Thanks for sending Examples in Finite Differences [1820] to WH's great-nephew Howard Elphinstone. John Brinkley's paper opened up new possibilities for permutations and combinations.
Thanks for sending Examples in Finite Differences [1820] to WH's great-nephew Howard Elphinstone. John Brinkley's paper opened up new possibilities for permutations and combinations.
Admires chimes analogy in JH's 'On Circulating Functions' [1818]. Resumed interest in partitions of numbers in development of periodic functions. Finds JH's method superior. Encourages him to publish it. WH and Augustus De Morgan developed original method, which WH erred in attributing to Leonhard Euler. De Morgan's paper to Cambridge [Philosophical] Society demonstrates theorem leading to proof of Euler's theorem.
Explains HW's method for periodic functions.
'Private & Confidential.' Urges JH to accept University of London's senate invitation to join Board, which JH previously declined. Names others invited.
'Private & Confidential.' Secretary of State George Grey disappointed that JH declined to join University [of London] Board. Extended offer again. HW offers conjecture on JH's non-periodic numbers.
'Private & Confidential.' All seven invited to join [University of London's] senate have agreed. Urges JH to reconsider.
R.S.L. sent JH's ['On the Algebraic Expression of the Number of Partitions...' (1850)], asking HW to judge its merits for publication in R.S.P.T.
Review of JH's paper [see HW's 1850-6-1] renewed HW's interest in 4- and 5-partitions of numbers. Will complete paper on combinations during vacation.
Favorable report to R.S.L. on JH's paper. Suggests minor changes. Verified only methods, not numerical values. Shows more general treatment of partitions than one that JH developed.
Heard JH plans new edition of Examples of Finite Differences [1820]. Will send list of errors HW found in original. Results of HW's investigation of self-repeating series of numbers.
Recalls JH's predecessor [Isaac Newton] at Mint was also interested in Bernoulli's 'Isoperimetrical Problems.' HW plans paper on new expression for coefficients of differences of zero in self-repeating series.
Cambridge [Philosophical] Society will publish HW's paper on self-repeating series. Suggests JH clarify some equations in new edition of [Examples of Finite Differences (1820)].
Additional suggestions for improving clarity of equations in new edition of JH's [Examples of Finite Differences (1820)].
Additional improvements for new edition of JH's [Examples of Finite Differences (1820)].
Discusses points raised about equations [see HW's 1854-8-19].
Further discussion of need for two constants [see HW's 1854-[5]-11]. Sends first installment of errata HW found in JH's [Examples of Finite Differences (1820)]. Realizes JH's duties [at Mint] afford little time to publish new edition. Suggests printing only errata list to first edition.
Sends copy of HW's paper, with manuscript listing properties of differences of zero. Is there a published table of such differences like that in JH's [Examples of Finite Differences (1820)]?
Learned to simplify expression for Bernoulli's number B=2n+1 using JH's formula.
Happy that JH may be leaving Mint and returning to scientific pursuits. HW resumed work on equations in finite differences. Hopes to reconcile discrepancy between JH's and P. S. Laplace's solutions. JH's solution renders only particular, not general, solutions.
Approves of JH sharing HW's findings. HW on excellent terms with Augustus De Morgan. Suspects two integrals exist, one real and one imaginary, for P. S. Laplace's equation.