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tokens: , and replace the bulge with a rotating bar using the analytic model from Long Murali ( 1992 ). For the bar parameters, we take a mass of 5 × 10 9 M ⊙ , a length of a = 3 kpc, a width of b = 1 kpc, and a present-day orientation of θ 0 = −30° (as in Hattori et al. 2016 ; Erkal et al. 2017 ). We vary the pattern speed between 0 and −100 km s −1 kpc −1 in steps of 0.1 km s −1 kpc −1 (where negative pattern speeds are prograde with the MW disc), more than encompassing the observed constraints on the pattern speed (e.g. Bland-Hawthorn Gerhard 2016 ). We find that the bar has a small effect on the stream, giving slightly different stream tracks depending on the pattern speed of the bar. Thus, the properties of the bar will also need to be marginalized over in order to measure the LMC mass from the misaligned proper motions. 5.4 Effect of LMC on other streams in the Milky Way The predicted misalignment between the stream track and proper motions should also be seen in any streams which receive a large tidal force from the LMC. Given the orbit of the LMC, we expect that the most affected streams will likely be in the southern Galactic hemisphere, e.g. the 11 streams newly discovered in Shipp et al. ( 2018 ), the Phoenix stream (Balbinot et al. 2016 ), the Jet stream (Jethwa et al. 2017 ), or the atlas stream (Koposov et al. 2014 ). In order to determine which are the most affected, each stream will need to be evolved in the presence of the LMC. Interestingly, some works have proposed assuming that stream tracks are aligned with their proper motions to measure the Sun’s proper motion (Majewski et al. 2006 ; Malhan Ibata 2017 ). If the significant misalignment predicted for the Tuc III stream is verified, this means that these methods must account for the perturbation of the LMC or only use streams which have received a negligible perturbation (possibly those in the northern Galactic hemisphere). 5.5 Effect of Tuc III on the Milky Way disc Our analysis in Section 3 found that Tuc III is on a very eccentric orbit with a pericentre of ∼1.8 kpc. This close passage of Tuc III with the MW could induce perturbations in the inner disc of our Galaxy (Feldmann Spolyar 2015 ). For these perturbations to be significant, Tuc III would have needed a substantial mass of ∼10 8 −10 9 M ⊙ and hence would have to be a dwarf galaxy. Given the current data, it is difficult to determine whether Tuc III is a globular cluster or a dwarf (see Li et al. in preparation). However, assuming that Tuc III is a dwarf, if Tuc III’s recent pericentre was its first approach to the MW (and thus Tuc III still retained the bulk of its dark matter halo) there could be detectable perturbations in the MW centre. We note that although we have assumed a disruption age of 3 Gyr, during which our best-fitting orbits have experienced multiple pericentric passages (e.g. Fig. 3 ), our model is not designed to determine when Tuc III began disrupting. Instead, it is designed to match the observed