472 dellinger: planck's constant c 2 



PHYSICS. — The calculation of Planck's constant C 2 . 1 J. H. 

 Dellinger, Bureau of Standards. 



This constant, which is of great importance in high tempera- 

 ture measurements and in atomic theory, has heretofore been 

 obtained from radiation data by processes involving the use of 

 a graph. It may be calculated directly and very simply from 

 any two observations. A solution of Planck's equation for C 2 in 

 terms of the ratio of energies at any two wave lengths and 

 temperatures is readily obtained, C 2 appearing in a correction 

 term in the solution. The various relations which have been 

 used for obtaining C 2 from radiation data are deducible as special 

 cases. 



The equation for two observations of wave length at constant 

 temperature is of special interest; the following approximate 

 expression is sufficiently exact for most cases. 



2 = 



X2 — Xl - 



log — + 5 Jog — — e \ 2 

 J] Xi J 



An approximate value of C 2 always suffices for the last term. This 

 general method of solution is superior to the method of equal 

 ordinates. No curve has to be drawn, and the calculations are 

 not limited to particular pairs of points. The method is more 

 powerful in determining whether an observed curve fits the 

 Planck equation. In fact, curves which give normal values for 

 C 2 by the method of equal ordinates were found to give very 

 high values when calculations were made by this method for 

 two points both on the same side of the maximum. 



Points on the Planck curve for which Wien's displacement law 

 holds, in particular the maximum of the curve, have been con- 

 sidered as furnishing additional ways of determining C 2 . Such 

 methods are debarred by lack of accuracy, and in fact these 

 special points may themselves be obtained most accurately and 

 conveniently by the same process of using two observations 

 which is used for obtaining C 2 . Substantially the same simple 

 equation suffices to determine C 2 and all the special points. 



1 Detailed paper to appear as Bureau of Standards Scientific Paper No. 287 

 (Bull. Bur. Stds., 13: 535-545). 1916. * 



