The effect of hydrostatic pressure (P≤5.1 kbar) on the metamagnetic transition of heavy-fermion ${\mathrm{UPt}}_3$ has been investigated by means of high-field magnetoresistance measurements (B≤28 T) at a temperature of 2.0 K. The transition, which occurs at ambient pressure for a field directed in the hexagonal plane at ${\mathit{B}}^{\mathrm{*}}$=21 T, shifts upwards with pressure at a rate of 0.60 T/kbar. The deduced magnetic Grüneisen parameter, ${\mathrm{\Gamma }}_{\mathit{B}}$=-∂ ln${\mathit{B}}^{\mathrm{*}}$/∂ lnV equals 59. The value for ${\mathrm{\Gamma }}_{\mathit{B}}$ falls well within the range of values reported for the thermal Grüneisen parameter, 52≤${\mathrm{\Gamma }}_{\mathit{T}}$=-∂ ln${\mathit{T}}^{\mathrm{*}}$/∂ lnV<71, which verifies directly a close relation between the thermal and magnetic energy scales.

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