DISCUSSION OF LARSON’S
GRAVITATIONAL EQUATION
As brought out at the recent convention, some confusion
has arisen over Larson’s gravitational equation, eq. (2) of the original
edition of the Structure of the Physical Universe:
The correct expanded version of this equation is

(m × 3.7115 x 10^{32})
× (m’ × 3.7115 x 10^{32})


F = 
—————————————————

(2)


1521 × 1015 × (s/1)²


where 3.7115 x 10^{32}
sec³/cm³ is the value of the natural unit of mass and m and
m’ are simply numbers. The number .1521 x 10^{15}
sec is the natural unit of time. From equation (2), the natural value
of the gravitational constant can be determined:
G_{n.u.}= (3.7115 × 10^{32})²/.1521
× 10^{15 }= 9.0567 x 10^{48
} 
(3)

Thus equation (1) might better be written as
F_{n.u} = 9.0567 × 10^{48}
mm’/s² 
(4)

where all values are in natural units. The expression for G in equation
(3) can be converted to conventional units. First, the cgs system:

^{ }F_{n.u}.s_{n.u}.² 

dynes 
G^{cgs} = 9.0567 ×10^{48} 
———— 
× 109.7 
——– 

m_{n.u}² 

F_{n.u} 

(.456 x 10^{5 }cm 
m_{n.u}² 
× 
—————— × 
—————— 

s_{n.u}² 
(.5565 x10^{24 }g 
= 6.67 x 10^{8 }dynes
cm²/g² 
(5)

The MKS system

F_{n.u}s_{n.u}² 

N 
G_{MKS }= 9.0567 ×10^{48}

———– 
109.7 10^{5 } 
—— 

m_{n.u}² 

F_{n.u} 

(.456 × 10^{7 }m)² 
m_{n.u}² 
× 
—————— × 
——————— 

s_{n.u}² 
(.5565 × 10^{27 }kg)² 
= 6.67 × 10^{11 }Nm²/kg² 
(6)

Both check. The importance of this cannot be overestimated. These equations
completely confirm Larson’s identification of all the fundamental
units.
Note that if in equation (2), the value 3.7115 ×
10^{26 }sec³/m³ 

is used then the correct time value must be .1521 × 10^{3}
sec for the denominator (or 10^{12} units
of time).
