OUR METHOD OF DETERMINATION. 73 



apple had come from the moon " was not he guilty of extra- 

 polation? But his extrapolation we call the law of univer- 

 sal gravitation, and it has been so called for two centuries. 



If you have the truth, you may extrapolate, and nature 

 will vindicate you. 



But if you are surrounded by frauds and lies, and if your 

 very soul has been filled by this contamination, then do not 

 get out of the miry hole, do not extrapolate either yourself 

 or anything else next to you, for the Light of God's Sun will 

 show to all the world where you have been and what you 



The Ratio and the Excess. 



And now finally let us apply this little lesson also in a 

 strictly formal way, in numbers and by calculation, exactly 

 as if we had an " absolute " atomic weight ratio to compare 

 with the " analytical ratios" of actual experience. 



Here we have the legal weight of the Half Eagle as the 

 absolute standard of comparison, namely 8.359 grammes. 

 That is our unit. 



We have also the present actual "mean weight" of 20 

 Half Eagles of 1881, being 8.333 grammes. 



We have likewise the actual " mean weight " of 20 Half 

 Eagles of 1897, namely 8.357 grammes. 



We had to reject one of the coins of 1897 weighing only 

 8.235. 



We finally obtained by the dreadfully criminal operation 

 of extrapolation the estimated weight of a new Half Eagle 

 at the U. S. Mint to be 8.361, although we regretfully admit 

 we ne'r had such an one in hand. 



Let us calculate the corresponding " analytical ratios" 

 to our usual five places, exactly as we do in our absolute 

 atomic weight determinations. That will give us a very 

 useful case of comparison, from the best work that can be 

 done at the mint, on the most valuable material, gold, when 

 again picked up after having circulated in this sinful world 

 at large, and brought upon the balance and tested " only to 

 the milligramme," not to the thousandth of the milligramme ! 



