Reading Resistance-Thermometers. 715 



Since a 2 and /? are small let us neglect for the present the 

 terms beyond f 2 . 



If we can now make the term in t' 2 vanish, x will reduce 

 to the form 



The condition for this is 



(l+ ? )( ? « 2 -/3)=0. 

 The factor (1+^), being equal to — tj cannot vanish 

 since ,< is not zero, and thus the requisite condition is 



Hence ^ q 



s -i=*=«* 



therefore 



s=, -/3 (2) 



Since a and ft are both positive for platinum, f 1 + — j is 



positive and therefore 5 is a real resistance. When s is 

 made to have this value, then 



ar=.r (l ■*• mt) 



where x is the reading when £ = 0° C. 

 We have 



and 



t = 



s-V 



X — Xq 



(3) 



w^l-h^— , (4) 



Thus t is directly proportional to the increase of x above 

 the zero-reading x . 



Clearly this proportionality still holds when the bridge-arms 

 are not all equal, so long as x and s are kept in the proper 

 ratio. The compensating leads, being in the measuring arm, 

 must have resistance in proportion to it. In practice, it is 

 desirable to be abb' to use tor the variable part ZB an ordi- 

 nary resistance-box with sets of IP-ohm, L-ohm, and Ol-ohm 

 coils (with ro~o~ths also, if desired for the highest accnracy); 

 and, in order to do this with a platinum thermometer of 

 any resistance, the arm J)C (fig. 1) is made to have the 



