**I read with interest** the feature article “Dynamic similarity, the dimensionless science” by Diogo Bolster, Robert Hershberger, and Russell Donnelly. The authors give a simple example of dimensional analysis of the deflection of a light beam passing through a star’s gravitational field. But the example stretches the possibilities of dimensional analysis beyond its true limits. In fact, the deflection angle could be any nontrivial function of the dimensionless fraction *Gm*/*c*^{2}*r*. Thus at least one more assumption outside dimensional reasoning must be made—the simplest solution, as the authors imply in the given example.

A nontrivial solution may be demonstrated by performing the same exercise with the Planck law, which gives the radiation spectrum emitted by a blackbody. The relevant quantities are wavelength *λ*, temperature *T*, spectral emittance *B _{λ}*, speed of light

*c*, Planck’s constant

*h*, and Boltzmann’s constant

*k*. According to the Buckingham Pi theorem, two independent dimensionless quantities can be formed using this list of quantities. An example of a solution is

One dimensionless quantity forms the left-hand side of the equation; the second, independent one occurs in the exponent of the denominator of the Planck law. Such a result could not be found by dimensional reasoning alone.