John Napier, who is also credited with inventing logarithms and pioneering the use of the decimal point, first published his rule in 1614. While spherical trigonometry was the foundation for many scientific pursuits including astronomy, celestial navigation, geodesy (the measurement and mathematical representation of the Earth), architecture, and other disciplines, Napier’s Theorum remained largely unknown in America because of its complexity. Since it was so important to his own scholarly pursuits, Jefferson, the Sage of Monticello, was the perfect person to school a professor friend on this important, but complicated mathematical formula.

For instance, a navigator’s distance and position can be determined by “solving” spherical triangles with latitude and longitude lines—essentially very large triangles laid out on a curved surface. Astronomers apply similar principles; stargazers imagine the sky to be a vast dome of stars, with triangles laid out on curved (in this case concave) surface. The distance of stars can be calculated by the viewer, who is considered to be standing at the center (the Earth) and looking up at stars and planets as if they were hung on the inside surface of the sphere. In architecture, spherical triangles fill the corner spaces between a dome that sits on foursquare arches—called a dome on pendentives.

Thomas Jefferson, long since retired to private life, declines the request of Dr. James Mease for copies of Dr. Benjamin Rush’s correspondence with Jefferson. Mease had hoped to include them in a volume of Rush’s letters to be published and specifically requested letters pertaining to Rush’s personal views on religion and politics. After demurring, Jefferson discusses at length the differences between personal and official correspondence, with philosophical thoughts on public versus private expression. He closes with assurances that his decision is nothing personal, and of his great respect for Mease: “I hope, my dear Sir, you will see in my scruples only a sentiment of fidelity to a deceased friend.”

The intricate design of this handkerchief features images of Washington, Adams, and Jefferson, beneath an eagle and flags. In the center appears the text of the Declaration of Independence, together with facsimiles of the signatures. An oak wreath with acorns surrounds the text and features images of the seals of the thirteen original states. An image at lower left depicts the Boston Tea Party with the caption, “The Patriotic Bostonians discharging the British Ships in Boston harbour.” An image at lower right depicts “General Burgoyne’s Surrender to General Gates at Saratoga.” Around the edge runs a stars and rope border with anchors at each corner and at the center of each side. The design was printed with red ink using a copper plate.

The design draws much from prints of the Declaration of Independence by William Woodruff, published in February 1819, and John Binns, published in October 1819.