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In this short note, we repeat the calculations the jumps for the specificheat C$_{\sigma_{xy}}$, the elastic compliance S$_{xyxy}^{\sigma_{xy}}$ and thethermal expansion $\alpha_{\sigma_{xy}}$ due to a shear stress $\sigma_{xy}$ inthe basal plane of $Sr_2RuO_4$. Henceforth we clarify some issues regarding theelastic theoretical framework suitable to explain the sound speed experimentsof Lupien et al. (2001,2002), and partially the strain experiments of Hicks etal. (2014), and Steppke et al. (2016) in strontium ruthenate. We continue topropose that the discontinuity in the elastic constant C$_{xyxy}$ of thistetragonal crystal gives unambiguous experimental evidence that thesuperconducting order parameter $\Psi$ has two components with a brokentime-reversal symmetry state, and that the $\gamma$ band couples theanisotropic electron-phonon interaction to the $[xy]$ in-plane shear stressaccording to Walker and collaborators [4] and [3]. Some importants words aboutthe roll of the spin equal to one for the transversal phonons are added in theconclusion following Levine [34].

Anisotropic shear stress $\sigma_{xy}$ effects in the basal plane of Sr$_2$RuO$_4$