the Mercury Unit of Electrical Resistance* 



167 



we obtain the respective resistances* at 0° C. in millimetres, 

 that is to say, the resistance of a cubic millimetre of mercury 

 at 0° C. 



Table IV. 



No. millims. 



3 ..... . 556-051 



5 193-726 



7 1917-54 



8 2601-46 



10 1541-10 



11 438100 



12 165211 



13 1636-10 



14 1419-33 



15 1524-88 



But, in practice, the resistances with which the tubes enter into 

 the measuring-apparatus are greater than their calculated values 

 by so much as is due to the passage of the current from their 

 openings into the cups of mercury for the connecting wires. 



This resistance can, without sensible error, be considered as 

 the resistance of a hemispherical shell whose inner radius is 

 equal to r, the inner radius of the tube, and whose outer radius 

 is infinitely great in comparison with r. The resistance dy of a 

 shell of the thickness dx and radius x is expressed by 



7 dx 

 dy = 



whence 



dx 1 r 



Xxhc 2r7r ~~ 2r 2 7r 



It therefore amounts to increasing the length of each of the tubes 

 by the length of its radius f. 



* An idea of the exactness of this method of reproduction will be best 

 obtained by a direct comparison of the calculated values according to the 

 two previous and present determinations. 



2*V 



-r 



Tube. 



Original 

 determination 1 . 



First 

 reproduction 2 . 



Present 



reproduction 3 . 



3 

 5 



7 

 8 



555-87 

 19356 



555-99 



19373 



191732 



2600-57 



55605 



193-73 



191754 



2601-46 



1 PoggendorrPs Annalen, vol. ex. p. 9. 



2 Ibid. vol. cxiii. p. 95. 3 The above Table. 



t The value of the resistance y is a little too great, from the supposition 

 that the radii are in the proportion r : co , and a little too small, from the 



