 An infinitesimal rotation of the molecule is given by
where Δφ is an infinitesimal angle, Δφ » (Δφ)², and formula_27 is an arbitrary unit vector.From the orthogonality of formula_28 to the external space follows that the formula_20 satisfy
Now, under translation
Clearly, formula_20 is invariant under translation if and only if
because the vector formula_25 is arbitrary.So, the translational Eckart conditions imply the translational invariance of the vectors belonging to internal space and conversely.