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Herschel, John in addressee 
letter in document-type 
1840-1849::1847::12 in date 
Warburton, Henry in correspondent 
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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