74 TRANSACTIONS OF THE 



notation came through the Arabs, who, about the ioth century, ob- 

 tained it from Hindostan (where, it is asserted, the figures were 

 anciently the initial letters of the Sanscrit names for the digits), 

 and has rendered easy those calculations and deductions which dis- 

 play many curious properties of, and relations between, numbers. 

 But it behooves to distinguish the ideas elucidated through mathe- 

 matical experiments from the mere signs or value of the notation — 

 that is, the apparatus — so that the latter may not claim a retro- 

 active significance. 



Many of the curious and often beautiful results from combina- 

 tion of numbers have, on close examination, no more intrinsic 

 import than the also curious and beautiful reflections produced by 

 turning a kaleidoscope, and dependent on much the same principles 

 of mathematical relations between quantities and magnitudes. 



Devotees of symbolism, in their undue zealotry, seem to have 

 pried about with a number in their hands, determined to fit it into 

 some object, like trying a stray key to all accessible locks. A not 

 ■very ancient work set forth, among other attributes, of the number 

 7, with much flourish, that there are seven planets and seven metals, 

 which, indeed, was the limit then known, but we now recognize at 

 least fifty metals, and the planets have also increased on acquain- 

 tance apart from the asteriods, which, at the present rate of dis- 

 covery, may soon swell the list to two hundred. 



Belief in the mysticism of numbers has often retarded scientific 

 research. Huygens, in 1655, discovered a satellite of Saturn. He 

 then stopped observations because the six planets (Saturn then 

 being the oldest known planet) and the six satellites, one of the 

 earth, four of Jupiter, and that one of Saturn made the perfect num- 

 ber of twelve. So he asserted solemnly that nothing more of plane- 

 tary system was left to be discovered. This blunder warns us not to 

 build symbols needlessly on the shifting sands of ignorance, to be 

 demolished by the advancing ocean -wave of science. 



Symbols that have once reigned with perfect title may degenerate 

 into petty signs. The chevron, an honorable ordinary in heraldry, 



