Fine points on heat-conduction experiment

In his otherwise excellent article “Thermal Conductivity Through the 19th Century” (PHYSICS TODAY, August 2010, page 36 ), T. N. Narasimhan has erred in his description of an experiment of heat conduction and dissipation in a rod heated at one end (see his figure 1 and caption). He reports an experiment that was performed by Guillaume Amontons and described by Johann Heinrich Lambert; ¹ however, Narasimhan mistakenly attributes the experiment to Lambert. In fact, Lambert converted and plotted Amontons’s data and fit them with an exponential function. That is made clear on pages 185 and 186 of Lambert’s text.

Narasimhan later states that the distances along the rod are given “with units unspecified.” As may be seen from the German text in the figure, the units are given as “linien,” or lines, converted from the units Amontons used, namely, “Pariser Zollen und Linien,” or Parisian inches and lines. I have found three values for the length of the “line” (“ligne” in French). The 11th edition of the Encyclopædia Britannica ² gives it as 0.089 inch or 2.2606 mm. The French edition of Wikipedia states two values, ³ 2.268 mm (the value through the year 1667) and 2.256 mm (the value from 1668 onward). That value is also given by François Cardarelli. ⁴ Since Amontons was born in 1663, he most probably used the 2.256 value. Thus it seems safe to say that to convert lines to millimeters in Narasimhan’s figure 1, the values of the x coordinate should be multiplied by 2.26.