Chiefly correspondence with Alexander John Gaspard Marcet on chemistry, with references to Sir Joseph Banks, Jean Francois Berger, Johan Jakob Berzelius, Jean-Baptiste Biot, and others; a few letters to and from John Bostock, Thomas Cooper, John Wilson Croker, Giovanni Fabbroni, and Henry Penneck.

This diary records the individuals and sights that he saw while in England. There are many observations of life in London, e.g. parks, buildings, paintings, food. Outside of London he visited many towns, including Manchester and its cotton mills as well as the steel mills of Birmingham. He relates his visit to Drury Lane and the dramatic performance of Sarah Siddons. Some of the people he met included Sir Joseph Banks, Sir Charles Blagden, Matthew Boulton, Joseph Priestley, William Pitt the Younger, and Benjamin Vaughan. He also visited and described the gardens at Kew. The diary includes several sketches, including the plan of Blenheim Palace, and also a table of distances traveled.

This volume was kept while Piggott was imprisoned by Napoleon at Fontainebleau. Subjects mentioned include astronomy, comets, and botanical gardens.

The papers of the Italian natural philosopher and electrician, Giambatista Beccaria (1716-1781) contain letters to Benjamin Franklin, Joseph Banks, Laura Bassi, Gian Francesco Cigna, and others on a variety of scientific topics, including atmospheric and terrestrial electricity, the aurora borealis, earthquakes, meteorology, and phosphorescence. In addition to Beccaria's epistolary essays, the collection includes several journals of meteorological observations and notes for Giovanni Eandi's biography of Beccaria.

Though the Miscellaneous Manuscripts collection is composed of items that do not fall readily into any other existing collection, the two dominant intellectual areas represented in the collection are Early American History and History of Science.