4. A unit free physical law.

The physical law 


is unit free if it for all positive  holds that


if and only if

where qi are definied as in the previous part.

 The physical law


is unit free.

Proof: If we put 


we get




The law thus becomes


that is,


Remark: If x is given in centimeters and x is given in meters, we have that 


If t is given in seconds and t in minutes, we have that 


In this case, g is given in m/(min)2.