The historical connections between physics and music are discussed, and the questions “What is music?” and “What is physics?” are addressed. The area of overlap is presented as the topic for the remainder of the book. The use of numbers having limited accuracy, identified with units and possibly other qualifiers, to specify quantities measured by physicists is presented. Scientific notation and unit prefixes are reviewed.

In addition, even modest rotation rates can cause significant alterations to the internal structure of stars. Finally, knowing how stars are spun up and spun down is important if we are to study a star’s complete history, from a slowly whirling gas cloud to a swiftly spinning white dwarf or a millisecond pulsar.

Since this was about 50 times the Kelvin–Helmholtz time for the Sun, a non-gravitational source of energy was obviously required to keep the Sun shining over the age of the solar system. A hint of what that energy source could be was provided by the physicist Francis Aston in 1920.

Up to this point, we have mainly been treating stars as if they exist in splendid isolation. However, stars are frequently found in binary systems, with two stars orbiting their barycenter. If the stars are sufficiently close to each other, then they will be tidally distorted, destroying the spherical symmetry of the standard equations of stellar structure.

Article 102 of the UN Charter requires that every treaty shall be registered with the UN Secretariat, and published by it. Over 75,000 treaties have now been registered. The UN General Assembly has drawn up detailed regulations on registration, which the chapter summarises. It also explains the documents which should be submitted to the UN Treaty Section to register a treaty. Where there is a dispute as to whether an instrument is a treaty, the fact that it has been submitted for registration may be evidence of the intention of the states concerned as to its status. But registration is not of itself conclusive of its status. The UN publishes treaties which have been registered in the UN Treaty Series. Each state will also usually have its own treaty series, in which treaties which it has signed or to which it is a party are published. Examples are the UK Treaty Series (UKTS) and the Treaties and Other International Acts (TIAS) of the United States.

Since all stars other than the Sun are at a distance that is large compared to their diameter, discerning their detailed structure is challenging. In this chapter, we start with the Hoyle-ish assumption that a star is a pretty simple structure: a static, isolated sphere.

Treaties may be amended by agreement between the parties. Bilateral treaties can be amended more easily than multilateral treaties. Bilateral treaties will sometimes include a provision on amendment but, in the absence of that, the parties will often simply proceed to amend the treaty by means of an exchange of notes, with provision concerning the entry into force of the amendment. Multilateral treaties too will often have express provision specifying amendment procedures. The chapter analyses various examples of these, including the use of supplementary treaties or protocols. If there is no such provision, residual rules are provided by Articles 40 and 41 of the Vienna Convention on the Law of Treaties.

Sound in one-dimensional systems, pipes, is considered in the context of modeling of the physics of wind instruments. Acoustic impedances are defined, which are used to characterize a system’s response to a force. The convenience of using complex numbers, which have real and imaginary parts, to describe impedance for waves, which have an amplitude and phase, is presented. Reflection and transmission of sound at points where a pipe’s impedance changes are considered, along with how these lead to resonances. The differences between sound propagation in cylindrical, conical, and Bessel horn-shaped pipes are presented. A model pipe with periodic holes is used to model the finger holes found in woodwinds. Such a pipe exhibits a critical frequency below which the impedance is imaginary, resulting in reflection, and above which is real-valued, allowing sound to propagate. An explicit example is shown using simple calculations for a fife, illustrating that the critical frequency becomes important for the upper range of woodwinds. A solution method for more advanced pipe models is presented. One more advanced model is that used for the human vocal tract, which can be modeled with pipes and acts as a time-dependent filter.

The Vienna Convention on the Law of Treaties remains the yardstick for the interpretation of treaties. International tribunals generally base their decisions on Convention rules, although, as different areas of law with their own dispute settlement systems have developed, there are also particular approaches. The Convention rules are contained in Articles 31--33, and the chapter focuses on these. Each element of the general rule of interpretation in Article 31 and the supplementary means of interpretation in Article 32 is analysed, including the role of subsequent agreement or subsequent practice. Further sections summarise other supplementary means of interpretation and look at treaties in more than one language.