312 THE ELECTRIC TELEGRAPH. 



this is rarely the case, the value of x is given with the 

 nearest approximation to the truth by the formula 



x = W 1,000 +0 a' 

 1,000 + d a 



When double readings are made that is, when in each 

 experiment the comparison and measured resistances are in- 

 verted there is no need for having the bisected wire so 

 rigidly in contact at both ends, provided the contact at the 

 end from which the lengths are measured is without sensible 

 resistance, and the resistance of the other end does not 

 change during the double observation. On this principle 

 we have constructed a bridge-balance of this kind, in which 

 the bisected wire is soldered between good contact clamps at 

 one end, and at the other is held by a metallic block running 

 upon an adjusting screw, by which the wire can be strained 

 or slackened at pleasure, the total length not appearing, the 

 resistance x being given by 



Tir & 



X = W r 



a 



A method of increasing very materially the sensibility of 

 the system was used by us in Dr. Siemens' laboratory in 

 1861. It consisted in inserting between the ends of the 

 platinum wire and the points branching to the galvanometer 

 and resistances W and x, an equal resistance coil, r, which 

 amounts, in fact, simply to lengthening the bridge-wire. 

 With this arrangement, the contact rollers can be moved' 

 considerably farther from the middle point with less error. 

 The resistance a? by a single reading, in this way, therefore, 

 is 



x = W 



1,000 a +r 



This method of testing with continuations was not prac- 

 tised to any great extent, however, and was, we believe, 

 never published until Dr. Matthiessen constructed a similar 

 arrangement with his apparatus, in connection with the Unit 



