io ELEMENTS OF SCIENCE 



taking account of the whole quantities, whereof such 

 figures form part. Thus, in adding together the quan- 

 tities expressed by 104, 92, and 8, according to this 

 mode, we need take no heed of the three whole numbers 

 as whole numbers, but simply add together their super- 

 imposed constituent parts : 



8 



92 

 104 



204 



The result of the above simple sum in addition takes 

 the form it does, because as the three superimposed units 

 at the right hand together make 14, we know that the 

 number of simple units is 4, together with one group of 

 ten. When this one group is added to the two super- 

 imposed figures which form the second column, the 

 product (because one of them is a zero) is ten groups 

 of ten. But a symbol of that value cannot be written 

 down in the second place, but must appear in the third, 

 which is that set apart for groups of ten times ten. It 

 is therefore carried to the third column, which consists 

 of but a single figure i, and, being added thereto, 

 makes with it two groups of ten times ten, or 200, so 

 that the result must be 204. 



That the results obtained by thus working with mere 

 symbols of abstractions applicable to all things which 

 can be counted, accurately correspond with real rela- 

 tions which exist between substantial things, is, of 

 course, most easily proved. For instance, if we take 

 three parcels of things e.g., marbles one of 104, 

 another of 92, and the third of 8, and mix them 

 together, then if we count the whole, thus mixed, we 

 shall find their number to be 204. 



