Adjustment of Resistance- Coils. 269 



fiftieth part of $t, and need not, with care, exceed one two- 

 hundredth. This reduces the expression for the error to 



6 = 



O+i) 2 



Suppose the error r made in measuring the shunt is as much 

 as 2 per cent., and the value of the shunt-ratio n only 10 ; 

 then, as the formula shows, the final error is only *0165 per 

 cent., or in a 1-ohm coil amounts to 0*000165 ohm. But if, 

 as is in practice much more frequently the case, the shunt- 

 ratio n is 50 instead of 10 (and often more), then with a 2-per- 

 cent, error in the shunt the final error is only '000767, or in 

 a 1-ohm coil amounts to 0*00000767 ohm. In practice, the 

 error made in cutting off the shunt wire is nothing like 

 2 per cent.: one half per cent is easily attainable. 



6. The special advantages possessed by this method of adjust- 

 ment cease to be available for resistances exceeding 10 ohms, 

 as it is not convenient to measure off shunts of 500 to 800 

 ohms ; for the wire is either inordinately long, or too thin for 

 a reliable proportion to exist between length and resistance. 

 For resistances exceeding 10 ohms we therefore modify the 

 process of adjustment as follows. The wire is roughly mea- 

 sured out as before, to a value slightly exceeding the final 

 correct resistance. It is soldered to the usual stout copper 

 terminals ; but before it is doubled, twisted, and wound up, a 

 spot is bared at about one tenth or less of its length from one 

 end. At this point a short piece of copper, about 2 millim. 

 thick and 3 centim. long, is soldered. The resistance of the 

 whole wire is then very accurately measured by Foster's 

 method, and the resistance of the short portion between the 

 terminal and the copper piece is also very accurately mea- 

 sured. We next calculate the value to which the resistance 

 of this short piece must be reduced in order to bring the total 

 resistance to its correct desired value, and then the short 

 portion is shunted down to the required amount by a shunt- 

 wire calculated, measured out, and soldered on, exactly as 

 described before. 



7. In conclusion, I would remark that in advancing from 

 coils of 1-ohm to coils of higher values we have followed the 

 suggestion made by Lord Rayleigh in 1881, of passing by 

 three threes plus one to ten, and three thirties plus ten to one 

 hundred. We have, however, found it much more convenient 

 not to use the ingenious but complicated system of mercury- 

 cups suggested by Lord Rayleigh for facilitating this operation. 

 Instead of this we have employed the following simpler device. 

 Six holes are drilled in a block of paraffin for mercury-cups. 



