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CURIOUS MEMORIAL OF SWEDENBORG. 189
difficulties arise in numerical calculations. Whereas, had the periodical number
been 8 or 16, a great facility would have resulted, the first being a cube number,
of which the root is 2, and the second a square number, of which the root is 4,
and that these numbers being divided by 2, their primitive, the number I would
be obtained, which would be highly useful with regard to money and measures,
by avoiding a quantity of fractions. The king, after speaking at great length on
this subject, expressed a desire that we should make a trial with some other
number than 16. Having represented to him, that this could not be done, unless
we invented new figures, to which, also, names altogether different from the
ancient ones must be given, as, otherwise, great confusion would arise, he de-
sired ns to prepare an example in point.
" We chose the number 8, of which the cube root is 2, and which, being
divided by 2, is reduced to the primitive number 1. We also invented new
tigures, to which we gave new names, and proceeded according to the ordinary
method ; after which we applied them to the cubic calculations, as well as to
naoney and to measures. The essay having been presented to the king, he was
pleased with it : but it was evident that lie had wished something more ex-
tended, and less easy, in order that he might display the superiority of his genius
and his great penetration. To this end he proposed to adopt some number
which should contain a square as well as a cube, and which, when divided by
% might be reduced to the primitive number 1. He made choice of 64 ; but we
observed to him that it was too high a number, and, consequently, very incon-
venient, and, indeed, that it was almost impossible to employ it ; that, besides,
if we were obliged to reckon up to 64, before recommencing, and that upon
reaching 64 times 64, or 4096, only three figures were used, calculation would be
rendered immensely difficult, especially with regard to multiplication and divi-
sion ; because it would be necessary to commit to memory a multiplication
cable composed of 4096 numbers, while the common table comprised only 80
or 90 numbers. However, the more we urged our difficulties, the more he was
determined to put his idea into pra-ctice ; and to show the possibility of what
appeared to us to require long and profound reflection, he undertook to devise
this method himself, and to lay down the plan of it, which he sent to us the
next morning. He had invented new figures, each with its particular name.
The 64 figures were divided into 8 classes, each being designated by a particu-
lar symbol. Upon a closer inspection, I found that these symbols or signs were
composed of the initial and final letters of his own name, in a manner at once
so clear and exact, that when the first 8 numbers were known, all the rest up
to 64 were attainable without the least difficulty. The names of the 8 numbers
of the first class were very simple, and those of the others so well contrived,
that one could easily remember them, without fear of confusion. Having ar-
rived at the number 64, when it became necessary to proceed with three figures,
up to 64 timee 64, he had invented new names, admirably arranged, and so easily
and naturally varied that there was not any number, however high, for which
there was not a name ; and this might be carried on ad infinitum, following the
principles and rules laid down.
" It was to me that the king committed this plan, in his own hand-writing
[the original of which I still preserve], in order to arrange from it a table show-
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