136 PROCEEDINGS OF THE AMERICAN ACADEMY 



Compare now the experimental values before given with the four 

 series of values below. 



The third and fourth fail to satisfy condition (2), as this condition 

 was discovered too late to change our figures, but they will serve 

 equally well for illustration. 



It will appear at once that wliile the first two curves lie very close 

 to the experimental curve, and parallel with it, even such close approx- 

 imations to the one-term equation as those above cut at an angle. The 

 use of residual curves will make the fact still clearer. Equations of 

 three, four, or more terms, will yieUl like results. 



Even if an equation could be found of this kind which was equally 

 good %\ith the simple form, it would still be improbable that the sim- 

 pler should not be the form preferred by nature. 



Since then the temperature is shown experimentally to be constant 

 along the family of curves ry"'r^ = e, a function f(v) can be found, 

 the same for all bodies, whose derivative in any direction in a given 

 body, when multiplied by a constant quantity depending on the nature 

 of the body, measures the flux of heat in that direction. 



* Computed. t Approximate. 



