By Prof. Steven H. Weintraub
Dept. of Mathematics
Lehigh University

18 November 1859

Cayley thanks Harley for his paper on quintics, which appeared as: Rev. Robert Harley, On the Theory of Quintics, Quarterly Journal of Pure and Applied Mathematics 3 (1860), 343-359.

26 January 1860 and 1 February 1860

Cayley discusses calculations by Harley that appear in Cayley's paper: [262] Arthur Cayley, On the Equation of Differences for an Equation of any Order and in particular for the Equations of the Orders two, three, four, and five, Phil. Trans. Royal Soc. London CL (1860), 93-112. (In that paper Cayley thanks Harley for his assistance with calculations.)

5 February 1860

Cayley discusses calculations by Harley that appear in Cayley's paper: [268] Arthur Cayley, On a New Auxiliary Equation in the Theory of Equations of the Fifth Order, Phil. Trans. Royal Soc. London CLI (1861), 263-276. (In that paper Cayley begins by discussing work of Cockle and Harley.)

15 September 1860

Cayley acknowledges receipt of Harley's paper, which he promises to present to the Royal Society. This paper appeared as: Rev. Robert Harley, On the Method of Symmetric Products, and Certain Circular Functions Connected with that Method, Phil. Trans. Royal Soc. London CLI (1861), 327-356. In that paper Harley refers to Cayley's letters of 28 September 1859 and 22 March 1860 in this collection.

19 February 1861

A relatively long letter in which Cayley discusses a number of computations about quintics, and at the end of which he points out to Harley an error in Harley's paper on quintics. This error is acknowledged by Harley in part II of this paper: Rev. Robert Harley, On the Theory of Quintics II, Quarterly Journal of Pure and Applied Mathematics 5 (1862), 248-259.

Cayley unsuccessfully nominated Harley for election to the Royal Society in 1862 but successfully nominated him in 1863. In this connection there are the following three letters:

19 February 1862

Cayley writes to Harley "I had much pleasure in signing myself and procuring two other signatures for your certificate for the Royal Society. You will have my best wishes for your success."

14 April 1862

Cayley writes to Harley that "I am sorry" to tell you that the Council of the Royal Society has not nominated you for election to the Society and hence that "your election therefore cannot take place until next year."

2 May 1863

Cayley writes to Harley "to tell you of your being one of the selected candidates for the Royal Society" and that "your election is practically quite certain," as indeed it was.