it off on the graduated meridian as nearly as possible opposite the two points. A better method, however, is to take off from the graduated meridian, opposite and near the middle latitude, with the dividers, a convenient unit, such as 2, 3, or 5 minutes, and find how many times this unit is contained in the distance between the two points. For

example, let it be required to measure the distance between e and g, Fig. 33. Find the center f, and from this point draw a line mf parallel to the latitude parallels. This is the middle latitude between e and g. On the graduated meridian, and on the opposite side of the middle latitude, take a distance, say 5 miles or minutes, and step this off from e to g or from g to e. Suppose e g contained 20 of these steps; the distance between the two points would then be equal to

5 X 20 or 100 miles. In practice, it is not necessary to draw the middle parallel, but simply to be guided by the eye in taking the unit from the scale midway between the two places.

91. To Find the Course and Bearing Between Any Two Points on the Chart. - For this purpose, use either the parallel ruler or the course protractor. When using the former, place an edge over the two given points; then move the two parts of the ruler in succession until the edge of one of them passes through the center of a compass diagram. This edge will then point out, by its intersection with the graduated circumference of the compass rose, the required course or bearing (see Art. 80 and accompanying figures).

When a course protractor is used, the course, or bearing, between the two places is found by methods described and illustrated in Arts. 82 and 83.

92. If the compass course is to be shaped from the course, or bearing, thus obtained, the various corrections must be applied according to the compass diagram showing true or magnetic directions.

93. To Find the Ship's Position on the Chart When the Course and Distance From Any Given Place Is Known. - Place the edge of a parallel ruler over the given place in the direction of the given course according to the nearest compass diagram, and take the given distance with the dividers from that part of the graduated meridian that lies opposite the given place and the supposed position of the ship. Thus, if e, Fig. 33, is the given point, N 35° E the ship's true course, and 100 miles the distance run, the position arrived at g is found by drawing a line from e N 35° E, and on this line lay off a distance of 100 miles. according to a selected unit taken from the latitude scale, as. near as possible to the middle parallel between the given and supposed place of the ship.

94. To Lay Off the Ship's Position on the Chart by Cross-Bearings. - When the bearings of the two selected . objects are corrected for deviation, due to the direction of the ship's head at the time of observing them, place the parallel ruler on the nearest compass diagram so that the edge passes through the center and the requisite degree or point on the circumference. Then move the ruler, step by step, until the edge passes through the object, when the line drawn along the edge will represent one of the bearings. The ship will then be somewhere on that line. Proceed similarly with the other bearing. Now, the ship will be somewhere on this line, also, and since the only common point of two lines intersecting each other is at their point of intersection, the position of the ship on the chart must necessarily be at the point where the two bearings intersect.

95. It is evident that the objects selected for crossbearings should be so situated that the lines of bearing do not intersect at a very acute angle, since the point of intersection in such a case is somewhat doubtful. To obtain good results, the angle between the bearings should be as near as possible to 90°, or 8 points.

SIMPLE METHOD OF CONSTRUCTING A MERCATOR'S CHART

96. In connection with the use of charts and the solution of chart problems in general, it may prove useful to the student to know how to construct a Mercator's chart. Many possibly think that this is a complicated problem and something that cannot be mastered by the average man. In the following, however, we shall proceed to show that the problem instead of being difficult is very simple. All that is needed is a Table of Meridional Parts and the usual outfit of drawing materials.

The order of procedure is then as follows: First determine the limits of the proposed chart-in other words, the number of degrees and minutes it is to contain, both of latitude and

of longitude. Then draw a straight line near the lower margin of the paper, if the chart is to represent north latitude; near the upper margin, if it is to represent south latitude; or at a suitable position toward the center, if both north and south latitudes are to be represented. Divide this line into as many equal parts as the number of degrees of longitude required; for instance, if the chart is to contain 15° of longitude, divide the line into 15 equal parts. At each extremity erect lines perpendicular to it. Take from the tables referred to in Art. 76 the meridional parts for each convenient degree of latitude, for the limits between which the chart is to be drawn, and take the difference between each successive pair, thus obtaining the meridional differences of latitude. Reduce these meridional differences to degrees by dividing them by 60; the result will be the lengths on the longitude scale between the chosen degrees of latitude. Lay off these lengths successively on the perpendicular lines, and through the points thus obtained draw straight lines parallel to the original line, to represent latitude parallels. At convenient intervals, or through each division on the base line, draw lines parallel to the perpendiculars to represent meridians.

The accuracy of the frame of the chart thus completed should be tested by measuring the two diagonals of the rectangle formed; if they are of the same length, the frame is perfect. The principal points in the chart are now laid down according to their respective latitudes and longitudes, and whatever formations and contours of water or land are required, together with other useful items, are drawn in freehand. A compass diagram may also be inserted, but it should be remembered that the direction of the meridians indicates true north and south.

97.

Illustration. - In order to illustrate the foregoing, let it be required to construct a chart on the Mercator's projection, extending from latitude 43° N to 46° N, and from longitude 81° W to 85° W, on a scale of 2 inches to 1° of longitude, the chart to embrace Lake Huron. In order to

do this, draw a horizontal line a b, Fig. 34, at the bottom margin of the paper to represent the forty-third parallel of latitude. On this line lay off four lengths of 2 inches each,

81° d 46°

-45'

30'

15'

45

45'

+30'

15'

44°

45'

30'

15'

43°

82 55 50 45 40 35 30 25 20 15 10 5 81°

2 Inches-1 Longitude.
FIG. 34

and divide each length into 60 equal parts, representing minutes of longitude. At the extremities of the line, carefully erect the perpendiculars a c and b d, to represent meridians. Then consult the Table of Meridional Parts and