470 WENNER AND WEIBELI TESTING OF POTENTIOMETERS 



where 



E is the value of the unknown electromotive force 



/ is the range readings 



ei is the reading of the highest dial 



62 is the reading of the next highest dial, etc. 



s — 2 

 c = where s is the value of the known electromotive force 



s 



and s is the reading of the known electromotive force dial or dials, 

 and b, d, ai and ^2, etc., are small corrections due to errors in the 

 adjustment of the varioi5s resistance sections. 



The correction ai depends only on the reading ei, a<> depends 

 only on the reading 62, etc., 6 depends only upon the reading 

 s, and d depends only upon /. A table can therefore be con- 

 structed for each dial giving the corrections corresponding to 

 each of its possible readings. 



Let i?e be the resistance in the potentiometer between the 

 JS'-terminals and R^ that between the *S-terminals. Then if 

 the total current is independent of the settings of the various 

 switches or plugs, 



E = .S R,/R, = f[{e, + a,) + {e, + a,) + etc.] {I + h + c + d) (2) 

 Thus if Re/Rs is determined for the various readings of /, of e 

 and of s the corrections h, d, ai, ^2, etc., can be determined. 



In order to reduce the time required for making the measure- 

 ments and to obtain the data in such form that the corrections 

 can be more easily calculated, a special piece of apparatus was 

 constructed and has been in use during the past two years. This 

 apparatus which we shall call a ratio-set has been found to 

 furnish a rapid and direct means for calibrating all types of 

 potentiometers which have so far been submitted to the Bureau 

 of Standards for test. It is equivalent to 211,110 resistance 

 sections of 0.01 ohm each, connected in series and so arranged that 

 a branch connection (either to battery or galvanometer) can be 

 made between any two adjacent sections. Or it is equivalent 

 to a slide wire on which contact can be made at 211,110 points. 

 The apparatus is made of 100 resistance sections, 20 of each of 

 the following denominations; 100 ohm, 10 ohm, 1 ohm, 0.1 ohm, 

 and 0.01 ohm. Five dial switches serve to shift resistance sections 



