94 THE ROYAL SOCIETY OF CANADA 



One of the simplest ways to find out if a recalibration is necessary- 

 is to measure resistances in several such ratios as 1 to 10, 1 to 8, 1 to 6, 

 1 to 4, and 1 to 2, then to interchange the terminal connections and 

 repeat the observations. If after applying the corrections determined 

 by the last calibration it is found that there are discrepancies between 

 the two sets of observations, then it is evident that the slide needs 

 recalibrating. If the magnitude of the discrepancy appears to vary 

 systematically with the magnitude of the ratios compared, it is pro- 

 bable that some particular coil is responsible for the whole trouble. 

 These can easily be singled out, and a complete recalibration becomes 

 unnecessary. 



Theory of the Calibration. 



The method finally adopted by Prof. Callendar for the calibration 

 consists in determining the relative values of the coils of the main dial 

 in pairs by comparison with the 2000 ohms of the vernier dial. The 

 connection between F and F' is disconnected and replaced by a pair 

 of 2000 ohm coils in series which form ratio arms. A battery is con- 

 nected to the point between the two 2000 ohm coils and the terminal 

 E ; and a galvanometer is placed in parallel with the ratio arms P and 

 Q, thus forming a Wheatstone's Bridge for comparing the vernier 

 dial F with any pair of consecutive coils. Readings may now be taken 

 with the slider at any reading and if we designate the 101 coils by R\, 

 i?2, Rz, ... i?ioi, we can get a hundred equations of the same type as 

 (4), viz. 



Rx + Rt = V^ + kdo 



R 2 + Rz= V^r+kdx 



R W0 +Rl0l = V^r +M, 



(8) 



Q 



where d , d\, . . . .dm are the deflections on the galvanometer correspond- 

 ing to the readings 0, 1 . . . . 100 on the slider, and k is a constant 

 which can at once be obtained by changing P or Q by one ohm. It 

 is necessary to know one more equation, and using two one thousand 

 ohm coils in series between the terminals E, F and following the same 

 plan as that used for the determination of the ratio of the two halves 

 of the main box we can at once get equations of the types (4) and (6) 

 and by altering one of the thousand ohm coils by one ohm we can 

 obtain an equation corresponding to (5) and from these we get 



■f = l + ô (9) 



where b represents the small known quantity. 



