This chapter explains the role played by reservations, the application of the rules of the Vienna Convention on the Law of Treaties, and practice in dealing with reservations. It defines reservations and distinguishes them from interpretative declarations and political declarations. It examines whether reservations are permissible or impermissible, including the test whether a reservation is incompatible with the object and purpose of the treaty. It also discusses the rules governing acceptance and objection, the legal effect of reservations, the question whether a prohibited reservation can be severed, and special cases such as human rights treaties, reservations relating to internal law, vague or general reservations, reference to Islamic law, late reservations, and the role of treaty monitoring bodies. It analyses the procedure for making or objecting to reservations or withdrawing them, and the functions of the depositary in relation to reservations.

The harmonic vibrational frequencies of an ideal string under tension, fixed at the ends, are developed, starting with the results from the harmonic oscillator. The corresponding resonances result in sinusoidal standing waves. The end conditions restrict the possible solutions to be those with an integer number of half wavelengths between the ends of the string. A general vibration of the string, such as from a pluck, can be described as the sum of sinusoidal solutions. More general end conditions include a free end, in which case there is an odd number of quarter wavelengths between the ends.

When a treaty prescribes how disputes can be settled, it usually provides for a preliminary phase involving direct negotiations or consultations. In the case of bilateral agreements, more binding mechanisms tend to be found in agreements with more specific obligations, or those directly affecting individual interests, such as trade. Otherwise, bilateral agreements will often specify that disputes are to be resolved by the diplomatic channel or other avenue of voluntary settlement. Both bilateral and multilateral treaties may provide for conciliation or mediation. The parties may, however, wish to resort to compulsory binding settlement. The two principal features are a prior agreement to submit disputes to a third party, and a provision that the decision of the third party is legally binding on the parties in dispute. Procedures of arbitration and judicial settlement, including the International Court of Justice, are analysed. In respect of remedies, the chapter examines countermeasures and the principles underlying them, sacrosanct obligations and necessity.

A star remains on the main sequence as long as it is powered by fusion of hydrogen into helium in its central core.

This chapter examines both entry into force and provisional application. A treaty enters into force in such manner and on such date as may be specified in the treaty or as the negotiating states may agree. Ways include ratification (or an analogous procedure) by all or a minimum number of negotiating states; exchange of instruments of ratification; notification by each state of the completion of domestic procedures; on the date of a reply note in the case of an exchange of notes; or on a date specified in the treaty; or on signature only by all the negotiating states. There can be more complex provisions, particularly with treaties that amend a previous treaty. The ‘date of entry into force’ is analysed. States may also provisionally apply all or part of a treaty prior to entry into force, subject to their constitutional provisions. Where a treaty has been terminated, the parties or some of them can agree to revive it.

The issue of successive treaties arises where all or some of the parties conclude a later treaty relating to the same subject matter. The relevant rules of the Vienna Convention on the Law of Treaties are in Articles 30 and 59, which have to be read together. The chapter analyses how these rules might apply. In the case of bilateral treaties, the parties will often include express provisions to clarify the position in respect of an earlier treaty. If not, it may be possible to resolve any inconsistency by interpretation of the two treaties, or the earlier treaty may be treated as terminated or suspended in accordance with Article 59. Or the residual rules of Article 30 may apply, by which the earlier treaty may apply only to the extent that its provisions are compatible with a later treaty. The principles are the same in respect of multilateral treaties but there is a greater variety of express provisions, which are not always clear. The fact that all the parties to an earlier treaty may not be parties to a later treaty also adds complexity. These issues are analysed, together with the residual rules of Article 30.

This chapter presents a discussion and derivation of the ideal gas law, starting with atoms and molecules. Collisions are characterized by the impulse, the change in momentum due to the collision, determined by the product of the average force during and the time duration of a collision. A free atom or molecule in a box is used to develop the concept of pressure on a wall and, ultimately, the ideal gas law for many noninteracting molecules. The distinction between gauge pressure and absolute pressure is necessary to understand before applying the gas laws. The root mean square (rms) speed for a typical molecule is estimated to be a bit faster than the speed of sound. That is, the molecules can be expected to be supersonic. Included is a discussion of isotopes and carbon dating and their connection to the musical scale.

The basics of magnets, magnetism, induced magnetism, magnetic fields, and electromagnets are introduced. The force between a magnet and an electromagnet is the basis for speakers, devices that turn electrical signals into sounds, as well as other electromechanical devices. The process works in reverse, in that a sound incident on a speaker can produce an electrical signal. The latter principle is used for some microphones. In general, a time-dependent magnetic field, for example, due to a moving magnet, will tend to induce electrical currents that oppose the change. This is known as Faraday’s law of induction. Several of the principles of magnetism are used together to create an electric guitar pickup. A scheme to use a pair of pickups to cancel out environmental signals, known as a humbucker, is shown. Electrical transformers work based on a time-changing magnetic field from one electromagnet experienced by another, and they are useful for generating electrical signals that better match the destination for the signals—typically an amplifier.

The depositary keeps custody of the original text of the treaty, prepares certified texts and performs a number of other important functions relating to the verification and notification of acts relating to the treaty. The principal functions are listed in Article 77 of the Vienna Convention on the Law of Treaties, but treaties may include specific provisions on the role of the depositary. Under Article 78, unless a treaty otherwise provides, states shall make notifications to the depositary or, if there is none, direct to the states to which they are intended. The depositary has a duty to act impartially. Often, bilateral treaties will not have a depositary but, if they do, the duties will be confined to custody or provision of certified texts. Multilateral treaties will almost always have a depositary, since they play an essential role in ensuring that the necessary formalities and procedures are performed. The depositary for many multilateral treaties is the UN Secretary-General or the chief administrative officer of a relevant international organisation. If a state is the depositary, the functions should be performed by its foreign ministry. The function in respect of correction of errors is examined in more detail.

Does a treaty apply to all of a party’s territory? How is territory defined? In the absence of an express definition or other contrary intention, the territory comprises the metropolitan territory of a state and any other territory under its sovereignty. But practice varies. Many bilateral treaties have provisions expressly extending them to overseas territories or enabling such extension by notification or subsequent agreement. Multilateral treaties may also include an express territorial application clause. UK practice from 1967 has been to apply multilateral treaties only to its metropolitan territory unless it makes a specific declaration of extension to any of its overseas territories. On rare occasions, a state may conclude a treaty only so that it applies to a specific overseas territory. The issues posed for federations are discussed, together with certain methods by which the problems can be reduced: territorial clauses, federal clauses and federal reservations. The case of the Hong Kong and Macao Special Administrative Regions is also analysed.