330 THE ELECTRIC TELEGRAPH. 



To ascertain the values of the radii, B, and r, for each 

 tube to be used as a measure, the only way is to fill the 

 tube with pure mercury at a known temperature and weigh 

 it, and to accept the reciprocal-lengths of the mercury drop, 

 with which the tube is calibrated, as the relations of its 

 sectional area, at different points. 



The weight, Gr, of the mercury is arrived at by repeatedly 

 filling and weighing, making the necessary reductions for 

 temperature and atmospheric pressure, and taking the 

 mean of several observations. If a is the specific gravity 

 of mercury at C, the volume V is 



For the value of V we have also the geometrical expression 

 for the contents of a truncated cone. 



which, divided by R r, becomes 



IfrV" " E/S 

 And if we make 



-5- > 



Whence 



_ Y 



^ "~T^r 



n . . 



1 + </<* + ^ 



v/a 



Or, with the value Y = - inserted, 



9 3 



which is now substituted for R r in equation I., and gives 

 for the whole resistance of the cone 



