58 MR. F. E SMITH ON THE CONSTRUCTION OF 



The International Ohm. 



At a meeting of the British Association Committee at Edinburgh in 1892, the 

 question of establishing identical electric standards in various countries was discussed. 

 Eventually, the following resolutions, amongst others, were agreed to : 



1. That the resistance of a specified column of mercury be adopted as the 



practical unit of resistance. 



2. That 14*4521 grammes of mercury in the form of a column of uniform cross- 



section, 106 '3 centims. in length, at C., be the specified column. 



In the construction of such a standard the accurate measurements are, therefore, 

 those of length and mass. For the purposes of this paper the above definition has 

 l>een extended as implying 106 '300 centims. 



Theory of Construction. 



If L be the length, and s the uniform cross-section of a column of mercury, then 

 its resistance R is given by the equation 



R = P L/s (1), 



where p is the specific resistance of the liquid. 



If W be the mass of the column, and A its density, then 



R=pAL 2 /W ....... (2). 



Since, when L = 106 '300 centims. and W = 14 '4 521 grammes, R = 1 inter- 

 national ohm, the resistance of any uniform column of mercury is such that 

 R = 14-452lL 2 /(106-3) 2 W. 



The departure of the column from a truly cylindrical form is, however, unavoidable. 

 In a well-chosen standard the tube is conical, preferably uniformly so, but more often 

 in practice it is best likened to a series of truncated cones of various lengths. It is 

 true that unless the section changes by more than 1 per cent., the value of the 

 resistance as calculated from equation (2) is correct to O'OOl per cent., but such a 

 tube is exceptional. In consequence, a correction for this conicality termed the 

 conical correction has to be applied. 



In the case of tubes varying considerably in cross-section, an elaborate calibration 

 is necessary, and a preliminary set of observations is therefore advisable. 



If W be the mass of a small quantity of mercury introduced into the tulie for the 

 purpose of calibration, X the length of the mercury thread when its mid-point is at a 

 distance x from some fixed mark, and A the density of mercury, then n = W/AX. 

 where s is the mean section of that portion of the tube occupied by the thread. 



If the length X be measured at n points at equal distances along the tube, then the 

 mean section of the whole tube is, to a first approximation (2W/AX)/w. 



