IT'S PROBABILITY. 



We term a precision " high " when the limit of the final 

 possible error is small. 



To make our demonstration as strong as possible, we will 

 suppose the degree of precision to be o.oi only in all cases^ 

 and count only 12 of the thirteen elements we actually have. 



On another occasion we may take the full value of all; 

 here we desire to give every advantage to the other side. 



If we limit the precision to one hundredth only, we have 

 50 such on either side of the atomic weight terminating .00 

 (to the hundredth exactly). Half of these are negative, the 

 others positive; in all, one hundred distinct possible values. 



Hence for any one element, the value terminating with 

 .00 is just one in one hundred possible ones. 



For tivo elements, any one of these 100 decimals might be 

 combined with every one of the 100 of the first; hence, the 

 total number of possible combinations of such decimals is 

 iooX IO f r ^vo elements. 



Only one combination out of these 10 ooo equally possi- 

 ble ones is the one in which both atomic weights terminate 

 in .00. 



It will be readily seen, that for twelve elements , the 

 chance that all twelve atomic weights terminate .00 is only 

 one in 100 raised to the I2th power, that is 



as I tO I OOOOOO 000000 OOOOOO OOOOOO. 



In case we had counted the thirteenth element in, this 

 number would have been hundred times as large, and con- 

 tained 26 ciphers. 



For every element for which the precision reaches the 

 thousandth, we would have gained one additional cipher in 

 this big number. 



We see that we could have insisted on a million times as 

 targe a number as the one above given. 



But I think the above number is large enough for our 

 purpose of demonstration. Let us try to express the result 

 in words. 



The chance that all the twelve chemical elements have their 

 atomic weight^ expressed to the hundredth of a unit, terminate 

 -with tivo ciphers, is as ONE to the number 



I OOOOOO OOOOOO OOOOOO OOOOOO. 



