THE VEGETABLE AND ANIMAL KINGDOMS. 141 



2 

 3 

 4 

 5 



99,999,999 



100,000,000 



regularly as far as 100,000,001 



100,010,002 the law changes. 



100,030,003 



100,060,004 



100,100,005 



100,150,006 



100.210,007 



100,280,008 



" The law which seemed at first to govern this series failed 

 at the hundred million and second term. This term is larger 

 than we expected by 10,000. The next term is larger than 

 was anticipated by 30,000, and the excess of each term above 

 what we had expected forms the following table : 



10,000 



30,000 



60,000 

 100,000 

 150,000 



being, in fact, the series of triangular numbers, 1 each multi- 

 plied by 10,000. 



1 The numbers 1, 3, 6, 10, 15, 21, 28, &c., are formed by adding the 

 successive terms of the series of natural numbers thus : 



1 +2 = * 



1 = 1 

 3 



1+2+3=6 

 1 + 2 + 3 + 4 = 10, &c. 



They are called triangular numbers, because a number of points corre- 



