Some miscellaneous topics pertaining to economic measurement are discussed, including the idealized "units" (dimensions) of economic variables; the effect that quarterly and annual averaging can have on the time series properties of a variable; and how growth rates are computed by U.S. statistical agencies.

It is important to limit statistical testing of context–mechanism–outcome configurations (CMOCs) to those which are most plausible. This is because testing too many hypotheses will lead to some false positive conclusions. Qualitative research conducted within process evaluations is a useful way to inform refinement of CMOCs before they are tested using quantitative data. Process evaluations aim to examine intervention implementation and the mechanisms that arise from this. They involve a mixture of quantitative (for example, logbooks completed by intervention providers) and qualitative (for example, interviews or focus groups with recipients) research. Qualitative research can be useful in assessing and refining CMOCs because intervention providers and recipients will have insights into how intervention mechanisms might interact with context to generate outcomes. These insights might be explored directly (for example, by asking participants how they think the interventions works) or indirectly (for example, by asking participants about their experiences of an interventions, and the conditions and consequences of this). Sampling for such qualitative research should ensure that a diversity of different participant accounts is explored. Analyses of these accounts can draw on grounded theory approaches which aim to build or refine theory based on qualitative data.

In this chapter, a concept known as scaling is introduced. Scaling (also known as nondimensionalization) is essentially a form of dimensional analysis. Dimensional analysis is a general term used to describe a means of analyzing a system based off the units of the problem (e.g. kilogram for mass, kelvin for temperature, meter for length, coulomb for electric change, etc.). The concepts of this chapter, while not entirely about the fluid equations per se, is arguably the most useful in understanding the various concepts of fluid mechanics. In addition, the concepts discussed within this chapter can be extended to other areas of physics, particularly areas that are heavily reliant on differential equations (which is most of physics and engineering).

Dimensional analysis for stratified turbulence defines the variables describing turbulence in the ocean, which are then used with the Reynolds decomposition to develop equations of motion and define key parameters, such as turbulent kinetic energy and the viscous dissipation rate. These are used in developing the Kolmogorov energy cascade and the accompanying cascade of scalar variance. Considering turbulent evolution and decay leads to consideration of strongly stratified turbulence and pancake eddies. Turbulent intermittence and statistics include expressions for estimating confidence limits. The turbulent equations are then used to develop expressions for estimating turbulent eddy coefficients from what can be measured. The chapter ends with a consideration of mixing efficiency.

James Clerk Maxwell’s field theory of electromagnetism had important and previously unrecognized roots in the cable industry of the mid-nineteenth century. When he took up electrical physics in 1854, the subject was permeated by a concern with cable problems. Guided by William Thomson, Maxwell soon adopted Faraday’s field approach, which in 1861 he sought to embody in a mechanical model of the electromagnetic ether. Seeking evidence to bolster the electromagnetic theory of light to which this model had led him, Maxwell joined the British Association Committee on Electrical Standards, which had been formed in 1861 largely to meet the needs of the submarine telegraph industry. Maxwell’s work on the committee between 1862 and 1864 brought home to him the value of framing his theory in terms of quantities he could measure in the laboratory—particularly the “ratio of units”—rather than relying on a hypothetical mechanism. Maxwell’s shift from his mechanical ether model of 1861 to his seemingly abstract “Dynamical Theory of the Electromagnetic Field” of 1864 thus reflected the often overlooked role concerns rooted in cable telegraphy played in the evolution of his thinking.

The majority of physics problems are impossible to solve by analytic means. Various strategies have been developed to cope with the highly non-linear nature of many of these problems. Dimensional analysis provides a powerful tool for addressing many complex problems, suggesting the form the solutions must have. Examples include the non-linear pendulum, explosions, flow at high Reynolds number and the law of corresponding states. The study of chaotic phenomena became feasible with the development of high speed computers and revealed regularities despite the apparent unpredictability of the systems. Scaling laws for extremely complex and non-linear problems lead to the concept of self-organised criticality, illustrated by the model computations for rice and sand piles.