ELECTEICAL MEASUREMENT BY ALTERNATING CURRENTS 295 



the fixed and the other through the suspended coil of an electrodynamo- 

 meter. By this means a heavy current can be passed through the fixed 

 coils and a minute current through the movable coil, thus multiplying 

 the sensitiveness possibly 1000 times over the zero current method. 



I have also found that many of the methods become very simple if 

 we use mutual inductances made of wires twisted together and wound 

 into coils. In this way the self inductances of the coils are all practi- 

 cally 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 

 connections 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 y^ is desired. 



By these various methods the measurement of capacities and induc- 

 tances 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 ra, C or c, E or r with the same suffixes 

 when they apply to the same circuit, the mutual inductance having two 

 suffixes. Let & be 2 TT times the number of complete periods per second, 



or & = 2-n. The quantities &L, bM or ^ are of the dimensions of 



resistance and thus -^., &*LC or b*MC have no dimensions. I'LM, -^ 



M 



or -fy 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 t and L 2 . When these coils are joined in the 

 two possible manners, the self inductance of the whole is 



L, + Z 2 + ZM U or L! + L, - 2M n . 



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

 L 1 L 2 3/ 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 



