18 Messrs. Hutchinson and Wilkes's Comparison of 



section at 0° C. is found by weighing the volume of mercury, 

 contained at that temperature, and dividing this by L multi- 

 plied by the density of mercury (p) in grammes per cubic 

 centimetre. 



The resistance of a column of mercury of varying cross 

 section is calculated as follows (Maxwell's ' Electricity and 

 Magnetism ') : — 



Let s be the cross section of the tube at a distance x from 

 one end ; let X be the length of a short thread of mercury, 

 when its middle point is distant x from this end ; then, assu- 



c 



ming s constant, throughout the length X, we have s=~ y 

 where C is the constant volume of the thread. 

 The weight of mercury that fills the tube is 



w= P J^= P c2(l)L _ _ (1) 



in which n is the number of points, at equal distances along 

 the tube, where X is measured. 



The resistance of the tube full of mercury is 



E= jY„ = £ 2(x) L ..... (2) 



where / is the specific resistance of mercury for unit volume. 

 Hence, from (1) and (2), 



WB=^ 2W2 (l)g, 



or 



10 4 WRn 2 

 r= - -r^> 



pPsWsg) 



in which r is the resistance of a column of mercury 1 metre 

 long and 1 square millimetre in cross section, at 0° C, ex- 

 pressed in British Association units. 

 In this equation put 



* x O 



!=fl. 



The equation for r now becomes 

 ,= 10*™. 



(3) 



