1) In Wright the ‘sign-tree’ or ‘sine-tree’ is explained firstly as ‘one of the principal timbers of a roof’, and secondly as the ‘centerings of an arch’ (EDD).
The word was in use in both Lancashire and Yorkshire. As no examples are quoted, either there or in the OED, the following references to its use as a roof timber are of interest. In 1817, a Slaithwaite diarist called Hirst wrote of damage to the ‘thack’ or roof of his house: he had been awakened in the middle of the night by a very loud noise and discovered that the sine tree [had] slipped out of the mortis in the balk end. In 1686, the accounts for the building of an extension to a house in Conistone mention Fower paire of finetrees [sic for sinetrees?] bought of … John Piccard. In this case the dimensions of the timbers are given as 10 inches deep and 5 inches in thicknesse. In 1739, 1 pair of signtrees at Lofthouse measured 10 fot and cost one shilling. The following references support the idea that ‘sine-tree’ and ‘sign-tree’ share the same origin as ‘centre’. For example, signetrees were required for the arches of Elland Bridge in 1579 and in 1698 one paire of senters referred to timbers for Pickering tithe barn. In 1747, sintrees for Clapham church bridge were listed in the same context as the frame and the arch. The semantic change can perhaps be explained by the fact that both meanings carry the idea of ‘load-bearing timbers’, and the orthographic connection may be via the word ‘tree’, commonly used in the past instead of ‘wood’ or ‘timber’. As ‘sine’ is an early and alternative spelling of ‘sinew’, Wright plausibly suggested that it was the first element in ‘sine-tree’ but the Yorkshire evidence points to an alternative explanation.