296 HENRY A. KOWLAND 



12 + 2M 1 



2. 

 3. 



Connecting them in pairs, we have the self inductances 



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



There are many advantages in twisting the wires of the standard 

 inductance together, but it certainly increases the electrostatic action 

 between the coils. This latter source of error must be constantly in 

 mind, however, and, for great accuracy, calculated and corrected for. 

 But by proper choice of method we may sometimes eliminate it. 



For the most accurate standards, I do not recommend the use of 

 twisted wire coils, at least without great caution. But for many pur- 

 poses it certainly is a great convenience, especially where only an 

 accuracy of one per cent is desired. In some calculations I have made, 

 I have obtained corrections of from one to one-tenth per cent from 

 this cause. 



For twisted wires the above results reduce to 3L -f- 61f, 3L 2M . 

 Similar equations can be obtained for a larger number of wires. For 

 twisted wire coils, n wires joined abreast, the self induction is 



-=1 , which is practically equal to L or M. The resistance 



is E/n. 



When we have n = p -\- m wires twisted and wound in a coil and we 

 connect them p direct and m reverse, the resistance and self induction 

 will be 



nR*+FR[AC+CnAB] , If [n (A + B) 0~\ + VABC 

 (nR)*+(bC? 2 



where R is the resistance of one coil and 



A = L + (n 

 B=L - M 



This gives self inductances and resistances equal or less than L and R. 

 The correction for electrostatic induction remains to be put in. For 

 the general case, the equation is very complicated for coils abreast, 

 with mutual inductances. 



The number of mutual inductances to be obtained is M for two 

 wires, 0, M, 2M for three wires, 0, M, 2M, 3M for four wires, etc. From 



