Émilie du Châtelet2× The Speed. 4× The Dent.

The sticker says 2× The Speed. 4× The Dent. In the 1720s that was an argument conducted in clay.

Natural philosophers of the early 1700s fought over what a moving body carries. Followers of Descartes measured it as mass times speed. Followers of Leibniz said mass times speed squared, which Leibniz called vis viva, living force.

In Leiden, Willem 's Gravesande put it to the test by dropping balls into soft clay, after similar work by Giovanni Poleni. Balls of the same size but different masses made identical dents when their drop heights were inversely proportional to their masses. The height needed grows as speed squared, so equal dents meant equal mass times speed squared, not equal mass times speed. A ball arriving twice as fast does the same damage as one four times as heavy.

Émilie du Châtelet put this experiment at the heart of the chapter on the force of bodies in her Institutions de physique (1740). She describes a ball of mass 3 at speed 1 beside a ball of mass 1 at speed 3, the faster making by far the larger dent, and argues for vis viva. She reported and championed the experiments; they were 's Gravesande's. On this sticker she drops the balls herself, which is our dramatic licence.

Clay did not really settle the quarrel. Momentum and energy are both conserved, both useful, and measure different things. Mass times speed squared survives, halved, as kinetic energy. Du Châtelet also translated Newton's Principia into French. It was published in 1759, ten years after her death, and is still the leading French translation.

The dents here are drawn at exactly one to four. Double the speed, quadruple the dent.