In 1976, when S. Gibbs published her survey and catalogue, Greek and Roman Sundials, she included 256 objects – already an impressive number. But there has been an explosion of new finds (some archaeological, but many from the re-finding in museums of objects that had never received proper publication). The online catalogue of the Berlin research project ‘Ancient Sundials’ now lists 667 objects (http://repository.edition-topoi.org/collection/BSDP). The dials in the Gibbs and Berlin catalogues are for the most part of stone and were intended to be used in a fixed position.

But the ancients were also ingenious in devising sundials that were small and convenient enough to carry about as a portable timekeepers. Vitruvius, in a list of dial types and their inventors (De arch. 9.8.1), alluded to them. In 1969, when D. De Solla Price published ‘Portable Sundials in Antiquity, Including an Account of a New Example from Aphrodisias’ (Centaurus 14, 242–66), he listed 11 known artefacts. Recently, K. Schaldach was able to list 26 (in A. Jones [ed.], Time and Cosmos in Greco-Roman Antiquity [2016], p. 91). T.’s book is focused on the 16 objects that he classifies as ‘geographical portable sundials’. He calls them ‘geographical’ (p. 19) because they include one or more geographical names and usually the associated numerical values of the latitude, inscribed as an aid to the user. T.’s long Chapter 2 contains a catalogue of the 16 known geographical portable dials, with good photographs of most of them. (In the cases of several, the dials have disappeared and they are known only from eighteenth- or nineteenth-century drawings and descriptions.) Much of the remainder of the book explores the meanings of these sundials. As T. remarks, many sundial publications have focused on the technical details of their design, mode of use and accuracy. But a large enough corpus now exists that we may practically interrogate it to see what we can find out about the mentalities and cultural practices of the makers and users of these dials. In particular, he argues that there was a change in mentality, as people learned to ‘think latitudinally’ (p. 167).

The great majority of ancient sundials were designed for use in a single clima or latitude. Early Roman dial enthusiasts were often oblivious of this fact. According to Pliny (HN 7.213), in the third century bce the Romans took a sundial from Catania in Greek Sicily to Rome and set it up in the Forum. For nearly a century, no one objected that it was designed to tell the time in a different latitude. And, among the hundreds of surviving stone dials, it is not unusual to find one that was recovered from a location well removed from the latitude for which it was designed. The ancient Greeks and Romans specified latitude in three different, interconvertible ways. Most popular in everyday life, from the Hellenistic period and well into the Roman period, was a specification in terms of the length of the longest day of the year. One might say that the Hellespont lies in the clima of 15 hours, because the sun is up for 15 hours on the day of the summer solstice. A second way of specifying latitude was in terms of the length of the shadow of a vertical gnomon on the day of the equinox. A number of equinoctial shadow lengths are preserved in Pliny and Vitruvius. For example, at Athens, at noon on the equinox, the shadow is ¾ of the length of the gnomon. Astronomers also measured latitude in our fashion, in terms of degrees, by specifying the altitude of the celestial pole. It is a simple theorem of geometry that the altitude of the celestial pole above the horizon at any place is equal to the latitude of that place (angular distance of the place from the plane of the equator). But, as T. points out, there is no large body of geographical latitudes specified in degrees before Ptolemy's Geography (second century ce), though Ptolemy's predecessor Marinus, whose works are lost, used latitudes in our fashion, too. T. argues that the Geography helped change the way in which people thought about their locations on the globe, and that they began to think latitudinally. The length of the solstitial day is not directly proportional to the latitude – and neither is the length of the equinoctial shadow. (The relations are mathematically more complicated.) Thus, thinking in terms of degrees more readily gives one a pictorial sense of north–south distances.

Even some portable dials were also intended for use at a single latitude. This is true of the cylinder dial (sometimes called in modern times a shepherd's dial). When one wants to tell the time, one takes the detachable gnomon from the inside of the cylinder and inserts it into a hole in the side meant to receive it. One holds the cylinder upright (or sets it down on a horizontal surface), then turns it so that the gnomon faces the sun and its shadow falls vertically along the side of the cylinder. One then selects the curve for the proper month for reading the time. This dial can be carried about, but will only function correctly near the latitude for which it was designed.

Much more sophisticated are the portable dials that Vitruvius characterised as πρὸς πᾶν κλίμα – ‘for every latitude’. Of these, by far the most common are the dials that J. Bonnin calls ‘portable dials of Type 6’ (La mesure du temps dans l'Antiquité [2015], p. 108). The great majority of T.’s geographical portable dials are of this type. These are metal and disk-like in form. One must set the suspension for a particular latitude. To facilitate this, there is an inscribed list of cities, with their latitudes, usually found on the back. On the surviving dials of this type, the number of locations ranges up to three dozen. Having set the suspension for the particular latitude, the user must now turn a vane that carries the shadow-casting gnomon so that it indicates the correct part of the year. Finally, holding the dial from its suspension ring, the user turns it until the shadow of the gnomon falls along the curved edge of the vane and reads off the time by means of the hour marks engraved on the vane.

T. analyses in detail the lists of places. He shows, for example, that they contain only cities and regions – never rivers, mountains, capes or lakes, although these figure in Ptolemy's Geography. And this shows us how people thought about the defining geography of the empire. A study of clusters of names may also tell us something about how the makers and users visualised the interiors of regions. T. claims that in the case of several dials the cities are arranged in order of an imagined itinerary.

Because T. focuses more on mentalities than on the technical details, it is not too surprising to see a minor slip in technical matters. In the description of the workings of the most common type of πρὸς πᾶν κλίμα dial, T. writes (p. 16) that the shadow of the gnomon vanishes at noon and is longest at sunrise or sunset. Actually, it is just the reverse – after all, the gnomon is a horizontal rod. It must be said, however, that the functioning of this particular dial is complicated (it functions differently in the morning and the afternoon, for example, and during most times of the year it tells only approximate time) and that many writers on dials have slipped a little when discussing this one.

The book concludes with sections addressing the utility of knowing the time in Antiquity (in astrology, for example), the diffusion of knowledge and design features among dial makers, and echoes of the ancient traditions in some post-classical objects.