relations of these weights are governed is this, that the product of either weight multiplied into its distance from the fulcrum must be equal to the product of the other weight multiplied into its distance from the fulcrum; or if there are more weights than one on each side of the fulcrum, the sum of the products on one side must equal the sum of the products on the other.

=

In the case before us, suppose the arms of the lever to be each 12 feet in length, and the weight w to be 3 lbs. -3 x 12 36. Then any weight as w placed at the extremity of the other arm of the lever must also be 3 lbs., being at an equal distance from the fulcrum; but supposing it desirable to restore the level of the lever by placing a weight nearer the fulcrum (say at 9 feet from it), as at w', then the number of pounds weight of w' must be such as when multiplied into 9 feet, will make 36, which in the present instance would be 4, as 4 x 9-36. The same principle holds good whether the lever be moving in a vertical or horizontal plane. If the lever A B were fixed on a vertical axis passing through the point c, so that its motion should be in a horizontal plane, the power requisite to alter its direction would require to be proportioned as above.

To apply this to the power of the sails on a ship, we may consider the ship herself as a lever turning round a vertical axis, called her axis of rotation, and the areas of the sails may be considered as so many weights or forces acting on her to turn her round her axis, the distances from the axis being measured from their centres of effort. It will be obvious that if we want to turn the ship away from the wind (or "bear up "), the full effect must be given to the sails that are nearest the bow; and the sails nearest the stern, or on the opposite side of the axis, (which may be assumed to be nearly at the middle of the ship) must as far as possible be neutralised; and vice versâ, to bring the ship's head up to the wind, the head sails must be neutralised, and the full effect given to the after sails. It will also be obvious that to keep the ship on a straight course, the amount of sail set on each side of the axis of rotation must be balanced by a consideration of the distances of the several sails, or, to speak more correctly, the distances of their centres of effort, from that axis.

Upon this balancing of the sail depends that quality of a ship called "carrying a good helm," by which it is meant that when

course.

all sail is set on a wind, the rudder hangs nearly in a line with the keel, very little action of the helm, and that only weather helm, being required to keep the ship from deviating from her The axis of rotation being a shifting line, this correct balance can never be attained by mere calculation - but an approximation sufficiently near for all practical purposes, has been arrived at by naval architects by means of comparison with ships known to have carried a good helm.

The desirable result has usually been attained by placing the common centre of effort of all the sails a few feet before the middle line of the ship, subject of course to some little modification to meet peculiarities in the form of particular ships.

From what has been said, it is to be hoped that the reader will have little difficulty in comprehending the principles which govern the different manœuvres executed on board a ship, such as Tacking and Wearing. But he must bear in mind that these manœuvres are not entirely carried out by means of the sails, but that the rudder plays the most important part. Now the action of the rudder is dependent on the speed with which the ship passes through the water, and this again upon the power of the sails. The example of the Lever must therefore be followed with some limitation. In Wearing, for instance, while we to a certain extent neutralise the after sail, it is desirable to keep such an amount of sail in full action as to keep up the speed of the ship. This is done by not only keeping the head sails full but the main top-sail also, or very slightly lifting, the mizen top-sail and driver alone being neutralised. Again, in tacking under ordinary circumstances, so much advantage is derived from keeping way on the ship to the last moment before the sails shake, that none of the head sails are neutralised at all.

CHAP. XIX.

MEASURES AND WEIGHTS.

THE earliest mark of time with which man could have been acquainted, must have been the successions of light and dark

ness, or the division of a certain portion of time into day and night. After that, the observation of the movements of the heavenly bodies, the length and direction of shadows, the rise and fall of tides, the escape of water from vessels, and the consequent subsidence of the fluid within - would all suggest themselves as so many means of marking the rate at which time was passing. The sun-dial of Ahaz, the clepsydra, the sand-glass of the Greeks, the notched candle of the Saxons were all inventions, more or less satisfactory, for ascertaining its movements; and there is good reason for believing, that the Eastern astronomers, in early ages, measured time during their observations by the vibration of the pendulum.

We know that a revolution of the earth on its axis is the natural measure of our time; that the time intervening between the appearance of a star, or the sun, on the meridian of a place, and its reappearance is called, in the former case, a sidereal day, which is twenty-four hours; and in the latter, a solar day, which, in consequence of the earth having advanced on its orbit, is on an average nearly four minutes longer. But it may not be quite understood how science has improved upon primitive modes, and constructed a machine which, self acting for several days (if need be), and independent of temperature and the visibility of heavenly bodies, computes time with almost undeviating accuracy.

When a pendulum, however long or short, is set in motion, every swing, vibration, or oscillation which it makes, until it comes to a standstill, is performed in exactly the same amount of time.

These times will be greater or less, as the pendulum is long or short; and it may therefore be made to perform any number of vibrations in a given time.

Say that it is made to beat 86,400 times in a day, and that we divide that number into certain portions, calling them minutes and hours, and the vibrations themselves seconds. The next requirements naturally will be to contrive some means for keeping the pendulum in motion for that, or even a longer, period. This is effected by a train of wheel-work, which is kept revolving during the descent of a weight suspended by a cord wound round one of its axles.

One of the teeth of that wheel which is in contact with the axis of the pendulum is disengaged in a particular direction at

each vibration, and thus the pendulum in return regulates the velocity of the descent of the weight.

An indicator and dial on the end of the last axis of the train will express this velocity; and this velocity is the time as measured by the pendulum in the instance of a common clock.

It was soon found that if the weight at the end of the pendulum were equally divided- -one half being fixed at each end of it, and the pendulum itself placed horizontally on an axis at its centre, and kept in motion by the constant pressure of a spring having a proportionate degree of strength- the same consequences would follow.

This arrangement, which is just the Balance Wheel produced in smaller proportions and adapted to smaller scales and any attitude or position, became the fundamental principle of the Chronometer and pocket watch.

"The compensation balance is a beautiful contrivance for counteracting the effect of changes of temperature, which, by causing an ordinary balance to expand and contract, occasion a variation in the extent of its vibration, and consequently in the rate of going of the timepiece of which it forms the essential feature. This correction is effected by forming the rim of the balance of two semicircular slips of metal, fixed at one end only, and each consisting of a very narrow riband of steel joined to an outer rim of brass. Each of these slips consisting thus of two metals differently affected by heat, is capable of altering its shape with every change in the temperature to which the chronometer is exposed, in such a way as to keep the vibrations of the balance always the same." *

The pendulum is also employed as an instrument in the measurement of space, as well as time. For things which we call fathoms, yards, feet, inches, &c., have no existence, excepting that which they derive from the pendulum.

The number of vibrations which a pendulum of a given length will make in a given time will depend on the locality of the instrument. In different latitudes, there is required a different length of pendulum to perform the same number of, vibrations. In the latitude of London, for example, a pendulum 39.13 inches

*National Encyclopedia.

long, will vibrate seconds, whereas near the Equator, a lesser length would be required to perform the same duty; and it may be observed that the bulbs are usually made capable of adjustment by means of screws.

"This difference is explained by the flattened shape of the earth, and the consequent diminished force of gravity near the equator.

66

Now, as a pendulum in this country, vibrating seconds at the level of the sea would, invariably be of a certain length, that length was adopted as a basis for a system of uniform measures throughout the British Islands; and in the absence, or total loss of the ordinary means, the standard measure could be declared with a line and plummet."

Table of the length of pendulum that will vibrate seconds at every fifth degree.

In France the measures,

The system of Weights in England is arbitrary, almost every county having a quantity of its own. weights, and coinage have a definite relation to the dimensions of the earth. The meridian of Paris measured from the pole to the equator, is divided into ten million parts, each of which is called a Metre.

This metre is 39-376 inches in length, and has been adopted as the basis of a decimal system; the multiples and divisions being expressed by a certain prefix to the metre.

As boat midshipmen are frequently employed upon commissariat service, the following tables may be found useful.