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Warburton, Henry in correspondent 
1850-1859 in date 
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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
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
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
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
From:
Henry Warburton
To:
Sir John Herschel
Date:
[7 January 1855]
Source of text:
RS:HS 18.77
Summary:

Corrects calculations relating to arbitrary constants in HW's previous letters. Encourages JH to avail himself of this information in second edition [of Examples of Finite Differences (1820)] .

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[9 January 1855]
Source of text:
RS:HS 18.78
Summary:

Relative to previous letter [see HW's 1855-1-7], HW found two possible equations, due to ambiguity of signs.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[28 April 1856]
Source of text:
RS:HS 18.79
Summary:

Heard JH not well. Offers him 'a nosegay, gathered from [JH's] own garden of the Differences of the Powers of Zero.' More notes on the self-repeating series. Developed two equations that HW may submit to Cambridge [Philosophical] Society.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[7 May 1856]
Source of text:
RS:HS 18.80
Summary:

HW neglected to state principle from which he derived equation for eliminating differences. Expresses it in formula.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[15 May 1856]
Source of text:
RS:HS 18.81
Summary:

Glad that JH shows renewed interest in mathematics. Besides HW, JH, Augustus De Morgan, and Mr. Gerard, there appear to be no others interested in researching the differences of the powers of zero. Gave outline of HW's paper at Cambridge Philosophical Society. Plans to revise it according to suggestions from JH and De Morgan.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[17 May 1856]
Source of text:
RS:HS 18.82
Summary:

Quick way to determine coefficients in tables of differences of powers of zero.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[25 May 1856]
Source of text:
RS:HS 18.83
Summary:

Sends law of coefficients, for developing summation theorem.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[26 May 1856]
Source of text:
RS:HS 18.84
Summary:

Coefficients of differences of odd powers of zero observe same law as those of even powers. Example of table of coefficients of differences of 015. Table took 15 minutes to compute by HW's process of summation. Notes error in table for 012 sent earlier.

Contributor:
John Herschel Project
From:
Sir John Herschel
To:
Henry Warburton
Date:
[27 May 1856]
Source of text:
RS:HS 18.85b
Summary:

Compliments HW's expression for the formula for coefficients of differences of the odd powers of zero. JH busy, but hopes soon to develop demonstration.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[30 May 1856]
Source of text:
RS:HS 18.86
Summary:

Glad for JH's renewed interest in mathematics. At 72, HW expects to do no more. Reviewed JH's letter of 14 May [1856]. Fears JH misunderstood meaning of symbol HW employed. Quotes explanation from HW's paper on self-repeating series.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[2 June 1856]
Source of text:
RS:HS 18.87
Summary:

Reflects on relations between differences of same power of zero. Reviews procedure developed for determining terms and law of coefficients. JH's critique expanded role for these, but HW disagrees with JH's latest comments.

Contributor:
John Herschel Project