BYRNE'S DUAL ARITHMETIC.
Dual Arithmetic. A new art. By Oliver Byrne.[[322]] London, 1863, 8vo.
The plan is to throw numbers into the form a(1.1)b (1.01)c (1.001)d... and to operate with this form. This is an ingenious and elaborate speculation; and I have no doubt the author has practised his method until he could surprise any one else by his use of it. But I doubt if he will persuade others to use it. As asked of Wilkins's universal language, Where is the second man to come from?
An effective predecessor in the same line of invention
was the late Mr. Thomas Weddle,[[323]] in his "New, simple, and general method of solving numeric equations of all orders," 4to, 1842. The Royal Society, to which this paper was offered, declined to print it: they ought to have printed an organized method, which, without subsidiary tables, showed them, in six quarto pages, the solution (x=8.367975431) of the equation
1379.664 x622 + 2686034 × 10432 x152 - 17290224 × 10518 x60 + 2524156 × 10574 = 0.
The method proceeds by successive factors of the form, a being the first approximation, a × 1.b × 1.0c × 1.00d.... In my copy I find a few corrections made by me at the time in Mr. Weddle's announcement. "It was read before that learned body [the R. S.] and they were pleased [but] to transmit their thanks to the author. The en[dis]couragement which he received induces [obliges] him to lay the result of his enquiries in this important branch of mathematics before the public [, at his own expense; he being an usher in a school at Newcastle]." Which is most satirical, Mr. Weddle or myself? The Society, in the account which it gave of this paper, described it as a "new and remarkably simple method" possessing "several important advantages." Mr. Rutherford's[[324]] extended value of π was read at the very next meeting, and was printed in the Transactions; and very properly: Mr. Weddle's paper was excluded, and very very improperly.
HORNER'S METHOD.
I think it may be admited that the indisposition to look at and encourage improvements of calculation which once
marked the Royal Society is no longer in existence. But not without severe lessons. They had the luck to accept Horner's[[325]] now celebrated paper, containing the method which is far on the way to become universal: but they refused the paper in which Horner developed his views of this and other subjects: it was printed by T. S. Davies[[326]] after Horner's death. I make myself responsible for the statement that the Society could not reject this paper, yet felt unwilling to print it, and suggested that it should be withdrawn; which was done.