Unpublished paper, 'On the Abelian systems of differential equations, and their rational and integral algebraic integrals, with a discussion of the periodicity of their Abelian functions' by W R [William Ralph] Westropp Roberts Before entering on the discussion of the Abelian system of differential equations, Roberts treats of some general algebraic theorems having reference to the differences of various sets of 'facients', and gives a wider definition to the term 'source', hitherto used to signify the source of a covariant, and treat of two operators, δ and ∆. He then shows how, by forming a 'square-matrix', all the conditions can be obtained which are fulfilled when a polynomial f(2) of the degree 2n in z is a perfect square. With regard to these conditions, Roberts remarks that any one of them being given all the others can be found by successive operations of the operator δ. Subject: Mathematics / Algebra Received 17 January 1895. Read 7 February 1895. Communicated by G [George] Salmon. Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 57 of the Proceedings of the Royal Society as 'On the Abelian system of differential equations, and their rational and integral algebraic integrals, with a discussion of the periodicity of Abelian functions'. 1895