1887.] ^^1 [Taylor. 



priceless blessings whose first and feeble preparations were planned in 

 former, unenjoying ages. Shall we reap the rich fruits grown from the 

 unselfish providence of ancestral culture, and shall posterity be less 

 favored ? Patriotism and humanity reject the doubt. The octonary algo- 

 rithm is pregnant with such great and widespread benefits — benefits to 

 extend throughout all coming time, that its acquisition should be estimated 

 as cheaply purchased by whole generations of transitional confusion. 



The measure thus imperfectly advocated is by no means a new one. It 

 is an incident of the highest interest and moment in the reign of that dis- 

 tinguished monarch, Charles XII of Sweden, that he not only contem- 

 plated the introduction of an octonary arithmetic, but that he commis- 

 sioned Swedenborg (at that time celebrated for his scientific and mathe- 

 matical attainments) to draw up the necessary details of the plan for 

 establishing this system, together with an octonary scale of weights, mea- 

 sures and coins throughout his kingdom.* It appears that the premature 

 death of the liing very shortly afterward, alone prevented the consumma- 

 tion of this most sagacious and philosophic enterprise. But for this unto- 

 ward circumstance this admirable meclianism would have thus been put 

 into practical operation more than a century and a half ago ! Had it 

 proved as successful as there is every reason to suppose it would, who can 

 estimate the influence this engrafting would have had upon the present 

 mathematical condition of Europe? Might we not now have been in the 

 full and assured enjoyment of that happier system? The subject of this 

 improved numerical notation had doubtless often occupied the minds of 

 mathematicians long before this time, but this is probably the first occa- 

 sion on which a deliberate and well-designed attempt was ever made to 

 give it a practical existence and establishment. As such it is an event of 

 no trivial importance, and must be I'egarded as ever memorable in the his- 

 tory of arithmetical reform. 



In contemplating the practical working of this untried system, and 

 forming an estimate of the character of the change required in the popu- 

 lar habits of thought, comparison and judgment, there can be no doubt 

 tliat the octonary scale could be generally introduced with far greater 

 facility, and made thoroughly familiar in a much shorter time, in its appli- 

 cation to the divisions of money, weight and measure, than it could be in 

 its more abstract application to the operations of universal numeration ; 

 that in advance of the arithmetical reformation, it would be found highly 

 expedient to introduce the simple and convenient system of weights and 

 measures here proposed, as the best preparation for the successful intro- 

 duction of the other. 



Even were the octonary arltlimetic (with all its own intrinsic excel- 

 lences) not to be adopted, we still urge that these measures would be worthy 

 of an independent establishmeat. After the variety of arithmetical reduc- 

 tions to which we are now accustomed under our present incongruous 



* See note D, page 364. 



