20 TWO NEW WOKLDS 



world are increased 10 33 times, in order to account 

 dynamically for the motions we actually observe. 



We may therefore tabulate the various units in 

 the two worlds as follows : 



In the infra- world the unit of 



Length is reduced .... 10 22 times. 



Time is reduced 10 2 ' 



Velocity is unchanged . 



Mass is reduced 10 55 



Area is reduced 10 44 



Volume is reduced . . . . 10 66 



Acceleration is increased . . . 10 12 



Mechanical force is reduced . . 10 3S 



Density is increased .... 10 11 



The above calculations may appear somewhat 

 abstruse, and the immense quantities denoted by 

 the exponential figures may appal some readers who 

 are not used to deal with figures on that scale. 

 But it should be remembered not only that such 

 figures enter into the daily calculations of as- 

 tronomers, who practise what is acknowledged to 

 be the most exact of all sciences, but that their 

 manipulation, once acquired, is extremely easy and 

 peculiarly elegant. We are dealing with quantities 

 on a very small, instead of a very large, scale, and 

 the exponential notation enables us to " think in 

 millions" (or in millionths) with the same ease 

 and certainty as we experience in dealing with the 

 simple multiplication table. As a rule, indeed, our 

 operations are confined to addition and subtraction. 



