It raises a question: Is it really appropriate to shift the changes in circular ether towards the s orbital side and the rest towards the p orbital side for comparison? Could combining changes involving linear ether reveal their own patterns? Perhaps a more objective comparison is needed. Let's revisit the arrangement of values in helium.

s and p Orbital of Helium
s and p Orbital of Helium

In the previous section, we shifted the graph of s orbitals, which only have circular ether, to one reference point and moved the rest, with linear ether, towards the p orbital side. The new criterion to be proposed is to create coordinates from these two shifted graphs. By considering the graph shifted with [O] as 0 and the graph shifted with [-] as 100, the positions of the points will be marked. It is about placing the top purple line as 100 and the bottom red dot as 0 in the above diagram, and observing how the points move between them. By using this method, all points can be aligned based on a single criterion. Let's call this the “Between,” and let the previous one be called the “Transform.”

However, the above diagram cannot be used as is. What we want to understand is not the position of the points, but rather how much they have changed from their previous values. Therefore, we will use1x2−1(x+1)2\dfrac{1}{x ^ 2}-\dfrac{1}{(x + 1) ^ 2} instead of 1−1(x+1)21-\dfrac{1}{(x + 1) ^ 2}.

The bottom graphs serve as the reference
The bottom graphs serve as the reference
Rl(x)=r(1(x+kh)2−1(x+kh+1)2)R_{l}(x) = r(\dfrac{1}{(x + k_{h}) ^ 2}-\dfrac{1}{(x + k_{h} + 1) ^ 2})
R(x) with highest k
Rh(x)=r(1(x+kl)2−1(x+kl+1)2)R_{h}(x) = r(\dfrac{1}{(x + k_{l}) ^ 2}-\dfrac{1}{(x + k_{l} + 1) ^ 2})
R(x) with lowest k
Rh(x)−Rl(x):100=px−px−1−Rl(x):vR_{h}(x) - R_{l}(x) : 100 = p_{x} - p_{x-1} - R_{l}(x) : v
→v=100(px−px−1−Rl(x))Rh(x)−Rl(x)\to v = \dfrac{100(p_{x} - p_{x-1} - R_{l}(x))}{R_{h}(x) - R_{l}(x)}

Let's see if a pattern emerges

Hydrogen

Betweens in the Hydrogen Orbital Values
Betweens in the Hydrogen Orbital Values 2S1/2
Betweens in the Hydrogen Ether Values
Betweens in the Hydrogen Ether Values 2S1/2

Hydrogen exhibits patterns on both sides. This is because hydrogen is an element with very small errors that can be explained by the Rydberg formula.

Helium

Betweens in the Helium Orbital Values
Betweens in the Helium Orbital Values 1S0
Betweens in the Helium Ether Values
Betweens in the Helium Ether Values 1S0

The changes in the orbitals show a slight decrease and a slight increase, but it can be considered as noise. The variation in ether, on the other hand, is clearly evident. Let's examine elements with higher numbers to better observe the extent of the changes.

Higher Atomic Numbers

Betweens in the Beryllium Orbital Values
Betweens in the Beryllium Orbital Values 1S0
Betweens in the Beryllium Ether Values
Betweens in the Beryllium Ether Values 1S0
Betweens in the Sodium Orbital Values
Betweens in the Sodium Orbital Values 2S1/2
Betweens in the Sodium Ether Values
Betweens in the Sodium Ether Values 2S1/2
Betweens in the Cesium Orbital Values
Betweens in the Cesium Orbital Values 2S1/2
Betweens in the Cesium Ether Values
Betweens in the Cesium Ether Values 2S1/2

Commonly, it seems that the p orbital exhibits some irregularities, and there is still a clear pattern in the ether classification. If we were to create an equation based on this, we might need to treat p as an exception. As we go to higher elements like cesium, even d orbitals become exceptions.

Both in Transform and Between, there is a common trend. Shifting the Rydberg formula seems to yield predictions with relatively low errors. Even in these small errors, the ether classification method shows a more distinct pattern than the traditional orbital classification method. While this is not a conclusive proof, it suggests the possibility that the ether classification method might provide clearer patterns than the traditional method. This concludes the demonstration.