of finding the latitude and longitude of a ship by observation, and the variation of the compass, will be given in the next book.

CHAP. XI.-OF SEA CHARTS.

The charts usually employed in the practice of navigation are the Plane and Mercator's charts. The former of these is adapted to represent a portion of the earth's surface near the equator, where the change in the lengths of corresponding arcs of the parallel is very small; and the other for all portions of the earth's surface. (For a particular description of these, see the articles CHART and GEOGRAPHY.) We shall here only describe their use.

Use of the Plane Chart. PROB. I.-To find the latitude and longitude of a place on the chart.

Rule. Take the least distance of the given place from the nearest parallel of latitude; this distance applied to the graduated meridian from the extremity of the parallel will give the latitude of the place. In the same way the longitude is found by taking the least distance from the nearest meridian, and applying it to the graduated parallel.

Thus the distance between Bonavista and the parallel of 15° being laid from that parallel on the graduated meridian, will reach to 16° 5′, the latitude required.

PROB. II.-To find the course and distance between two given places on the chart.

Rule.-Lay a ruler over the given places; if a parallel ruler be used, keeping the edge of one ruler passing through the places fixed, move the other until it through the centre of one of the compasses on the chart; the point of the compass through which this edge passes will show the course.

Or, generally, let a line on the edge of another ruler be placed so as to be parallel to the first ruler, and to pass through the centre of a compass; it will cut the circumference in a point which will determine the course.

The interval between the places being applied to the scale will give the distance.

Thus the course from Palmas to St Vincent will he found to be about S.S.W.W., and the distance 131° or 795 miles.

PROB. III.-The course and distance sailed from a

known place being given, to find the ship's place on the chart.

Rule.-Lay a ruler over the given place parallel to another ruler laid over one of the compasses, with one edge passing through the centre, and the other the point on the circumference which shows the course, and lay off on it the distance taken from the scale; it will give the point representing the ship's present place.

Thus, supposing a ship has sailed S.W. by W. 160 miles from Cape Palmas; then by proceeding as above, it will be found that she is in Lat. 2° 57′ N.

The reader will have no difficulty in solving various other problems by means of this chart, being, in fact, only the construction of the various problems in plane sailing on this chart.

Use of Mercator's Chart.

The method of finding the latitude and longitude of a place, and the course or bearing between two given places, is the same as in the plane chart, which see.

PROB. I.-To find the distance between two given places on the chart.

CASE 1.-When the given places are under the same meridian.

Rule. The difference or sum of their latitudes, according as they are on the same or cn opposite sides of the equator, will be the distance required.

Lea Charts,

CASE 3.—When the given places differ both in latitude tion Instru- and longitude.

Observa

ments.

Rule. Find the difference of latitude between the given places, and take it from the equator or graduated parallel; then lay a ruler over the places, and move one point of the compass opened to the difference of latitude just found along the edge of the ruler till the other just touches a parallel; then the distance from the point of the compass on the ruler to the point of intersection of the ruler and the parallel, applied to the equator, will give the distance between the places in degrees and parts of a degree, which, multiplied by 60, will give it in miles.

PROB. II.-Given the latitude and longitude in; to find the ship's place by the chart.

Rule.-Lay a ruler over the given latitude, and lay off the given longitude from the first meridian by the edge of the ruler, and the ship's present place will be obtained.

PROB. III. Given the course sailed from the given place, and the latitude in; to find the ship's present place on the chart.

Rule.-Lay a ruler over the place sailed from, in the direction of the given course; its intersection with the parallel of latitude in, will give the ship's present place.

PROB. IV. Given the latitude and longitude of the place left, and the course and distance sailed; to find the ship's present place on the chart.

Rule.-Lay a ruler over the given place, in the direction of the given course, take the distance sailed from the equator, and put one point of the compass opened to this distance at the intersection of the ruler with any parallel, and the other point will reach to a certain place by the edge of the ruler. This point being kept fixed, draw in the other point of the compass until it just touch the above parallel when swept round; apply this extent to the equator, and it will give the difference of latitude. Hence the latitude in is known; and the intersection of the edge of the ruler with the parallel of this latitude will give the ship's present place. The above problems sufficiently illustrate the use of Mercator's Chart. The reader will have no difficulty in solving other problems by means of it.

BOOK II.

CONTAINING THE METHODS OF FINDING THE LATITUDE AND LONGITUDE OF THE SHIP AT SEA, THE VARIATION OF THE COMPASS, AND TIME OF HIGH WATER.

CHAP. I.-DESCRIPTION AND USE OF INSTRUMENTS USED IN OBSERVATIONS.

SECT. I.-OF HADLEY'S SEXTANT AND QUADRANT. The principal difference between these instruments is in the extent of the angle which can be observed by them; and in the more elaborate and careful workmanship of the latter of the two. Indeed the quadrant is only available for taking observations which determine the latitude. The distances of the moon from the sun or other heavenly body, which are frequently used for the determination of the longitude, can only be observed by the help of the sextant.

In the

Allowing for these differences, the principle on which the quadrant and sextant are constructed is the same. Royal Navy sextants are almost exclusively in use, although quadrants are still employed for the observation of altitudes in many trading vessels. The sextant, therefore, will first be described, and afterwards those points in which the quadrant differs from the sextant will be explained.

The reader is supposed to be aware of the ordinary laws with regard to the propagation and reflection of light, viz.,

that in the same medium, light is propagated in straight Observalines, the smallest conceivable quantity of which that can tion Inbe stopped or propagated alone is called a ray; and that struments. when a ray of light is incident on a plane reflecting surface, it is bent or reflected after incidence in such manner, that the incident and reflected rays and the straight line perpendicular to the mirror at the point of incidence (called the normal to the surface) lie all in one plane; and that the incident and reflected rays make equal angles with the normal or the surface.

Let MO (fig. 44) be an arc of a circle, CO and CM two radii, and CI be a moveable radius carrying a plane mirror, silvered through its whole extent, firmly fixed to it; EFG another mirror, the lower part of which FG only is silvered, while the upper part EF is unsilvered, so that a ray reflected from the lower portion FG in direction FH, and a direct ray PFH through the unsilvered part EF, may be seen together by an eye at K. This mirror is fixed to the radius CM in such a manner that when the moveable radius occupies the position ACO, the two mirrors ACB and EFG are both perpendicular to the plane of the instrument, and parallel to one another.

Let now S and P be two distant objects whose angular distance is required to be found. Let the instrument be placed so that its plane passes through S and P, and that a ray from P, passing through the unsilvered glass EF, may be seen directly by an eye at K; and while in this position let the bar be moved round C, CI carrying the mirror with it until a ray from S, falling on ACB, is reflected in the direction CF, and again reflected by FG in the direction FH; so that to the eye at K the images of the two objects S and P are seen together, or coincide.

Now angle of deflection SHP SCF - CFH

Produce SA to meet PFH in H; then SHP is the angle through which the ray SA has been deflected, and is also the angular distance between S and P. Let A'B' be the new position of the mirror AB; then ACA' is the angle through which the mirror has turned, and consequently also the angle through which CI has moved.

=

H

=

180°-2 FCB'-(180° -2 EFC) because by law of reflection,

=

SCA' FCB'; and therefore SCF 180° - SCA' - FCB' = 180° -2 FCB', and EFC-GFH; and therefore

CFH

180° - EFC-GFH = 180° - 2 EFC; .. SHP=2 EFC-2 FCB'.

But

EFC-FCB, because EFG is parallel to ACB;

or SHP-2 FCB -2 FCB'=2 ACA'

twice the angle through which CI has moved. Hence if the arc OM be divided into degrees, and each degree marked as two degrees, the reading off of the arc OI will be the angle between the distant objects S and P.