preponderant. For justice is like a balance, of which indeed that instrument is the emblem; in this balance good and evil are weighed, and if we act with impartiality in respect to our government, the result will prove that the good which proceeds from its constitution is, in every respect, paramount.

Nevertheless, since your honorable assembly commences this day its labors, I sincerely wish, that it will thoroughly examine, according to justice, all the abuses which may have arisen since the last Diet, that it will redress and correct those that have arisen through error, and that it will rigorously extirpate those which have been caused by departing from justice, and by perverting the spirit of the laws. But I especially desire that the Diet will exercise a particular care in preventing and obviating those symptoms of discontent, which restless and turbulent minds would excite against the established form of our government, as well in the provinces as in the Estates of the Realm, now assembled. These useful precautions, gentlemen, will prevent you from falling in Charybdis, whilst endeavoring to avoid Scylla.

Presented to the Diet held at Stockholm, January, 1761, by EMANUEL SWEDENBORG,

Member of the Senatorial Order of the Kingdom.

THE following memorial of Emanuel Swedenborg, concerning Charles XII. of Sweden, was printed in the Gentleman's Magazine, for September, 1754. It may, however, be proper to observe, that it was no doubt written by the author long prior to his being called to the sacred office which occupied the last twenty-nine years of his life; (which accounts for his speaking of the celebrated Charles XII. with so much greater respect than he is known to have afterwards entertained for his memory.) The editor of the Gentleman's Magazine does not state by what means he obtained possession of the article; he most probably translated it from some foreign journal, or the transactions of the Royal Academy at Stockholm; in which it might have appeared long before its publication in English.

Having been frequently admitted to the honor of hearing his late most excellent majesty Charles XII. discourse on mathematical subjects, I presume an account of a new arithmetic invented by him, may merit the attention of my readers.

His majesty observed then, that the denary arithmetic, universally received and practised, was most probably derived from the original method of counting on the fingers; that illiterate people of old, when they had run through the fingers of both hands, repeated new periods over and over again, and every time spread open both hands; which being done ten times, they distinguished each step by proper marks, as by joining two, three, or four fingers. Afterwards, when this

method of numeration on the fingers came to be expressed by proper characters, it soon became firmly and universally established, and so the denary computus has been retained to this day. But surely were a solid geometrician, thoroughly versed in the abstract nature and fundamentals of numbers, to set his mind upon introducing a still more useful computus into the world, instead of ten, he would select such a perfect square, or cube number, as by continual bisection, or halving, would at length terminate in unity, and be better adapted to the subdivisions of measures, weights, coins, &c.

Thus intent on a new arithmetic, the hero pitched upon the number eight, as most fit for the purpose, since it could not only be halved continually down to unity, without a fraction, but contained within it the square of two, and was itself the cube thereof, and was also applicable to the received denomination of several sorts of weights and coins, rising to 16 and 32, the double and quadruple of eight. Upon these first considerations, he was pleased to command me to draw up an essay or an octonary computus, which I completed in a few days, with its application to the received divisions of coins, measures, and weights, a disquisition on cubes and squares, and a new and easy way of extracting roots, all illustrated with examples.

His majesty having cast his eye twice or thrice over it, and observing, perhaps from some hints in the essay, that the denary computus had several advantages not always attended to, he did not at that time seem absolutely to approve of the octonary; or, it is likely, he might conceive, that though it seemed easy in theory, yet it might prove difficult to introduce it to practice. Be this as it will, he insisted on fixing upon some other that was both a cube and a square number, referrible to eight, and divisible down to unity by bisection. This could be no other than 64, the cube of 4, and square of 8, divisible down to unity without a fraction.

I immediately presumed to object, that such a number would be too prolix, as it arises through a series of entirely distinct and different numbers up to 64, and then again to its duplicate 4096, and on to its triplicate 262144, before the fourth step commences; so that the difficulty of such a computus would be incredible, not only in addition and subtraction, but to a still higher degree in multiplication and division. For the memory must necessarily retain in the multiplication table, 3969 distinct products of the 61 numbers of the first step multiplied into one another; whereas only 49 are necessary in the octonary, and but 81 are required in the denary arithmetic ; which last is difficult to be remembered and applied in practice, by some capacities. But the stronger my objections were, the

more resolute was his royal mind upon attempting such a computus.

Obstructions made him eagerly aspire

All to surmount, and nobly soar the higher.

He insisted that the alleged difficulties might be overbalanced by very many advantages.

A few days after this I was called before his majesty, who resuming the subject, demanded if I had made a trial? I still urging my former objections, he reached me a paper written with his own hand, in new characters and terms of denomination, the perusal of which he was pleased, at my entreaty, to grant me; wherein, to my great surprise, I found not only new characters and numbers, (the one almost naturally expressive of the other) in a continued series to 64, so ranged as easily to be remembered, but also new denominations, so contrived by pairs, as to be easily extended to myriads by a continued variation of the character and denomination. And further casting my eye on several new methods of his for addition and multiplication by this computus, either artificially contrived, or else inherent in the characters of the numbers themselves, I was struck with the profoundest admiration of the force of his majesty's genius, and with such strange amazement, as obliged me to esteem this eminent personage, not my rival, but by far my superior in my own art. And having the original still in my custody, at a proper time I may publish it, as it highly deserves; whereby it will appear with what discerning skill he was endowed, or how deeply he penetrated into the obscurest recesses of the arithmetical science.

Besides, his eminent talents in calculation further appear, by his frequently working and solving the most difficult numerical problems, barely by thought and memory, in which operations others are obliged to take great pains and tedious labor.

Having duly weighed the vast advantages arising from mathematical and arithmetical knowledge in most occasions of human life, he frequently used it as an adage, that he who is ignorant of numbers is scarce half a man.

Whilst he was at Bender he composed a complete volume of military exercises, highly esteemed by those who are best skilled in the art of war.

No. II. p. 17.

EXTRACTS FROM COUNT HOPKEN'S LETTERS TO GENERAL TUXEN. The late Swedenborg certainly was a pattern of sincerity, of virtue and piety, and at the same time, in my opinion, the