SOME CONTEMPORARY ADVANCES IN PHYSICS-X 109 



reasons with all the necessary background without too long a stoppage 

 of the main current of this argument.- I must therefore set it down 

 as an assertion, that the selection-rule is deducible from the assump- 

 tion that the value of k is the Azimuthal Quantum-number of the 

 valence-electron; which thus is 1 for all the Stationary States of the 

 s-sequence, 2 for each State belonging to the /^-sequence, 3 for the 

 (i-sequence, and 4 for the /-sequence. The feature common to the 

 various Stationary States of a sequence is, therefore, the Azimuthal 

 Quantum-number of the valence-electron — if this atom-model is valid. 

 This being assured, the conclusion is drawm that, since k is higher 

 for the /-terms than for the (/-terms, higher for the (/-terms than 

 for the ^-terms and higher for the ^-terms than for the 5-terms; since, 

 therefore, the /-orbits are ceteris paribus more nearly circular than 

 the (/-orbits and less inclined to stretch down into the neighbor- 

 hood of the kernel, the (/-orbits more nearly circular than the />-orbits 

 and the ^-orbits more nearly circular than the 5-orbits — therefore 

 the approximation of the sodium terms to the hydrogen terms will 

 be most nearly perfect for the / (and higher) sequences, less so for 

 the d, less for the p and worst for the 5-terms. This also is verified. 

 It reinforces the opinion that the ^-values assigned to the various 

 sequences are actually their azimuthal quantum-numbers. 



As the different States of a single sequence share a common Azimu- 

 thal Quantum-number, they must differ — supposing alw^ays that this 

 atom-model is valid— in their Total Quantum-number. Consecutive 

 States of a sequence presumably have consecutive values of the 

 Total Quantum-number (although sometimes one meets with a break 

 or a jolt in the continuity of a sequence, suggesting a departure from 

 this rule). The meanings of the Total Quantum-number n and of the 

 Azimuthal Quantum-number k for elliptical orbits are such, that n 

 can never be less than k. Hence the value of n for the first Station- 

 ary State of the 5-sequence may be unity, or greater; but the values 

 of n for the first terms of the /^-sequence, the (/-sequence and the /- 

 sequence may not be less than 2, 3, and 4, respectively. 



Strange as it may seem, there is no perfectly satisfactory way of 

 determining the value of n for all Stationary States. Generally 

 it happens that the various States of an /-sequence, that of sodium 

 for example, agree so closely with those States of hydrogen which 

 form an nt sequence, that there is little hesitation in attaching to 

 each of the /-States the same value of n as is borne by that State 

 of the hydrogen atom which coincides with it so nearly. For instance, 



2 These being (verbum sapieiiti) the argument associated with the name of Rubino- 

 wicz, and the argument deduced from the Principle of Correspondence. 



