THE FORCES OF THE INFRA -WORLD 21 



3. We have now laid a solid foundation for our 

 knowledge of this newly-discovered world. We see 

 that, while the appearances remain the same, the 

 central forces must necessarily be different, and 

 must, indeed, vastly exceed the mechanical forces 

 we are familiar with. If we take the visible universe 

 as it is, and reduce all its dimensions in the same 

 ratio, and accelerate the rates of revolution of the 

 various celestial bodies in the same ratio, so as to 

 keep their absolute velocities the same as before, 

 we find that this cannot be done with the simple 

 gravitational attraction as we know it. We must 

 have a more powerful centripetal force. 



We can give a simple illustration in the case of 

 the earth and the moon. Let all their dimensions 

 be halved, and let their velocities and densities re- 

 main the same as before, Then, since the volume 

 of each body will be one-eighth of what it was, its 

 mass also will be one-eighth, and the gravitational 

 ction, being proportional to the product of the 

 masses, will be ^Vth of the present attraction. On 

 the other hand, their distance will also be halved, 

 and this will increase the gravitational attraction 

 four times. So that on the whole we have a centri- 

 petal force one-sixteenth of the present force. 



As regards the centrifugal force, this is propor- 

 tional to m ^ , and depends only upon the revolving 

 body. Now V is the same as before, m is reduced 



