Since the unit of measure, the mile a minute of latitude, has a different value in every latitude, there is an appearance of distortion in Mercator's chart when covering any large extent of surface; for instance, an island near the pole of the same size as one near the equator will be represented as being much larger, due to the different scale used to preserve the character of the projection.

Art. 68. To Construct a Mercator's Chart.-If the chart for which a projection is to be made includes the equator, the values to be measured off are given directly by Table 3. If the equator does not come upon the chart, then the parallel of latitude to be laid down should be referred to a principal parallel; preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude from the principal parallel is then the difference of the values found for the two taken from Table 3.

The values so found may either be measured off, without previous numerical conversion, by means of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any properly divided scale of yards, metres, &c., after having been reduced to the scale of proportions adopted for the chart.

If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes of arc on the equator, a diagonal scale may first be constructed, on which ten meridional parts, or ten minutes of arc on the equator, have a length of half an inch; then, in the usual manner, multiples of one meridional part may be measured on the base line; multiples of 0.1 on the lines parallel to the base line; and multiples of 0.01 may be estimated between the parallel lines. If an inch scale be used, the meridional parts, before being laid down on the projection, must, of course, be multiplied by 0.05 or divided by 20, since 20 minutes of arc on the equator, or 20 meridional parts, have to be made equal to one inch.

Often it may be desirable to transfer a chart constructed according to any other projection to a Mercator projection, and to adapt the scale to a certain allotment of paper. In this case, the lowest and the highest parallels of latitude may first be drawn on the sheet on which the transfer is to be made. The distance between these parallels may then be measured, and the number of meridional parts between them ascertained. Dividing the distance by this number will then give the length of one meridional part, or the quantity by which all the meridional parts taken from the Table 3 must be multiplied. This quantity will represent the scale of the chart.

When a numerical conversion of all the values is thus required, it will, in general, be found convenient to prepare first a rough eye-sketch of the projection, and to note on it all the distances which will have actually to be measured off.

EXAMPLE. The process of constructing a Mercator projection is best shown by an example.

Let a projection be required for a chart of 14 extent in longitude between the parallels of latitude 20° 30′ and 30 25' (Fig. 24), and let the space allowable between the paper between these parallels measure, say, 10 inches. Entering the column in Table 3 headed 200, and running down to the line marked 30' in the side column, will be found 1249.1; then, entering the column 30, and running down to the line of 25, will be found 1905.7. The difference, or 1905.7—1249. I=656.6, is the value of the meridional arc between these latitudes, for which I' of arc of the equator is taken as the unit. On the intended projection, therefore, 1' of arc of longitude will measure =0.0152 inch, which will be the scale of the chart. For the sake of brevity call it 0.015. By this quantity 656.6 all the values derived from Table 3 will have to be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale of one inch.

Draw now, in the centre of the sheet, a straight line, ab, in Fig. 24, and assume it to be the Middle Meridian of the chart. Construct very carefully in this line a perpendicular, cd, near the lower border of the sheet, and assume this perpendicular to be the parallel of latitude 20° 30', and at the same time draw the southern inner neat line of the chart. From the point 6, which is the intersection of the lines ab and cd, lay off on the line cd, on each side of the Middle Meridian, ab, seven degrees of longitude, or the distances B and B', each equal to 0.015 X 60 X 7 6.3 inches; and through the points B and B' thus obtained draw parallel lines to ab, which lines, AB and A'B', will be the eastern and western neat lines of the chart.

=

In order to construct the parallel of latitude for 21° 0', find, in Table 3, the meridional parts for 21° 0', which are 1281.0. Subtracting from this number the number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inches, which is the distance on the chart between 20 30 and 21° 0'. On the lines BA, ba, and B'A', lay off the distances, BE, be, and B'E', each equal to 0.478 inch, and through E, e, E' draw the straight line, EE', which will be the parallel of 21° o'.

Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; that is, lay off BA, ba, and B'A' from B, b, B', respectively.

and draw the lines FfF', GgG', H/H', &c., which will be the parallels of latitude 22° 0', 23° 0′, 24° 0′, &c. Finally, lay down in the same way the parallel of latitude 30° 25′, which will be the northern inner neat line of the chart.

A degree of longitude will measure, on this chart, oin.015 × 60 oin.9. Lay off, therefore, on the lowest parallel of latitude drawn on the chart, on a middle one, and on the highest parallel, measuring from the meridian, on each side, the distances, respectively, of oin.9, 1in.8, 2in.7, 3in.6, &c., in order to determine the points where meridians answering to full degrees cross the parallels drawn on the chart. Through the points thus found draw the meridians. Draw then the outer neat lines of the chart at a distance, say, of the twentieth part of an inch outside of the inner neat lines, and extend to them the meridians and parallels. Between the inner and outer neat lines of the chart subdivide the degrees of latitude and longitude as minutely as the scale of the chart will permit, the subdivisions of the degrees of longitude being found by dividing the degrees into equal parts, and the sub divisions of the degrees of latitude being found in the same manner as the full degrees of latitude previous'v described.

Art. 69. The subdivisions between the two eastern as well as those between the two western neat lines will serve for measuring or estimating terrestrial distances. Distances between points bearing North and South of each other may be ascertained by referring them to the subdivisions between the same parallels. Distances represented by lines at an angle to the meridians (loxodromic lines) may be measured by taking a small number of the subdivisions near the middle latitude of the line to be measured between the dividers and stepping them off on that line. If, for instance, the terrestrial length of a line running at an angle to the meridians between the parallels of latitude of 24 o' and 29° o' be required, the distance shown on the neat space between 26 15′ and 26° 45′ = 30 nautical miles may be taken between the dividers and stepped off on that line.

Art. 70. A chart may be transferred from any other projection to that of Mercator by drawing a system of corresponding parallels of latitude and meridians over both charts, so close to each other as to form minute squares, and then the lines and characters contained in each square of the map to be transferred may be copied by the eye in the corresponding squares of the Mercator projection.

Art. 71. GREAT CIRCLE CHARTS.-This chart, useful to the Navigator in laying out his track in Great Circle Sailing, is supplementary to the Mercator chart; for, having drawn the track on it, a transfer can be made to the Mercator chart by means of the ordinates, latitude and longitude, of various points.

It is drawn on the Central, or Gnomonic, projection, and on it all great circles appear as straight lines. The pole is made the centre of projection, and the plane of projection is that of any parallel of latitude.

A series of concentric circles represents the parallels of latitude, the radius of any particular one being rcot L, where is any convenient linear magnitude and equals the radius of the parallel of 45°. The meridians are straight lines drawn from the centre, dividing each circumference into 360 equal parts.

These charts are only valuable to represent the higher latitudes, because within the tropics the difference between tracks by the Great Circle and by the Rhumb is so small that the Mercator chart will answer every purpose. And, again, the existence of the trade winds governs the track to be followed within their limits.

The application and use of the Great Circle Chart will be exemplified in Great Circle Sailing, Chap. III, Part I, Art. 129, &c.

12. THE LOG BOOK.

Art. 72. The LOG BOOK is a record or journal of the ship's cruise. It should afford not only the data from which the Navigator establishes the ship's position by that method commonly called Dead Reckoning, but be so complete in all its details as to be a valuable Meteorological Journal; to accomplish which, there should be a thorough knowledge of the various instruments used, a careful personal recording on the part of the Officer of the Watch, and as careful a revision on the part of the Navigator or Master.

Since the Masters of vessels in the Merchant Marine are requested to co-operate with the Navy in a uniform system of collecting and reporting meteorological data, this subject can best be illustrated by describing the LOG BOOK AND METEOROLOGICAL JOURNAL used in the United States Navy.

Art. 73. Of the instruments employed in collecting data for the Log Book, the Log, the Lead, and the Compass have heretofore been described. To ascertain the meteorological data there are necessary the BAROMETER, the THERMOMETER, and the HYGROMEter.

The Barometer shows the pressure of the air.

The Thermometer (in the shade) shows the temperature of the air.

The Hygrometer shows the degree of moisture of the air.

The three combined form an efficient weather guide.

THE BAROMETER.

Art. 74. The barometer consists of a brass tube (Fig. 25) terminating at top in a ring, A, for suspension, and at bottom in a flange, B, to which the several parts forming the cistern are attached.

The upper part of this tube is cut through so as to expose the glass tube and mercurial column within, seen in Fig. 28. Attached at one side of this opening is a scale, graduated in inches and parts; and inside this slides a short tube, c, connected to a rack-work, arrangement, moved by a milled head, D: this sliding tube carries a vernier in contact with the scale, which reads off to go (.002) of an inch. In the middle of the brass tube is fixed the thermometer, E, the bulb of which being externally covered, but inwardly open, and nearly in contact with the glass tube, indicates the temperature of the mercury in the barometer-tube, not that of the external air. This central position of the thermometer is selected that the mean temperature of the whole column may be obtained; a matter of importance, as the temperature of the barometric column must be taken into account in every scientific application of its observed height.

The cistern (Fig. 26) is made up of a glass cylinder, F, which allows the surface of the mercury q to be seen, and a top plate, G, through the neck of which the barometer tube passes, and to which it is fastened by a piece of kid leather, making a strong but flexible joint. To this plate, also, is attached a small ivory point,, the extremity of which marks the commencement or zero of the scale above. The lower part, containing the mercury, in which the end of the barometer-tube t is plunged, is formed of two parts, i,j, held together by four screws and two divided rings, L, M, in the manner shown in Figs. 26 and 27. To the lower piece j is fastened the flexible bag N, made of kid leather, furnished in the middle with a socket, k, which rests on the end of the adjusting-screw O. These parts, with the glass cylinder F, are clamped to the flange B by means of four long screws P' and the ring R; on the ring R screws the cap S, which covers the lower parts of the cistern, and supports at the end the adjusting-screw O. G, i, j, and k, are of boxwood; the other parts of brass or German silver. The screw O serves to adjust the mercury to the ivory point, and, also, by raising the bag, so as to completely fill the cistern and tube with mercury, to put the instrument in condition for transportation.

B

FIG. 25.

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E

D

Art. 75. The principle of the barometer is now so generally known, being, too, in almost universal use at sea, that it need hardly be mentioned here. While the mercury in the cistern falls, or is pressed down by the air, the column rises in the exhausted tube; and when the mercury in the cistern rises, owing to diminished pressure of the air, the column of mercury in the tube falls. But the actual length of the column of mercury is required (in order to know the weight or pressure of the atmosphere), as measured from the actual surface of the mercury, which is variable; therefore, a correction is required for most instruments on account of the difference from the neutral line or point, namely, that defining the base of the column when the scale attached to it was graduated.