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Warburton, Henry in correspondent 
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1840-1849 in date 
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From:
Henry Warburton
To:
Sir John Herschel
Date:
[19 October 1847]
Source of text:
RS:HS 18.39
Summary:

Sends copy of HW's paper on combinations of 'Plural Elements,' printed in Transactions of Cambridge Philosophical Society, based on the method of continued subtraction suggested by Augustus De Morgan. Shows solution for Bernoulli's fifth number.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[14 November 1847]
Source of text:
RS:HS 18.40
Summary:

Close to finding expeditious, symmetric method for computing Bernoulli's numbers. Resolves four formulas that HW sent to JH earlier today.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[22 November 1847]
Source of text:
RS:HS 18.41
Summary:

Thanks for comments on HW's paper and work on properties of Bernoulli's numbers. Claims HW's method of continued subtraction is convenient process for determining numerical coefficients. Found error, long perpetuated in literature, regarding Bernoulli's 13th number. Offers correct solution.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[23 November 1847]
Source of text:
RS:HS 18.42
Summary:

More calculations showing continued subtraction method in solution of Bernoulli's 13th number.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[24 November 1847]
Source of text:
RS:HS 18.43
Summary:

More calculations using continual subtraction method to test Bernoulli's 15th number.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[25 November 1847]
Source of text:
RS:HS 18.44
Summary:

More continual subtractions to resolve Bernoulli's 17th number. Error in official value given in Encyclopaedia Metropolitana. Also working on Bernoulli's 18th number.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[29 November 1847]
Source of text:
RS:HS 18.45
Summary:

Will submit paper to Cambridge [Philosophical] Society revising all [Leonhard] Euler's values for Bernoulli's numbers. Doubts accuracy of values up to B=49 quoted by George Peacock.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[5 December 1847]
Source of text:
RS:HS 18.46
Summary:

Error in Leonhard Euler's value for Bernoulli's 21st number. Promotes HW's method of continued subtraction as a reliable means of proving accuracy of values for higher Bernoulli numbers.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[13 December 1847]
Source of text:
RS:HS 18.47
Summary:

Destroy all HW's letters claiming errors in Leonhard Euler's values for Bernoulli's numbers. Mr. Hensley of Trinity College found weakness in HW's continued subtraction method. Clarifies symbols HW used to represent P. S. Laplace's expressions of Bernoulli's numbers.

Contributor:
John Herschel Project
From:
Henry Warburton
To:
Sir John Herschel
Date:
[14 December 1847]
Source of text:
RS:HS 18.48
Summary:

Continues explicating P. S. Laplace's formula for determining Bernoulli's numbers. Concerned that JH sees HW claiming too much for HW's continued subtraction method.

Contributor:
John Herschel Project
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
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
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
Document type
Transcription available