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For Planck's law per unit frequency, setting $x=h\nu /(k_{B}T)$ leaves a positive constant times $x^3/(e^x-1)$. Its logarithmic derivative givesThe same uniqueness argument as in the Derivation of Wien's displacement law, with $5$ replaced by $3$, selects the positive root. The maxima differ because corresponding positive spectral intervals obeyThe nonconstant Jacobian determinant $c/{\lambda }^2$ changes density heights. Consequently $c/{\nu }_{\max }=(x_{\lambda }/x_{\nu }){\lambda }_{\max }\simeq 1.75978{\lambda }_{\max }$. A peak is a property of a specified density, rather than an invariant point of the spectrum. For equal logarithmic intervals, the corresponding densities satisfy $\lambda B_{\lambda }=\nu B_{\nu }$ and have matching converted peak positions; this is a third convention, distinct from either linear-interval density.