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 J3TNA — AFFREIGHTMENT analytical expression of the relation (ii) assumes a more complex form ; we thus derive the most general equations of electrodynamic propagation for matter treated as continuous, anyhow distributed and moving in any manner. For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by dAQ + iry d /K-l ° dt V dx) 47rc2 47rc2 / ^ ' also the circuital relations here reduce to dQ __ <dy dy . ^- = ^TTV, dx dx dt ’ thus

d2Q

dv

giving, on substitution for v. d^Q= v d2Q_ d2Q (c2 dx* d£z Vdxdt' For a simple wave-train, Q varies as' sin m(x - Yt), leading on substitution to the velocity of propagation Y relative to the moving material, by means of the equation KY2 + 2vY = c2 — v2 ; this gives, to the first order of v/c, Y = c/Ki - u/K, which is in accordance with Fresnel’s law. Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wavegroups travelling with the slightly different velocity cf(yA-1)/(iA.-1, the value of K occurring in Y being a function of A determined by the law of optical dispersion of the medium. For purposes of theoretical discussions relating to moving radiators and reflectors, it is important to remember that the dynamics of all this theory of electrons involves the neglect of terms of the order (v/c)2, not merely in the value of K but throughout. The modification of the spectrum of a radiating gas by a magnetic field, such as would result from the hypothesis that the radiators are the system of revolving or oscillating electrons in the molecule, was detected by Zeeman in 1896 ; more minute investigation has largely confirmed the predictions as to its character that were made by H. A. Lorentz and others on the basis of the theoretical ideas here sketched. Reference may be made generally to—Maxwell. Collected Papers.—H. A. Lorentz. Archives Neerlandaises, xxi. 1887, and xxv. 1892; and a tract, Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Korpern, Leyden, 1895. — 0. Lodge. “Aberration Problems,” Phil. Trans. 1893 and 1897.—J. Larmor, Phil. Trans. 1894-5-7, and a treatise JEther and Matter, Cambridge Univ. Press, 1900, where full references are given. See also' in Ency. Brit. (9th ed.) articles Atom, Ether, Molecule, Electricity, Wave Theory. (j. l.*) Afforestation.

See Forests.

Affreightment. — Contract of Affreightment is the expression usually employed to describe the contract between a shipowner and some other person called the freighter, by which the shipowner agrees to carry goods of the freighter in his ship, or to give to the freighter the use of the whole or part of the cargo-carrying space of the ship for the carriage of his goods on a specified voyage or voyages, or for a specified time; the freighter on his part agreeing to pay a specified price, called “freight,” for the carriage of the goods or the use of the ship. A ship may be let like a house to some person who takes possession and control of it for a specified term. The person who hires a ship in this way occupies during the currency of his term the position of shipowner. The contract by

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which a ship is so let may be called a charter-party ; but it is not, properly speaking, a contract of affreightment, and is mentioned here only because it is necessary to remember the distinction between a charter-party of this kind, which is sometimes called a demise of the ship, and a charter-party which is a form of contract of affreightment, as will hereinafter appear. The law with regard to the contract of affreightment is, of course, a branch of the general law of contract. The rights and obligations of the shipowner and the freighter depend, as in the case of all parties to contracts, upon the terms of the agreement entered into between them. The law, however, interferes to some extent in regulating the effect to be given to contracts. Certain contracts are forbidden by the law, and being illegal are, therefore, incapable of enforcement. The most important example of illegality in the case of contracts of affreightment is when the contract involves trading with an enemy. The law interferes again with regard to the interpretation of the contract. The meaning to be given to the words of the contract, or, in other words, its construction, when a dispute arises about it, must be determined by the judge or court. The result is, that certain more or less common clauses in contracts of affreightment have come before the courts for construction, and the decisions in these cases are treated practically, though not perhaps quite logically, as rules of law determining the sense to be put upon certain forms of expression in common use in shipping contracts. A third way in which the law interferes is by laying down certain rules by which the rights of the parties are to be regulated in the absence of any express stipulation with regard to the matter dealt with by such rules. This is done either by statutory enactment, as by that part (Part YIII.) of the Merchant Shipping Act, 1894, which deals with the liability of shipowners; or by established rules of the unwritten law, the “ common law ” as it is called, as, for instance, the rule that the common carrier is absolutely responsible for the of'law safe delivery of the goods carried, unless it is prevented by the act of God or the King’s enemies. These rules of law, whether common law or statute law, regulating the obligations of carriers of goods by sea, are of most importance in cases which are uncommon though not unknown at the present day, in which there is an affreightment without any written agreement of any kind. It will, therefore, be convenient to consider first cases of this kind where there is no express agreement, oral or written, except as to the freight and destination of the goods, and where consequently the rights and obligations of the parties as to all other terms of carriage- depend wholly upon the rules of law, remembering always that these same rules apply when there is a written contract, except in so far as they are qualified or negatived by the terms of such contract. The rules of the common or ancient customary law of England with regard to the carriage of goods were no doubt first considered by the courts and established with regard to the carriage of goods by common carriers on land. These rules were applied to common carriers by water, and it may now be taken to be the general rule that shipowners who carry goods by sea are by the English law subject to the liabilities of common carriers. (See as to the grounds and precise extent of this doctrine the judgments in Liver Alkali Company v. Johnson, L.P., 7 Ex. 267, and Nugent v. Smith, 1 C.P.D. 423.) In practice goods are not often shipped without a written contract or acknowledgment of the terms upon which they are to be carried. For each separate consignment or parcel of goods shipped a bill of lading is almost invariably given, and when a whole cargo is agreed to be carried