Unpublished paper, 'Researches on the theory of invariants' by William Spottiswoode Invariants may be regarded from two points of view, the permutational and the functional. According to the former they are considered as arising from a process of permutation, according to the latter as derivatives from other functions. Spottiswoode adopts the latter course, and demonstrates his method. Annotations in pencil and ink throughout. Subject: Mathematics Received 20 December 1854. Read 18 January 1855. Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 7 of the Proceedings of the Royal Society as 'Researches on the theory of invariants'. 1854