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
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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.