98 



Mil. F. E. SMITH ON THE CONSTRUCTION OF 



Thus, since the resistance of a mercury column of length L and cross-section S is 

 L/106'300 ohms, the constant f must be such that 



106'SOO 



000669 



0-05597 |_ 



0-009841 ~ 



0-05638 

 0-009987 



whence /= 0795. We may now with some confidence apply this constant to obtain 

 the end corrections of the various tubes. In Table VI. these corrections are evaluated 

 and expressed as small lengths to be added to the standard length. The method of 

 calculation is as follows : 



Let r be the mean radius of the standard, and r lt r 2 the radii of the sections at the 

 ends. Then the end corrections are equivalent to two mercury columns at C. of 

 lengths 0795r, and 0795r 2 , and cross-sections irr^ and irr/. The lengths of two 

 columns of uniform section irr 2 which have the same resistance as these are 0795r 2 /r 1 

 and 0795r a /r 2 , and these are the two lengths to be added to the standard. The 

 complete correction is conveniently written in the form 0795r 2 (r l -\- ?* 2 )/?VV 

 Table VI. gives the necessary data for the calculations. 



TABLE VI. , in which the End Corrections are Evaluated. 



The values of the end corrections enable us to now calculate the resistance in 

 international ohms of the standards as erected by Method II. Approximately the 

 resistance is O'l per cent, greater than before. 



