RESISTANCE BOXES. 319 



for independently bringing into the circuit any of the resistances of 

 which the box is made up. 



927. Many different subdivisions may be adopted for graduating 

 the values of the resistances. The most economical would be to use 

 a series of coils, the resistances of which vary as the terms of the 



progression i, 2, 2 2 , 2 3 2 n . With n+ i coils we should have all 



the resistances from i to 2 n+l - i. By taking twelve coils, the first 

 of which is an ohm, we may obtain all resistances from i ohm to 

 8191 ohms. 



Thus, to get a given resistance 107, for instance it is sufficient 

 to write the number in the primary system 2 6 + 2 5 + 2 3 + 2 + i, or 

 iioion, and to leave open all the coils which correspond to the 

 ciphers i, closing by plugs those which correspond to the zeros. 



It is desirable to add to the series a supplementary coil equal to 

 unity, which would enable us to verify by comparison the relative 

 values of the various coils. 



The small calculation required by the preceding arrangement 

 makes its use very inconvenient. 



The coils may be combined like boxes of weights in taking for 

 the series the values 



i; I, 2, 2, 5; 10, 10, 20, 50; 100, 100, 200, 500; 

 1000, IOOO, 200O, 5000. 



We have thus a total of 10,000 units, and the means of verifying 

 all the coils. 



The coils are most frequently arranged in a linear series, and all 

 those which are not to be used are plugged ; but this arrangement is 

 so far inconvenient that a variable number of plugs is used for each 

 combination, and therefore a variable number of contacts, the effect 

 of which cannot always be neglected. 



A better arrangement is that of a dial box (Fig. 181). Each dial 

 consists of nine equal coils, connected by brass plates numbered 

 from to 9, there being no connection between the plates 9 and 0. 

 In the centre is a copper disc, connected with the plate of the next 

 dial by plates or bars of brass L, L', L". The plugs are placed 

 between the disc and the plates of the segments ; as their number is 

 fixed, one for each dial, and always at work, we may consider that 

 the resistance they introduce into the circuit is constant. 



The boxes usually contain four dials corresponding to the units, 

 tenths, hundreds, and thousandths, as seen in the lower part of 

 Fig. 1 8 1. With a supplementary unit placed inside the box, the 



