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.

Combinations of tones that are consonant (“nice”) are those that exhibit no slower beats. Beats occur when two periodic signals are close to the same frequency. For sinusoidal signals, the beat frequency is simply the difference between the two signals. For complex signals, one must also consider differences between multiples of the signal frequency. Thus, consonant combinations are those where the ratio of the frequencies is equal to a rational number. Of particular importance are rational numbers involving the ratio of small integers. The musical fifth corresponds to a frequency ratio of 3 to 2 and is an important part of music. A set of note frequencies used for a musical scale can be justified based on consonant combinations, and variations of the details of those choices, known as temperaments, are useful in music for practical reasons. In particular, the equal-tempered scale used for keyboards, based on multiples of the 12th root of 2, is very common.

A third state is a state not a party to a treaty. The general rule is that a treaty does not create obligations or rights for a third state without its consent. Articles 35 and 36 of the Vienna Convention on the Law of Treaties elaborate the general rule by setting out the circumstances in which a treaty can apply to a third state. Before a third state can be bound by an obligation to a treaty to which it is not a party, the parties must intend the provision to establish an obligation for the third state, and the third state must expressly accept that obligation in writing. A right arises for a third state under a treaty if the parties so intend and the third state assents. The chapter discusses the application of these rules, and obligations erga omnes, defined as obligations in whose observance all states can be held to have a legal interest.

International organisations include global organisations such as the United Nations and regional organisations such as the European Union. The chapter examines constituent instruments and their interpretation, membership (which may include non-state entities) and withdrawal, including the withdrawal of the United Kingdom from the European Union. International organisations have the capacity to enter into treaties but may only conclude agreements in those areas in which they are competent to act. The Vienna Convention of 1986 adapts the rules of the 1969 Convention to apply to international organisations, but it is not yet in force. The chapter examines bodies which play a role in recommending or negotiating treaty texts (including the United Nations, UN Sixth Committee and the International Law Commission) and those which play a role in settling disputes (such as the International Court of Justice) and in monitoring compliance (such as the Human Rights Committee). It looks at special cases, including the OSCE, Commonwealth and European Union.

Because stars are large and massive compared to a rocky planet like the Earth, we expect that a balance between pressure gradients and gravity inside a star will require very high internal pressure. However, there can be very different ways in which high pressure can be achieved, as two examples from the Earth make clear. Both the atmosphere and the oceans are in hydrostatic equilibrium; air pressure thus decreases with altitude above sea level, while pressure in the ocean increases with depth.

Various sound-recording technologies are presented that use different mediums and different encoding methods for the recorded signal. Analog and digital are two broad categories used for encoding. Sound signals can be recorded using a physical change to a material, as is used for vinyl records and some CDs and DVDs. Signals can also be recorded using magnetic materials and their interaction with electromagnets. Optically encoded signals involve a change in the reflection or transmission of light from a material, including the analog signals used in older movie films and digitally recorded signals for newer recordings. Two examples of digital recording encoding are 1-bit and base-2 binary. Nyquist folding, used when sampling is too slow, is introduced.