(2). By measuring the sun's semi-diameter.-Fitting the telescope and arranging the shades so that the reflected and direct images of the sun may be viewed clearly and seen of the same brightness, measure the sun's horizontal diameter, moving the index forward on the divisions until the images of the true and reflected suns touch at the edges; read off the measure which will be on the arc; then cause the images to change sides, by moving the index back; take the measure again and read off; this reading will (as is generally the case) be off the arc; half the difference of the two readings is the index correction.

When the reading on the arc is the greater, the correction is subtractive; when the lesser, additive.

If both readings are on the arc, or both off the arc, half their sum is the index correction-subtractive when both on, additive when both off the arc.

One-fourth of the sum of the two readings should be equal to the sun's semi-diameter in the Nautical Almanac for the day; but if both readings be on or both off the arc, one-fourth their difference should be the sun's semidiameter.

Thus, suppose the observations, in Example 1, to be made on September 26th, 1882; here one-fourth of the sum of the two readings is 16′ 0′′, agreeing with the semi-diameter as given in the Nautical Almanac for the given day.

This affords a test of the accuracy with which the observation has been made. But in order that the comparison may be a good criterion, we should measure the sun's horizontal diameter which is not sensibly affected by refraction.

Obs. In order to obtain the index correction with the greatest precision, the mean of a number of measurements of the sun's diameter should be taken; also, the limb should be placed (by hand, before the tangent screw is used) alternately a little open and a little overlapping, so that in making the contact the tangent screw may be turned different ways.

EXAMPLES FOR PRACTICE.

Ex. 1. 1882, April 17th, the reading on the arc 29′ 40′′, the reading off the arc 34′ 10′′: required the index correction and semi-diameter.

Ex. 2. 1882, July 4th, the reading on 33′ 10′′, off 29′ 50′′: find index correction and semi-diameter.

Ex. 3. 1882, November 13th, on 4′ 40′′, off 60' 10": find index correction and semidiameter.

Ex. 4. 1882, July 10th, on 32′ 45′′, off 34′ 30′′: find index correction and semi-diameter. Ex. 5. 1882, March 21st, off 1° 10' 0", off 6′ 40′′: find index correction and semi-diameter. Ex. 6. 1882, January 17th, on 67′ 40′′, on 2' 30": find index correction and semi-diameter.

355. The Prismatic Sextant.-In the form of instrument just described, and which is all but universally employed, the angle measureable is limited. to 140°; but we may perhaps add that PISTOR and MARTINS, of Berlin, have, by an ingenious modification of the horizon-glass (for which they substitute a prism), produced a sextant which will measure any angle up to 180°. This instrument is called the PRISMATIC SEXTANT.

The following shows the form of Examination Paper on the Adjustment of the Sextant.

Exn. 9a.

Port of

EXAMINATION PAPER.

Rotation No.

ADJUSTMENTS OF THE SEXTANT.

The applicant will answer in writing, on a sheet of paper which will be given him by the Examiner, all the following questions, numbering his answers with the numbers corresponding to the questions.

A. To set the index-glass perpendicular to the plane of the sextant.

-How do you make that adjustment?

2.

A. Place the index near the middle of the arc, and look into the index-glass so that you can see both the arc and its reflection; if they be in one line, the glass is perpendicular, but if not continuous, they are brought so by the screws in the frame upon which the glass stands.

3.-What is the second adjustment?

A. To set the horizon-glass perpendicular to the plane of the sextant.

4.-Describe how you make that adjustment?

A.-Place O of the vernier on O on the arc, hold the instrument obliquely, with its face upwards, and look from the sight vane at the horizon; if the reflected part and the direct portions of the horizon are in one line, this adjustment is perfect, but if not, they must be brought in line by gently moving a screw at the back (top) of the glass.

5.-What is the third adjustment?

A. To set the index and horizon-glasses parallel when the index is at O.

6.-How would you make the third adjustment?

A. Place the index at O, and holding the instrument vertically, look at the horizon; if the reflected and direct parts are in one line, this adjustment is perfect, but if they are not in one line, move a screw at the back of the horizon-glass until they are.

7.-In the absence of a screw how would you proceed?

A.—I would find the index correction, or as it is called, the index error.

8.-How would you find the index error by the horizon?

A.-Hold the instrument vertically, and, looking at the horizon, move the tangent screw until the horizon in both parts of the horizon-glass form one line; the reading is the index

error.

9.-How is it to be applied?

A.-To be added when the reading is off the arc, and to subtract when the reading is on the arc.

10.-Place the index at the error of

minutes to be added, clamp it, and leave it.

The Examiner will see that it is correct. This is a reading off the arc, i.e., on the arc of excess

11.-The Examiner will then place the zero of the vernier on the arc, not near any of the marked divisions, and the Candidate will read it.

In all cases the Candidate will name or otherwise point out the screws used in the various adjustments.

NOTE to 10 and 11.-When the Examiner is satisfied that the Candidate can read the arc of the sextant both on and off the arc, it will be sufficient to place his initials against 10 and 11 on the paper containing the

answer.

The above completes the examination of Second and Only Mates.

In addition to the above, First Mates and Masters will be required to state in writing :

12.-How do you find the index error by the sun?

A.-Place the index at about 30' on the arc, and holding the instrument vertically, look at the sun, two suns will be seen; bring their upper and lower limbs in exact contact, read off and mark down, then place the index at about 30 off the arc, or to the right of O, bring down the upper and lower limbs in contact as before, read off and mark down; half the difference of these two readings will be the index error.

13.-How is the same applied?

A.-To be added when the greater reading is off the arc, and subtracted when the greater reading is on the arc.

14.—What proof have you that those measurements or angles have been taken with tolerable accuracy?

A. By adding the two readings together, and dividing the sum by 4; if the measurements are correct, the result should be nearly equal to the semi-diameter for the day, as given in the Nautical Almanac. If they do not so agree, repeat the observations until they do.

CURRENT.-SOUNDINGS.

TO FIND THE COURSE TO STEER IN ORDER TO MAKE GOOD ANY COURSE IN A KNOWN CURRENT, AND ALSO THE DISTANCE MADE GOOD.

356. Draw a line on a chart to represent the course to be made good; from the ship's place on the chart lay off a line in the direction of the set of the current, on which mark off from the ship's place the rate of the current per hour; then take in the compasses the distance the ship sails in an hour by log, and put one foot on the last-named mark, and from the point where the other foot reaches the first line draw a line to the mark on the line representing the direction of the current. The course to be steered is represented by the line last drawn, and the parallel ruler being placed to it, and moved to the centre of the compass on the chart, will give the course of the ship; and that portion of the first line drawn, intersected by the last line drawn, will be the distance the ship will make good per hour.

On a chart, suppose A to be the place of the ship, B the port of destination; also AC the set of the current, the rate per hour being taken from the scale of miles and laid off in the direction of the line. Take the distance sailed by the ship per hour from the scale of miles, and with one foot of the dividers at C, make an arc cutting A at D. Join CD, and move the parallel ruler from CD to A, drawing A E parallel to CD; then A E will be the direction of the ship's head; and the parallel ruler being moved to the centre of the compass on the chart, will give the course of the ship on the chart; and AD will be the distance the ship will make good.

SOUNDINGS.

357. In the open sea, the tide requires about six hours and a quarter to rise from low to high water, and an equal interval to fall from high to low water. If the rise or fall was an uniform quantity throughout, by simply

taking a proportionate part of the rise or fall due to the time of tide, we should at once obtain the quantity required to reduce the soundings to the low water of that day. But the water does not rise in equal proportions, the rise during the first and last hours being very small (about one-sixteenth of the whole range); in the second hour there is a considerable increase of rise; in the third and fourth hours a still greater increase of rise; and then the rise begins to take off in the same proportion as it increased.*

The correct amount for every half-hour, and for various ranges, is given in the "Tide Tables for the English and Irish Ports for 1880," (p. 98, Table B), published by the Hydrographic Office, Admiralty.†

358. As the soundings upon the chart are all referred to or measured downwards from the mean level of low water of ordinary spring tides,‡ casts of the lead taken at any other time of the tide, or any other day than full and change, will exceed the depth marked on the chart (except when it happens to be low water of greatest spring tides). It is necessary for the seaman to be able to calculate the difference between the actual depth obtained by means of his lead, and that marked on his chart, in order to the identification of his ship's place, more especially when the range of the tide is considerable, and the depth not great. Also, when about to enter a port in a vessel whose draught of water is nearly equal to the depth, it is necessary to find the height of the tide as exactly as circumstances will permit.

359. Two classes of questions may be proposed in reference to this subject -firstly, to find the depth of water at a given place and time; secondly, having obtained the actual depth by a cast of the lead, to find the sounding on the chart corresponding thereto, and thence to identify the ship's place. Both these classes of questions require us to know the time of high water and the range of the tide on the given day; and for this purpose almanacs are published. The most correct, and by far the most useful of all these, are the "Tide Tables" published by the Admiralty, and to which we have already referred. In this book are given the times of high water and the height of the tide for every day in the year, at each of the principal ports in Great Britain.

The reader may obtain an idea of this law, sufficiently exact for practical purposes, in the following manner:-Describe a circle, and divide the circumference into six equal parts on each side, corresponding to the hours of the tide; then divide the diameter into proportional parts, corresponding to a given (assumed) range of tide. Connect the segments of the circle by straight lines drawn across the figure, when it will be perceived that they intersect the diameter at certain divisions of the range. These are the correct quantities respectively due to each hour's rise or fall of such a tide from low to high water, and vice versa. An examination of these quantities will show, that in the first hour of the tide the rise is equal to one-sixteenth of the whole range; at two hours from low or high water, the tide has risen or fallen one-fourth of the whole range; at three hours it has risen just half its range; at four hours it has risen three-fourths of the whole range; at five hours to within a sixteenth of the whole range. The above method, which is constructed on principles theoretically correct, will represent with sufficient exactness all that is necessary for practical purposes. + Table XIX, RAPER, which the author, in 1847, computed for RAPER's work, also shows the space through which the surface of the water rises and falls at given intervals from high or low water.

On most charts the soundings expressed are reduced to low water of ordinary spring tides; but in some charts, however, the soundings are reduced to the low water of extraordinary spring tides-such, for example, is the case on the chart of Liverpool, surveyed by Captain DENHAM, R.N., the soundings on which are reduced to a spring range of thirty feet, while the mean spring range for that place, as deduced from observations made for two years at the Tide Gauge, St. George's Pier, is 26 feet.