Discusses points raised about equations [see HW's 1854-8-19].
Showing 1–20 of 52 items
Discusses points raised about equations [see HW's 1854-8-19].
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.
Suggests changes for JH's paper on Swedish felspar submitted to Geological Society. Confusion between this and other silicates. Compares JH's analysis to that of Wilhelm Hisinger and others.
Discussed JH's proposed felspar paper [see HW's 1816-4-24] with W. H. Wollaston. Suggests using Wollaston's and [recently deceased Smithson] Tennant's unpublished method to test for alkalis and give Tennant credit for it. James Smithson first coined term 'silicate'.
Apologizes for delay in writing out what JH requested. He will have it tomorrow.
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.
Close to finding expeditious, symmetric method for computing Bernoulli's numbers. Resolves four formulas that HW sent to JH earlier today.
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.
More calculations showing continued subtraction method in solution of Bernoulli's 13th number.
More calculations using continual subtraction method to test Bernoulli's 15th number.
More continual subtractions to resolve Bernoulli's 17th number. Error in official value given in Encyclopaedia Metropolitana. Also working on Bernoulli's 18th number.
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.
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.
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.
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.
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.
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.
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.
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].
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.