OF ARTS AND SCIENCES. 289 



Means, 3149.49 68.7 3149.31 + 0.18 



In terms of the Brunner scale, therefore, my own unit is .000317 cm. 

 X 0.18 = .000057 cm. too short. Subsequent investigations have 

 shown that both units contain errors of considerable magnitude when 

 compared with the hundredth part of the Coast Survey meter at 68°. 



The following are the relative errors of each millimeter expressed 

 in terms of the entire length of the centimeter : — 



Notwithstanding the fact that great advances have been made in the 

 science of exact measurements since the construction of the normal 

 standards now in use, there are several problems connected with this 

 Bubject which require further investigation. It is a well-known fact, 



VOL. XV. (x. S. VII.) 19 



