[shaw] THE KELVIN-VARLEY SLIDE POTENTIOMETER 93 



for determining whether a recalibration is necessary or not, because 



the ratio of the two halves of the box can remain fairly constant 



while the ratio of a smaller number of the coils to the remainder alters 



appreciably. An examination of the tables given later will show that 



this was actually the case with our instrument. The following is the 



method for testing the two halves of the slide. 



A box of 100,000 ohms is arranged in parallel with the main slide 



box, between the terminals A and B. A battery is connected between 



the same terminals and a high resistance galvanometer is connected 



between the galvanometer terminal on the vernier box and the middle 



of the extra 100,000 ohms. The main slider is then placed at 50, and 



the vernier at zero. We now have an ordinary Wheatstone's bridge. 



If we call the first fifty coils A and the last fifty B, and if we let the 



two halves of the 100,000 ohm box be represented by C and D respec- 



C A 

 tively, then we would obviously have -^ = -=- if there were a perfect 



balance; but if the four arms differ slightly among themselves there 

 will be a small deflection in the galvanometer. Calling this deflection 

 d, we have then 



7>=i + kd (4) 



where k is a constant depending on the galvanometer and scale. The 

 vernier slider is now placed at the first coil and we get a new deflection 

 d' . We have now, therefore, 



■£- A + 1 ° +kd> (5) 



D 5-10 ^ 



The vernier slider is replaced at zero and A and B are interchanged 

 with respect to the rest of the circuit, giving another deflection d" . 

 Hence we also have 



-§ = 4 + u " (6) 



In practice it is advantageous to obtain the d's by reversing the 

 current through the galvanometer. Assuming that A and B each 

 differ from 50,000 by quantities relatively very small, and eliminating 

 C, D and k from these equations we find that 



i =1- -000200^' (7) 



If a high resistance galvanometer is used this measurement can be 

 made with great accuracy, and this ratio should not vary more than 

 one or two parts in a hundred thousand, during several years. From 

 the year 1894 to the year 1899 this ratio for our instrument fluctuated 

 up and down between .999832 and .999863. In January, 1911, it was 

 .999858. 



