1887.] 'J^^ [Taylor. 



of the Theological and Spiritual Writings of Emanuel Swerteuborg " (royal 

 octavo), published at Boston by Crosby & Xichols, 1854. In the life of Swe- 

 denborg, prefixed to the "Compendium," it is said: "In 1719 he published 

 four works ; first, 'A Proposal for Ji. ring the value of Coins and determining 

 the Measures of Sweden, so as to suppress fractions, and facilitate Calcula- 

 tions.' After which he was commanded by his Sovereign to draw up an 

 Octonary Computus (a mode of computing by eighths), wliich he completed 

 in a few days, with its application to the received divisions of Coins, Weights, 

 and Measures ; a disquisition on Cubes and Squares, and a new and easy way 

 of extracting Eoots; all illu.strated by appropriate examples " (Life, p. 'J). 

 As Swedenborg devised for his " Octonary Computus," both a set of charac- 

 ters and of new names, we were exceedingly anxious to have enriched this 

 Paper with tlieir representation. We have tailed, however, to find any clue 

 to these early publications in any of the public libraries or private collections 

 to wliich we have had access. The only additional reference to the subject 

 in the volume above referred to, is contained in a letter from Swedenborg to 

 M. Xordberg, written after the death of Charles XII, wliich appears to 

 detail the monarch's first conception of the project of a reformation in the 

 popular system of numeration. An extract giving all that relates to the 

 subject of octonary computation, is here copied : 



Letter of J/. Swedenhorg, Assessor of the Board of Mines, to M. JSfordherg, 

 AutJior of the History of Charles XII. 



"Sir: — As you are now actually engaged upon tiie Life of Charles XII, 

 I avail myself of the opportunity to give you some information concerning 

 that monarch, which is perhaps new to you, and worthy of being transmitted 

 to posterity. * Conversing one day with the King upon arithmetic, 



and the mode of counting, we observed that almost all nations, upon reaching 

 ten, began again ; that those figures which occupy the first place, never 

 change their value, while those in the second place were multiplied ten-fold, 

 and so on with the others; to which we added that men had apparently begun 

 by counting their fingers, and that this method was still practised by the 

 people ; that arithmetic having been formed into a science, figures had been 

 invented which were of the utmost service ; and, nevertheless, that the 

 ancient mode of counting had been always retained, in beginning again after 

 arriving at ten, and which is observed by putting each figure in its proper 

 place. 



The King was of opinion that had such not been the origin of our mode of 

 counting, a much better and more geometrical method might have been in- 

 vented, and one which would have been of great utility in calculations, by 

 making choice of some other periodical number than 10. That the number 

 10 had this great and necessary inconvenience, that wiien divided by 2, it 

 could not be reduced to the number 1, without entering into fractions. Be- 

 sides, as it comprehends neither the square, nor the cube, nor the fourth 

 power of any number, many 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 1 would be obtained, which would be highly 



