Laws are mathematical functions in the form of a formula. They are used to define how resulting objects are modified.
They are composed and selected in the Laws Editor which is specific to each tool that uses laws and can be opened from that tool.

To use a law:

1. Open the Laws Editor.
2. Select the desired law in the Laws table by double-clicking and press OK. The law that is applied is what is in the formula field.  

To create a law:

1. Type the desired formula into the formula field.

2. Press the + (plus) button.  

3. Type in a titke for the law and press OK. The new law will appear in the Laws table

To Delete a law:

1. Open the Laws Editor.
2. Click on the Law in the Laws table to select it.
3. Right click and select Delete, or press the - (minus) button.

Laws cannot be edited but double click a law will load it into the Formula field where it can be altered and then a new altered law added.

f(u)

In the Offset tool the function are defined as a function of U. Where U is the distance along the object being offset. Therfore the function is dependant upon the direction that the object is drawn. You can determine the direction by looking at the vertex values in the Selection Info palette. 
The effect of the formula is added to the Offset Distance.

Examples:

All of these examples are set with the Offset Distance set to Zero (0). 

Setting f(u) = u

Setting f(u) = 2

Setting f(u) = cos(u)

Setting f(u) = u

Notice that the distance between the start and end of the resulting spiral is ~Pi since the diameter of the original circle is 1.0.