When the Edinburgh and Northern Railway (E&N) and the Dundee and Perth Railway (D&P) were seeking Parliamentary approval in 1845, it was proposed by their engineers that from Perth both should share a line running along the south bank of the Tay as far as Newburgh, where the D&P would cross to the north bank, and the E&N leave the Tay and head south to a ferry crossing of the Forth. Matthew had been in a very small minority supporting this, and the D&P as built crossed the Tay at Perth. In 1864, when a bridge crossing the Tay at Dundee was proposed, Matthew urged that a bridge at Newburgh was preferable to a bridge at Dundee, a Newburgh bridge giving much the same reduction in the rail distance between Dundee and the Forth ferry-ports from which passengers could cross to Edinburgh as a bridge at Dundee but doing so by a shorter (and therefore cheaper) crossing of the Tay. He argued the costs of a Dundee bridge were being grossly under-estimated: "To erect a substantial bridge, not a flimsy spectral thing, which might or not vanish as a phantom the first storm, or break down under the vibration caused by a heavy, rapid, moving train, would, in my opinion cost nearly double, and probably much more than double, the sum the Engineer states; upon this I stake my judgement against that of the Engineer", noting in passing, "from the geological indices, I would expect the foundation to be more regular at Newburgh than at Dundee, consequently better".