e average (say 61) as 44
on one side or 78 on the other. There must be some reason why the number 7
is thus deprived of its fair share in the structure. Here is a field of
speculation in which two branches of inquirers might unite. There is but
one number which is treated with an unfairness which is incredible as an
accident; and that number is the mystic number _seven_! If the cyclometers
and the apocalyptics would lay their heads together until they come to a
unanimous verdict on this phenomenon, and would publish nothing until they
are of one mind, they would earn the gratitude of their race.--I was wrong:
it is the Pyramid-speculator who should have been appealed to. A
correspondent of my friend Prof. Piazzi Smyth[139] notices that 3 is the
number of most frequency, and that 3-1/7 is the nearest approximation to it
in simple digits. Professor Smyth himself, whose word on Egypt is paradox
of a very high order, backed by a great quantity of useful labor, the
results which will be made available by those who do not receive {66} the
paradoxes, is inclined to see confirmation for some of his theory in these
phenomena.

CURIOUS CALCULATIONS.

These paradoxes of calculation sometimes appear as illustrations of the
value of a new method. In 1863, Mr. G. Suffield,[140] M.A., and Mr. J. R.
Lunn,[141] M.A., of Clare College and of St. John's College, Cambridge,
published the whole quotient of 10000 ... divided by 7699, throughout the
whole of one of the recurring periods, having 7698 digits. This was done in
illustration of Mr. Suffield's method of _Synthetic division_.

Another instance of computation carried to paradoxical length, in order to
illustrate a method, is the solution of x^3 - 2x = 5, the example given of
Newton's method, on which all improvements have been tested. In 1831,
Fourier's[142] posthumous work on equations showed 33 figures of solution,
got with enormous labor. Thinking this a good opportunity to illustrate the
superiority of the method of W. G. Horner,[143] not yet known in France,
and not much known in {67} England, I proposed to one of my classes, in
1841, to beat Fourier on this point, as a Christmas exercise. I received
several answers, agreeing with each other, to 50 places of decimals. In
1848, I repeated the proposal, requesting that 50 places might be exceeded:
I obtained answers of 75, 65, 63, 58, 57, and 52 places. But one answer, by
Mr. W. Harris Johnston,[144] of Dundalk, and of the Ex