Probable Values ofe,h,em, andα

Calculation of general physical constants.—The calculation of the general physical constants offers a rich and almost untouched field of investigation. In general each equation for the calculation of a given constant contains also other general constants, and therefore does not, strictly speaking, evaluate any one of them. In 1929 the writer solved this problem by a method of successive approximations, i.e., the constant first evaluated was that one least dependent on others. This constant then became an auxiliary constant, of known magnitude, in the equations for other constants. The method breaks down when the probable error of any auxiliary constant is not small compared to the experimental error. This is the case in the calculation of $h$, which always involves $e$ and in which the error in $h$ is usually due mainly to the error in $e$. The present paper gives in detail a logically correct method for the simultaneous evaluation of $e$ and $h$, from the several known functional relations between these two constants. The method was suggested first by W. N. Bond, but was not carried by him to its logical conclusion. The writer also disagrees with portions of Bond's calculations and with the final values of the constants that Bond adopts.