12 ELEMENTS OF SCIENCE 



the science of number, which science is the arithmetical 

 part of the great science of mathematics. 



Thus by these arithmetical symbols we can elucidate 

 most important results as to real things, without paying 

 attention to anything more than the symbols themselves, 

 till the result sought is attained. If we know that the 

 numbers used refer to marbles or any other set of things, 

 we can freely use them and work out results without 

 thinking of the objects to which they refer till the end 

 of the process. This is of enormous assistance and a 

 prodigious economy of human effort. 



There is no special difference between multiplication 

 and addition. Multiplication is the addition of any 

 number to itself a certain number of times over, and a 

 number is said to be multiplied by that number which 

 expresses how many times the former number has to be 

 added to itself. Thus if 10 be multiplied by 2, it has 

 to be added to itself (or taken) twice ; if it is multi- 

 plied by 9, it has to be taken nine times, and so 

 becomes 90. Nevertheless though multiplication is 

 essentially but a form or mode of addition, practically it 

 is a very different process, and it is one by which we 

 can most clearly see the great convenience of the system 

 of numeration adopted, and of the practice of placing 

 figures in such a way that they express their value by 

 their mere position. 



The results of a definite small number of additions of 

 a few small numbers have been calculated for committal 

 to memory according to what we know as the multiplica- 

 tion table. This being learnt, two sums, the figures of 

 which have been superimposed in due order of value, can 

 be multiplied together, by the process of multiplying the 

 separate figures which compose such two sums, just 

 as we have seen that two sums can be added together 



