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revolution round the sun affect it, though very slightly. It is divided into 24 hours, and the hour, like the degree, is subdivided into successive sixtieths, called minutes and seconds. The usual subdivision of seconds is decimal.

It is well to observe that seconds and minutes of time are distin. guished from those of angular measure by notation. Thus we have for time 134 43" 27'58, but for angular measure 13° 43' 27":58.

When long periods of time are to be measured, the mean solar year, consisting of 366-242203 sideral days, or 365*242 242 mean solar days, or the century consisting of 100 such years, may be conveniently employed as the unit.

359. The ultimate standard of accurate chronometry must (if the human race live on the earth for a few million years) be founded on the physical properties of some body of more constant character than the earth for instance, a carefully-arranged metallic spring, hermetically sealed in an exhausted glass vessel. The time of vibration of such a spring would be necessarily more constant from day to day than that of the balance-spring of the best possible chronometer, disturbed as this is by the train of mechanism with which it is connected: and it would certainly be more constant from age to age than the time of rotation of the earth, retarded as it now is by tidal resistance to an extent that becomes very sensible in 2000 years; and cooling and shrinking to an extent that must produce a very considerable effect on its time-keeping in fifty million years.

360. The British standard of length is the Imperial Yard, defined as the distance between two marks on a certain metallic bar, preserved in the Tower of London, when the whole has a temperature of 60° Fahrenheit. It was not directly derived from any fixed quantity in nature, although some important relations with natural elements have been measured with great accuracy. It has been carefully compared with the length of a second's pendulum vibrating at a certain station in the neighbourhood of London, so that should it again be destroyed, as it was at the burning of the Houses of Parliament in 1834, and should all exact copies of it, of which several are preserved in various places, be also lost, it can be restored by pendulum observations. A less accurate, but still (unless in the event of earthquake disturbance) a very good, means of reproducing it exists in the measured base-lines of the Ordnance Survey, and the thence calculated distances between definite stations in the British Islands, which have been ascertained in terms of it with a degree of accuracy sometimes within an inch per mile, that is to say, within about yoouu

361. In scientific investigations, we endeavour as much as possible to keep to one unit at a time, and the foot, which is defined to be one-third part of the yard, is, for British measurement, generally adopted. Unfortunately the inch, or one-twelfth of a foot, must sometimes be used, but it is subdivided decimally. The statute mile, or 1760 yards, is unfortumately often used when great lengths on land

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are considered; but the sea-mile, or average minute of latitude, is much to be preferred. Thus it appears that the British measurement of length is more inconvenient in its several denominations than the European measurement of time, or angles.

362. In the French metrical system the decimal division is exclu. sively employed. The standard, (unhappily) called the Mètre, was defined originally as the ten-millionth part of the length of the quadrant of the earth's meridian from the pole to the equator; but it is now defined practically by the accurate standard metres laid up in various national repositories in Europe. It is somewhat longer than the yard, as the following Table shows :

Inch = 25.39977 millimètres. Centimètre = '3937043 inch. Foot = 3'047972 decimètres.

Mètre = 3·280869 feet. British Statute mile

Kilomètre = *6213767 British = 1609'329 mètres.

Statute mile. 363. The unit of superficial measure is in Britain the square yard, in France the mètre carré. Of course we may use square inches, feet, or miles, as also square millimètres, kilomètres, etc., or the Hectare = 10,000 square mètres.

Square inch = 6:451483 square centimètres.
foot =

9*290135 decimètres.
yard = 83.61121 decimètres.
Acre

'4046792 of a hectare. Square British Statute mile = 258.9946 hectare.

Hectare = . 2.471093 acres. 364. Similar remarks apply to the cubic measure in the two countries, and we have the following Table:

Cubic inch = 16.38661 cubic centimètres.

foot = 28.31606 decimètres or Litres. Gallon

4'543808 litres. = 277'274 cubic inches, by Act of Parliament,

now repealed. Litre

= '035315 cubic feet. 365. The British unit of mass is the Pound (defined by standards only); the French is the Kilogramme, defined originally as a litre of water at its temperature of maximum density; but now practically defined by existing standards.

Grain - 6479896 milligrammes. Gramme = 15'43235 grains. Pound = 453-5927 grammes. Kilogram. = 2.20362125 lbs.

Professor W. H. Miller finds (Phil. Trans., 1857) that the 'kilogramme des Archives' is equal in mass to 15432 349 grains : and the 'kilogramme type laiton, deposited in the Ministère de l'Intérieure in Paris, as standard for French commerce, is 15432'344 grains.

366. The measurement of force, whether in terms of the weight of a stated mass in a stated locality, or in terms of the absolute or

kinetic unit, has been explained in Chapter II. (See SS 221–227.) From the measures of force and length we derive at once the measure of work or mechanical effect. That practically employed by engineers is founded on the gravitation measure of force. Neglecting the difference of gravity at London and Paris, we see from the above Tables that the following relations exist between the London and the Parisian reckoning of work:

Foot-pound = 0'13825 kilogramme-mètre.

Kilogramme-mètre = 7'2331 foot-pounds. 367. A Clock is primarily an instrument which, by means of a train of wheels, records the number of vibrations executed by a pendulum ; a Chronometer or Watch performs the same duty for the oscillations of a flat spiral spring-just as the train of wheel-work in a gas-meter counts the number of revolutions of the main shaft caused by the passage of the gas through the machine. As, however, it is impossible to avoid friction, resistance of air, etc., pendo lum or spring, left to itself, would not long continue its oscillations, and, while its motion continued, would perform each oscillation in less and less time as the arc of vibration diminished: a continuous supply of energy is furnished by the descent of a weight, or the uncoiling of a powerful spring. This is so applied, through the train of wheels, to the pendulum or balance-wheel by means of a mechanical contrivance called an Escapement, that the oscillations are maintained of nearly uniform extent, and therefore of nearly uniform duration. The construction of escapements, as well as oi trains of clock-wheels, is a matter of Mechanics, with the details of which we are not concerned, although it may easily be made the subject of mathematical investigation. The means of avoiding errors introduced by changes of temperature, which have been carried out in Compensation pendulums and balances, will be more properly described in our chapters on Heat. It is to be observed that there is little inconvenience if a clock lose or gain regularly; that can be easily and accurately allowed for : irregular rate is fatal.

368. By means of a recent application of electricity, to be after, wards described, one good clock, carefully regulated from time to time to agree with astronomical observations, may be made (without injury to its own performance) to control any number of other lessperfectly constructed clocks, so as to compel their pendulums to vibrate, beat for beat, with its own.

369. In astronomical observations, time is estimated to tenths of a second by a practised observer, who, while watching the phe pomena, counts the beats of the clock. But for the very accurate measurement of short intervals, many instruments have been devised. Thus if a small orifice be opened in a large and deep vessel full of mercury, and if we know by trial the weight of metal that escapes say in five minutes, a simple proportion gives the interval which elapses duting the 'escape of any given weight. It is easy to con.

trive an adjustment by which a vessel may be placed under, and withdrawn from, the issuing stream at the time of occurrence of any two successive phenomena.

370. Other contrivances are sometimes employed, called Stopwatches, Chronoscopes, etc., which can be read off at rest, started on the occurrence of any phenomenon, and stopped at the oco currence of a second, then again read off; or which allow of the making (by pressing a stud) a slight ink-mark, on a dial revolving at a given rate, at the instant of the occurrence of each phe. nomenon to be noted. But, of late, these have almost entirely given place to the Electric Chronoscope, an instrument which will be fully described later, when we shall have occasion to refer to experiments in which it has been usefully employed.

371. We now come to the measurement of space, and of angles, and for these purposes the most important instruments are the Vernier and the Screw.

372. Elementary geometry, indeed, gives us the means of dividing any straight line into any assignable number of equal parts; but in

practice this is by no means an accurate Р.

or reliable method. It was formerly used in the so-called Diagonal Scale, of which the construction is evident from the dia. gram. The reading is effected by a sliding piece whose edge is perpendicular to the length of the scale. Suppose that it is PQ whose position on the scale is. required. This can evidently cut only one of the transverse lines. Its number gives the number of tenths of an inch (4 in the figure), and the horizontal line next above

the point of intersection gives evidently the number of hundredths (in the present case 4). Hence the reading is 7:44. As an idea of the comparative uselessness of this method, we may mention that a quadrant of 3 feet radius, which belonged to Napier of Merchiston, and is divided on the limb by this method, reads to minutes of a degree; no higher accuracy than is now attainable by the pocket sextants made by Froughton and Simms, the radius of whose arc is virtually little more than an inch. The latter instrument is read by the help of a Vernier.

373. The Vernier is commonly employed for such instruments as the Barometer, Sextant, and Cathetometer, while the Screw is applied to, the more delicate instruments, such as Astronomical Circles, Micrometers, and the Spherometer.

374. The vernier consists of a slip of metal which slides along a divided scale, the edges of the two being coincident. Hence, when it is applied to a divided. circle, its edge is_circular,

29

in.

and it moves about an axis passing through the centre of the 'divided limb.

In the sketch let 0, 1, 2, 10 denote the divisions on the vernier, 0, 1, 2, etc., any set of consecutive divisions on the limb or scale along whose edge it slides. If, when 0 and o coincide, 10 and 11 coincide also, then 10 divisions of the vernier are equal in length to is on the limb; and therefore each division of the vernier is idths, or i io of a division on the limb. If, then, the ver. nier be moved till 1 coincides with 1, 0 will be sth

30 of a division of the limb beyond o; if 2 coincide with 2, 0 will be ths beyond o; and so on. Hence to read the vernier in any position, note first the division next to o, and behind it on the limb. This is the integral number of divisions to be read. For the fractional part, see which division of the vernier

10 is in a line with one on the limb; if it be the 4th (as in the figure), that indicates an addition to the reading of oths of a division of the limb; and so on. Thus, if the figure represent a barometer scale divided into inches and tenths, the reading is 30-34, the zeroline of the vernier being adjusted to the level of the mercury.

375. If the limb of a sextant be divided, as it usually is, to thirdparts of a degree, and the vernier be formed by dividing twenty-one of these into twenty equal parts, the instrument can be read to twentieths of divisions on the limb, that is, to minutes of arc.

If no line on the vernier coincide with one on the limb, then since the divisions of the former are the longer there will be one of the latter included between the two lines of the vernier, and it is usual in practice to take the mean of the readings which would be given by a coincidence of either pair of bounding lines.

376. In the above sketch and description, the numbers on the scale and vernier have been supposed to run opposite ways. This is generally the case with British instruments. In some foreign ones the divisions run in the same direction on vernier and limb, and in that case it is easy to see that to read to tenths of a scale division we must have ten divisions of the vernier equal to nine of the scale.

In general to read to the nth part of a scale division, n divisions of the vernier must equal n + 1 or n-1 divisions on the limb, according as these run in opposite or similar directions.'

377. The principle of the Screw has been already noticed (8 114). It may be used in either of two ways, i.e. the nut may be fixed, and the screw advance through it, or the screw may be prevented from moving longitudinally by a fixed collar, in which case the nut, if prevented by fixed guides from rotating, will move in the direction of the common axis. The advance in either case is evidently proportional to the angle through which the screw has turned about its

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