THE FORCES OF THE INFRA-WORLD 1 9 



v. This is a purely kinematical theorem; but 

 in order to account for it dynamically, we must con- 

 sider the forces at work in the infra-world. 



Now, centrifugal force is proportional to the square 

 of the velocity of the revolving body, and inversely 

 proportional to its distance from the centre of 

 attraction. In symbols, F=^g- where ra is the 

 mass, V the velocity, and R the radius of the orbit. 

 Now, in descending into the infra-world, V remains 

 substantially the same, m is reduced 10 55 times, and 

 R is reduced 10 M times. Hence the centrifugal force 

 is reduced to 10" 33 times the force, say, between the 

 earth and the sun. 



How is this force balanced ? The distance between 

 two bodies in the infra-world is 10 22 times less than 

 between two bodies in this world, and hence the 

 gravitational force must be multiplied by 10 44 . But, 

 on the other hand, the gravitational force is pro- 

 portional to the product of the masses, which are 

 both reduced 10 65 times. Hence the gravitational 

 attraction is in the infra- world ] } Rpri or on ^y 

 10~* times what it is with us. This is 10 88 times too 

 small to balance even the reduced centrifugal force 

 of 10~ M dynes found above. Still, if our dynamical 

 :s hold good and everything we know 

 points in that direction wo may be sure that that 

 attractive force of 10~ M dynes is somehow provi 



s that all central forces -in the infra- 



