Sometimes, he combatted his loneliness and the monotony of the work by solving mathematical problems in his head. He was in an advanced math class at Boston Latin, and had been privately tutored after hours in high-school algebra and quadratic equations. Clipping a sponge into the desired spherical or oblong shape, he would contemplate the mathematics of its curves—the elegant sweep of parabolas between vertical and horizontal axes. Or he would ponder the theory behind celestial navigation. Will did not have the faintest idea about the theory—why bother, when the Nautical Almanac and the Reduction Tables had worked all the problems for you? But, Drew had wondered, what would a navigator do if, by chance, he lost the Almanac and Tables? Will’s edition of the American Practical Navigator contained an explanation of the astronomical triangle and complex trigonometric formulas that, if mastered, allowed you to calculate your position without reliance on the reference books. He studied it at night, but with all the arcane terms—cosine course, sine of the course angle, secant of the course angle—it was as impenetrable to him as to Will, the difference being that the impenetrability nagged him while it troubled Will not at all. It isn’t necessary to reinvent the wheel, Will said; yet Drew wanted to.

Sort. Clean. Clip. Haul the traps up. Lower the traps down. Stack unfinished sponges in the drying shed. Stow the finished ones in the storage rooms, Drew musing upon the aspects of the theory that were within his grasp. The sextant reading measures the height of a star, let’s say Vega, he would think. Ninety degrees minus the reading equals the distance between the observer’s position and Vega’s geographic position over the earth. But why? How? He made a mental picture of a diagram in Will’s celestial navigation textbook: the globe and three lines. One line plunged vertically from the north pole to the imaginary center of the earth and represented the zenith angle, 90 degrees; the other two represented the observer’s sextant angle and the angle of the star’s geographic position. So, what’s really being measured isn’t the actual height of the star, he said to himself, but the internal angle of its GP with the zenith line, which should equal the difference between the observer’s sextant angle and 90 degrees. If the sextant angle is 50 degrees, then Vega’s internal angle is 40 degrees, and 40 degrees of arc over the earth’s surface equals 2,400 nautical miles, because there are 60 nautical miles in each degree of arc.… Therefore, the observer’s position is 1,400 miles from the point on the earth where Vega is directly overhead.