62 



MR. F. E. SMITH ON THE CONSTRUCTION OF 



the mercury column of section irr 2 , to which it is equivalent, is OD (1 + OD*/3?~). 

 A measurement of OD and of r enables us, therefore, to calculate the length of a 

 mercury column equivalent to the meniscus. 



1 



O 



B 



Fig. 1. 



Fig. 2. 



It was this latter method which was adopted. When calibrating a tube, the value 

 of OD was variable, but since the value of 1 -j- OD 2 /3r 2 never exceeded T03, the 

 equivalent length ^ OD has been assumed as correct, the discrepancy being beyond 

 the degree of accuracy desired. This approximation does not, however, suffice for 

 determinations of cross-section. In such cases the complete formula has been 

 employed. 



The fact that in any determination of L and W the mercury column may not 

 completely occupy the interior of the tube is not a serious disturbing factor, since, if 

 L e /W is accurately known for any one portion of the tube, its value for any other 

 portion may be estimated from the calibration data. 



Let Li,, L 2 , Si, S 2 , W,, and W 2 represent the relative lengths, mean cross-sections, 

 and masses of mercury occupying two different portions of the same tube. Then 



(2W 2 /A 2 + a 3 W 2 /A, t , + 



L, 2 /W, LjS s _ 

 L 4 /W 2 "" LjSi " 



where the values of n u 2 , a lt a 2 , &c., are obtainable from the calibration data. The 

 ratio SS/B! is, however, more conveniently obtained from the calibration curve. 



Fig. 3. 



Let the limits AB (fig. 3) represent that portion of the tube employed for a mercury 

 standard, and let OX be the mean line of the curve AB. The ordinate value of OX 

 is the mean value of A, the thread length employed in the calibration, and may be 



