## Mathematical Geography by Willis Ernest Johnson

Before the advent of coordinated universal time and internationally-recognized time zone boundaries, practical, day-to-day considerations of time measurement quickly became entangled in geographical, political, historical, and legal problems of surprising recalcitrance.

If you live in the northern hemisphere, does the sun pass due south of you every 24 hours? Perhaps surprisingly, no! An hour is 1/24 of a sidereal day, the time required for the earth to rotate once with respect to the stars. Because the earth orbits the sun, the sun’s position on the celestial sphere traverses a circle once per year. Consequently, the mean solar day is shorter than the sidereal day by a factor of roughly 1/365.25: The sun therefore passes due south on average every 23 hours, 56 minutes, 4 seconds. The actual length of the solar day varies seasonally because the earth’s orbit is not circular and the dates of perihelion and aphelion (when the earth is closest or furthest from the sun) do not coincide with the solstices (when the north pole is tipped most nearly toward or away from the sun).

A related phenomenon is said to have confounded Ferdinand Magellan’s crew briefly upon return to Spain after circumnavigating the globe. Their careful reckoning gave the date of September 6, 1522, but the Spaniards assured them the date was the 7th. Eventually the crew realized they had lost a day over their long voyage by traveling west, with the sun. Today we would say Magellan lost a day crossing the date line.

Civilizations successfully used local (solar) time for millennia. Only when consistent time measurements were required over extended longitudes did standard time become important. Of course, time standards were not immediately or universally adopted. Consequences ranged from minor confusion for travellers to legal cases with substantial financial stakes.

During the late Nineteenth Century in the United States, railroads and cities used their own time conventions for many years. When Mathematical Geography was written, the vicinity of El Paso Texas used four systems of time, due to the confluence of three U.S. time zones and an entirely separate Mexican standard time used in Juarez, across the Rio Grande.

In 1902, thirteen lawsuits were brought in the courts of Kentucky over the wording of fire insurance policies. In one case, the policy expired at noon on April 1, 1902, but left unspecified whether solar or standard time was to be reckoned. On the date in question, a warehouse fire began at 11:45 A.M. standard time, namely at 12:02:30 P.M. local time. Nearly \$20,000 of insurance money hung in the balance of the court’s decision. Such improbable occurrences were not as rare as one might expect. Willis’s book does not divulge the outcome of these cases, but does highlight the need for pedantic attention to issues we might all regard as too obvious to warrant detailed consideration.

In the modern world of the global positioning system, universal time, and largely undisputed geopolitical boundaries, we easily forget that divisions of time and space are nothing more than social agreements. The earth has no intrinsic clocks convenient for international travel and commerce, nor many geographical features that unambiguously separate neighboring states, provinces, territories, or countries.

Mathematical Geography is not a mere catalogue of amusing events and curious factoids, but a clear, engaging, and systematic exposition of the shape and movement of the earth as an astronomical body, and the consequences for time-keeping, map making, and geodesy. Written in 1907 for use in American secondary schools and for teacher preparation, the book intertwines purely scientific issues of astronomy and geography with the historical growth of the United States in the 1800s as the political entity expanded across the North American continent, and with then-current legal and practical issues related to time and place. Much of the factual content is up-to-date, and even the remainder should be of historical interest.

Despite the book’s imposing title, the mathematical content is light, entailing only trigonometry, plane geometry, and basic algebra. Mathematical Geography is easily accessible to a modern reader with a good high school education. A curious and intelligent younger reader can also learn much, skipping brief mathematical derivations as needed or even learning useful mathematics in a realistic context.

This enjoyable book deserves, and earns, the attention of anyone who wants to understand more about the planet we inhabit and how the earth’s shape and motion affect our daily lives.

This review was contributed by DP-volunteer adhere.

### One Response to Mathematical Geography by Willis Ernest Johnson

1. Sue Clark says:

Sounds like an interesting book. I’ll have to remember to mention it to my DH–he loves this type of book.