A letter of Robert Leslie Ellis to William Walton on probability

Abstract

The paper discusses the background to and provides a transcription of a letter from Robert Leslie Ellis (1817–59) to William Walton (1813–1901) of 1849 on probability theory.

Acknowledgments

I would like to thank John Gibbins for his support and the anonymous referee for his/her valuable comments. For the material from the Ellis Papers held by Wren Library (Cambridge), I duly acknowledge the kind permission of the Master and Fellows of Trinity College, Cambridge.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ The present paper is part of a larger research project that is to cover all aspects of Robert Leslie Ellis’ life and work.

² For discussions of Ellis’ contributions to probability theory see, for example, Dale (1999, 370–372), Kilinc (2000), Salmon (1980), and Verburgt (2013).

³ Given the content of Ellis’ letter to Walton, the background sketch in what follows is limited to the first part of Ellis’ contributions to probability theory.

⁴ Ellis, for his part, wrote the lengthy ‘General Preface’ to Bacon's Philosophical works (Ellis 1860). About this preface, Whewell remarked that ‘Mr. Ellis has [here] given a more precise view than any of his predecessors had done of the nature of Bacon's induction and of his philosophy of discovery’ (Whewell 1860, 149–150).

⁵ As De Morgan wrote to Ellis in a famous letter about the four-colour problem: ‘On looking at the question I perceived that the thing depends upon the following [...]. On looking for demonstration of this, I found nothing more simple on which to found it, and on thinking of it, it became an axiom to my mind, and I quoted it in a paper sent to Cambridge (but not yet published) as an instance of Whewell's views about latent axioms, things which at first are not even credible, but which settle down into first principles’ (Augustus De Morgan to Robert Leslie Ellis, 24 June 1854, Wren Library, R L Ellis Papers, Add.Ms.c. 67/111–12).

⁶ See footnote 2.

⁷ From the known sources, it can be seen that the Ellis–Forbes correspondence commenced as early as February 1836, when Ellis was nineteen, and Forbes twenty-seven, years old. See Shairp et al. 1873, 121.

⁸ The Ellis Papers in the Wren Library, Cambridge, contain some 81 letters from Ellis to Walton.

⁹ Henry Wilbraham, who is known for discovering and explaining the Gibbs phenomenon nearly fifty years before William Gibbs himself did, was admitted to Trinity College, Cambridge in 1841 at the age of sixteen. He finished Seventh Wrangler in the Tripos of 1846 and became a Fellow of his college in 1848 (see Venn 1854, 464). As to probability theory, Wilbraham's contributions primarily lay in his criticisms of Boole's method of treating (inverse) probability in the Laws of thought of 1854—his point being that ‘Boole does in the great number of questions relating to chances solvable by his method [...] tacitly assume certain conditions expressible by algebraical equations, over and above the conditions expressed by the data of the problem, and to show how these assumed conditions may be algebraically expressed’ (Wilbraham 1854, 465).

Additional information

Funding

This work was supported by a VENI grant from the Netherlands Organization for Scientific Research (NWO) [grant number 016.Veni.185.299]. A Grattan-Guinness Archival Research Travel Grant allowed me the travels and stays needed to undertake the research for the present paper.