Sends law of coefficients, for developing summation theorem.
Sends law of coefficients, for developing summation theorem.
[Form letter] Offers to send Commercium epistolicum J. Collins et aliorum... (1856), by J. B. Biot and Francisque Lefort, a critical edition of works by mathematician John Collins.
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.
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.
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.
Has procured an actinometer and would like details of the scale.
Would he answer some of his queries when he has leisure? Queries on the law of beats for unison sounds. Met JH's daughter on Monday, who gave a fair account of JH and his recent work.
Has long held the view that a pipe underneath the strings of a piano would increase the resonance. Had not conceived such an instrument as JH suggested. Why are 3rds and 6ths more agreeable to the ear than 4ths and 5ths?
Regrets letter read the night before at the R.A.S. of JH's wish to resign and hopes JH's health allows him to come occasionally and be a nominal member. Discusses Piazzi Smyth's preparations for voyage to Teneriffe.
Sending him a copy of her Familiar Astronomy and inviting his comments on this work. His works are well known in America.
Writes to clarify his understanding of the word 'fluorescence.' Asks JH to review a paper on color-blindness.
Death of his sister a blow to John Bullar [father of writer].
Recent observations of specified stars and their variations.
Further thoughts [see GS's 1856-6-27] on the nature of fluorescence, including that it is a transient phosphorescence.
Continues comments on fluorescence from letter of 1856-7-8; then shows mathematically that JH's solution for the problem of Mahomet's coffin [see GS's 1856-7-1] will not work.
Comments on one of the magnetism experiments JH described in his letter of 1856-7-14.
Describes R.S.L.'s compound magnet. Recommends cleaning and remagnetizing. Awaits JH's instructions.
Their whole family is grateful for JH's letter of sympathy to JB's father.
Will give him great pleasure to call at Collingwood in the near future. Grieved to hear of JH's illness. Begs acceptance of a set of papers of Dr. William Griffith.
Sending a pamphlet, which may give JH some amusement.