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Warburton, Henry in correspondent 
1850-1859::1854 in date 
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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

Herschel7865

From:
Henry Warburton
To:
Sir John Herschel
Date:
[26 September 1854]
Source of text:
RS:HS 18.69
Summary:

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)]?

Contributor:
John Herschel Project

Herschel7866

From:
Henry Warburton
To:
Sir John Herschel
Date:
[5 October 1854]
Source of text:
RS:HS 18.70
Summary:

Learned to simplify expression for Bernoulli's number B=2n+1 using JH's formula.

Contributor:
John Herschel Project

Herschel7868

From:
Henry Warburton
To:
Sir John Herschel
Date:
[15 November 1854]
Source of text:
RS:HS 18.72
Summary:

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.

Contributor:
John Herschel Project

Herschel7869

From:
Henry Warburton
To:
Sir John Herschel
Date:
[17 November 1854]
Source of text:
RS:HS 18.73
Summary:

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.

Contributor:
John Herschel Project

Herschel7870

From:
Henry Warburton
To:
Sir John Herschel
Date:
[10 December 1854]
Source of text:
RS:HS 18.74
Summary:

Testing recent work on equations analogous to P. S. Laplace's but of higher order. Solution so simple that HW expects to find it published elsewhere. Corrects error in previous letter regarding generality of arbitrary constants.

Contributor:
John Herschel Project

Herschel7871

From:
Henry Warburton
To:
Sir John Herschel
Date:
[11 December 1854]
Source of text:
RS:HS 18.75
Summary:

Demonstrates easier way to treat equations analogous to P. S. Laplace's.

Contributor:
John Herschel Project

Herschel7872

From:
Henry Warburton
To:
Sir John Herschel
Date:
[12 December 1854]
Source of text:
RS:HS 18.76
Summary:

Please correct error in HW's earlier calculations.

Contributor:
John Herschel Project
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