38 TWO NEW WORLDS 



ously; but the dimensional calculus again gives us 

 a rapid method of arriving at the new quantities. 



We have seen that the units of length and time 

 are reduced 10 22 times, thus leaving the velocities 

 unchanged. Volumes are reduced 10 66 times, but 

 masses only 10 65 times, thus implying a density 10 11 

 times greater than before. Electric charges are 

 diminished as the square root of the mass, i.e., 10 27 * 6 

 times. The increase or diminution of any other 

 physical quantity is deducible from these four, and 

 a complete set of the physical constants of the infra- 

 world is thus obtained by multiplying the new units 

 in accordance with the dimensional formulae. I 

 append a table below. The first column gives the 

 physical quantities, the second their dimensions, 

 and the third the extent to which they are increased 

 (positive index) or reduced (negative index) in the 

 infra-world. The electrical formula} are taken from 

 my ''Electron Theory" (p. 296). 



Time T 10' 22 



Length L 10~ 22 



Area L 10-" 



Volume L 3 ICT 66 



Angle A = LL-! 1 



Angular velocity AT- 1 10 22 



Velocity LT' 1 1 



Acceleration LT~ 2 10 22 



Mass M 10-" 



Force MLT~ 2 10~ 33 



Moment ML 2 T- 2 10~ M 



Work . ML 2 T~ 2 1(T 55 



