Dr. Alfred's Partheil's Paper, Page 11

We can therefore put A.W. / o = i, from which the above mentioned formula A.W. = o * i follows without further ado.

We saw that for most elements the interval numbers we calculated correspond satisfactorily with the ones we found, mostly even surprisingly well. In some cases the correspondence is less pleasant. In two cases there are not enough intervals to cover all elements. Cerium and preasodymium as well as osmium, iridium, platinum and gold do not find enough space in the 8th. Octave. At the moment I have to leave it open, whether these difficulties found within the periodic system can be overcome by a future more accurate determination of the atomic weights, or if they are caused by choosing the wrong octave numbers. Maybe they will disappear if we use a different element than oxygen = c as the "basic note". These calculations can be very difficult and time consuming; outer circumstances have so far prevented their execution.

Now I would like to draw your attention to an interesting part of the system of elements. Iodine with its atomic weight of 126.85 should have its place in the periodic system before tellurium, which surely has an atomic weight higher than 127. Only numerical inconsequence allows the application of the systematic here. We have a similar situation with argon and potassium. Our table of intervals is showing the interval cb for iodine and the interval b# for tellurium. Although with the other notes the interval of the sharp lower note is smaller than that of the flat higher note, the interval of fb is smaller as e# and cb is smaller than b#. This almost matches the situation with iodine and tellurium, but argon and potassium still do not fall in the right place, but one note too low.

Maybe this difficulty can be overcome with an appropriate calculation.

When you rise to the tower on winding stairs, it appears to you
often the same picture, but it expands always.
The same, you mostly come, when rising in the reign of knowledge
Back to a well known thing, but see it heightened.

Gentlemen, I have shown you today in a new light something already known. The clarification of the simple relationships of the apparently irregular atomic weight numbers to each other and to the frequencies of the notes seems