NATURAL PHILOSOPHY. 175 



FATALITY OF NUMBERS. 



The laws governing numbers are so perplexing to the unculti- 

 vated mind, and the results arrived at by calculations are so aston- 

 ishing, that it cannot be a matter of surprise if superstition has 

 attached itself to numbers. 



But even to those who are instructed in numeration there is 

 much that is mvsterious and unaccountable, much that onlv an 



*. . . 



advanced mathematician can explain to his own satisfaction. The 

 neophyte sees the numbers obedient to certain laws; but why 

 they obey these laws he cannot understand ; and the fact of his 

 not being able so to do tends to give to numbers an atmosphere 

 of mystery which impresses him with awe. 



For instance, the property of the number 9, discovered, I be- 

 lieve, by W. Green, who died in 1794, is inexplicable to any one 

 but a mathematician. The property to which I allude is this, that 

 when 9 is multiplied by 2, by 3, by 4, by 5, by 6, etc., it will be 

 found that the digits composing the products, when added to- 

 gether, give 9. Thus : 



2 multiplied by 9 equals 18, and 1 plus 8 equals 9 



3 " 9 " 27, " 2 " 7 " 9 



4 " 9 " 36, " 3 " 6 " 9 



5 " 9 " 45, " 4 " 5 " 9 



6 " 9 " 54, " 5 " 4 " 9 



7 " 9 " 63, " 6 " 3 " 9 



8 " 9 " 72, " 7 " 2 " 9 



9 " 9 " 81, " 8 " 1 " 9 

 10 " 9 " 90, " 9 " " 9 



It will be noticed that 9 multiplied by 11 makes 99, the sum of 

 the digits of which is 18 and not 9, but the sum of the digits 1 

 multiplied by 8 equals 9. 



9 multiplied by 12 equals 108, and 1 plus plus 8 equals 9 

 9 " 13 " 117, " 1 " 1 " 7 "9 



9 " 14 " 126, " 1 " 2 " 6 "9 



And so on to any extent. 



M. de Maivan discovered another singular property of the same 

 number. If the order of the digits expressing a number be 

 changed, and this number be subtracted from the former, the re- 

 mainder will be 9 or a multiple of 9, and, being a multiple, the 

 sum of its digits will be 9. 



For instance, take the number 21, reverse the digits, and you 

 have 12; subtract 12 from 21, and the remainder is 9. Take 63, 

 reverse the digits, and subtract 36 from 63 ; you have 27, a mul- 

 tiple of 9, and 2 plus 7 equals 9. Once more, the number 13 is 

 tiie reverse of 31 ; the difference between these numbers is 18, or 

 twice 9. 



Again, the same property found in two numbers thus changed 

 is discovered in the same numbers raised to any power. 



Take 21 and 12 again. The square of 21 is 441, and the square 

 of 12 is 144; subtract 144 from 441, and the remainder is 297, a 

 multiple of 9 ; besides, the digits expressing these powers added to- 



