This series largely comprises the notes of Robert Payne on mathematical and scientific subjects. It includes Payne's notes on other authors' works with page references as well as his own problems in geometry, optics, proportion, geometry of the circle, duplication of the cube and chronology. It includes notes on weights, coins and astronomy. There are some notes of Payne's on works by Hobbes (HS/C/3/5 and HS/C/4/2) which show the connection between the two and how Hobbes relied on Payne to improve his work.
Apart from the two items listed above and HS/C/2/1, HS/C/7/10, HS/C/7/11 which are in Hobbes's hand and HS/C/1/6 which is a scribal manuscript probably acquired by Hobbes, all other items in this collection are in Robert Payne's hand and represent a sizeable collection of primary source material left by Payne illuminating his interests, influences and exposure to other scholars as well as his way of working and note-taking in the field of mathematics and physics.
For a long period, Payne's notes were assumed by scholars to be the work of Hobbes on account of the similarity in hand between Hobbes and Payne. However, when Hobbes scholar K. Schuhmann consulted some of this material in the 1990s he noted to Peter Day, then keeper of Chatsworth Collections, that much of HS/C/7 was not like any of Hobbes' published works. Schuhmann believed the notes not to be in Hobbes's or Charles Cavendish's handwriting. And indeed later Noel Malcolm, identified the notes in this series as Robert Payne's and laid out the reasonings for this in a chapter of "Aspect of Hobbes" (2002, pp. 80-145).