Dr. Alfred's Partheil's Paper, Page 6

the cubic roots of the atomic weights are divided up into 16 groups, the result is a wavelike line in which the waves have an approximate regularity. Just like other attempts to express the atomic weights through formulae, this one also fails because of the irregular differences.

Ramsay's exposition has prompted me over the last time to more intensely consider the problem of the numerical relationship of the atomic weights. During these considerations I found a solution to the mystery in the following way:
From an energetic point of view, assuming that matter is not an opposite of energy but that our human senses perceive certain forms of energy as matter, just as we perceive other forms of energy such as sounds, as warmth, as light, as electricity, then the thought is not far-fetched that also what we perceive as matter consists of a similar form of movement to those other forms of energy.

If we let a drop of water fall into a bowl of water, wave motions are triggered. Sounds, warmth and light have long been recognized as wave-like vibrations. The wave nature of electric vibrations has been proven through the famous experiments of Hertz. And through the investigations of Balmer, Ames, Kayser and Runge as well as von Rydberg we know that harmonic conditions also reign over the spectral lines. Shouldn't we be able to find at least traces of similar laws governing the form of energy called matter?

The further pursuit of this thought has led to surprising results.