Inspired by a problem posed in a 1924 issue of English Mechanics and the World of Science, Martin Beech has written a book covering a variety of geophysical notions related to the shape, density and internal structure of Earth. Humans have never penetrated much below Earth's surface, so Beech spends most of his time discussing thought experiments, particularly those that involve bodies falling through the interior of Earth. Along the way Beech touches on numerous discoveries, speculations and fictional expositions related to Earth's structure.

The first few chapters lay out what Beech calls ‘Cymro's problem’, which involves describing the motion of a body falling along a tunnel through a uniform spherical Earth, and its solution via Newtonian mechanics. Beech then segues into a discussion of the geology and temperature of Earth's interior, from Athanasius Kircher's fire caverns to the realization that Earth is heated internally by the decay of radioactive nuclei. The next set of chapters focuses on three Astronomers Royal: Nevil Maskelyne, John Flamsteed and George Biddell Airy (in that non-chronological order). It seems that Maskelyne may have originated Cymro's problem with a question published in the Ladies Diary in 1781, and may have been inspired to do so because of a deep well Flamsteed had dug at Greenwich for use in observing stellar parallax around 1679. Airy comes into the story because in 1826 he attempted to measure differences in the period of a pendulum, on Earth's surface and at the bottom of a mineshaft, in hopes of determining Earth's density, but Beech quickly moves on to Henry Cavendish's more successful experiments and a digression on the period of a pendulum with a length that exceeds Earth's radius.

The following chapter presents an argument against flat-Earth theories, though it is unlikely that any of Beech's readers will subscribe to such theories, and if they do they may not find his argument against them fully convincing. Beech then discusses literary accounts of Earth's interior from Verne to Burroughs to Flammarion. Then begins a series of chapters devoted to the history of physics and astronomy with connections made, whenever possible (and in some cases straining possibility), to Cymro's problem. Beech discusses ancient Greek attempts to determine the size of Earth, medieval ideas about motion, Galileo's Two New Sciences and Dialogo (in that order), the debate between Hooke and Newton over the path of a body falling through Earth, Edmond Halley's proposal that planets may be hollow (to explain their densities), and the efforts of Maupertuis and others to measure the shape of Earth. Beech makes sure to mention Maupertuis's proposal to dig a tunnel to Earth's core (and Voltaire's ridicule of that idea), but he neglects to mention Galileo's idea that falling bodies follow a semicircular path ending at Earth's centre.

The next several chapters connect Cymro's problem to various areas of engineering, mathematics and physics. Beech discusses proposals for using gravity tunnels as a transit system (doomed because of air resistance), the relation between Cymro's problem and the famous brachistochrone and tautochrone problems, actual attempts to drill deep into Earth (as well as the possibility of a self-tunnelling capsule that uses heat to melt its way down), and the motion of a black hole oscillating around Earth's center while accreting mass. The penultimate chapter of the book provides further discussion of flat-Earth, as well as hollow-Earth, theories and the author's attempt to demarcate psuedoscientific claims from scientific thought experiments that, like Cymro's problem, may be impossible to carry out in practice but still provide some real insight into the workings of nature. The book closes with a chapter that leaps from satellite measurements of Newton's gravitational constant, to gravity tunnels on other planets, to the idea of drilling through the surface ice on Europa and Enceladus, to actual drilling through the Antarctic ice above Lake Vostok.

Beech's writing is generally clear and engaging. Although some mathematical content is relegated to an appendix, there is quite a bit (e.g. trigonometric, exponential and logarithmic functions, as well as differential equations) in the main text. His science is generally good, but readers of BJHS will likely find his historical material superficial and in some cases erroneous (like his claim that the Copernican theory bruised humanity's ego because it displaced Earth from the centre of the universe). Citations are almost exclusively to secondary literature, although Beech mentions several primary sources without citing them (even for direct quotes), making the book less useful as a guide to further historical study. Perhaps the most interesting bits, from a historical perspective, are Beech's exploration of early popular-science journals and textbooks (Chapter 5) and his discussion of speculative accounts of Earth's interior in fiction (Chapter 9) and non-fiction (Chapter 21). As the listing of topics above suggests, the book does not adhere to any coherent structure but is instead a series of fascinating vignettes. Most of the topics are related to Cymro's problem and the interior structure of Earth, but not all (e.g. neutrinos, parallax, Richard of Wallingford's clock and the principle of least action). Beech has given us something like a flight of ideas, in which he hops from topic to topic while making some insightful commentary but occasionally missing opportunities to delve deeper. There is no doubt, though, that Beech enjoys his material. His book, like the fin de siècle popular-science magazines that inspired it, is a potpourri of ideas and questions that, although it provides no overarching argument or deep historical insight, will delight readers interested in how we can think about, if not actually explore, the interior of Earth.