Electricity in a uniform plane conducting Surface. 481 



between the sliders D and H. To measure the resistance between 

 A and B in terms of that of the wire E F, it is then only neces- 



f.3. 



sary to press successively the keys 1 and 2, and each time to 

 adjust the slider D so as to give no deflection on the galvano- 

 meter, and then to connect the battery with H, by the key 3, 

 and to find the positions of D required to keep the galvanometer 

 at zero for two positions of H separated by the known amount h. 

 If we denote by s the distance through which D has to be shifted 

 on the wire E F when the battery-contact on the disk is trans- 

 ferred from A to B, and by d the shift of D corresponding to the 

 shift of H over the distance h, we have 



resistance between A and B resistance of h 



resistance of 5 



resistance of d ' 



and since s, h } and d are all of them lengths measured on the 



same wire, their resistances are simply as their lengths. Hence, 



taking as unit of resistance the resistance of unit length of the 



wire EF, we have . , . , ^ h 



resistance A to ±> = $-.• 



d 



It will be observed that the ratio -, which we will hereafter de- 

 note bv -, is the same as that of the resistances E ABF and 



EDF. 



51. In all measurements of resistance it is necessary, not only 

 that the contact of the electrodes A and B with the disk should 

 be constant and easily reproduced, but also that the area of con- 

 tact should be measurable; the difficulty of realizing these 

 conditions with accuracy is by far the most important source of 

 error to which the determinations of resistance are liable. In 

 order to obtain a measurable and constant surface of contact, the 

 spring contact-pieces employed in the experiments for plotting 



Phil. Mag. S. 4. Vol. 50. No. 333. Dec. 1875. 2 I 



