If x ∝ y, y ∝ z and z ∝ x. Let us find the relation among three constants of variation.

Given: x ∝ y , y ∝ z and z ∝ x

It can be written as,

x = k y, y = m z and z = n x

where k, m and n are constant of variations.

Put the value of y in x,

We get,

x = k m z

Now put the value of z in x,

⇒ x = k m n x

⇒ k m n = 1

This is the required relation among three constants of variation i.e. k, m and n.