The relationJn′(x)Nn′(kx)−Jn′(kx)Nn′(x)=0arises in certain resonant cavity problems having cylindrical symmetry. The first roots of this relation are presented here as a function ofkforn= 1, 2, 3, 4. The M'Mahon relation does not allow calculation of the first roots despite statements to the contrary in several places. It is shown that the functionsJn′(x)/Nn′(x)have relative maxima atx = nexcept forn= 0.