any error must be corrected before commencing work. All chaining must be horizontal (on 0 and scales) and not along the surface of sloping ground. In chaining on sloping ground too long a portion of the chain should not be used at once. In chaining lines the chain must be extended, but neither stretched too tightly nor allowed to rest too slackly. A line with an error of two links in every 1,000 will be passed."

=

The land surveyors' chain known as Gunter's chain, of 66 feet, is divided into 100 "links," each link being therefore 7.92 inches, or 1 foot of chain 1.515 link. This chain of 66 feet is a convenient measure of superficies as by it 1 acre is equal to 10 square chains or 100,000 square links. Professor Edmund Gunter, who invented the chain of 66 feet about the year 1620, also invented, in 1624, the " line of numbers," and he introduced several improvements into surveying instruments during the time he was connected with Gresham College in the City of London.

The old Scotch acre was also divided into ten square chains, each chain into 16 "falls," and the whole into 100,000 square links.

Engineers also use iron or steel chains of 50 or 100 feet, divided into links, each iron or steel link with its connecting ring being 1 foot long, having their true lengths at the temperature of 62° Fahr. Although chain measures are usually made of iron or steel, those used in mines are often made of brass. In metalliferous mines (Brough's treatise on mine surveying, 1889) a chain of 10 fathoms, or 60 feet, is stated to be used, each link being 6 inches long, the chain being provided with brass marks at every fathom. It would appear that for colliery use the chain may be left half an inch longer than the true length since it is rarely drawn out into a straight line. In continental countries the metric chain is used for mining, but a unit

somewhat similar in length to the "fathom" is also used. The fathom is declared by the Weights and Measures Act, 1878, to be equal to 2 yards, or 1.8288 metres.

Deal rods and glass rods were subsequently substituted for chains, and in the measurement of the base line on Hounslow Heath in 1784 the difference obtained between the measurements by glass rods and the more convenient steel chains was only 2 inches in 27,404 feet. Rods made of deal, pine, or lance wood, are used in surveying and in checking chain measurements; such rods are usually 5, 6, or 10 feet in length, and mostly have their ends protected by brass plates, after being soaked in boiling oil and well protected by varnish, so as to lessen the effect of humidity. Even, however, with the utmost care rod measurements can hardly be relied on beyond 0.03 inch in 100 feet.

In Russia base lines of over 2 miles in length have been measured with steel wires with an accuracy of 0.1 inch in the whole length of the line.

Measurements can be made more accurately by steel Measurements by ribands or steel wires than by linked chains, a measure- ribands. ment by riband may be taken as one and a half times more accurate than a chain measurement. For all surveying purposes a steel riband of 50 feet should have a width of not less than inch and be about 4-inch thick. Of course much depends on the mode in which a chain measure or a steel riband may be used; for we have not only to ascertain the absolute length of a chain in yards or metres, but we must allow for the "sag" of the chain, for which latter purpose the modulus of elasticity of a steel chain may be found experimentally by applying to it varying stretching weights or "pulls." At the Standards Office a pull or normal tension of 56 lbs. is given to steel 100 feet chains; 40 lbs. on steel 66 feet chains; and 10 lbs. on steel ribands. The distance indicated by a 500 feet steel riband when subjected to

Mural and reference

a normal tension has been found to be 500-082 feet. On the best wire woven linen tapes a normal tension of 12 lbs. is given, on ordinary linen tapes the tensions are 5 lb. on 100 feet, 4 lb. on 66 feet, 2 lbs. on 30 feet linen tapes. A wire-woven 100 feet linen tape will stretch nearly 2-inch with a 12 lb. pull.

As

In the measurement of ships the Board of Trade "Instructions and Regulations" (1895) permit the use to some extent of the measuring tapes, but all tapes are required to be frequently tested as to their accuracy. all flaxen and hempen manufactures are liable to contraction by moisture no tapes are to be used which are not waterproof; and those only of such length as (15 feet, 60 feet) which involve no practical error arising from sag" or deflexion, or from extension by long continued use, and it is also stated that a strong waterproof tape of 100 feet long, decimally divided into feet, held moderately tight, will be found convenient in measuring the lengths of vessels, and the breadths of the areas, and in measuring the lengths and breadths of closed-in spaces.

66

Of whatever material a chain or tape may be made it Standards. requires to have its accuracy periodically verified by a fixed mural or reference standard, and hence long standards, or small base lines of 100 feet and 66 feet, with their subdivisions, including the land measure of the pole or perch (5 yards) have been laid down by the Board of Trade on the north side of Trafalgar Square, London, and by different local authorities throughout the United Kingdom. The standards at Trafalgar Square were made legal measures by an Order in Council dated 27th June 1876, and copies of these standards were subsequently laid down at the Arts Museum, Edinburgh, the Guildhall, London, the City Hall, Dublin, the Assize Courts, Manchester, the Municipal Buildings, Glasgow, the Town Hall, Bradford, &c.

Besides these public standard chain measures, bronze mural tablets are also exhibited at the places above referred to, as well as on the outside of the Royal Observatory, Greenwich, (the original mural standards), and in the vestibule of the Science Galleries at South Kensington Museum. These tablets show the length of the yard, foot, and inch (and at Kensington and Dublin of the metre, decimetre, and millimetre also), so that any workman can at once test his 2-foot rule to one hundredth of an inch.

measure

The connection between our system of weights and Pendulum measures and pendulum measurements is no longer a direct ments. one, for the yard measure is no longer based on the length of the seconds' pendulum. Pendulum observations, however, form an important part of geodetic surveys, as those in India carried out by Capt. J. P. Basevi, Col. W. J. Heaviside, and Col. Herschel, or those carried out at the United States Geodetic Survey by Mr. Peirce; and by M. Sawitsch in Russia. The object of pendulum observations may be said to be to determine the figure of the earth, as the length of the seconds' pendulum varies with the latitude at which the pendulum may be swung. The ratio of the earth's axes, as deduced from pendulum observations, is, according to Clarke ("Geodesy," Oxford, 1880), as 292 to 293.

In the C. G. S. (centimetre-gram-second) system of units the following values may be taken for the apparent acceleration of a body falling freely under the action of gravity in vacuo (g), and for the length (1) of the seconds pendulum connected with the value of (g) :

PART IV.

Scientific

measurements.

13. SCIENTIFIC MEASURING INSTRUMENTS.

In the measurement of physical quantities the units of such quantities may be classified as follows:

Fundamental units, as those of length, mass, and time.

Geometric units, as those of surface, volume, and angle.

Mechanical units, as those of velocity, acceleration,

force, work, power, pressure, and moment of inertia.

With reference to the units of length and mass, standards are determined, to which reference has been already made, and in connection with other units various forms of measuring instruments become necessary, of which, in some instances, the Legislature has taken cognizance, as in the measurement of electricity, gas, &c., and to these some reference may be offered here. (See also Guillaume's "Unités et Étalons" (Paris, 1890), Everett's "Illustrations of the C.G.S. System of Units" (Macmillan, 1891), Lupton's " Numerical Tables" (Macmillan, 1892).