DI = kIo
DI is the just noticeable difference between two stimuli.
Io is the reference stimulus
k is a constant.
If we define I* as the comparison stimulus then DI could be rewritten as |Io - I*|, where |Io - I*| is the smallest just noticeable absolute difference between two stimuli.
The above equation can be rewritten as
DI/Io = k which means that if you take the size of the just noticeable difference between two stimuli and divide it by the reference stimulus this fraction is a constant. In other words the larger the stimulus the larger a comparison stimulus has to be to be seen as just noticeably different.
For example. Suppose you had two lights and you wanted to know how much brighter (or dimmer) the comparison light had to be than the reference light for the two to appear just noticeably different. You would adjust the comparison light until it appeared either just noticeably brighter or dimmer than the reference light. Then you would plug the values of the reference and comparison lights in the above equations.
You'll find that the brighter the reference light, the brighter (or dimmer) the comparison light has to be to be seen as just noticeably different.