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Herschel7845

From:
Henry Warburton
To:
Sir John Herschel
Date:
[20 December 1847]
Source of text:
RS:HS 18.49
Summary:

Verified Leonhard Euler's values for Bernoulli's numbers up to B=25 by method previously outlined and to be stated fully in this letter. Mr. Hensley [of Trinity College] proposes to revise incorrect values given in Penny Cyclopaedia. Computing a Bernoulli number by P. S. Laplace's formula takes three days. HW's method of continued subtraction requires only 24 hours.

Contributor:
John Herschel Project

Herschel7846

From:
Henry Warburton
To:
Sir John Herschel
Date:
[23 December 1847]
Source of text:
RS:HS 18.50
Summary:

Proved accuracy of Leonhard Euler's values for Bernoulli's 27th number. Plans to test number 29. Will investigate Thomas Clausen's theorem, the generality of which JH appears to have disproved.

Contributor:
John Herschel Project

Herschel7847

From:
Henry Warburton
To:
Sir John Herschel
Date:
[30 December 1847]
Source of text:
RS:HS 18.51
Summary:

Demonstrates property of 'Coefficients of the terms of the Numerators of the Fractions which generate the odd powers of the Numbers of the Natural Series.' Claims this method can compute Bernoulli's numbers 37, 39, and 41.

Contributor:
John Herschel Project

Herschel7848

From:
Henry Warburton
To:
Sir John Herschel
Date:
[28 January 1850]
Source of text:
RS:HS 18.52
Summary:

Thanks for citing (18 months ago) John Brinkley's paper on 'General Term.' Heard that Augustus De Morgan notified JH of deductions HW drew from Brinkley's theorems, extending them into permutations and combinations. Re-read JH's ['On the Development of Exponential Functions' (1816)]. Asks where to buy JH's Examples in Finite Differences [1820] for HW's great-nephew [Howard Elphinstone].

Contributor:
John Herschel Project

Herschel7849

From:
Henry Warburton
To:
Sir John Herschel
Date:
[31 January 1850]
Source of text:
RS:HS 18.53
Summary:

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.

Contributor:
John Herschel Project

Herschel7850

From:
Henry Warburton
To:
Sir John Herschel
Date:
[24 February 1850]
Source of text:
RS:HS 18.54
Summary:

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.

Contributor:
John Herschel Project

Herschel7851

From:
Henry Warburton
To:
Sir John Herschel
Date:
[25 February 1850]
Source of text:
RS:HS 18.55
Summary:

Explains HW's method for periodic functions.

Contributor:
John Herschel Project

Herschel7852

From:
Henry Warburton
To:
Sir John Herschel
Date:
[27 February 1850]
Source of text:
RS:HS 18.56
Summary:

'Private & Confidential.' Urges JH to accept University of London's senate invitation to join Board, which JH previously declined. Names others invited.

Contributor:
John Herschel Project

Herschel7854

From:
Henry Warburton
To:
Sir John Herschel
Date:
1850-[2-27 or later]
Source of text:
RS:HS 18.58
Summary:

'Private & Confidential.' All seven invited to join [University of London's] senate have agreed. Urges JH to reconsider.

Contributor:
John Herschel Project

Herschel7853

From:
Henry Warburton
To:
Sir John Herschel
Date:
[4 March 1850]
Source of text:
RS:HS 18.57
Summary:

'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.

Contributor:
John Herschel Project

Herschel7855

From:
Henry Warburton
To:
Sir John Herschel
Date:
[1 June 1850]
Source of text:
RS:HS 18.59
Summary:

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.

Contributor:
John Herschel Project

Herschel7856

From:
Henry Warburton
To:
Sir John Herschel
Date:
[5 June 1850]
Source of text:
RS:HS 18.60
Summary:

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.

Contributor:
John Herschel Project

Herschel7857

From:
Henry Warburton
To:
Sir John Herschel
Date:
[5 June 1850]
Source of text:
RS:HS 18.61
Summary:

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.

Contributor:
John Herschel Project

Herschel7858

From:
Henry Warburton
To:
Sir John Herschel
Date:
[10 April 1854]
Source of text:
RS:HS 18.62
Summary:

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.

Contributor:
John Herschel Project

Herschel7859

From:
Henry Warburton
To:
Sir John Herschel
Date:
11 [May] 1854
Source of text:
RS:HS 18.63
Summary:

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.

Contributor:
John Herschel Project

Herschel7860

From:
Henry Warburton
To:
Sir John Herschel
Date:
[16 August 1854]
Source of text:
RS:HS 18.64
Summary:

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)].

Contributor:
John Herschel Project

Herschel7861

From:
Henry Warburton
To:
Sir John Herschel
Date:
[17 August 1854]
Source of text:
RS:HS 18.65
Summary:

Additional suggestions for improving clarity of equations in new edition of JH's [Examples of Finite Differences (1820)].

Contributor:
John Herschel Project

Herschel7862

From:
Henry Warburton
To:
Sir John Herschel
Date:
[19 August 1854]
Source of text:
RS:HS 18.66
Summary:

Additional improvements for new edition of JH's [Examples of Finite Differences (1820)].

Contributor:
John Herschel Project

Herschel7863

From:
Sir John Herschel
To:
Henry Warburton
Date:
[20 August 1854]
Source of text:
RS:HS 18.67
Summary:

Discusses points raised about equations [see HW's 1854-8-19].

Contributor:
John Herschel Project

Herschel7864

From:
Henry Warburton
To:
Sir John Herschel
Date:
[25 August 1854]
Source of text:
RS:HS 18.68
Summary:

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.

Contributor:
John Herschel Project
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