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352. HAVING seen in the preceding chapter that for the investiga. tion of the laws of nature we must carefully watch experiments, either those gigantic ones which the universe furnishes, or others devised and executed by man for special objects-and having seen that in all such observations accurate measurements of Time, Space, Force, etc., are absolutely necessary, we may now appropriately describe a few of the more useful of the instruments employed for these purposes, and the various standards or units which are employed in them.

353. Before going into detail we may give a rapid résumé of the principal Standards and Instruments to be described in this chapter. As most, if not all, of them depend on physical principles to be detailed in the course of this work, we shall assume in anticipation the establishment of such principles, giving references to the future division or chapter in which the experimental demonstrations are more particularly explained. This course will entail a slight, but unavoidable, confusion-slight, because Clocks, Balances, Screws, etc., are familiar even to those who know nothing of Natural Philosophy ; unavoidable, because it is in the very nature of our subject that no one part can grow alone, each requiring for its full development the utmost resources of all the others. But if one of our departments thus borrows from others, it is satisfactory to find that it more than repays by the power which its improvement affords them.

354. We may divide our more important and fundamental instru. ments into four classes

Those for measuring Time;

Space, linear or angular ;
, Force ;

, Mass. Other instruments, adapted for special purposes such as the measurement of Temperature, Light, Electric Currents, etc., will come more naturally under the head of the particular physical energies to whose measurement they are applicable. Descriptions of self-recording instruments such as tide-gauges, and barometers, thermometers, electrometers, recording photographically or otherwise the continuously varying pressure, temperature, moisture, electric potential of the atmosphere, and magnetometers recording photographically the continuously varying direction and magnitude of the terrestrial magnetic force, must likewise be kept for their proper places in our work.

Calculating Machines have also important uses in assisting physical research in a great variety of ways. They belong to two. classes:

I. Purely Arithmetical, dealing with integral numbers of units. All of this class are evolved from the primitive use of the calculuses or little stones for counters (from which are derived the very names calculation and “The Calculus"), through such mechanism as that of the Chinese Abacus, still serving its original purpose well in infant schools, up to the Arithmometer of Thomas of Colmar and the grand but partially realized conceptions of calculating machines by Babbage.

II. Continuous Calculating Machines. These are not only useful as auxiliaries' for physical research but also involve important dynamical and kinematical principles belonging properly to our subject.

355. We shall now consider in order the more prominent instru. ments of each of these four classes, and some of their most important applications:

Clock, Chronometer, Chronoscope, Applications to Observation

and to self-registering Instruments.
Vernier and Screw-Micrometer, Cathetometer, Spherometer,

Dividing Engine, Theodolite, Sextant or Circle.
Common Balance, Bifilar Balance, Torsion Balance, Pendulum,

Dynamometer. . Among Standards we may mention1. Time.-Day, Hour, Minute, Second, sidereal and solar. 2. Space.-Yard and Métre: Radian, Degree, Minute, Second. 3. Force. -Weight of a Pound or Kilogramme, etc., in any par

ticular locality (gravitation unit); poundal or dyne, Kinetic

Unit 4. Mass.-Pound, Kilogramme, etc.

356. Although without instruments it is impossible to procure or apply any standard, yet, as 'without the standards no instrument could give us absolute measure, we may consider the standards firstreferring to the instruments as if we already knew their principles and applications.

357. First we may notice the standards or units of angular measure:

Radian, or angle whose arc is equal to radius

Degree, or ninetieth part of a right angle, and its successive subdivisions into sixtieths called Minutes, Seconds, Thirds, etc. The division of the right angle into go degrees is convenient because it makes the half-angle of an equilateral triangle (sin-' }) an integral number (30) of degrees. It has long been universally adopted by all Europe. The decimal division of the right angle, decreed by the French Republic when it successfully introduced other more sweeping changes, utterly and deservejly failed.

The division of the degree into 60 minutes and of the minute into 60 seconds is not convenient; and tables of the circular functions for degrees and hundredths of the degree are much to be desired. Meantime, when reckoning to tenths of a degree suffices for the accuracy desired, in any case the ordinary tables suffice, as 6' is to of a degree.

The decimal system is exclusively followed in reckoning by radians. The value of two right angles in this reckoning is 3:14159... , or 17. Thus # radians is equal to 180°. Hence 180° -7 is 57°29578 ..., or 57° 17' 44":8 is equal to one radian. In mathematical analysis, angles are uniformly reckoned in terms of the radian.

358. The practical standard of time is the Siderial Day, being the period, nearly constant', of the earth's rotation about its axis (S 237). From it is easily derived the Mcan Solar Day, or the mean interval which elapses between successive passages of the sun across the meridian of any place. This is not so nearly as the former, an absoJute or invariable unit; secular changes in the period of the earth's

'In our first edition of our larger treatise it was stated that Laplace had calculated from ancient observations of eclipses that the period of the earth's rotation about its axis had not altered by roodrody of itself since 720 B.C. In § 830 it was pointed out that this conclusion is overthrown by farther information from Physical Astronomy acquired in the interval between the printing of the two sections, in virtue of a correction which Adams had made as early as 1863 upon Laplace's dynamical investigation of an accelerauon of the moon's mean motion, produced by the Sun's attraction, showing that only about half of the observed acceleration of the moon's mean motion relatively to the angular velocity of the earıh's rotation was accounted for by this cause. Quoting from the first edition, $ 830.] “lo 1859 Adams communicated to Delaunay his final result :-hat at “the end of a century the moon is 5"69 before the position she would have, • relatively to a meridian of the earth, according to the angular velocities of the “two motions, at the beginning of the century, and the acceleration of the "moon's motion truly calculated from the various disturbing causes then recog. “nized. Delaunay soon after verified this result : and about the beginning of "1866 suggested that the true explanation may be a retardation of the earth's

solation by tidal friction. Using this hypothesis, and allowing for the conse** quent retardation of the moon's mean motion by cidal reaction (3 276), Adams, in an estimate which he has communicated to us, founded on the rough as., sumprion that the parts of the earth's retardation due to solar and lunar tides are as the squares of the respective tide-generating forces, finds 22• as the

error by which the earth would in a century get behind a persect clock rated "at the beginning of the century. If the retardation of rate giving this integral "effect were uniform ($ 32), the earth, as a timekeeper, would be going slower " by '22 of a second per year in the middle, or '44 of a second per year at the "end, than at the beginning of a century."

revolution found 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 distinguished from those of angular measure by notation. Thus we have for time 136 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•242 203 siderial days, or 365*242242 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 jodou.

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 1700 yards, is unfortimately often used when great_lengths on land

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. I Centimètre = '3937043 inch. Foot = 3.047972 decimètres.

Mètre = 3·280869 feet. British Statute mile

Kilomètre = 6213767 British = 16094329 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 = .2471093 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 defiħed by existing standards.

Grain = 64979896 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

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