Measurement of some Standard Resistances. 



415 



to be accurately known, the value of the 100-ohm coil can be 

 found. In this way the following results were obtained : — 



Table II. 



Method IV. 



Method III. 



Difference expressed 



as a fraction of the 



whole. 



103017 1 

 100-020 . J 



100045 1 

 100-047 J 



1000-37 1 

 1000-36 J 



100051 "j 

 1000-52 ) 



100-022 

 100045 

 1000-31 

 1000-50 



- 00003 

 +■00001 

 + -00005 

 4- -00001 



In one case only is the difference greater than that due to 

 an error in temperature comparable with o, l C, and it will 

 be noticed that the difference between two determinations of 

 the same coil by Method IV. is comparable with the differences 

 between the results of the two methods. 



It thus appears that to an accuracy of some two or three 

 parts in one hundred thousand, the various methods lead to 

 the same results. To reach a higher accuracy would involve, 

 if the coils were of platinum-silver, the knowledge of their 

 temperature to less than 0°'l C. The end might, however, 

 better be attained by employing manganin or some such 

 alloy. 



Possibly this paper may serve a useful purpose by calling 

 attention to the various methods which may be employed to 

 build up multiples of a unit resistance and by giving some 

 account of the accuracy attained. 



A source of uncertainty in resistance measurements is due 

 to the fact that the coils are heated by the current. It is 

 clear that the currents traversing the 1000-ohm coil in the 

 two arrangements described above were different ; the concord- 

 ance of the results tends to show that the error due to heating- 

 was in these experiments negligible. 



Appendix. — Added Sept. 18, 1900. 



In the theory of Method I. given above, no notice is taken 

 of the fact that the length of copper connecting each of 



