Spencer Heath Archive

Item 58

October 1944

 

Original is in item 56.

 

Divide any mass-motion product by the time involved to get the mass-motion product pertaining to one unit of time. (M x Mo)/T = Ratio of mass-motion to time. The quantity of energy flowing through one unit of time. Multiply this quantity of energy (mass-motion) by its duration and we have energy multiplied by time or “action.”

Mass = 3   Motion = 2   Time = 1

(3 x 2)/1 = 6 = Rate of Energy per unit of time or quantity of “action” during a unit quantity of time.

dynes           cm         sec

    Mass 12     Motion 9    Time 8

 

     Energy = dynes x cm = 12 x 9

     = 12 x 9 = 108 dyne-centimeters or ergs.

 

Energy in relation to time is (12 x 9)/8 = 13.5 ergs per second. 13.5 is the number of ergs per second.

 

12 dynes having a velocity of 9/8 = 1 1/8 centimeters per second equals 12 x 9/8 = 13.5 ergs per second.

 

13.5 is a quantity of energy. In the present case it is also the quantity of energy per unit of time or rate of energy. Since the action continued for 8 seconds the quantity of action is 13½ ergs x 8 seconds = 108 erg-seconds.

 

12 dynes   9 centimeters   in 8 seconds

12 x 9 = 108 ergs of energy in 8 seconds = 13.5 ergs if it had happened in one second. If it had all happened in one second it would have been 8 times as much per second = 8 x 108 ergs = 864 ergs in one second, and that would have been at the rate of 864 ergs per second.

But, as it was, that rate per second was only 13.5 ergs per one second and 8 x 13.5 = 108.0 ergs in 8 seconds. If it continued for 8 seconds at the rate of 13.5 ergs per second the quantity of energy would be 108 ergs at the end of 8 seconds. 12 dynes x 9 centimeters is a quantity of energy, namely, 108 ergs. If this energy is spread out over 8 seconds, then there will be only 13.5 ergs for each second. The rate will be 13.5 ergs per second and since it continued for 8 seconds at this rate the total amount of energy was 8 x 13.5 = 108 ergs.

 

If 108 ergs happen in 8 seconds the frequency of the 108 ergs is .125 per second — 1/8 of a flow per second. Now if I multiply the energy in ergs by the frequency it gives 108 x .125 = 13.5

If 108 ergs is the packet of energy and this is multiplied by the frequency of the packet, then 108 x .125 = 13.5 which is the number of ergs per second or rate of energy

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Units     Webster’s

a     Unit acceleration, a = V/T  an acceleration of one centimeter   per second each second.     (L VT) /See original; could not                                        transcribe this symbol./

F     Unit of force,  F = M x a , a force which acting for one

second upon a mass of one gram increases its velocity at the rate of one centimeter per second. (L M VT) Called a dyne. Approx one milligram.

Force is considered a fundamental quantity and mass as a

quantity derived thus: M = F/a.

Unit of mass is then defined as a mass which when acted on by unit force for one second has its velocity changed at the rate of one centimeter per second.

 

The Erg     Dimensions of the physical quantity are given

           in parentheses.

Unit of kinetic energy, W = Mv²/2

     The energy of a mass of one gram moving with a velocity of one centimeter per second L²M Vt  called erg.

Unit of momentum, M x v . The momentum of 1 gram moving with a velocity of 1 centimeter per second LM/T^-1  V/2

 

Unit of power, P = W/T, the power when work is done at

the rate of one erg per second  (L² MT^-3) = L² M³ Vt

 

    Unit of Work (Erg), F x L , the work done by a force of one dyne acting through a distance of one centimeter. (L²MT^-2) = L²m Vt  ??? Ho time element

 

An erg is simply a dyne-centimeter. Just like a foot-­pound or pound-foot. The number of Ergs in a body at any velocity is the same as the number of centimeters it would have moved under a force of one dyne to attain that velocity. Simply the number of dyne-centimeters in it.

An erg is only a force (dyne) times distance, motion (centimeter. It is mass and motion without duration, there­fore only an abstraction that can be conceived but cannot be experienced outside of the mind. Real energy is energy that can be experienced as an objective unity of mass, motion and time.

A dyne-centimeter (erg)-second is an actual amount of energy. It is a quantity of energy (action) in terms of the three units of mass-length-time. It is thus a three-fold unit—

 

Mass units   1

Motion units 1     Energy units 1

Time units   1

The three are not multiplied together unless there are more units than one each. When the factor is one there is no multiplication.

 

Units of force or mass (Unit quantities)

Unit of Work (Unit quantities)

Units of Power (Rate of Work—quantity of work per unit of time)

 

1 Pound 1 Gram 1 Dyne

1 Pound-foot

 

1 Dyne-centimeter or Erg

1 Horsepower—(minute)

(33000 pounds feet per minute) 1 Horsepower-hour

(Sixty horsepower minutes) 1 Pound-foot per minute 1 Dyne-centimeter per second or one erg per second

 

Quantities of Energy (Rate of work times duration)

 

Horsepower x minutes Horsepower hour x hours Pound-foot per minute x minutes Dyne-centimeter per sec or erg per second     x seconds