HW neglected to state principle from which he derived equation for eliminating differences. Expresses it in formula.
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HW neglected to state principle from which he derived equation for eliminating differences. Expresses it in formula.
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.
Quick way to determine coefficients in tables of differences of powers of zero.
Sends law of coefficients, for developing summation theorem.
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.
Describes R.S.L.'s compound magnet. Recommends cleaning and remagnetizing. Awaits JH's instructions.
New method for constructing circular lenses up to 10-feet diameter for £50. Focusing power sufficient to melt metals. Wants to send 3-inch sample to JH.
Sends small lens. Its components neither parallel nor concentric; contains water. Suggests new polishing method. Estimates 4-foot lens would cost £7-£8. [JH Note: Tested and returned lens. Noted advantages and deficiencies and suggests improvements. Listed others who built similar lenses.]
Lens safely returned. Not aware of lenses in 1851 Exhibition or of C. F. Sturm's solid lenses. Notes advantages of plate glass. Offers to make three foot by three foot square lens. Recognizes limitations for use in astronomy; hopes for other applications.
Sad to hear of JH's suffering and retirement from Mint. Describes production rates, problems, equipment, personnel, and quality of gold at Sydney mint. Starting an observatory. G. B. Airy promises to send astronomer. New South Wales legislature is not friendly to scientific research. Describes Australian society.
Sending his completed universal alphabet with comments.
Pleased to hear from Capt. E. W. Ward's letter that JH still remembered him. Grieves to hear of his bad health. Mint at Sydney is progressing. Rich gold fields at Victoria. Looks forward to the re-establishment of steam communication.
Thanks for the check. Will search for the deeds.
Congratulations on the success of his son at Addiscombe.
Pleased to hear of his improved health. Has sent some of the substance he requested. Affairs at the Mint not very satisfactory.
Thought that the book presented by JH had come from Algernon Percy (4th Duke of Northumberland); regrets the error.
Would like a letter from JH giving him authority to have the box to open. Is busy with the Report.
Has he repeated his experiments with the photographic representation of the prismatic structure? Regarding a numerical nomenclature for the colors.