Newton's Scala Graduum Caloris. A Numerical Simulation

Abstract

Sir Isaac Newton, in the Scala graduum Caloris, published in 1701, presented a scale with “the degree of heat” of the bodies which extended the measurements far beyond the values available at that time. To determine it, Newton followed two paths. The first was by using an expansion thermometer with linseed oil as the liquid, whose measurements followed an arithmetical progression, but its maximum was limited by the inflammation of the oil. The second using a completely new method, which consisted of measuring the cooling times of a body previously heated in a small kitchen fire, and relating these times to the temperatures according to a new law, which gave rise to a new scale that followed a geometric progression. Both scales were partially overlapped, allowing him to extend the arithmetic measurements up to more than six times the water boiling point. This new law is known as Newton’s Cooling Law.

Here, we intend to carry out a numerical simulation of the hot body cooling process, conjecturing the instruments he may have used and the environmental conditions in which it took place. All this following what Newton himself reflects in his article. We will end with some reflections on the law, which we believe he enunciated in an integral manner.