Measurements of Precision in Platinum Thermometry. 563 



Q is the variable arm of tlie bridge, and hence a must auto- 

 matically change with Q if the relation a = &(R + Q)/(S — R) 

 is always to be satisfied. Fortunately, this is easily possible, 

 as will presently be seen. 



It is now necessary to indicate the most favourable values 

 for the constant arms of the bridge, and to get an idea of 

 the probable errors introduced by assuming P = QR/S to be 

 an exact equation. 



We suggest as values for the arms of the bridge 



R=l ohm. 

 S = 100 ohms. 

 b = 100 ohms. 



Q and a are variable arms, the value of Q being about 

 254 ohms when P, the platinum thermometer, has a resistance 

 of 2 '54 ohms. 



With regard to the probable errors we will consider two 

 cases: (lj when the thermometer leads are equal in resistance, 

 (2) when they are not equal. 



For this purpose equation (10) is conveniently recast in 

 the form 



p - ~: 



-d QR RLo L, /b ~ b T T \ , 10X 



P = ^- + -S- + (a + 6 + L 1 + L,) (§ Q - a+ S L *- L '> • (13) 



Substituting a value for Q obtained from the relation 



a = 6(R + Q)/(S-R), we obtain 



QR Rf (« + &) j ( a + fr + L 2 +gL 3 \ ^ 



S ,+ Sl 8 ^(a + ^-hLi + La)/ ^V a + 6 + Li + L// 



The nominal value of R/S is 0*01, that of 6/S is 1'0, of L 1? 

 L 2 , L 3 , and L 4) 0*15 ohm, and the minimum value of (a-\-b) 

 is 354 ohms. Hence, if L 1 = L 2 = L 3 , the total value of all 



the terms after -~- cannot exceed 0*00000 1 4 ohm, corre- 

 sponding to a little more than one ten-thousandth of a 

 degree. If now L l5 L 2 , and L 3 differ in resistance by 1 per 

 cent., a total error of 0-"00001 5 ohm or 0°*001 5 C. is introduced. 

 As the leads are readily adjusted within much lets than 1 

 per cent., we may take the simple equation 



P=QR/S 



to be sufficiently correct. 



