430 H. A. Rowland — Electrical Measurement. 



together and wound into coils. In this way the self induc- 

 tances of the coils are all practically equal and the mutuaL 

 inductances of pairs of coils also equal. Hence we have only 

 to measure the minute difference of these two to reduce the 

 constants of the coil to one constant, and yet by proper connec- 

 tions we can vary the inductances in many ratios. Three 

 wires is a good number to use. However, the electrostatic 

 induction between the wires must be carefully allowed for or 

 corrected if much greater accuracy than yi-g- is desired. 



By these various methods the measurement of capacities and 

 inductances has been made as easy as the measurement of 

 resistances, while the accuracy has been vastly improved and 

 many sources of error suggested. 



Relative results are more accurate than absolute as the period 

 of an alternating current is difficult to determine, and its wave 

 form may depart from a true sine curve. 



Let self inductances, mutual inductances, capacities and 

 resistances be designated by L or I, M or m, C or <?, and R or 

 r with the same suffixes when they apply to the same circuit, 

 the mutual inductance having two suffixes. Let b be 27T 

 times the number of complete periods per second, or b = 27m. 



The quantities &L, bM. or — are of the dimensions of resist- 



ance and thus — , 6 2 LC or & 2 MC have no dimensions. & 2 LM, 



L M . M 



— or — have dimensions of the square of resistances. 



Where we have a mutual inductance M 12 , we have also the 

 two self inductances of the coils L 1 and L 2 . When these coils 

 are joined in the two possible manners, the self inductance of 

 the whole is 



L 1 +L a + 2M ia orL 1 +L 2 -2M 12 . 



In case of a twisted wire coil the last is very small. Likewise 

 L^— M 2 12 will be very small for a twisted wire coil, as is found 

 by multiplying the first two equations together. 



If there are more coils we can write similar equations. For 

 three coils we have 



L x + L 2 + L 3 + 2M ia + 2M 13 + 2M 23 



1. L 1 +L 2 + L 3 -2M 12 -2M 13 + 2M 23 



2. L 1 + L 2 + L 3 -2M 12 + 2M l3 -2M 23 



3. L 1+ L 2 + L 3 + 2M 12 -2M 13 -2M 23 



Connecting them in pairs, we have the self inductances 



L 1 + L 2 + 2M 12 L t + L 3 + 2M 13 L 2 + L 3 + 2M 23 



L X + L 2 ^2M 12 L 1 + L 3 -2M J3 L 2 + L 3 -2M 23 



There are many advantages in twisting the wires of the 

 standard inductance together, but it certainly increases the 



