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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 ist error fast, and 2nd error faster
With ist error slow, and 2nd error not so slow
With ist error slow, and 2nd error fast

Gaining rate.

With ist error slow, and 2nd error slower

With ist error fast

, and and error not so fast | Losing rate.

With ist error fast, and 2nd error slow

4. For the Greenwich Date, Mean Time.-To the approximate Greenwich date apply the accumulated rate, subtracting it if gaining, but adding it if losing.

Example.--A chronometer showed 8h. om. 425. on December 4th ; on June ist it had been found om. 12s. slow on mean noon at Greenwich, but on July ist it was 4m. 275. fast on mean noon at Greenwich. Find the Greenwich mean time on December 4th.

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NOTE.—In these cases the dates have been considered as astronomical : their interpreta. tion in reference to the longitude will always have to be taken into account.

In order that the longitude found shall be worthy of confidence, the greatest care must be bestowed upon the determination of the rate of the chronometer. As a single chronometer might deviate very greatly without being distrusted by the navigator, it is well to have at least three chronometers, and to take the mean of the longitudes which they severally give in every case.

But, whatever care may have been taken in determining the rate on shore,

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the sea rate will generally be found to differ froin it more or less, as the instrument is affected by the motion of the ship; and, since a cause which accelerates or retards one chronometer may produce the same effect upon the others, the agreement of even three chronometers is not an absolutely certain proof of their correctness. The sea rate may be found by determining the chronometer correction at two ports whose difference of longitude is well known, although the absolute longitudes of both parts may be somewhat uncertain. But for this purpose a small pamphlet—" List of Time Signals, established in various parts of the World”—is published by the Hydrographic Department of the Admiralty, compiled for the use of the navigator, as an aid for ascertaining the errors and rates of chronometers : this you should always have at hand with your epitome and charts.

An unknown error in the chronometer will have the following effect on the position of the ship as determined by an altitude of a heavenly body and the supposed known error and rate : (1) If the chronometer is

Fast, and also faster than supposed, or

Slow, but not so slow as supposed; thenthe true position will be eastward of that by observation, and as a consequence, when expecting to make land, sailing eastward, it will be made earlier, but sailing westward, later, than anticipated. (2) Similarly, if the chronometer is

Slow, and also slower than supposed, or

Fast, but not so fast as supposed; thenthe true position will be westward of that by observation, and as a consequence, when expecting to make land, sailing westward, it will be made carlier, but sailing eastward, later, than anticipated.

THE COMPASS The invention of the compass has been placed at many dates; there are numerous indications that it was used in China over 2,000 years ago. It was in use in Europe in the twelfth century.

Almost the first historical compass is supposed to have been made by Flavio Gioja of Amalfi in the south of Italy. It was only marked to eight points.

A compass consists of four parts—the pivot, the bowl, the card, and the needles. There are many patterns, all of which aim at the same idea, that is, sensitiveness of action, which is obtained by two types, the dry compass and the wet or spirit compass.

The one most in favour is the compass patented by Sir William Thomson, afterwards Lord Kelvin, in 1877. The principal features of this most excellent compass are :-(1) reduction to the least possible weight; (2) short, light needles symmetrically arranged on each side of the central point; (3) mode of suspension ; (4) its slow period of oscillation or swing.

The above features are attained by the application of well-known laws, and each will now be explained.

(1) Reduction of Weight.This is attained by using short, light needles, and by cutting away the unnecessary central portion of the card, and, in order to give the necessary rigidity to the card, the rim is made of aluminium and suspended to the central cap by means of silk threads, which latter also absorb some of the vibration set up by the screw or other causes. The cap is of sapphire and the pivot iridium-pointed, and these two substances being amongst the hardest known, and the card being extremely light, friction is reduced to a minimum. The weight of a 10-inch Thomson compass card is about 180 grains, and will be found written on the under side.

(2) Short, light Needles. The practical rules on which a compass adjuster works are based on the assumption that the compass-needle is a magnetic particle having no length. This assumption much facilitates the theory of calculation and compensation, and is most nearly attained by using a number of short needles-eight in the compass under consideration—the longest of which in a 10-inch card is only 31 inches.

(3) Mode of Suspension.—By keeping the point of suspension of the card and needles well above their centre of gravity the card has stable equilibrium, which has the effect of rendering the compass steadier and constrains it to move in a horizontal plane, which obviates the necessity of a counterpoise, in the form of a sliding weight, which was a feature of old pattern compasses.

(4) Period of Oscillation or Vibration.-One of the chief features of the Thomson compass is its slow period of swing which, in England, is about 40 seconds for the 10-inch card. The period of oscillation being slow conduces to greater steadiness, and practically eliminates the possibility of synchronising with the period or roll of the ship in a seaway, as a ship's period is much quicker. The period of vibration of a compass can be lengthened by two different

methods ; firstly, by increasing its moment of inertia ; secondly, by decreasing the magnetic moment of the compass (the magnetic moment of a magnet is the product of the amount of magnetism imparted to one of its poles multiplied by the distance between its poles).

The moment of inertia of a compass can be increased by increasing its weight, but this would render the compass sluggish and also nullify the first point, viz., reduction of weight. It is, therefore, to the second point that we must look for the desired result, and this is attained by using short, weakly-magnetised needles. The loss of directive force in the needles is more than compensated for by the enormous reduction in the weight of the card as compared with old patterns. The period of oscillation is marked on the under side of the card.

A well-constructed compass will last for many years. Compasses are sometimes condemned as faulty when they are in good order and condition, the trouble being due to position on board, not construction.

THE LIQUID OR SPIRIT COMPASS The card is made of mica, the degrees and points are painted on the outer edge; it is attached to a frame and central hollow float which is immersed in a mixture of distilled water and pure alcohol to prevent freezing; the liquid prevents any undue oscillation of the card. It is important that the point of suspension of the card should be in the horizontal plane passing through the gimbal ring, that the centre of flotation should be below the point of suspension, and that the centre of gravity of the card should be below the centre of flotation. The needles are sheathed in brass and are strongly magnetised, and are placed low on the card so as to prevent the card dipping with large changes of magnetic dip. The bowl should be kept full of the liquid. All air is removed by air pump before the cover is finally screwed down. The expansion and contraction of the liquid is met by having an elastic corrugated metal box attached to the bottom of the bowl. There should be no air bubbles present, and the card should not press upon the pivot with a weight of more than 100 grains. Both types of compass are fitted with a shadow pin and azimuth mirror with which to take bearings. Bearings, by the mirror, of objects more than 30 degrees high are not reliable.

GYROSCOPE AS A COMPASS Originally constructed by M. Foucalt to make visible the rotation of the earth, the gyroscope is familiar to most people in the form of a spinningtop. Its adaptability as a compass depends upon the law that when a body symmetrical about an axis of figure is set rotating about that axis the tendency is for the axis to retain unchanged its directional position in space. The principle on which it proceeds is this—that unless gravity intervene, a rotating body will not alter the direction in which its permanent axis points.

In the gyroscope there is a rotating metal disc, the middle point of whose axis is also the centre of gravity of the machine. By this device the action of gravity is eliminated. It is so constructed that the axis of rotation can be made to point to some star. Then as the heavy disc revolves at great speed it is found that the axis continues to point to the moving star, though

in consequence of this apparently altering its direction relative to bodies on the earth. But if the axis be pointed to the celestial pole which is fixed no alteration in its position relative to bodies on the earth takes place. It has the dynamical property known as the moment of momentum (mass x velocity) into the distance from the axis. A gyroscope free to move in two planes, at any place on the earth other than the poles, tends to set itself with its axis of rotation parallel to the axis of the earth by reason of the relative rotations of the two bodies, meeting in this position the least resistance.

Used as a compass it has to possess a very large gyroscopic resistance strongly opposing any attempt to tilt its axis to any angle. It must therefore rotate at a very high speed, usually 20,000 revolutions per minute. The centrifugal force developed at the periphery is enormous, the stress amounting to 10 tons per square inch; the air friction consumes 95 per cent. of the energy. The disc and spindle are constructed from one solid piece of special nickel steel, so that nothing about it should work loose. The directive force developed is 15 times that of the best form of magnetic compass.

Owing to what is called the precession or swing to or from the meridian, a serious difficulty had to be overcome which was added to by the movements of the ship and the earth's rotation, causing the axis of the gyroscope to wobble ; as the gyro is rigidly attached to the compass card, the axis and the north and south line being exactly parallel, this caused the north point of the card to swing steadily three or four degrees on each side of the meridian. This fault had to be overcome before the gyro could be used as a compass.

It was accomplished in a very ingenious manner. The gyro revolves inside a case and acts as a high speed centrifugal blower ; a strong air blast is created which incidentally serves to keep the motor cool. A stream of this air was diverted through two small pipes led on opposite sides of the disc; the pipes were fitted with valves, which opened or closed with the inclination of the gyro; the jet of air opposed the inclination first one side, then the other, gradually reducing the amplitude of the swing, until in about two and a half to three hours the gyro ran with perfect steadiness; this process is called damping. The gyro must be free to move in two directions. The card, floats, and gyro are all attached and float in a bowl of mercury; the bowl is slung in gimbals in the same manner as an ordinary compass.

In order to keep the whole floating system central a steel stem is fixed in the centre of the glass cover and the lower end dips into a cup containing mercury carried on top of the float.

The gyro contains a motor by which it is driven. The best position for a gyro compass is as near the centre of gravity of the ship as possible.

If a" master compass” is thus carried transmitters worked electrically can be used in any place, in any position, either horizontally or vertically inclined. The gyro compass is of no service at the North or South Pole. It has to be corrected for course and speed. Tables for that purpose are supplied with the compass.

The Advantages are : Independence of magnetic disturbance and vibration (as the syro points true north there is neither variation nor deviation to

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