1898.] of temperature by means of Platinum Thermometry. 527 



" By whatever amount the resistance of one arm of the shunt 

 is increased, that of the other is to be diminished." Thus the 

 sum of the resistances of the arms of the shunt is constant. 

 Let it equal 8. It will be shewn that if S is chosen rightly at 

 the outset, and if the above rule is obeyed, then the condition 

 that the bridge is balanced is that the arms of the shunt are 

 linear functions of the temperature. By suitable choice of con- 

 stants we may make the resistance in one arm numerically equal 

 to the temperature. The rule is most easily followed by connect- 

 ing two ordinary resistance boxes in parallel and transferring 

 plugs from one to the other, so that one box gains in resistance 

 what the other loses. 



§ 3. Demonstration of the accuracy of the Method suggested. 



Since the equation connecting resistance and temperature is 

 that of a parabola with axis inclined, any of the following equa- 

 tions may be used in which R t is the resistance at t, R the 

 resistance at 0°, <f> is the change of resistance between 0° and 

 100°. 



R t = C + at - fit"- (1), 



R t = a'(t + z)-/3'(t4-zy (2), 



V 100=s 14-iy (S) - 



The constants in the three equations are connected as follows: 

 C — ol'z — fi'z- = R , 



(loo + SH 



a = a' - 2/3z 



/3 = (3' 



100-' 

 8<f> 

 100 3 



Now equation (2) can be written as follows : 



1 



Rt 



+ 



«(t + z) a' 2 



which will at once be recognized as the expression for the effective 

 resistance of two conductors in parallel whose individual resistances 



are a (t + z) and - _ — a' (t + z) respectively. Since these two are 



each linear functions of the temperature and since their sum is 



