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tyranny. Thus during the critical years before 1775, when resistance to London’s attempt to impose taxes on its colonists began to create a distinct sense of being American, two different struggles for democracy were building against two different governments—the colonies against Britain, and western farmers against east coast authority.
    In Pennsylvania, the attempt by Penn and his heirs to regain control from Cresap and his fellow banditti began with a prolonged legal battle in London to have the boundaries in their royal charter drastically revised. Not until 1732, long after Penn’s bankruptcy and death, did they succeed in persuading the Court of Chancery in London, the senior English court dealing with equity and contracts, to shift the entire commonwealth of Pennsylvania south. The northern boundary was now to be the forty-second degree, and the southern was to run exactly fifteen miles south of Philadelphia along a line that did intersect the arc round New Castle.
    Once more, what seemed clear-cut on a map proved impossibly complicated on the ground. For thirty years the difficulties of drawing straight lines, arcs, and tangents across the curvature of the earth and getting them to meet at the right point bamboozled the best surveyors in the colonies. Eventually Penn’s heirs agreed with the Calverts, the earl of Baltimore’s family who owned Maryland, to share the enormous cost of having a definitive boundary run by the eminent British astronomers Charles Mason and Jeremiah Dixon .
    The pair had already worked together on the world’s first great international scientific project, the observation of the 1761 transit of Venus across the face of the sun, an enterprise that involved scientists from most of the nations of Europe. Although they had successfully viewed the phenomenon from Cape Town, the restless, inquisitive Mason, forever striking up conversations with strangers and traveling, as he put it, “for curiosity to see thecountry,” appeared to be an odd match with the dour, concentrated Dixon, who rarely stirred far from his precious telescopes. Nevertheless, in the four years from 1763 to 1767, the two of them not only untangled the geometrical confusion around Philadelphia, but more impressively solved the problem of running an accurate parallel or line of latitude due east-west, a feat never before accomplished in North America, and probably not in Europe.
    Although the United States’ longest frontier is a parallel, as are the top and bottom borders of many states, it is easy to overlook the fiendish challenge each presented its maker—to draw a straight line across the rounded surface of the globe. At sea, mariners would simply follow a constant compass bearing—270 degrees to head due west—but on land ordinary compasses became too unreliable due to magnetic variation, the presence of mountains, and the action of other distorting forces. Until the invention of the solar compass in the 1840s, a boundary-maker intent on the utmost accuracy had to rely on celestial navigation. But then, a second, more horrible predicament presented itself—on the surface of the three-dimensional earth the shortest line between two points lying east and west of each other is not straight but, paradoxically, a curve, known as a Great Circle or a circumference of the globe (see appendix).
    The complex solution found by Mason and Dixon was to run a Great Circle from one observation point to the next, a distance of about a dozen miles, then track back along the line of the parallel. Close to a week of star sightings was required at each point, and the use of the finest scientific instruments in the British empire. The combined wealth of the Penns and Calverts had purchased for them a six-foot-tall, vertically suspended telescope known as a zenith sector, a transit and equal-altitude instrument, and a Hadley quadrant, all constructed in brass and mahogany with achromatic lenses