ELECTRICAL MEASUREMENTS 333 



The above results show to what accuracy self-inductances of different 

 values can be compared to each other, or to one of the self-inductances 

 taken as a standard. The reason that the agreement between the 

 different determinations is not greater than it is, even though the elec- 

 trodynamometer was sensitive to a change of 1 part in 10000 in R -\- r, 

 is that there was always some little heating of the resistances, and 

 although they were measured in each determination on a Wheatstone 

 bridge, still it was impossible to determine the exact resistance at the 

 time that the experiment was made. This slight effect of the heating 

 of the resistance would not enter in the comparison of two nearly equal 

 self-inductances, that is the comparison of a coil with a standard. The 

 accuracy of this comparison can be made to depend on the accuracy 

 with which R -j- r can be determined for zero deflection, and this can 

 be done to about 1 part in 10000. To do this, first the standard coil 

 and the coil to be compared are substituted in turn in place of L in 

 figure; they are thus compared separately to a third coil. But as the 

 standard and the coil to be compared are nearly equal in self-inductance, 

 the difference or self-inductance can be determined by the amount 

 necessary to change R -\- r, and this change will be nearly independent 

 of the slight heating of the resistances. To make a coil of the same 

 self -inductance as the standard, the standard is placed in the R -\- r 

 circuit and the value of R -\- r is found that produces no deflection. 

 The coil to be compared is then substituted in place of the standard 

 keeping R -)- r fixed, and the self-inductance of this coil is changed 

 until there is no deflection, as in the case of the standard. The 

 accuracy with which this can be done depends on the accuracy with 

 which R -f- r can be set or 1 part in 10000. The method therefore 

 gives a means of comparing and constructing coils to agree in self- 

 inductance to within 1 part in 10000 with a standard. 



Method 6. Zero Method for the Comparison of 8 elf -Inductance with 



Capacity 



This method resembles method 12 and the connections are made as 

 in the figures when both the hanging coil and fixed coils of the electro- 

 dynamometer are shunted off the main circuit. 



Let the currents be denoted by C>>*, C^+M, (7 2 e*(W+W, O.eW+fc), 

 and (7 4 itbt+<M . The resistance by R", /, R and r. The capacity by C. 

 The self -inductance by L. A' and A" are reversing commutators and 

 F the terminals of the fixed coils and H the terminals of the hanging 

 coil of the electrodynamometer. 



