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Published online by Cambridge University Press: 18 August 2016
The paper which I have the honour to submit is so elementary in its details that I have to claim the indulgence of the meeting; but, as the practical application of the simple formulæ to which I shall have occasion to refer may be interesting, I trust I may not unworthily occupy a short portion of your time.
A few months ago it occurred to me that tables to facilitate the process of multiplication, based upon the identity
would be of extensive use in actuarial and other calculations, and would effect a considerable saving of labour—to an extent even greater than that acquired by the use of logarithms. This led me to give attention to the subject; and after a trial on a small scale, I deemed it of sufficient importance to construct for my own use a series of tables of the fourth parts of the squares of all integer numbers up to 100,000.
page 122 note * By Sylvester, J. J. M.A., F.R.S., (Assurance Mag., vol. iv., p, 236.)Google Scholar
page 126 note * Since the above was written the author has received a valuable suggestion from Mr. Peter Gray, to insert in the tables the tabular differences and proportional parts, which will materially enhance the advantages afforded by them.
page 128 note * Practically, these figures need not be set down; they are here only inserted for perspicuity.