Roger Cotes and William Whiston, Lectures and Experiments

  • This material is held at
  • Reference
      GB 133 Eng MS 1494
  • Dates of Creation
      c. 1707-1710
  • Name of Creator
  • Language of Material
  • Physical Description
      255 x 195 mm. 1 volume. 65 folios, foliated 64. Medium: boards, paper. Binding: covers detached, some leaves are discoloured.
  • Location
      Collection available at The John Rylands Library, Deansgate

Scope and Content

Contents: Described "A course of lectures for the hydrostatical and pneumatical experiments begun at Cambridge and continued at London, composed by Mr Roger Cotes and William Whiston". There are 19 lectures in total. These relate to a course of lectures delivered by Cotes and Whiston at Trinity College, Cambridge from 1707 up to 1710.

Some of the lectures compare exactly or very closely with the version published in Cotes' Hydrostatical and pneumatic lectures, (1738), which had been edited for publication by his literary executor, Robert Smith. Smith excluded lectures which were the work of Whiston. It could be assumed that lectures present in this manuscript, but not in the published version, were authored by Whiston, although there is no direct evidence for this in the document. The fact that some lectures were delivered at London may indicate Whiston's lectures are present in this manuscript, and that the lectures may post-date his expulsion from Cambridge in 1710, although again there is no internal evidence for this. The correlation between the manuscript version and published version is as follows:

  • Ms lecture I - Published lectures I and II
  • Ms lecture II - Published lecture III
  • Ms lecture III- Published lecture IV
  • Ms lecture IV- Published lectures V and VI
  • Ms lecture V - Published lectures VII-VIII
  • Ms lecture VI- Published lecture IX
  • MS lecture VII- Published lecture X
  • Ms lecture VIII - Published lecture XII and XIII
  • Ms lecture IX - Published lecture XIV
  • Ms lecture XVI- Published lecture XV
. Manuscript lectures X, XI, XII-XIII, XIV-XV, XVII-XVIII and XIX do not appear in Hydrostatical and pneumatic lectures; correspondingly published lectures XI, and XVI do not appear in this manuscript.

On the cover has been written "Lectures and Experiments by Francis Haukesbee [crossed through], William Whiston and Roger Cotes." This is in a different hand to the lecture notes, and it is assumed to have been added later. The excised reference to Hauksbee is clearly an error made at a later date The author of the volume has not been identified, and there is no internal evidence to suggest it was either Cotes' or Whiston's own copy.

Administrative / Biographical History

Roger Cotes

Roger Cotes (1682-1716) was born at Burbage, Leicestershire, the son of the rector of that parish. While a pupil at Leicester School, he attracted attention for his precocious mathematical skills. He went on to study at St Paul's School, London, and entered Trinity College, Cambridge in 1799. He was elected a minor fellow of Trinity in 1705, and a major fellow in 1706. In the same year he was elected as first Plumian professor of astronomy and experimental philosophy (this new chair had been endowed by Thomas Plume (1630-1704), archdeacon of Rochester, to support astronomy at Cambridge). Cotes' rapid rise owed much to the patronage of Richard Bentley, the master of Trinity, Isaac Newton and William Whiston.

As part of his duties as professor, Cotes was in charge of an observatory at Trinity College, and he undertook regular astronomical research. However his most important work was editing and revising the second edition of Newton's Philosophiae Naturalis Principia Mathematica, which was issued in 1713. Cotes made important contributions to the sections on the theory of tides, lunar motion and cometary paths, and he also included an influential and lengthy essay describing Newton's method. Cotes' other work was published posthumously, after his sudden death in 1716. In 1722 his Harmonia Mensurarum was published, which made novel contributions to the mathematics of area, and in 1738, his literary executor, Robert Smith edited Cotes' Hydrostatical and Pneumatical Lectures, for publication. These lectures delivered at Trinity between 1707 and 1710, with his colleague, William Whiston, were important for incorporating practical experiments into teaching. The Lectures went through three edition between 1738 and 1775; Smith excluded those lectures which were delivered by Whiston.

William Whiston

William Whiston was born at Norton-juxta-Twycross, Leicestershire in 1667, the son of the rector of Norton. He attended grammar school at Tamworth between 1684 and 1686, before entering Clare College, Cambridge. He graduated in 1689, was elected to the Exeter fellowship at Clare in 1691, and became a senior fellow in 1693. Whiston was also ordained a deacon of the Church of England in the same year, and in 1694, became chaplain to John Moore, the bishop of Norwich.

In 1694 Whiston met Isaac Newton, and they became friends. Whiston was an enthusiastic proponent of Newton's work, and in 1696 published A new theory of the Earth, which was heavily influenced by Newton's ideas, and to whom the book was dedicated. The New Theory was highly successful, and earned Whiston a formidable academic reputation. From 1698 to 1701, Whiston was involved with his religious duties as vicar of Lowestoft-cum-Kessingland, Suffolk. but with Newton's patronage, he returned to Cambridge in 1701 to lecture, and in May 1702 he succeeded Newton as Lucasian professor of mathematics.

During the next decade, Whiston's output was prolific, publishing an edition of Euclid's Elements, an edition of Newton's lectures on algebra in 1702 (Arithmetica universalis) as well as his own lectures on astronomy,Praelectiones astronomica (1707)), and the Praelectiones physico-mathematicae in 1710, which was revised as Sir Isaac Newton's Mathematical Philosophy more easily demonstrated in 1716. Whiston was regarded as a highly effective communicator of the Newtonian system.

As well as his scientific work, Whiston had a long-standing interest in theology, especially of the early Church. He published An Essay on the Revelation in 1706, and The Accomplishment of Scripture Prophecies in 1708. Whiston was a defender of Biblical prophecy, and attempted to show evidences for the truth of prophecy in the Bible. Although critical of deism, he was sympathetic to some aspects of Arianism and highly critical of the Athanasian creed; in Sermons and Essays (1709), he set out these views, which attracted immediate and largely hostile attention. In 1710, Whiston was charged under a University heresy statute, and expelled from his Cambridge chair.

Whiston's academic career was now over, and thereafter he earned a living a popular lecturer, tutor and publishing entrepreneur. He worked with Francis Hauksbee the younger (1687-1763) to deliver a very successful biannual scientific lecture course on mechanics, hydrostatics, pneumatics and optics, as well as another course on astronomy. Whiston also founded the Society for Promoting Primitive Christianity, which discussed the theology of the early Church. Whiston also published an edition of Josephus, which proved highly successful. He published his memoirs in 1749-50. Whiston died in 1752 at his son-in-law's home, Lyndon Hall, Rutlandshire.

Access Information

The manuscript is available for consultation by any accredited reader.

Acquisition Information

The manuscript was purchased by the University of Manchester Library for £30 from Dawsons, booksellers, on 9 June 1966 [accession reference.: 513708)

Conditions Governing Use

Photocopies and photographic copies of material in the manuscript can be supplied for private research and study purposes only, depending on the condition of the manuscript.

Prior written permission must be obtained from the Library for publication or reproduction of any material within the manuscript. Please contact the Head of Special Collections, The John Rylands Library, 150 Deansgate, Manchester, M3 3EH.

Custodial History

The volume is stamped "Bibliotheca Halliwelliana" and "Lib Ms Bib Hall no.7". There is also a note on flyleaf, "Purchased this volume Aug 1 1837 at a sale by Hodgson no.192 Fleet Street" [poss Edmund Hodgson, bookseller].

Related Material

Cambridge University Library, Department of Manuscripts and University Archives, has a manuscript of the Lectures on Hydrostatics and Pneumatics, MS Add.9302. King's College, London have a student's notes of Cotes' lectures, Wheatstone Collection QC19 COT.


Ronald Gowing, Roger Cotes: natural philosopher (Cambridge University Press, 1983) and J. E. Force, William Whiston: honest Newtonian (Cambridge University Press 1985) .The DNB entries for Cotes and Whiston have been used to compile this description: Domenico Bertoloni Meli, 'Cotes, Roger (1682-1716)', Oxford Dictionary of National Biography, Oxford University Press, 2004 [, accessed 23 July 2016] and Stephen D. Snobelen, 'Whiston, William (1667-1752)', Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Oct 2009 [, accessed 23 July 2016]

Geographical Names