Spencer Heath Archive

Item 699

Pencil by Heath on notepad paper.

September 23, 1957

 

Assume some Mass in grams as so many dynes.

Then, let M stand for so many dynes of force.

Now, let 1 stand for the number of centimeters through which the dynes of force (M) act.

Now, let t stand for the time it takes the force d to act through distance 1.

Then 1/t is the distance 1 in one second (velocity)

When 1/t = velocity of light—rate of motion, action, and t is the time it takes,

Then 1/t x t = the whole distance.

Let (V) = velocity of light — 1/t = (V) = the number of centimeters in one second

Let (V) also stand for the number of seconds the force acts through (V) centimeters per second.

Then (V) x (V) = total distance 1

Then M—total number of dynes— x (V)² = total work done,

total number of dyne-centimeters — ergs

So then (V)² = number of ergs when the number of grams

or dynes is 1 — When M = 1

 

So 1 dyne acting at (V) velocity through (V) seconds has the energy to do (V)² ergs of work.   energy to act through (V)² centimeters or (V)² ergs.    1 dyne through

(V)² centimeters = (V)² ergs and (V)² dynes through 1

centimeter also equals (V)² ergs

 

So if either of these is done in one second it will be 1 erg-second, and, if repeated, will be at the rate of (V)² ergs per second — (V)² ergs per second x the number of seconds

 

 

 

units of force   units of velocity   units of time   units of        in dynes         in centimeters      in seconds      work in    

                per second                       ergs

1 dyne    x       (V)       x        (V)     =    (V)²

A quantum of work is the least fraction of an erg. It is the fraction h of an erg or h ergs. Like the erg, it is composed of: units of force x distance l (units of velocity x units of time).

All quanta are equal, so, if there is a least or single indivisible unit of force, then when there is only 1 unit of force then velocity must be at its maximum and, conversely, when velocity is maximum there can be only 1 unit of force, hence under those conditions 1 quantum is composed of

units of force      units of velocity           units time

   least          units of motion

    per unit of time

1 sub-quantal       maximum number of            1 sub-quantal

fraction of a       sub-quantal fractions        fraction of a

dyne or gram       of a centimeter              second.

 

The product of these 3 components is h erg-seconds

When force is 1 dyne and velocity is 1 centimeter per second and time is 1 second, then the total action is 1 erg in one second.

But if the velocity is (V), then the number of dynes must be

 

1/(V) and (V)  and  1 second and

h  x  1/(V)  x (V)  x   1 = 1 quantum

or

1/(V)  x  (V)  x  h  x  1 = 1 quantum

In the quantum

When velocity is maximum, the composition is either

In its own units:

FORCE              VELOCITY             TIME

H = 1 sub-quantal  x   maximum number  x  1 sub-quantal
mass or force    of sub-quantal        time unit
unit             motion units

In G.C.S. units:

either

(1) 1/(V) dynes  x  (V) centimeters  x  1 second per second

or

(2) 1 dyne  x  (V) centimeters  x  1/V seconds

Reducing to quantum size:

 

(1)  h/(V)|  x  (V)  x  1 second

 

or

 

(2)  (V)  x  (V)  x  h seconds

(1) is least possible (imperceptible) force or mass with highest possible velocity at lowest frequency—longest period. (2) is largest possible force or mass with highest possible velocity at highest frequency — shortest period.

(1)  = h x (V) x 1

(2)  = (V) x (V) x h