Primacy of AtomicNumberPlusValence versus AtomicWeight
The realization of an inverse integral relationship between atomic and hydration numbers respectively, in combination with the observation of an improved order of agreement when atomic numbers are adjusted per unit valence, led to Flint's adoption of use of Z+C as measure of relative mass, in preference to Atomic Weight.
The below table (AW versus Z versus Z+C) exhibits calculations of hydration numbers using each of three ions as the base ion (H+, Rb+ or La+3) in each of three sets of calculations, inputting Atomic Weights, versus Atomic Numbers, versus Atomic Numbers + Valence, respectively. Thus, within the first set of calculations, that inputting Atomic Weights, for the middle column using Rb+ as the base ion, the result is that which is also illustrated in the paper "Direct Calculation of Hydration Numbers for the Lighter Ions"; the other columns merely substitute H+ and La+3 resp. as the base ion in place of Rb+; and the other sets of calculations substitute Z or Z+C resp. for AW:A
As is shown, the order of agreement between calculations using all three base ions is clearly preferable using Z+C versus either Z or AW:
INPUT: AW (Atomic Weights)  INPUT: Z (Atomic Number)  INPUT: Z + C (Atomic No. + Valence)  
BASE =  H+  Rb+  La+3  H+  Rb+  La+3  H+  Rb+  La+3  
OH  0.77  0.21  0.01  0.59  0.32  0.19  0.19  0.23  0.21  
H+  0  0.17  0.25  0  0.08  0.13  0  0.01  0.04  
Li+  4.19  18.84  24.7  7.87  14.68  18.23  17.73  16.65  21.22  
Be++  2.88  13.69  18.01  5.63  10.69  14.74  12.75  11.95 


Na+  1.45  10.18  13.67  3.77  7.83  9.94  9.5  8.86  11.58  
Mg++  1.08  8.86  11.97  3.14  6.75  9.59  8.09  7.52  9.95  
Al+3  0.23  5.74  7.95  1.78  4.34  6.31  5.07  4.66  6.38  
K+  0.9  3.15  4.77  0.36  2.25  3.23 