H. A. Rowland — Electrical Measurement. 431 



electrostatic action between the coils. This latter source of 

 error must be constantly in mind, however, and, for great accu- 

 racy, 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 purposes it certainly is a great convenience, espe- 

 cially 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 + #M, 

 3L— 2M. Similar equations can be obtained for a larger num- 

 ber of wires. For twisted wire coils, n wires joined abreast, 



the self induction is - — r , which is practically equal to 



L or M. The resistance is R/?i. 



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 



nU 3 + b 2 R[AC + BC-nAB] R 2 [;i(A + B)-C]+5 2 ABC 



(nUf+lbCy^ " " (™R) a + (6C) 2 



where R is the resistance of one coil and 



A = L + (»-l)M 

 B = L-M 



C = nL + (4mp — w)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 com- 

 plicated 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 these results we see that we are always able 

 to reduce mutual to self inductance. Measuring the self induct- 

 ance of a coil connected in different ways, we can always deter- 

 mine the mutual inductances in terms of the self inductances. 



Thus we need not search for methods of directly comparing 

 mutual inductances with each other, although I have given 

 two of these, but we can content ourselves with measuring 

 self inductances and capacities. Fortunately most of the 

 methods are specially adapted to the latter, the ratio of self 

 inductance to capacity being capable of great exactness by 

 many methods. 



In the use of condensers I have met with great difficulty 

 from the presence of electric absorption. I have found that 

 this can be represented by a resistance placed in the circuit of 

 the condenser, which resistance is a function of current period 



A.M. Jour. Scr.— Fourth Series, Yol. IY, No. 24. — Dec, 1897. 

 30 



