Duration Time

   (Frequency)

Units

Appreciable Unappreciable Indivisible Equal

Let us suppose that there are ultimate units respectively of Mass, Velocity and Duration (period).

Then, in the quantum there is some number of each of these ultimate units.

And, the product of these three numbers is the quantum unit h — one quantum

This product is the number of sub-quantum units that constitute the single quantum unit.

The respective numbers of sub-quantum units are either equal or they are unequal.

When they are equal, each is the cube root of the whole number of sub-quantum units.

Let N represent the whole number of sub-quantal units.

 

(1) Then N^1/3 x N^1/3 x N^1/3 = N^3/3 = N sub-quantal units.

There cannot be less than one sub-quantal unit in any of the three quantal categories of Mass, Velocity and Period. Then in (1) above we divide N^1/3 by itself — N^2/3 — to express a single sub-quantal unit of Mass. We then multiply velocity by N^1/3 (to preserve the quantum whole).

So, when mass is minimum, velocity is squared.

1 x (N^1/3)² x N^1/3 = N^3/3 = N.  1 x 4 x 2 = 8

Likewise we may preserve the quantum whole by squaring the Period — 1 x N^1/3 x N^2/3 = N^3/3

                                                            ^{1      2      4      8}            

/Note: Some additional calculations were assumed to be preliminary to this and were not transcribed from the original./