60 



MR. F. E. SMITH ON TIIK INSTRUCTION OF 



uniformly conical column this becomes p\dxjir (t\ -j- x tan .). If the length of the 

 column be L/ri, its resistance R is equal to pL/irnr^a, where r 1 and r. 2 are the radii 

 of the terminal sections (see fig. 1, p. 62). Now the mean section of the cone is 

 ^TT (r 2 2 -4- r, 2 -j- r,r 2 ) ; hence, in the evaluation of //, the resistance K' of the column 

 is assumed to be SpL/irn (r., 2 + r \ z + r \ r z) ; whence 



R/R' = (r 2 2 + r, 2 + r^/^r,, = 1 + * (*V - rtf/r* 



approximately, which ratio is hereafter denoted by /*", and referred to as the conical 

 correction for the 5-centim. lengths. 



The values of jj." for each of the n -\- a -j- b . . . lengths can now be evaluated, since 

 the manner in which the cross-section changes is known. The mean value must then 

 be multiplied by the mean value of /*' already calculated. Thus a conical correction 

 designated by /i, and equal to the product ////'> is obtained for the standard, the bore 

 of which is to be regarded, not as a series of uniform tubes, but as one of gradually 

 changing section typified by the calibration curve. The resistance of the column of 

 mercury at 0'0 C. may now be written 



L 2 



14-4521 

 106-3 2 



For the evaluation of p." a table of the following form was found very useful. In 

 it j and 2 refer to the terminal sections of the cone, and values of p." are tabulated 

 for various ratios of , to 2 . When the difference of sections exceeds 2 per cent., 

 the value of p." rises rapidly. In practice the ratio a T /a 2 did not exceed 1'015 per 

 cent. 



TABLE I. 



Determination of L and W. 



The ratio of the square of the length of the mercury column at 0'0 C. to its mass 

 may be determined in different ways. The difficulties encountered in any ordinary 

 method of procedure are {!) the mercury column is not terminated by plane 

 surfaces ; (2) the column may not completely fill the tube ; (3) films of air and 

 moisture separate the mercury from the glass. With respect to the last of these 



