what does the triple tau actually symbolise in the Royal Arch

The triple tau, formed by three tau crosses conjoined at their feet, serves as the emblem and badge of the Royal Arch 1. Symbolic explanations of the emblem focus on the nature of the Deity, geometry, sacred history, and spiritual distinction.

In traditional ritual lectures, the symbol's intersecting lines form angles corresponding to mathematical combinations equal to the five Platonic bodies, which represent the four elements and the sphere of the universe 1. Symbolically, its three united taus signify the threefold nature of the Deity as one God whose three aspects share the attributes of each other 2.

Albert C. Mackey suggested that the emblem draws upon the tau mentioned in Ezekiel as a mark of salvation, acting as a sign of distinction that separates those who know and worship the true name of God from those who remain ignorant of that mystery 1.

In a paper read in 1887 by C. W. Shackles, writing in The Freemason, the triple tau is further stated to signify the Temple at Jerusalem (Templum Hierosolymae) and to mean the key of knowledge.

Monogrammatic origins of the emblem trace back to the eighteenth century, where the letter T was placed over the letter H as an abbreviation for Templum Hierosolymae, Latin for the Temple of Jerusalem 1. This T over H badge was formally specified for the Royal Arch apron in the Charter of Compact of 1766, the founding document of England's first Grand Chapter, and was documented during that period by Thomas Dunckerley as standing for Templum Hierosolymae.

In a paper read before the Lodge, Bernard E. Jones explained that the triple tau developed directly from this T over H monogram rather than originating as three conjoined T's. E. Comp. Harry Mendoza, writing on the Warwickshire Freemasons' website, records that the emblem visually evolved into the modern triple tau shape between approximately 1810 and 1821, as the letters lost their serifs and the vertical stem of the T dropped down to rest upon the crossbar of the H. Albert C. Mackey noted that the phrase Templum Hierosolymae was long recognised by scholars of the Order as the Latin phrase concealed under the monogram 1.

Albert Mackey and George Oliver differed in their symbolic interpretations of the triple tau, though they held common ground regarding the historical origin of the Royal Arch degree itself.

In an article by Albert G. Mackey hosted on Phoenixmasonry, Oliver is described as believing that the triple tau—by virtue of its connection with the circle and triangle in the Royal Arch jewel—was intended to typify the sacred name as the Author of Eternal Life. Mackey recorded Oliver's interpretation among various speculations without affirming agreement. Instead, Mackey proposed his own view based on the mark of the tau in Ezekiel, arguing that the triple tau serves as a mark of favorable distinction separating those who know and worship the true name of God from those ignorant of that mystery 1.

Regarding the historical origin of the degree, the two scholars shared a unified perspective. An article on the Grand Lodge of British Columbia and Yukon website records that both Mackey and Oliver maintained the theory that the Third Degree had been mutilated to create the Royal Arch degree.